The Chemistry of alkanes and cycloalkanes

The alkanes chemistry and of cycloalkanes The chemistry of alkanes and cycloalkanes Edited by Saul Patai and Zvi Rap...

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The alkanes

chemistry and

of

cycloalkanes

The chemistry of alkanes and cycloalkanes Edited by Saul Patai and Zvi Rappoport © 1992 John Wiley & Sons, Ltd ISBN: 0-471-92498-9

THE CHEMISTRY O F FUNCTIONAL GROUPS A series

of advanced

treatises Professor

under

the general

Saul

Patai

editorship

of

T h e chemistry of a l k e n e s (2 v o l u m e s ) T h e chemistry of t h e c a r b o n y l g r o u p (2 v o l u m e s ) T h e chemistry of the ether l i n k a g e T h e chemistry of the a m i n o g r o u p T h e chemistry of t h e nitro a n d nitroso g r o u p s (2 parts) T h e c h e m i s t r y of c a r b o x y l i c a c i d s a n d esters T h e chemistry of t h e c a r b o n - n i t r o g e n d o u b l e b o n d T h e chemistry of a m i d e s T h e chemistry of t h e c y a n o g r o u p T h e c h e m i s t r y of t h e hydroxyl g r o u p (2 parts) T h e chemistry of t h e a z i d o g r o u p T h e chemistry of acyl h a l i d e s T h e chemistry of t h e c a r b o n - h a l o g e n b o n d (2 parts) T h e chemistry of t h e q u i n o n o i d c o m p o u n d s (2 v o l u m e s , 4 parts) T h e c h e m i s t r y of t h e thiol g r o u p (2 parts) T h e chemistry of t h e h y d r a z o , a z o a n d a z o x y g r o u p s (2 parts) T h e chemistry of a m i d i n e s a n d i m i d a t e s (2 v o l u m e s ) T h e chemistry of c y a n a t e s a n d their thio derivatives (2 parts) T h e chemistry of d i a z o n i u m a n d d i a z o g r o u p s (2 parts) T h e chemistry of t h e c a r b o n - c a r b o n triple b o n d (2 parts) T h e chemistry of k e t e n e s , a l l e n e s a n d related c o m p o u n d s (2 parts) T h e c h e m i s t r y of t h e s u l p h o n i u m g r o u p (2 parts) S u p p l e m e n t A: T h e chemistry of d o u b l e - b o n d e d f u n c t i o n a l g r o u p s (2 v o l u m e s , 4 parts) S u p p l e m e n t B: T h e chemistry of a c i d derivatives (2 parts) S u p p l e m e n t C: T h e chemistry of t r i p l e - b o n d e d f u n c t i o n a l g r o u p s (2 parts) S u p p l e m e n t D: T h e chemistry of h a l i d e s , p s e u d o - h a l i d e s a n d a z i d e s (2 parts) S u p p l e m e n t E: T h e chemistry of ethers, c r o w n ethers, hydroxyl g r o u p s a n d their s u l p h u r a n a l o g u e s (2 parts) S u p p l e m e n t F: T h e chemistry of a m i n o , nitroso a n d nitro c o m p o u n d s a n d their derivatives (2 parts) T h e chemistry of t h e m e t a l - c a r b o n b o n d (5 v o l u m e s ) T h e chemistry of p e r o x i d e s

T h e CHEMISTRY of ORGANIC SELENIUM AND TELLURIUM COMPOUNDS (2 VOLUMES) T h e chemistry of t h e c y c l o p r o p y l g r o u p T h e CHEMISTRY of s u l p h o n e s a n d s u l p h o x i d e s T h e chemistry of o r g a n i c silicon c o m p o u n d s (2 parts) T h e chemistry of e n o n e s (2 parts) T h e chemistry of sulphinic a c i d s , esters AND their derivatives T h e chemistry of s u l p h e n i c a c i d s a n d their derivatives T h e chemistry of e n o l s T h e chemistry of o r g a n o p h o s p h o r u s c o m p o u n d s (2 v o l u m e s ) T h e chemistry of s u l p h o n i c a c i d s , esters a n d their derivatives T h e chemistry of a l k a n e s a n d c y c l o a l k a n e s UPDATES T h e chemistry of a - h a l o k e t o n e s , a - h a l o a l d e h y d e s a n d a - h a l o i m i n e s Nitrones, n i t r o n a t e s a n d nitroxides C r o w n ethers a n d a n a l o g s C y c l o p r o p a n e derived reactive i n t e r m e d i a t e s Synthesis of c a r b o x y l i c a c i d s , esters a n d their derivatives The silicon-heteroatom

bond

Ratal's 1992 g u i d e to t h e chemistry of f u n c t i o n a l

I C—H I

groups—Saul

Patai

he chemistry o1 alkanes and cycloalkanes

Edited

by

SAUL PATAI and ZVI R A P P O P O R T The

Hebrew

University,

Jerusalem

1992

JOHN WILEY & SONS CHICHESTER-NEW

YORK-BRISBANE-TORONTO-SINGAPORE

An Interscience®

Publication

Copyright ©

1992 by John Wiley & S o n s Ltd Baffins L a n e , C h i c h e s t e r West Sussex P 0 1 9 l U D , England

All rights reserved.

N o part of this b o o k m a y be r e p r o d u c e d by any m e a n s , or transmitted, or translated into a m a c h i n e language w i t h o u t the written permission of the publisher.

Other Wiley Editorial

Offices

J o h n W i l e y & S o n s , Inc., 6 0 5 T h i r d A v e n u e , N e w York, N Y 10158-0012, U S A Jacaranda Wiley Ltd, G.P.O. B o x 859, Brisbane, Queensland 4001, Australia J o h n Wiley & S o n s (Canada) Ltd, 22 Worcester R o a d , Rexdale, O n t a n o M 9 W I L l , Canada J o h n W i l e y & S o n s (SEA) Pte Ltd, 37 Jalan P e m i m p i n # 0 5 - 0 4 , B l o c k B, U n i o n Industrial Building, S i n g a p o r e 2 0 5 7

Library of Congress Cataloging-in-Publication Data T h e Chemistry of alkanes and cycloalkanes / edited by Saul Patai. p. c m . — ( T h e Chemistry of functional groups) 'An Interscience publicadon.' Includes bibliographical references a n d indexes. I S B N 0 471 9 2 4 9 8 9 (cloth) 1. A l k a n e s . 2. C y c l o a l k a n e s . I. P a t a i , S a u l . II. R a p p o p o r t , Z v i . III. Series. QD305.H6C46 1992 90-26878 547.411—dc20 CIP

Bridsh Library Cataloguing-in-Publication Data T h e chemistry of alkanes a n d c y c l o a l k a n e s . — ( T h e chemistry of functional groups) I. P a t a i , S a u l . II. R a p p o p o r t , Z v i . III. S e r i e s . 547 I S B N 0 471 92498 9

T y p e s e t b y T h o m s o n Press (India) Ltd., N e w D e l h i a n d P r i n t e d in G r e a t B r i t a i n b y B i d d i e s L t d , G u i l d f o r d , S u r r e y

Contributing authors W. Adam

Department of Organic Chemistry, University of Wiirzburg, D-8700 Wiirzburg, G e r m a n y

Zeev Aizenshtat

Department of Organic Chemistry a n d Casah Institute of AppHed Chemistry, T h e Hebrew University of Jerusalem, Jerusalem 91904, Israel

William C. Agosta

The Rockefeller University, 1230 York Avenue, New York, N Y 10021-6399, USA

J. E. Anderson

Chemistry Department, University College London, Gower Street, L o n d o n W C I E 6BT, U K

Richard F. W. Bader

Department of Chemistry, M c M a s t e r University, Hamilton, Ontario L8S 4 M I , C a n a d a

Derek V. Banthorpe

Department of Chemistry, University College London, 20 G o r d o n Street, L o n d o n W C I H OAJ, U K

S. W. Benson

Loker H y d r o c a r b o n Research Institute, University of Southern California, Los Angeles, California 90089, USA

Stefan Berger

Department of Chemistry, Philipps-Universitat M a r b u r g , Hans-Meerwein-Strasse, D-3550 M a r b u r g , G e r m a n y

James H. Brewster

D e p a r t m e n t of Chemistry, P u r d u e Lafayette, Indiana 47907-1393, USA

N. Cohen

The Aerospace Corporation, P.O. Box 92957, Los Angeles, California 90009, USA

Robert H. Crabtree

Department of Chemistry, Yale University, P.O. Box 6666, New Haven, Connecticut 06511-8118, USA

Tino Gaumann

Institute of Physical Chemistry, Federal Technology, CH-1015 Lausanne, Switzerland

Lowell H. Hall

Department of Chemistry, Quincy, M A 02170, USA

Eastern

University,

West

School

Nazarene

of

College,

VI

C o n t r i b u d n g authors

E. Heilbronner

Grutstrasse 10, CH-8704 Herrliberg, Swhzerland

A. C. Hopkinson

D e p a r t m e n t of Chemistry, York University, Downsview, O n t a r i o M 3 J IPS, C a n a d a

A. Hummel

Interfaculty Reactor Insdtute, Delft University of Techno logy, Mekelweg 15, 2629 JB Delft, The Netherlands

Marianna Kahska

D e p a r t m e n t of Chemistry, T h e University of Warsaw, Warsaw, P o l a n d

Lemant B. Kier

D e p a r t m e n t of Medicinal Chemistry, Virginia C o m m o n wealth Univershy, Richmond, VA 23298, U S A

Goverdhan Mehta

School of Chemistry, University of H y d e r a b a d , Central University P O , Hyderabad-500 134, India

George A. Olah

Katherine B. a n d D o n a l d P . Loker H y d r o c a r b o n Research Institute a n d D e p a r t m e n t of Chemistry, University of Southern California, Los Angeles, C A 90089-1661, U S A

T. Oppenlander

Fachhochschule Furtwangen, Abteilung Vihingen-Schwenningen, Fachbereich Verfahrenstechnik, D-7730 VS-Schwen ningen, G e r m a n y

Eiji Osawa

D e p a r t m e n t of Knowledge-Based Information Engineer ing, Toyohashi University of Technology, T e m p a k u - c h o , Toyohashi 441, J a p a n

G. K. Surya Prakash

Katherine B. a n d D o n a l d P . Loker H y d r o c a r b o n Research Institute a n d D e p a r t m e n t of Chemistry, University of Southern California, Los Angeles, CA 90089-1661, USA

H. Surya Prakash Rao

D e p a r t m e n t of Chemistry, Pondicherry University, Pondicherry-605014, India

Glenn A. Russell

D e p a r t m e n t of Chemistry, Iowa State University, Ames, Iowa 50011, U S A

Hans J. Schafer

Organisch-Chemisches Institut der Westfahschen WhhelmsUniversitat, Correns-Strasse 40, 4400 Munster, G e r m a n y

G. Zang

D e p a r t m e n t of Organic Chemistry, University of Wurzburg, D-8700 Wurzburg, G e r m a n y

Mieczys/aw Zielihski

Isotope Laboratory, Faculty of Chemistry, University, Cracow, Poland

Jagiehonian

Foreword In nearly thirty years the series The Chemistry of Functional Groups has treated all the major groups of organic chemistry. During all this time we were aware of the omission of the treatment of the C — H group, which may be regarded as the parent of all these groups even though most authors do not include it in the list of functional groups. F o r a long time we did not dare to deal with the C — H group, but in 1987 the publication of a volume on the cyclopropyl group served as a natural link to approach the 'non-functional' C — H group and the present volume is the result of this approach. Two chapters of the originally planned list of contents did not materialize: these were on 'Combustion and pyrolysis' and on 'Bioinorganic oxidation'. Again, we succeeded in securing worldwide cooperation of authors. In the present volume these include contributors from ten countries, a m o n g them from Canada, Germany, India, Israel, Japan, The Netherlands, Poland, Switzerland, the U K and USA. The literature coverage in most chapters in until 1991. We would be grateful to readers who would draw our attention to mistakes or omissions in this volume as well as in all other volumes of the series. SAUL PATAI Z V I RAPPOPORT

Jerusalem November 1991

The Chemistry of Functional Groups Preface to the series The series 'The Chemistry of Functional G r o u p s ' was originally planned to cover in each volume all aspects of the chemistry of one of the important functional groups in organic chemistry. The emphasis is laid on the preparation, properties and reactions of the functional group treated and on the effects which it exerts both in the immediate vicinity of the group in question and in the whole molecule. A voluntary restricdon on the treatment of the various functional groups in these volumes is that material included in easily and generally available secondary or terdary sources, such as Chemical Reviews, Quarterly Reviews, Organic Reactions, various 'Advances' and 'Progress' series and in textbooks (i.e. in books which are usually found in the chemical libraries of most universities and research institutes), should not, as a rule, be repeated in detail, unless it is necessary for the balanced treatment of the topic. Therefore each of the authors is asked not to give an encyclopaedic coverage of his subject, but to concentrate on the most important recent developments and mainly on material that has not been adequately covered by reviews or other secondary sources by the time of writing of the chapter, and to address himself to a reader who is assumed to be at a fairly advanced postgraduate level. It is realized that n o plan can be devised for a volume that would give a complete coverage of the field with no overlap between chapters, while at the same d m e preserving the readabihty of the text. The Editor set himself the goal of attaining reasonable coverage with moderate overlap, with a minimum of cross-references between the chapters. In this manner, sufficient freedom is given to the authors to produce readable quasi-monographic chapters. The general plan of each volume includes the fohowing main sections: (a) An introductory chapter deals with the general and theoretical aspects of the group. (b) Chapters discuss the characterization and characteristics of the functional groups, i.e. qualitative and quantitative methods of determination including chemical and physical methods, MS, UV, IR, N M R , ESR and P E S — a s weh as activating and directive effects exerted by the group, and its basicity, acidity and complex-forming ability. (c) O n e or more chapters deal with the formation of the functional group in question, either from other groups already present in the molecule or by introducing the new group directly or indirectly. This is usually followed by a description of the synthetic uses of the group, including its reacdons, transformadons and rearrangements. (d) Additional chapters deal with special topics such as electrochemistry, photochemis try, radiation chemistry, thermochemistry, syntheses and uses of isotopicahy labelled compounds, as weh as with biochemistry, pharmacology and toxicology. Whenever ix

X

Preface to the series

apphcable, unique chapters relevant only to single functional groups are also included (e.g. 'Polyethers'. 'Tetraaminoethylenes' or 'Siloxanes'). This plan entails that the breadth, depth and thought-provoking nature of each chapter will differ with the views and inclinations of the authors and the presentation will necessarily be somewhat uneven. Moreover, a serious problem is caused by authors who dehver their manuscript late or not at all. In order to overcome this problem at least to some extent, some volumes may be published without giving consideration to the originally planned logical order of the chapters. Since the beginning of the Series in 1964, two main developments occurred. The first of these is the publication of supplementary volumes which contain material relating to several kindred functional groups (Supplements A, B, C, D , E and F). The second ramification is the publication of a series of 'Updates', which contain in each volume selected and related chapters, reprinted in the original form in which they were published, together with an extensive updating of the subjects, if possible, by the authors of the original chapters. A complete hst of all above mentioned volumes published to date will be found on the page opposite the inner title page of this book. Advice or criticism regarding the plan and execution of this series will be welcomed by the Editor. The publication of this series would never have been started, let alone continued, without the support of many persons in Israel and overseas, including colleagues, friends and family. The efficient and patient co-operation of staff members of the publisher also rendered me invaluable aid. M y sincere thanks are due to all of them, especially to Professor Zvi R a p p o p o r t who, for m a n y years, shares the work and responsibility of the editing of this Series. The Hebrew University Jerusalem, Israel

SAUL PATAI

Contents 1.

Atomic and group properties in the alkanes Richard F . W. Bader

2.

Structural_chemistry of alkanes - a personal view Eiji O s a w a

79

3.

Conformational analysis of acyclic and alicyclic saturated hydrocarbons J. E. Anderson

95

4.

Chiroptical properties of alkanes and cycloalkanes James H. Brewster

135

5.

Enumeration, topological indices and molecular properties of alkanes Lowell H . Hall a n d L e m o n t B. Kier

185

6.

The thermochemistry of alkanes and cycloalkanes N . C o h e n a n d S. W. Benson

215

7.

The analysis of alkanes and cycloalkanes Zeev Aizenshtat

289

8.

NMR spectroscopy of alkanes Stefan Berger

351

9.

The mass spectra of alkanes Tino G a u m a n n

395

10.

The photoelectron spectra of saturated hydrocarbons E. Heilbronner

455

11.

Acidity and basicity A. C. H o p k i n s o n

531

12.

Alkanes: modern synthetic methods G o v e r d h a n M e h t a a n d H . Surya P r a k a s h R a o

553

13.

Electrophilic reactions on alkanes George A. O l a h a n d G. K. Surya P r a k a s h

609

14.

Organometallic chemistry of alkane activation R o b e r t H. C r a b t r e e

653

15.

Rearrangements and photochemical reactions involving alkanes and cycloalkanes T. O p p e n l a n d e r , G. Z a n g a n d W. A d a m

681

xi

1

xii

Contents

16.

Radiation chemistry of alkanes and cycloalkanes A. H u m m e l

743

17.

Electrochemical conversion of alkanes H a n s J. Schafer

781

18.

Syntheses and uses of isotopically labelled alkanes and cycloalkanes Mieczys)âw Zielihski a n d M a r i a n n a K a h s k a

809

19.

Natural occurrence, biochemistry and toxicology Derek V. B a n t h o r p e

895

20.

Inverted and planar carbon W i h i a m C. Agosta

927

21.

Radical reactions of alkanes and cycloalkanes

963

Glen A. Russell Author index

999

Subject index

1061

List of abbreviations used Ac acac Ad Alk All An Ar

acetyl (MeCO) acetylacetone adamantyl alkyl allyl anisyl aryl

Bz Bu

benzoyl (CgHsCO) butyl (also t-Bu or Bu')

CD CI CIDNP CNDO Cp

circular dichroism chemical ionization chemically induced dynamic nuclear polarization complete neglect of differential overlap f] ^ -cyclopentadienyl

DBU DME DMF DMSO

l,8-diazabicyclo[5.4.0]undec-7-ene 1,2-dimethoxyethane N,N-dimethylformamide dimethyl sulphoxide

ee EI ESCA ESR Et eV

enantiomeric excess electron impact electron spectroscopy for chemical analysis electron spin resonance ethyl electron volt

Fc FD FI FT Fu

ferrocene field desorption field ionization Fourier transform furyKOC^Hs)

Hex c-Hex HMPA HOMO

hexyl(C6Hi3) cyclohexyKC^Hii) hexamethylphosphortriamide highest occupied molecular orbital

xni

XIV

List of abbreviations used

1-

Ip IR ICR

ionization potential infrared ion cyclotron resonance

LCAO LDA LUMO

hnear c o m b i n a d o n of atomic orbitals lithium diisopropylamide lowest unoccupied molecular orbital

M MCPBA Me MNDO MS

metal parent molecule m-chloroperbenzoic acid methyl modified neglect of diatomic overlap mass spectrum

n Naph NBS NMR

normal naphthyl N-bromosuccinimide nuclear magnetic resonance

Pen Pip Ph ppm Pr PTC Pyr

pentyl(C5Hii) piperidyKCsHioN) phenyl parts per mhlion propyl (also f-Pr or Pr') phase transfer catalysis pyridyl (C5H4N)

R RT

any radical room temperature

sSET SOMO

secondary single electron transfer singly occupied molecular orbhal

tTCNE THF Thi TMEDA Toi Tos or Ts Trityl

tertiary tetracyanoethylene tetrahydrofuran thienyl(SC4H3) tetramethylethylene diamine tolyKMeC^HJ tosyl(p-toluenesulphonyl) triphenylmethyKPhgC)

Xyl

xylyl(Me2C6H3)

M

In addition, entries in the 'List of Radical N a m e s ' in lUPAC Nomenclature of Organic Chemistry, 1979 Edidon. P e r g a m o n Press, Oxford, 1979, p. 305-322, wih also be used in their unabbreviated forms, both in the text and in formulae instead of explicidy drawn structures.

CHAPTER

Atomic and group properties in the alkanes R I C H A R D F. W. B A D E R Department

of Chemistry,

McMaster

University,

Hamilton,

Ontario,

L8S 4M1,

Canada

I. A T O M S I N C H E M I S T R Y A. A Theory of Molecular Structure B. Additivity and Transferability of G r o u p Properties » C. Atoms and the Charge Distribution 11. T O P O L O G Y O F T H E C H A R G E D E N S I T Y A. The D o m i n a n t F o r m in the Charge Density B. Critical Points and Their Classification C. Critical Points of Molecular Charge Distributions D. Gradient Vector Field of the Charge Density E. Chemical Bonds and Molecular G r a p h s F. Rings and Cages G. Calculation of the Charge Density III. S T R U C T U R E A N D S T R U C T U R A L STABILITY A. The Molecular Structure Concept B. The Conflict and Bifurcation Mechanisms of Structural Change . . . C. A Theory of Molecular Structure lY. C L A S S I F I C A T I O N O F C H E M I C A L B O N D S A. Bond Order B. Bond P a t h Angle C. Bond Ellipticity V. L A P L A C I A N O F T H E C H A R G E D E N S I T Y A. The Physical Basis of the Electron Pair Model B. Characterization of Atomic Interactions C. The Laplacian and Reactivity VI. A T O M I C P R O P E R T I E S A. Q u a n t u m Mechanics of an Atom in a Molecule B. Definition and Calculation of Atomic Properties C. Atomic Charges and the Hybridization Model D. Atomic and G r o u p Volumes E. Acyclic Hydrocarbons and Additivity of the Energy F. Physical Basis For Transferabihty of G r o u p Properties The chemistry of alkanes and cycloalkanes Edited by Saul Patai and Zvi Rappoport © 1992 John Wiley & Sons, Ltd ISBN: 0-471-92498-9

2 2 2 5 6 6 8 9 9 12 16 17 17 17 18 20 21 21 27 31 35 35 37 40 41 41 43 48 52 59 61

2

Richard F . W. Bader

VII. T H E O R I G I N O F S T R A I N E N E R G Y A. Definition of Strain Energy B. Cyclic Molecules C. Bicyclic Molecules D. Physical Consequences of Strain VIII. A D D I T I V I T Y O F G R O U P D I P O L E S A N D P O L A R I Z A B I L I T I E S A. Definition of G r o u p M o m e n t s B. Definition a n d Additivity of G r o u p Polarizabilities C. Vibrationally Induced Molecular Dipole M o m e n t s IX. C O N C L U S I O N X. R E F E R E N C E S

61 61 62 64 66 67 67 70 74 76 76

I. ATOMS IN CHEMISTRY A. A Theory of Molecular Structure

The title of this series of books, 'Chemistry of the Functional Groups', is a mirroring of the cornerstone of experimental chemistry, that atoms a n d functional groupings of atoms exhibit characteristic sets of properties (static, reactive a n d spectroscopic) which, in general, vary between relatively narrow limits. I n chemistry we recognize the presence of a g r o u p in a given system a n d predict its effect u p o n the static a n d dynamic properties of the system in terms of a set of properties assigned t o that group. Thus, the knowledge of chemistry is classified, understood a n d predicted in terms of the chemistry of the functional groups. T h e functional group is the central concept in the working hypothesis of chemistry, that a molecule is a collection of a t o m s linked by a network of bonds, the molecular structure hypothesis. The purpose of theory is t o provide the conceptual framework in o u r pursuit of the prediction a n d understanding of observation. T h u s it should be possible t o recover from theory the concepts that m a k e u p the molecular structure hypothesis, since this hypothesis is itself a synthesis of ideas developed t o account for the observations of chemistry. It has been demonstrated that q u a n t u m mechanics can be generalized t o a particular class of open systems, i.e. t o pieces of some total system, a n d that these open systems faithfully recover the characteristics that are ascribed t o the chemical a t o m ^ T h e resulting theory of atoms in molecules, since it defines the concept central t o the molecular structure hypothesis, recovers as well the structural aspects of the hypothesis, namely the network of b o n d s which link the atoms a n d defines a molecular structure, together with a theory of structural stability which describes the changes in structure resulting from the making and breaking of chemical bonds^. This chapter describes the application of this theory of molecular structure^ t o a study of the atoms a n d their groupings which determine the chemistry of the alkanes. B. Additivity and Transferability of Group Properties

The finding that the variations in g r o u p properties through certain series of molecules can be so slight as to enable one to establish a group additivity scheme played an important role in establishing the concept of the functional group in chemistry. A g r o u p additivity scheme requires n o t only that a molecular property be additive over the groups in a given molecule, b u t that the contribution from each group, a n d hence the group itself be transferable amongst a series of molecules. T h e earliest a n d best studied of the systems exhibiting such group additivity schemes were the alkanes, both acyclic a n d cyclic. T h e

1. Atomic and group properties in the alkanes

3

study of the molar volumes of the normal alkanes at their boiling point by K o p p in 1855"^* provided the earliest example of the transferability and additivity of g r o u p properties. This was followed by the demonstration of characteristic a n d additive group contributions to the molar refraction"^^ and the related property of molar polarization^, as m a d e possible by the introduction of the Abbe refractometer in 1874. The molar refraction provided the first example of a measured physical property being used to establish the presence of a group in a given molecule through its additive contribution to the total property.^ Even a property as sensitive as the energy can exhibit additive group contributions as was once again first demonstrated in the experimentally determined heats of formation of the normal hydrocarbons^"^. Benson^^ has demonstrated how this and other thermodynamic properties of molecules and the changes in these properties upon chemical reaction can be usefully tabulated and predicted in terms of g r o u p contributions. The properties of the alkanes, both acyclic and cyclic, are so well ordered and classified in terms of atomic and group contributions that the use of the theory of atoms in molecules as the basis for the theoretical discussion of alkane chemistry is most appropriate. The theory, in addition to predicting these properties from fundamental principles, leads directly to an understanding of their additive a n d constitutive nature. The discussion of atomic properties will focus on the transferability of the volumes, energies and polarizabilities of the methyl and methylene groups, as these are important properties from both the historical and operational points of view. T h e discussion of a group's contribution to the molecular polarizability, a property important to the understanding of intermolecular interactions and chemical reactivity, requires a study of the atomic charges and first moments, as a basis for obtaining an understanding of how the atomic charge distributions respond to an externally applied field. O n e finds that the response of the charge distribution to an electric field is a characteristic group property, whether the field be externally applied or internally generated by a vibrational displacement of the nuclei. Having defined the transferable methylene group one may inquire as to how its properties, in particular its energy, change when it is subjected to the geometrical constraints found in the cyclopropane molecule. It is shown that a small a m o u n t of charge is transferred from the hydrogens to carbon when the methylene group is introduced into cyclopropane, causing a correspondingly small increase in its energy, an increase which equals the measured and so-called strain energy. T h r o u g h the use of the theory of atoms in molecules one may use q u a n t u m mechanics to predict not only the properties of a total system, but to predict as well the properties of the atoms which comprise it. In this m a n n e r one obtains a direct hnk between chemical concepts such as strain energy and the underlying physics. O n the other hand, it is at the limit of near-perfect transferability of group properties as exhibited by the alkanes that one can detrmine whether or not a proposed theory meets the requirements of experiment, for at this limit one may experimentally determine to high precision the properties of atoms in molecules via their additive contributions. By demonstrating that the atoms defined by q u a n t u m mechanics account for and recover the experimentally measured properties of atoms in molecules, one establishes that the atoms of theory are the atoms of chemistry. There is no test of theory other than the demonstration that it predicts what can be measured. There have been many previous attempts to define certain properties of atoms in molecules, particularly atomic charges. Arbitrary definitions of an a t o m or of some of its properties d o not account for the characteristics ascribed to the a t o m within the molecular structure hypothesis and hence play no operational role in the prediction and understanding of chemical observations. Aside from the obvious statement that all definitions should follow directly from q u a n t u m mechanics using only information

4

Richard F. W. Bader

contained in the state function, it is instructive to review what are the essential requirements imposed upon the definition of an a t o m in a molecule by the observations of chemistry. T h e reader may judge for himself the correctness of these criteria and whether any definition other than the q u a n t u m definition of an a t o m is able to fulfill them. The first requirement stems from the necessity of two identical pieces of matter exhibiting identical properties, with the important understanding that the form of a substance in real space is determined by its distribution of charge. T h u s two systems, macroscopic or microscopic, are identical only if they have identical charge distributions. This requires that atoms be defined in real space and that their properties be directly determined by their distribution of charge. Thus if an atom has the same form in the real space of two systems, i.e. the same distribution of charge, then it contributes the same a m o u n t to every property in both systems. This condition demands in turn that the atomic contributions M(Q) to some property M are additive over the a t o m s in a molecule to yield the molecular average < M > (equation 1). The b o u n d a r y of the atom, <M> = X^(Q)

(1)

as defined by a partitioning which necessarily exhausts all of real space, must be such as to maximize the transferability of an a t o m between systems, i.e. maximize the transfer of chemical information. These three requirements must be met if one is to predict that atoms and functional groupings of atoms contribute characteristic and measurable sets of properties to every system in which they occur. It is because of the direct relationship between the spatial form of an a t o m a n d its properties that we are able to identify them in different systems. The existence of an additivity scheme is a limiting situation wherein not only equation 1, that each a t o m make an additive contribution to every property, must hold, but requiring in addition that the a t o m be transferable amongst a set of molecules without change. The definition of an a t o m which meets these requirements will recover those properties of atoms in molecules which are directly measurable in the limiting situation wherein the properties for a series of molecules follow an additivity relationship. There is no k n o w n relationship between the energy and the distribution of charge in a molecular system of the form outlined above as being a requirement for a theory of atoms in molecules, although such a relationship is thought to exist Yet the atoms of theory, as is to be demonstrated in this chapter, exhibit just this requirement, a constancy in their contribution to the total energy of a system paralleling the constancy in their charge distribution. This property, together with the definition of an atom's energy which sums to the total energy of a system according to equation 1, are unique to the q u a n t u m atom. The reader is invited to consider how one might go a b o u t devising a non-arbitrary partitioning into atomic contributions of the electron-electron, electron-nuclear and nuclear-nuclear interactions, all of which contribute to the total energy of a molecule, and do so in such a way that when the a t o m is transferred to a second system with differing numbers of electrons and nuclei, thereby causing all of the individual contributions to the energy to change, its form and energy remain unaltered. This is the substance of chemistry. The total energy of a methyl group is in excess of twenty-five thousand k c a l m o l " ^ Yet it is an experimental fact that it can be transferred between members of the homologous series of saturated alkanes with a change in energy of less t h a n one k c a l m o l ~ \ and this in spite of changes of thousands of k c a l m o l " ^ in the individual potential energy contributions to its total energy. The energy is singled out only because it is a non-trivial and fundamental property. A theory which properly accounts for the transferability of an atom's energy will so account for all properties. It is hoped that a critical reading of this account, which describes how the theory of atoms in molecules is able to account for the properties of the alkanes in a m a n n e r


5

which parallels the historical role which the experimental study of this series of molecules played in the development of the concept of a functional group, will convince the reader that the predictions of q u a n t u m mechanics have been extended to the realm of the atom. It is time t o forego the arbitrary a n d subjective definitions of chemical concepts a n d bring the full predictive power of theory to bear on chemistry. The concepts of chemistry, of atoms and bonds, of structure and changes in structure, evolved from experimental chemistry, a n d they are part of the c o m m o n vocabulary of chemistry. Unfortunately, while chemistry has a single vocabulary, every individual has his or her own dictionary, the term a t o m or b o n d leading to different images in different minds. Theory offers the opportunity of greatly extending the operational usefulness of this c o m m o n vocabulary by providing a single dictionary, one based o n physics. C. Atoms and the Charge Distribution

F o r the reasons discussed above, an a t o m is t o be defined in real space. Thus, while the theory of atoms in molecules is obtained from q u a n t u m mechanics, its vehicle of expression is the electronic charge density, the distribution function which determines an atom's form in real space. Because the charge density must exhibit a cusp at the position of a nucleus and satisfy a particular condition there, the information contained in the electronic charge density serves also t o determine the positions of and the charges on the nuclei in a molecule. Because of t h e dominance of the nuclear-electron force, the electronic charge distribution exhibits local maxima at the positions of the nuclei with t h e result that recognizable atomic forms are created within a molecular system. These forms are so dominant in determining the structure of the charge distribution that their individual properties make characteristic contributions to the properties of the total system. Thus the atomic basis for the classification of chemistry could and did evolve as the working model of chemistry before its underlying physical basis was known. Schrodinger's state function W contains all the information that can be k n o w n about a q u a n t u m system. Among the properties of a system it predicts is the distribution of charge. T h e quantity ^*^^dxj^dx2'--dx„, where dxi denotes a n infinitesimal volume element (^Tj) and the spin component for electron i, is the probability that each of the N electrons in a system will be in some particular volume element with a particular spin component. If this quantity is summed over all spins and integrated over the spatial coordinates of all electrons b u t those of electron n u m b e r one, what remains is the probability that electron number one is in some particular volume element dz^. T h a t is, probability that electron one is in Jt^ =

Jt'^*^|Jti

(2)

where the summation over all spins and integration over all spatial coordinates but one is denoted by the symbol jdz'. Since ^ is a n antisymmetrized function, all electrons are equivalent and multiplication of the result given in equation 2 by N will give the total probability of finding electronic charge in ^t^. T h e probability per unit volume, the electronic charge density p(r), is therefore given by /»

p(r) = N ^ * 4 ^ J t '

(3)

«

The electronic charge density is responsible for scattering the X-rays in a crystal structure determination, a determination made possible by the charge density exhibiting its maximum values at the positions of the nuclei. Such experiments can be used to determine the charge density, averaged over the thermal motions of the nuclei. Rather than a

6


probabihty, p(r) c a n be and, for t h e present purposes, is more usefully interpreted as providing a description of the static (or nuclear motion averaged) distribution of negative charge t h r o u g h o u t real space. T h e model of matter employed here is o n e wherein the distribution of negative charge is measurably finite over a relatively large volume of space a n d is most highly concentrated at the positions of the point-like nuclei which are embedded in it. T h e atomic forms defined by the topology of the charge density are open systems a n d their boundaries, as defined in real space, satisfy the q u a n t u m condition for a n open system. T h u s all of the properties of a n a t o m in a molecule or a crystal employed in the atomic classification of the properties of matter are predicted by q u a n t u m mechanics. The same topological properties of the charge density which define the a t o m also lead to the definition of bonds, structure a n d structural stability a n d the whole of the molecular structure hypothesis is given a basis in physics^. This chapter, which describes the application of the theory of atoms in molecules t o the chemistry of the alkanes, gives only a curtailed account of the q u a n t u m mechanical basis of the theory, as full accounts have been presented e l s e w h e r e ^ T h e development of the theory of molecular structure is presented in somewhat more detail a n d the application begins with a review of the topological features of molecular charge distributions a n d the associated definitions of atoms, bonds a n d molecular structure. II. TOPOLOGY OF THE CHARGE DENSITY A. The Dominant Form in the Charge Density

The d o m i n a n t topological feature of the electronic charge d e n s i t y — t h a t it exhibits local maxima at the positions of the nuclei—is illustrated in Figure l a which gives a display of p{r) for the tetrahedrane molecule, C4H4. T h e plane shown contains t w o carbon nuclei a n d their associated protons. T h e density exhibits a m a x i m u m at the position of a nucleus for any plane containing the nucleus. This behaviour of the charge density is t o be contrasted with that exhibited at the mid-point of a C — C internuclear axis. T h e charge density has the appearance of a saddle at this point for the t w o carbon nuclei in the plane of Figure l a , b u t appears as a maximum in p at the corresponding point between the t w o carbon nuclei lying above a n d below the plane shown in the

F I G U R E 1. (a) Relief map of the electronic charge density p, for tetrahedrane in a plane containing two carbon and two hydrogen nuclei with an arbitrary cut-off in p at the positions of the carbon nuclei. The rounded maximum in the foreground lies at the mid-point of the axis between the two out-of-plane carbon nuclei, (b) M a p showing the trajectories traced out by the gradient vectors of the charge density for the same plane as in (a). Most of the trajectories terminate at the positions of the nuclei whose positions are encompassed by large open circles. A set of trajectories also terminates as the critical point denoting the two-dimensional maximum in the foreground of (a). This is the bond critical point between the out-of-plane carbons, and the associated set of trajectories defines their interatomic surface. The critical point in the interior of the molecule, a cage critical point, serves as an origin for trajectories. Bond or (3, — 1) critical points are denoted by black dots. The pairs of trajectories which originate at each of these points and terminate at the neighbouring nuclei are drawn in heavy bold and they denote the bond paths. The pairs of bold trajectories which, in this plane, terminate at each such critical point, denote the intersections of the corresponding interatomic surfaces with the plane of the diagram, (c) Contour map of the charge density for the same plane overlaid with bond paths and the intersections of the interatomic surfaces. The contour values in atomic units (au) increase in the order 2 x 10", 4 x 10", 8 x 10" with n beginning at — 3 and increasing in steps of unity (open crosses mark the projected positions of out of plane nuclei)

1. Atomic and g r o u p properties in the alkanes

(a)

(b)

(c)

FIGURE 1. {caption opposite)

8


figure. Knowledge of p in o n e o r t w o dimensions is insufficient t o characterize its three-dimensional form. W h a t is needed is a m e t h o d for summarizing in a succinct m a n n e r the principal topological features of a charge distribution. B. Critical Points and Their Classification

Each topological feature of p(r), whether it be a maximum, a minimum o r a saddle, has associated with it a point in space called a critical point, where the first derivatives of p(r) vanish. Thus at such a point, denoted by the position vector r^, Vp(r J = 0, where Vp denotes the operation Vp = \dp/dx + }dp/dy + kdp/dz

(4)

Whether a function is a maximum or a minimum at an extremum is, of course, determined by the sign of its second derivative or curvature at this point. In general, for a n arbitrary choice of coordinate axes, one will encounter nine second derivatives of the form d^p/dxdy in the determination of the curvatures of p at a point in space. Their ordered 3 x 3 array is called the Hessian matrix of the charge density, or simply, the Hessian of p . This is a real, symmetric matrix a n d as such it c a n be diagonalized. The new coordinate axes are called the principal axes of curvature. T h e trace of the Hessian matrix, the sum of its diagonal elements, is invariant t o a rotation of the coordinate system. T h u s the value of the quantity V^p, called the Laplacian of p, V V = V • Vp = d^p/dx^ + d^p/dy^ + d^p/dz^

(5)

is invariant t o the choice of coordinate axes. The principal axes a n d their corresponding curvatures at a critical point in p are obtained as the eigenvectors a n d corresponding eigenvalues in the diagonalization of the Hessian matrix of p. T h u s the pairs of names 'curvature a n d eigenvalue' a n d 'axes of curvature a n d eigenvectors' c a n be used interchangeably in describing the properties of a critical point in p . While all of the eigenvalues of the Hessian matrix of p at a critical point are real, they may equal zero. The rank of a critical point, denoted by cd, is equal to the n u m b e r of non-zero eigenvalues o r non-zero curvatures of p at the critical point. The signature, denoted by a, is simply the algebraic sum of the signs of the eigenvalues, i.e. of the signs of the curvatures of p at the critical point. The critical point is labelled by giving the d u o of values (co, a). With relatively few exceptions, the critical points of charge distributions for molecules at or in the neighbourhood of energetically stable geometrical configurations of t h e nuclei are all of rank three. The near ubiquitous occurrence of critical points with co = 3 in such cases is another general observation regarding the topological behaviour of molecular charge distributions. It is in terms of the properties of critical points with (D = 3 that the elements of molecular structure are defined. A critical point with coono c5on"^ VOÔONOO^ ONOOT-h

iVDON

00

O 03 X

C 3 PQ

CH2 > C H > C. A methyl g r o u p linked t o a methylene g r o u p withdraws a n almost constant a m o u n t of charge from methylene, as ^ ( M e ) = — 0.0165 ± 0.0005e in p r o p a n e t h r o u g h t o hexane. This n u m b e r changes slightly t o — 0.0175e for the 6-3IG** and D — H basis sets. The reader is referred t o Table 4 for the net charges o n the M e a n d methylene groups obtained using t h e D — H basis. The methylene g r o u p in p r o p a n e is linked t o t w o methyls a n d its net charge of + 0.034e is, within integration error, twice that of a methylene linked to a methyl and a second methylene, as found in butane t h r o u g h t o hexane. A methylene linked only t o other methylenes as found in pentane a n d hexane has a zero net charge (Table 4). Thus the inductive transfer of charge from methylene t o methyl is a nearly

49


TABLE 4. Net charges in methyl and methylene groups and their energies relative to standard values" Molecule

Ethane Propane n-Butane n-Pentane n-Hexane

^(CH3)

+ 0.000 -0.017 -0.018 -0.018 -0.017

AE{CH^)

^(CH,) (e)

+ + + +

0.034 0.018 0.018 0.017

AECCHJ" (kcalmopi)

+ 0.002 + 0.001

-10.7 -10.4 -10.3 -10.4

+ + + +

21.1 10.5 10.4 10.6

-0.6 -0.3

"ECCHa) in ethane = = - 39.62953 au, £(CH2) = B° = - 39.04743 au using the D — H basis set. ''This C H j is bonded only to other methylenes.

constant quantity, equal to 0.017e per methyl, and this transfer is d a m p e d by a single methylene group, as a CH2 group once removed has a zero net charge. The net charges on the individual atoms in these groups also exhibit a similar constancy. The H a t o m of methyl in the plane of the carbon framework has a charge of — 0.025e, 0.003e smaller in magnitude than that of the two other H atoms of methyl. The H of CH2 linked to a single methyl bears a charge of — 0.040e, while that for a H on a carbon linked only to other methylenes has a charge of — 0.043e. O n e correctly anticipates, as illustrated in Figure 12, that these constancies in average populations are a result of essentially constant distributions of charge over corresponding atoms in these molecules and that this will in turn result in these atoms making essentially constant contributions to the total energies. The two central methylene groups in hexane and the single such group in pentane have essentially zero net charge and their energies are found to be equal to the additive contribution per methylene group in the energy additivity scheme for the normal alkanes. These groups will be taken to define the properties of the 'standard' CH2 group for comparison with the methylene groups of the cyclic and bicyclic hydrocarbons. W h e n three methyls are attached to a single carbon as in isobutane, each withdraws significantly more electronic charge than when bonded to methylene and this effect is further enhanced in neopentane. The net charges on the carbon atoms in CH3, CH2 (linked only to methylenes), CH2 (linked to one methyl), C H and C are, respectively, + 0.065, +0.085, +0.097, +0.129 and +0.137e. There is a dramatic decrease in the average population of a hydrogen a t o m when it is linked to a carbon a t o m in a system with ring strain. Figure 13 gives net atomic and group charges for all cyclic structures. By symmetry, a CH2 group of the three-, four- and six-membered cyclic molecules has zero net charge as does the standard methylene group of the acyclics defined above. C o m p a r e d to the hydrogens of this standard group, the hydrogens of cyclopropane have 0.048 fewer electrons, the same decrease in population as predicted using the D — H basis. In cyclobutane this difference has decreased to 0.014e and in cyclohexane the average of the axial and equatorial H populations is only 0.003e less t h a n that in the standard methylene group. Correspondingly, the average electron population of a carbon atom in these molecules increases with increasing strain, the net charge of a C a t o m in the six-, five-, four- and three-membered cychcs being + 0.086, +0.077 (average), +0.057 and — O.OlOe, respectively. The value for cyclohexane, which may be considered to be strain free, is within 0.006e of the standard value. The bridgehead carbon atoms in bicyclobutane 13 and in the propellanes 21 and 22 bear the largest negative charges of all the carbon atoms and the order of electron-withdrawing ability found in the unstrained acyclic molecules is reversed. In the strained molecules the C H and C groups

50

Richard F. W. Bader

F I G U R E 12. Contour plots of the charge distributions in the normal alkanes, ethane to hexane, for the plane containing the carbon nuclei and the in-plane protons of the Me groups. Also shown are the charge distributions for the methylene groups for a plane containing the C and H nuclei: (a) in propane, (b) in butane, (c) in pentane, (d) in hexane, (e) the central group in pentane, (f) an equivalent group in hexane. The atomic boundries and bond paths are shown. The plots for the Me groups in propane to hexane are superimposable, as are plots (b), (c) and (d) as well as (e) and (f) for the methylene groups. The outer contour has the value 0.001 au with remaining values being the same as those given in Figure 1

withdraw charge from the CH2 groups. These observations indicate that a carbon becomes more electronegative as it is subjected to more angular strain and this fact is of primary importance in understanding the gross effects of geometrical constraints on the charge distribution and its energy. Orbital theories relate an increase in the electronegativity of a carbon a t o m relative to that of a bonded hydrogen to an increase in the s character of its bonding hybrid orbital. Thus the decrease in b o n d length and pK^ and the increase in force constant and b o n d dissociation energy for C — H through the series cyclohexane, ethylene and


51

q(C)= -.010

A q(H)=.oo5 9 . 6

.036 -.011 .025

/\q(CH2)=o.o 28.7(275)

42.3

.043 -.030 - 5 . 2 -.017

69.0(68.0)

26.8(26.5)

.068

4.2

.084 -.037 .010

--035 -.002

*°^®

22

A

..yjf 077f -.040 -.2 -.003 71(6.2^

104.6(105.0)

-.033 .041 3 0 . 5 ^058

-.9 15.2(14.4)

-.036

-5.1

-.012

-.016 -.016 -- 1 5 . 1 -0I3 20.9 ^^^3(89^0P

.005

23 .111

35.2

.0.0 11.4(74)^^^^

- 7 3

-.019 68.6(63.9)

24

q(C)=-.107 4 4 . 0 104.2(98.0)

:0|6

.072 ^.-.003 _ _ .002 2 . 5 58.5(54.7)

3.2

.056 -.029 -.002

15 54.0(51.8)

.003 -.003 1 9 . 9 0.0

.072

.068

^

140.8(140-0)

159.1(164.7)

25

0.0

.030 -.028 .002 2 0 . 9 .059 -.030 0.0

-.149

».003 106.6(104.0)

2.9

12.5 11.4

21

.036 .019 1 1 . 3 .074

614(63.2)

-^^

12.2

26

F I G U R E 13. Structure of strained hydrocarbons showing opposite each CH2, CH or C group the net charge on carbon, the average net charge on hydrogen, the net charge for the group and the strain energy of the group in k c a l m o l " ^ The total calculated strain energy followed by the value in parentheses is given beneath each structure.

acetylene is accounted for by a change in hybridization on carbon from sp^ to sp^ to sp, respectively. The increasing electron populations of these carbons to yield net charges of +0.080e, — 0.035e a n d -0.177e, respectively, quantify the accompanying increase in electronegativity. An empirical expression has been proposed to relate the C — H coupling constant J ( ^ ^ C — H ) to the percent s character of the bond"^^ a n d the values of this constant for cyclohexane, ethylene and acetylene (123,156 a n d 249 Hz, respectively) yield values of 25, 31 and 50% for the s character.

52


The hybridization model also predicts that the smaller b o n d angles found in a system with angular strain should result in a n increase in the p character of the strained C — C bonds a n d hence t o a n increase in the s character of the associated C — H bonds"^^. I n this way one can account for the increase in the electronegativity of carbon relative t o hydrogen which, as noted above, accompanies the introduction of strain into a cyclic system. The validity of this model can be demonstrated by showing that the properties of the CH2 group in cyclopropane resemble those for ethylene, a point emphasized by Coulson a n d Moffitt'^'^. T h e C — H b o n d length a n d H C H b o n d angle, both observed and calculated at the 6-3IG* level, are similar for the CH2 groups in cyclopropane a n d ethylene, the observed values being 1.082 and 1.090 A, and 116.6° a n d 116.5°, respectively. The similarity in properties extends t o the C — H coupling constants, the value for cyclopropane being 161 Hz, t o the C — H force constant a n d b o n d dissociation energies as well as t o their pK^ values"^^ of 46 a n d 44, ethylene being more acidic. T h e carbon is negatively charged in both molecules, slightly more so in ethylene. Similarly, the properties for the C — H bridgehead g r o u p in bicyclo[ 1.1.0]butane a n d the still larger net negative charge o n this carbon are understood by noting that its properties a p p r o a c h those observed for the same group in acetylene. A value of 205 H z for J^^C—H) correlates with 41%s character. T h e C — H b o n d length of 1.070 A, while larger t h a n the value of 1.057 A in acetylene, is less t h a n that found in ethylene. Since bicyclobutane reacts with phenyl hthium whose pK^ is 43, the pK^ of this bicyclic molecule is probably less than 40 which makes it more acidic than ethylene or cyclopropane b u t less acidic than acetylene itself, which has a pK^ of 25. The atomic charges for the cyclic molecules are considered in detail below in the discussion of the origin of strain energy a n d its variation with structure throughout this series of molecules. T h e ultimate argument for an increase in electronegativity with increasing s character is, of course, based on energy, an s electron being more tightly b o u n d than a p electron. As described below, one indeed finds that the energy of a carbon a t o m decreases as the s character of its hybrids t o dissimilar neighbouring atoms increases. The bridgehead carbon a t o m in bicyclobutane, for example, is found to be only 9.5 kcal mol ~ ^ less stable than the carbon in acetylene. D. Atomic and Group Volumes

The study of the molar volumes of hydrocarbons by K o p p in 1855"^^ provided the earliest example of the addivitity of group properties. Table 5 a n d 6 list the molecular volume a n d the contribution of each a t o m a n d functional group t o this volume as determined by b o t h the 0.002 a n d 0.001 au envelope of the charge density for a n u m b e r of hydrocarbons obtained from 6-31G**/6-31G* calculations. Table 5 also lists the fraction of the total electronic charge of the a t o m contained within the stated envelope"^"^. The volumes of the methyl a n d methylene groups in the homologous series of normal hydrocarbons exhibit the same pattern of transferable values noted above for the group populations. T h e volume of the methyl group in ethane is slightly larger than that of the methyl groups in the remaining members whose volumes vary by only + 0 . 0 2 a u from their average value. T h e volume of the methylene group bonded t o t w o methyls in p r o p a n e is slightly greater than the volumes of the methylene bonded t o one methyl, their volumes varying by ± 0 . 0 2 a u a b o u t the average value. Finally, the methylene groups bonded only to other methylenes also have a characteristic volume. T h e small differences between the latter t w o kinds of methylene groups are evident in Figure 12. The methylene bonded t o one methyl is less compressed than one bonded only t o other methylenes and this is reflected in this larger volume. This effect is enhanced for p r o p a n e where the single methylene is larger still. T h e volume varies in the reverse order t o the population and energy of the methylene group: the more contracted the group, the larger its population a n d the lower its energy. T h e same is true for the methyl group, the

1. A t o m i c a n d g r o u p properties in the alkanes

53

TABLE 5. Atomic energies, populations and volumes"

v{Q) Molecule

Atom^

-EiQ)

N{Q)

0.001

0.002

0.001

0.002

CH4

C H C H C H H C H C H H C H C H H C H C H C H H C H C H C H H C H C H C C H C H H axial C H H axial C H axial H C H C H

37.6097 0.6480 37.6328 0.6621 37.6502 0.6615 0.6625 37.6539 0.6744 37.6470 0.6622 0.6632 37.6695 0.6750 37.6469 0.6621 0.6629 37.6716 0.6747 37.6910 0.6753 37.6480 0.6615 0.6627 37.6707 0.6751 37.6884 0.6756 37.6649 0.6625 0.6627 37.6759 0.6845 37.6746 0.6634 37.6938 37.7115 0.6557 37.6905 0.6683 0.6686 37.6896 0.6729 0.6754 37.6702 0.6577 0.6557 37.8253 0.6322 37.7330 0.6494

5.754 1.062 5.762 1.079 5.774 1.079 1.082 5.778 1.092 5.773 1.079 1.083 5.791 1.095 5.773 1.080 1.082 5.791 1.095 5.803 1.098 5.775 1.079 1.082 5.790 1.095 5.804 1.098 5.781 1.084 1.082 5.808 1.102 5.786 1.084 5.851 5.894 1.053 5.830 1.086 1.084 5.809 1.092 1.099 5.814 1.062 1.055 6.061 1.009 5.864 1.033

76.90 52.31 64.66 52.30 63.45 52.44 52.59 54.75 52.10 63.36 52.38 52.52 53.79 52.20 63.64 52.37 52.41 53.64 52.09 52.36 52.13 63.57 52.40 55.59 53.60 52.16 52.76 52.21 61.29 52.21 52.41 47.28 51.49 59.75 52.10 40.97 70.84 50.21 60.83 52.64 52.12 53.70 52.25 52.24 68.14 51.49 50.72 78.69 48.05 65.86 48.39

64.94 38.61 57.90 38.79 57.31 38.87 39.45 51.37 38.83 57.29 38.80 39.44 50.72 39.43 57.30 38.85 39.49 50.69 39.38 49.98 40.03 57.29 38.89 39.44 50.55 39.42 50.30 39.99 56.23 39.99 39.38 45.74 38.65 55.25 39.76 40.97 62.11 37.47 55.34 38.93 38.66 50.67 38.85 39.99 59.62 38.51 37.54 68.22 36.10 58.08 36.83

99.7 97.8 99.8 98.0 99.9 98.0 98.1 98.0 98.0 99.9 97.9 98.1 99.9 98.2 99.9 97.9 98.1 99.9 98.2 100.0 98.3 99.9 97.9 98.1 99.9 98.3 100.0 98.4 99.9 99.9 98.1 100.0 98.3 99.9 98.3 100.0 99.8 97.9 99.9 98.0 98.1 99.9 98.0 98.3 99.8 98.1 97.9 99.8 97.8 99.8 98.2

99.4 96.0 99.6 96.1 99.7 96.1 96.4 97.9 96.3 99.7 96.2 96.4 99.9 96.6 99.7 96.1 96.4 99.9 96.6 99.9 96.8 99.7 96.1 96.3 99.9 96.6 99.9 96.8 99.8 98.2 96.4 99.9 96.6 99.8 96.6 100.0 99.6 96.2 99.7 96.2 96.3 99.9 96.3 96.7 99.6 96.3 96.1 99.5 96.1 99.6 96.5

C2H6 C3H8

n-QHio

n-CsH,^

iso-C4Hio

neo-C5Hi2

C-C3H, c-QHg

C-QH12

Bicyclo[1.1.0]butane

[l.LljPropellane

(continued)

54


TABLE 5. (continued) v(Q) Molecule

CH3 +

C4H9^

Atom'' C C H C H C H C H*^ H C

-E(Q)

N(Q)

37.8041 37.7250 0.6473 37.8418 0.5691 37.6826 0.5179 37.7136 0.6170 0.5896 37.9288

6.102 5.919 1.041 6.121 0.879 5.757 0.748 5.796 0.969 0.934 6.099

%iV(Q)

0.001

0.002

0.001

0.002

93.77 92.37 50.30 121.06 41.35 95.46 35.70 68.22 45.18 44.53 64.58

76.83 77.27 37.31 98.46 31.18 77.01 26.61 60.39 34.91 34.21 60.21

99.7 99.6 97.8 99.4 97.7 99.5 97.5 99.8 98.1 97.9 99.9

99.2 99.3 96.0 98.8 96.1 99.0 95.8 99.6 96.6 96.4 99.8

"All results in atomic units and calculated from 6-31G**/6-31G*. *'The carbon atom of a methyl group, if present, is listed first. This is followed by the unique H of a methyl and then by one of the two equivalent hydrogens of a methyl. Given next are the carbon and hydrogen atoms of methylene. The final entries are for carbon and hydrogen of methine and finally a single carbon as in neopentane. În plane.

transferable methyl having a smaller volume, but larger population and lower energy t h a n the methyl of ethane. It has also been shown that the methyl and methylene g r o u p dipole moments and their correlation energies as determined by a density functional exhibit the identical pattern of transferable v a l u e s T h e group contributions to the molecular dipole are discussed in Section VIII. The methyl groups in isobutane and neopentane have still larger net charges and still lower energies since they withdraw charge from C H and C, respectively. Correspondingly they have smaller volumes, the smallest being found for the most stable, that in neopentane. O n e notes that the volume and contained charge of the central carbon in this latter molecule is independent of the choice of envelope as it is interior to b o t h the 0.001 or 0.002 au contour. This observation is borne out by the fact that b o t h choices of envelope recover 100% of the charge of this atom. The stability and electron population of a carbon a t o m increases with the extent of methyl substitution, as methyl is less electron-withdrawing t h a n is hydrogen. The volume of a substituted carbon, however, exhibits the opposite order, its value decreasing in the order ethane > p r o p a n e > isobutane > neopentane. W h a t might at first seem surprising from the next entries in Table 5 is that the volume of a carbon a t o m increases as it is subjected to increased geometric strain. The extent of geometric strain present in a molecule is measured by comparing the b o n d p a t h angle with the normal b o n d angle (see Table 2). T h e b o n d p a t h angle of 78.8° in cyclopropane, for example, is considerably less than the normal tetrahedral C — C — C b o n d angle. The strain in this molecule is, however, less t h a n that suggested by the geometric angle which is less than the b o n d p a t h angle by 18.8°. The strain is still less in cyclobutane and, correspondingly, the b o n d path angle exceeds the geometric angle of 89.0° by only 6.7°. In the strain-free cyclohexane molecule the b o n d p a t h angle is actually closer to the tetrahedral value t h a n is the geometric one since the latter, equal to 111.4°, exceeds the former by 1.3°. Correspondingly, the volume of the carbon in cyclopropane is greater t h a n that for the carbon in cyclobutane which in turn is greater t h a n that for cyclohexane. Unlike the variation in volume of a carbon with extent of methyl substitution discussed above, one finds both the electron population and stability of a strained carbon to parallel

1. Atomic a n d g r o u p properties in the alkanes TABLE 6. Molar volumes of molecules and functional groups FM(cm^mol-i) Molecule and group CH4 CH3 C2H, CH3 C3H8 CH3 n-C4Hio CH3 CH^ n-CsHi^ CH3 CH2 CH2" n-C6Hi4 CH3 CH2 CH/ CH3 CH neo-C5Hi2 CH3 C C-C3H6

cn. C-C4H8 en. C-QH12 CH,

Bicyclo[1.1.0]butane

CH,

CH [l.l.l]Propellane

CU,

c C2H4 CH2 C2H2 CH CH3 + t-C4H/ CH3 C

0.001

0.002

25.53 20.87 39.54 19.77 53.64 19.73 14.18 67.64 19.70 14.12 81.56 19.71 14.08 13.98 95.71 19.74 14.09 14.03 67.34 19.51 8.81 80.78 19.28 3.66 45.85 15.28 59.11 14.78 84.25 14.04 53.02 15.20 11.31 60.28 14.51 8.37 34.44 17.22 28.99 14.49 18.14 59.97 18.07 5.76

19.58 16.13 31.10 15.55 42.76 15.62 11.51 44.13 15.61 11.56 65.96 15.63 11.55 11.61 72.49 15.62 11.56 11.63 54.36 15.61 7.53 65.95 15.57 3.66 36.69 12.23 47.45 11.86 69.35 11.53 42.83 12.02 9.31 48.98 11.76 6.86 27.11 13.56 23.24 11.62 14.00 49.19 14.61 5.37

"These methylenes are bonded only to other methylenes.

N-^^NiQ) + 0.0003 + 0.0006 + 0.002

+ 0.002

+ 0.004

+ 0.003

-0.002

+ 0.002

+ 0.002 + 0.001 + 0.002 + 0.001

+ 0.002

-0.00007 + 0.00006 -0.001 + 0.002

55

56

Richard F. W. Bader

the increase in its volume. These observations, together with an understanding of strain energy itself, can be rationalized in terms of the hybridization model. As illustrated above in the discussion of the atomic and group populations, the smaller C — C — C b o n d angles found in hydrocarbons with angular strain should result in an increase of the p character of the strained C — C bonds and hence in an increase in the s character of the associated C — H bonds. Since s electrons are b o u n d more tightly t h a n are p electrons, the effect of the angular strain is to increase the stability of a strained carbon a t o m and increase its electronegativity relative to its bonded hydrogen atoms. T h e atomic volume of carbon is another property like its population iV(C), whose value increases with increasing s character, the values of v(C) in ethane, ethylene a n d acetylene being 65, 92 a n d 121 au, respectively, paralleling the trend in N{C) values which at this basis set in the same order as 5.76, 5.92 and 6.12e. O n the basis of these results one anticipates that the atomic volume of carbon will also exhibit an increase with increasing geometric strain, as this also causes an increase in the s character of the carbon atom. T h e increase in stabihty, charge and volume of a carbon atom with increasing geometric strain is illustrated by the results for the three cyclic molecules cyclohexane, cyclobutane and cyclopropane'^''". It is i m p o r t a n t to note that the theory of atoms in molecules, as illustrated in a subsequent section, again recovers the experimental findings regarding the values of the strain energies for these molecules. The energy of the methylene g r o u p in cyclohexane differs from the energy of the standard methylene group (a value fixed independently by the partitioning of the energies of the normal hydrocarbons) by only 0.06 kcal m o l " ^ The charges of the carbon and hydrogen atoms in this g r o u p and in the transferable methylene g r o u p in pentane and hexane are also very similar. T h u s in agreement with experiment, cyclohexane has a zero strain energy. The strain present in the four- and three-membered rings results in a transfer of charge from hydrogen to carbon relative to their values in the standard methylene group. The extent of this charge transfer increases with an increase in strain. The result is an increase in the stability of the carbon atom, but an even greater decrease in the stability of the two hydrogen atoms relative to their values in the standard methylene group, and the net result is a strain energy. The strain energy per methylene group is greater for cyclopropane t h a n for cyclobutane, the values being 9.3 and 6 . 5 k c a l m o l ~ \ respectively. In agreement with experiment, the predicted total strain energies of 27.9 and 26.0 kcal m o l " ^ for the two molecules are very similar. The volume changes for the hydrogens attached to the strained carbon atoms parallel the shifts in charge, their volumes being slightly less than the volumes of the hydrogen atoms in the standard methylene group. The increase in volume of the carbon a t o m dominates the volume change accompanying the introduction of geometric strain into a cyclic molecule. T h e reason for this can be seen from Figure 14, which shows the boundaries of the carbon atom of the standard methylene group superimposed on the carbon a t o m of cyclopropane in the plane of the carbon nuclei. The effect of decreasing the angle between the c a r b o n - c a r b o n b o n d paths subtended at the nucleus of the standard methylene carbon to its value in cyclopropane is a fan-like opening up of the carbon a t o m and a corresponding increase in its breadth. There is a loss in its relative volume where the boundaries of the three ring atoms meet, but this is small compared to the gain in the outer regions of the atom. It is also important to note that this result of an increase in volume of the methylene group with increase in strain is not an artifact of the partitioning method. T h u s the incremental increase in the total molecular volumes, p r o p a n e through to hexane, is 14.0 au. This increment per added methylene group is less t h a n one-third and one-quarter, respectively, of the total molecular volumes of cyclopropane and cyclobutane. Gavezzotti has noted that the surface area of a methylene group increases with geometric strain and decreases with steric crowding"^^.


57

F I G U R E 14. Contour plot of the charge distribution of the cyclopropane molecule in the ring plane showing the bond paths and the C — C interatomic surfaces. Also shown for one carbon (and its out-of-plane hydrogens) is the corresponding boundary of the standard methylene group in the acyclic hydrocarbons. The outer contour value is 0.001 au, the remainder as in Figure 1

Also included in Tables 5 and 6 are the results for bicyclo[1.1.0]butane and [ l . l . l j propellane. In both these molecules all four bonds to a bridgehead carbon a t o m he on one side of a plane through its nucleus. In keeping with the considerable geometrical strain present at the bridgehead positions, these atoms are the most stable, and possess the largest net charges and volumes of all the saturated carbon atoms considered here. The bridgehead carbon in bicyclo[ 1.1.0] butane is over one and one-half times larger than the methine carbon in isobutane. It is only 10.4 kcal mol ~ ^ less stable than the

58

Richard F. W. Bader

sp-hydridized carbon atom of acetylene with a net charge one-half as great, suggesting a considerable degree of s character in its bonds to neighbouring groups from which it withdraws charge. The volume of a bridgehead carbon in [1.1.1]propellane is nearly 50% larger than that of a methyl group carbon a t o m and more t h a n twice as large as the central carbon in neopentane. The bridgehead carbons are large and exposed in these two molecules. In keeping with this observation, both molecules undergo acetolysis by protonation of the bridgehead carbons, as previously discussed in Section V.C. in terms of the Laplacian of the charge density. In the normal and branched alkanes the general behaviour, as noted above, is for the volume of a carbon a t o m to decrease as its stability and electron population increase. This behaviour is what is observed for atomic volumes of the free atoms across a short row of the periodic table, from an alkali metal to an inert gas. In the strained hydrocarbons, on the other hand, just the opposite behaviour is observed, with the volume increasing along with an increase in population and stability of the carbon. The parallel increases in electron population, stability and volume of a carbon a t o m which accompany an increase in its s character is further illustrated by the series ethane, ethylene and acetylene. The idea extends to carbocations as well (Table 5), the sp^ carbons of CH^^ and € ( € 1 1 3 ) 3 ^ having volumes in excess of those for an sp^ carbon in the hydrocarbons from which they are derived. Correspondingly, they also have greater electronegativities as reflected in their net charges and stabilities. T h u s the positive charge in CH3^ is shared equally over all four nuclei. As anticipated in terms of hyperconjugation model, the electron population of the central carbon increases with increasing methyl substitution, the central carbon in tertiary butyl carbon bearing a net negative charge. While v(C) is greater for the sp^ carbon of a carbocation than it is for the corresponding carbon in the saturated hydrocarbon from which it is derived, the value of v(C) for the sp^ carbon is found to decrease, rather than increase, with N{C). T h e width of an sp^ carbon in the plane perpendicular to the plane of the nuclei does indeed increase with the increase in hyperconjugative electron release to this carbon which accompanies an increase in methyl substitution, from 5.7 au in CH3^ to 6.7 au in € ( € 1 1 3 ) 3 ^ . In the plane of the nuclei, however, the C of CH3^ extends between the H atoms while in C(CH3)3^ the central carbon is totally enclosed by the interatomic surfaces with other carbons. In addition to the net charges on the carbon in CH3^ and in methane being the same, the former is more stable than the latter by 45.7 kcal mol The stability of the carbon which changes from sp^ to sp^ on formation of a carbocation increases with the extent of methyl substitution, equalling 147 kcal mol in the case of tert-huty\ cation, thereby accounting for the observation that the acidity of a branched hydrocarbon increases with the extent of methyl substitution. The volume of a methylene group decreases along with a decrease in the number of adjacent methyl groups. This is evident in Figure 12, where the methylene carbon adjacent to the methyl carbon appears less confined than the one next to it which is bonded only to methylenic carbons. The volume of the carbon atom in a methyl g r o u p and of the group itself decrease as the number of methyl groups substituted on a single carbon increases. The volume of a carbon a t o m also decreases with the extent of methyl substitution. In all of these cases, the volume decrease of the carbon a t o m is accompanied by an increase in its electron population and stability. If these are examples of what could be termed increases in steric strain, then such strain and its consequences must be sharply distinguished from the geometric strain found in small ring systems as described above. The two types of strain exhibit opposite behaviour with respect to the volume change accompanying increases in the stability and electron population of a carbon atom. This study of the properties of atoms in molecules shows that a carbon a t o m subjected to geometrical strain, an unsaturated carbon a t o m a n d an sp^ carbon in a carbocation exhibit similar properties with respect to changes in their atomic populations, energies

1. Atomic a n d group properties in the alkanes

59

and volumes. F o r example, reactions leading t o a reduction in geometric strain, in unsaturation or in positive charge will all proceed at a faster rate with a n increase in pressure, for all these reactions lead t o a decrease in the volumes of the associated carbon atoms. (The atomic volume decrease associated with the loss of charge in a reaction of a carbocation could be offset t o some extent by a n accompanying decrease in the electroconstriction of a solvent.) Most important, a carbon a t o m subjected t o a n increasing degree of geometric strain behaves increasingly like a n unsaturated carbon atom with respect t o the paralleling behaviour of its charges, stability a n d volume. T h e hydrocarbons also demonstrate that the volumes of atoms and of functional groups can be a characteristic property, one that is transferable between systems. E. Acyclic Hydrocarbons and Additivity of the Energy

It is clear from Figure 12 that t o within the accuracy of the plots shown in that figure, the charge densities of the chemically equivalent methyl a n d methylene groups a r e superimposable, as are the interatomic surfaces which define t h e atoms a n d t h e boundaries of the groups. This suggests that t h e groups are transferable a m o n g t h e molecules. This is further borne o u t by t h e corresponding constancies in t h e group populations and volumes discussed above. The energy is the most sensitive of properties and it is shown here that the energies of these same equivalent groups change by less than o n e kcal mol ~ ^ u p o n transfer a m o n g members of the series a n d thus the charge distributions a n d all of the properties of each group, including its polarizability, a r e predicted t o be transferable t o within the same experimental accuracy, as is indeed observed. The transferability of the polarizability of these same groups is demonstrated in a subsequent section. This constancy in properties a n d charge distributions requires that the equilibrium geometries of the groups remain essentially unchanged t h r o u g h o u t the series of molecules, as predicted by S C F calculations at the different levels of basis set. Table 1 permits a comparison of b o n d lengths at the 6-3IG* level of basis. Examples of the constancy in geometrical parameters using the D — H basis set are as follows: the b o n d lengths of the in-plane (H') a n d out-of-plane (H) hydrogens in the transferable methyl groups in p r o p a n e t o hexane all equal 1.0841 a n d 1.0850 A, respectively, while the corresponding bond angles vary by 0.02° about the value of 107.76° for H C H a n d by 0.01° about the value 107.67° for H C H ' , except for propane where it has the value 107.80°. A methylene bonded t o a methyl group has a C — H bond length of 1.0867 A a n d a n H C H angle of 106.25 + 0.01°. It is possible t o fit t h e experimental heats of formation of t h e members of the homologous series CH3(CH2);nCH3 starting with m = 0, with t h e expression AH° = 2A + mB where A is the contribution from the methyl group a n d B that from the methylene group. T h e generally accepted value of B at 25 °C is — 4.93 kcal mol ~ ^ while A = — 10.12 kcal m o l W i b e r g ^ ^ a n d Schulman a n d Disch^^ have shown that the correlation energy correction, the zero point energies a n d t h e change in AH° o n going from 298 t o 0 K are well represented by group equivalents. This is borne o u t by the fact that the additivity of t h e energy is recovered by single determinant S C F calculations which refer t o the vibrationless molecules at 0 K. Thus the total calculated molecular energies E can be fitted t o a similar relationship, with E = 2 ^ ° + mB° for all three basis sets with a m a x i m u m error of 0.05 kcal mol~ ^ This means that the calculated state functions, energies a n d charge distributions contain the necessary information t o account for the additivity observed in this homologous series of molecules. F o r the D — H basis set ^1° = - 39.62953 a u a n d B° = - 39.04743 au, where A° is the energy of a methyl group in ethane, equal t o |E(C2H6). It is clear from the group populations given in Table 4 that t h e methyl group in

60

Richard F. W. Bader

ethane is not identical to the corresponding group in the other members of the homologous series, and similarly, the methylene group differs slightly depending on whether it is bonded to one methyl or to two other methylenes. The small differences in populations found for these groups are to be anticipated as their environments change by correspondingly small a m o u n t s in these cases. In ethane, methyl is bonded to methyl, while in the other molecules it is bonded to methylene, from which it withdraws charge. Table 4 also lists the energies of the methyl groups relative to the constant A°, the energy of a methyl group in ethane. T o within the accuracy of the numerical integrations, the energy and populations of methyl are constant when it is bonded to methylene, and the M e group is the same in all members of the homologous series past ethane. T h e M e group in these molecules is more stable relative to methyl in ethane by an a m o u n t A £ = — 1 0 . 4 + 0.4 kcal mol ~^ a n d its electron population is greater by an a m o u n t AN = 0.0176 ± 0.0005e. The charges and energies obtained using the results of the 6-31G*/6-31G* and 6-31G**/6-31G* calculations behave in the identical manner, their values of A £ and AN being - 10.7 ± 0.9 kcal m o l " ^ and 0.0165 ± 0.005e for the former and - 1 0 . 5 ± 0.5 kcal m o l " ^ and 0.018 ± O.OOle for the latter. The charge and energy gained by methyl is taken from the methylene groups. W h a t is most remarkable, and what accounts for the additivity observed in these molecules is that the energy gained by methyl is equal to the energy lost by methylene. Table 4 Hsts the energies and charges of the methylene groups relative to the energy increment B°. O n e finds that in propane, where it is bonded to two methyls, the energy of the methylene group is B° — 2AE and it transfers 2AN e to the methyl groups, where AE and AN are the differences obtained above for the M e group bonded to a methylene. In butane, a methylene is bonded to a single methyl, its energy is given by B° — AE and its population decreases by AN to give a net charge qiCHj) = + 0.018. The corresponding CH2 groups in pentane and hexane, those bonded to a single methyl, have the same properties as the CH2 groups in butane. T h u s the central methylene in pentane and the two such groups in hexane, those b o n d e d only to other methylenes, should have an energy equal to the increment B° and a zero net charge. This is what is found to within the uncertainties of the integrated values. Therefore, methylene groups bonded only to other methylenes, as found in pentane and in all succeeding members of the series, possess zero charge and contribute the standard increment 5 ° to the total energy of the molecule. The group additivity scheme for the energy in hydrocarbons is not the result of methyl and methylene groups having the same energies in every molecule in spite of small changes in their environments. Instead, their properties d o change with changes in environment to give two kinds of methyl groups and three kinds of methylene groups. There are only three different CH2 groups because the change in environment is d a m p e d by a single such group. The underlying reason for the observation of additivity in the face of these small differences is the fact that the change in energy for a change in population, the quantity AE/AN, is the same for both the methyl and methylene groups. Thus the small a m o u n t of charge shifted from methylene to methyl makes the same contribution to the total energy. Reference to Table 1 shows that nearly all of this small shift in charge and its accompanying change in energy are restricted to the carbon atoms of the methyl and methylene groups, the properties of corresponding hydrogen atoms remaining essentially unchanged. This is to be expected, as it is the carbons that are bonded and share a c o m m o n interatomic surface and the charge transfer is accomplished by a small shift in this surface. This shift is reflected in the movement of the C — C b o n d critical point 0.003 or 0.004 A in the counter direction of the charge transfer and the bonded radius of the methyl carbon is slightly greater than that for the methylenic carbon. Since the transfer of charge occurs between chemically similar atoms, the resulting change in energy is zero. It is also necessary that the change in correlation energy for a change in population be the same for both groups if one is to account for the experimental observation of group additivity of the energy.

1. Atomic a n d group properties in the alkanes

61

It is t o be emphasized that there is n o a priori reason why the energy of the central transferable methylene g r o u p in pentane or hexane, as defined by t h e surfaces of zero flux in the gradient vector field of the charge density, should have a n energy equal t o the constant B° appearing in the expression E = 2A° + for t h e total calculated energies, a n equation which mirrors the expression for the experimental heats of formation. It is straightforward to use q u a n t u m mechanics to relate a spectroscopically measured energy t o the theoreticafly defined difference in energy between two states of a system. I n a less direct, b u t n o less rigorous manner, q u a n t u m mechanics also relates the difference in the experimentally determined heats of formation of pentane and hexane to the corresponding, theoretically defined energy of the methylene group. F. Physical Basis For Transferability of Group Properties

According t o equation 23, which determines the mechanics of an a t o m in a molecule, an a t o m responds only t o the total force 23

5.5 9.0

52 90 103

4.9 4.9

83 79

TABLE 6. Rotational barriers (kcal mol ^) in hexaalkylethanes Compounds

Ri

R2

expt.

References

McgC—CMeRiR^

Me Me Me i-Pr i-Fr

Me Et

CMe2Bu-t i-Pr t-Bu

8.4 9.4 11.7 8.7 11.0

64 61,83 61 90 89

H Me i-Pr t-Bu

H Me i-Pr t-Bu

8.4 10.4-10.7 10.3 13.8

64 57,61,83 57 57,63

RiCH2C(Me)2—C(Me)2CH2R2

3. Conformational analysis of acyclic and alicyclic saturated hydrocarbons TABLE 7. Rotational

barriers

(in kcal mol

in

compounds

117

tert-

butyl—C(X)RiR^ Rotational barrier

Ri Me Me Me i-Fr t-Bu t-Bu

R2

r-Bu—C(Me)RiR2

Me

8.4 9.4 8.7 11.0

Et i-Fr i-Fr i'Fr t-Bu

-(CHJ3-(CH^)^-

-(CHJv-(CH^),-

t-Bu—CHR^R2 References 6.9 6.3 6.0 7.3 7.6,8.4 8.0 6.0 6.3 7.4 7.8 7.3 7.3

64,83,107 61,83 83 52 89 117 118 118 118 118 118 118

barrier^^'^^^'^^^. It is reasonable to expect R^ a n d R^ in such molecule to prefer a position anti to the C(Me)2R group, and thus to have no interactions with groups at the other end of the central b o n d either in the g r o u n d or the transition state for rotation. The undeniable affect of R on the barrier must therefore be indirect, a n d a buttressing of the CH2 g r o u p to which it is attached has been suggested^^'^^^. With one fewer substituent, barriers to tert-butyl g r o u p rotation in pentasubstituted ethanes are rather smaller. Table 7 shows the reduction in rotation barriers in tert-butyl—C(Me)R^R^ when the methyl g r o u p is replaced by a hydrogen atom, and barriers for some other pentaalkylethanes. The measured t^rt-butyl rotational barriers in c o m p o u n d s t - B u — C H 2 R are 4.9 a n d 4.3 kcal m o l " ^ for R = C H 3 a n d R = H, respectively^^'^^'^^'^^. The values are also for a straightforward rotation, although in the former case there is undoubtedly some slight skewing away from perfect staggering in the g r o u n d state. F u r t h e r examples exist in highly branched hydrocarbons which involve a considerable degree of co-operative rotation of several groups. Such conformational interconversions are normal when alkyl groups, particularly the unsymmetrical ethyl a n d isopropyl groups, interact with each other a r o u n d a centre or other simple structural feature. The subject has been reviewed recently^ in a slightly wider context t h a n that of hydrocarbons. An example, tris-isopropylmethane, is now given in some detail.^^ The preferred conformation is calculated to be one in which two of the groups have the isopropyl hydrogen gauche in the same sense to the unique hydrogen while the third g r o u p is anti, although skewing makes dihedral angles quite different from the perfectly staggered values implied by conformation 35 (and methyl g r o u p hydrogens are skewed as well). This conformation is only slightly m o r e stable than a conformation like 36 with all three groups gauche in the same sense, a n d there is a barrier to interconversion of 35 and 36 which is calculated to be 3.4 kcal mol N M R coupling constants agree with an equilibrium involving these structures, but the picture has to be extended somewhat, because there are clearly three equivalent versions of 35 depending on which of the three isopropyl groups is anti, a n d these with 36 m a k e u p one set of conformations. There is a second set of conformations equivalent to the first except that all gauche groups are gauche in the opposite sense, e.g. 37 and 38. The barrier to interconversion of the sets is calculated to be 5.3 kcal mol " \ and this is borne out by N M R observations of a dynamic process with a barrier of 6.6 kcal mol

118

T h e analyst m a y well feel that in a molecule like this, interactions along any one b o n d and rotation a b o u t that b o n d are only a small part of the picture. T h e methyl hydrogens in adjacent isopropyl groups thus help define the molecular conformation by interacting t h r o u g h space (their relationship t h r o u g h b o n d s is 1,7). Immediate interactions along any o n e b o n d a n d rotation a b o u t that b o n d are only a small part of the picture so that comparison of the size of 'barriers' in different molecules, as m a d e earlier in this section with simpler molecules are not particularly helpful. When all groups are branched, every molecule is a special case.

V. CYCLOHEXANE AND ALKYLCYCLOHEXANES A. Cyclohexane

The conformation of cylcohexane is a chair, as described in the chapter o n structure. The twist-boat conformation has been measured^ t o be 5.2 kcal mol ~^ less stable t h a n the chair a n d the barrier t o interconversion of the chair a n d twist boat is a b o u t 10.1 kcal m o l " ^ in the liquid phase^^^'^^^ a n d slightly higher in t h e gas phase^^^ (10.4 kcal mol ~^), while pressure increases the rate of the p r o c e s s ^ A s u m m a r y of a considerable body of experimental work o n this topic is given in these last references M a n y calculations have been m a d e of cyclohexane, for the success of such calculations is a measure of the success of a program. Some accounts of these have been given^^'^^"^. B. Monoalkylcyclohexanes

The conformational questions here are n o t only of axial o r equatorial preference {A value^^^'^^^), but also of the rotational conformation a b o u t the alkyl-to-cyclohexyl bond. The ethyl, isopropyl a n d tert-butyl groups serve as models for a n y primary, secondary or tertiary alkyl group, a n d the methyl a n d tert-butyl groups have a rotational isotropy not present in the ethyl a n d isopropyl groups. T h e A value is a treacherous universal measure of steric size because of the restraints t o reducing steric strain by rotation o r

3. Conformational analysis of acyclic and alicyclic saturated hydrocarbons

119

other distortions that the cyclohexyl ring must obey. M u c h of the interest of the acyclic alkane conformational analysis comes from the complexity of additional choices in such molecules compared with cyclohexane. There is nothing remarkable about the conformation of the exocyclic b o n d in methylcyclohexane^^^'^^^ and, in both axial and equatorial ethylcyclohexane, the conformation with the methyl group gauche to both ring-CH2 groups is less stable than those where it is gauche to one ring-CH2 group and to the methine h y d r o g e n I n the equatorial conformation of isopropylcyclohexane, behaviour quite analogous to that of 2,3-dimethylbutane is observed. The opening-up of the methyl-C-methyl and C H 2 — C — C H 2 b o n d angles at either end of the exocyclic b o n d means that enantiomeric conformations 39 and 40, and conformation 41 are of apparently equal energy, as shown by observation^ of the ^^C N M R spectrum at - 1 6 5 °C, and by calculation

Me Me Me

Me

(39)

(40)

Me kMe H (41) O n the question of how cyclohexane accommodates a tert-butyl group substituent, calculation s u g g e s t s ^ t h a t torsion about the exocyclic b o n d relieves strain a n d the perfectly staggered arrangement is a transition state between conformations skewed by 6-10° in the equatorial and 15-27° in the axial conformation, where parallel 1,3-interactions are n o d o u b t greater. H o w the ring distorts in these monoalkylcyclohexanes has also been studied^^^'^^^'^^^ The A value, the free-energy difference between the two chair conformations with axial and equatorial alkyl groups, is widely used as a measure of steric size^^^'^^^. F o r all alkyl groups there is less than 7% of the axial conformation present at ambient temperature and direct quantitative observation of the equilibrium is not possible. Historically, indirect examination of conformational equilibria in disubstituted cyclohexanes has been used to predict equihbria in monoalkyl c o m p o u n d s (assuming additivity of substituent effects), and reviews of early work in this field and of the pitfalls encountered have been given M o r e recently, direct observation of the conformational mixture by N M R spectroscopy at low temperatures^^^'^^^'^^"^j sometimes using enrichment of the axial isomer population by rapid cooling of a high-temperature equilibrium mixture, has been possible. Along with this, the reliabihty of molecular mechanics calculations of saturated hydrocarbons has led to a clear picture of the equilibrium. One important point to emerge is that, while the enthalpy of methyl, ethyl and isopropyl groups is similar, there are important differences in entropy between some axial and equatorial conformations as well as between s u b s t i t u e n t s ^ S o m e of this is due

120

J. E. Anderson

to easily understood conformational entropy. F o r isopropylcyclohexane there is only one likely axial conformation 42, b u t three equatorial conformations which have been measured experimentally to be of equal e n t h a l p y ^ T h e r e is therefore expected t o be three times as much of the equatorial conformation t h a n is predicted o n considerations of enthalpy alone. W h a t is less clear is whether other terms such as vibrational entropy differ between conformations. In the case of methylcyclohexane, which has been m u c h studied a n d in which there is n o possibility of conformational entropy, there does a p p e a r to be an entropy term favouring the equatorial conformation slightly, so that steric strain n o t only disfavours the axial conformation enthalpically, b u t also by restricting higher frequency vibrations a n d torsions it has a n effect o n the entropy term. Calculated values for the enthalpy difference^^^ are 1.78, 1.81 a n d 1.71 k c a l m o l " ^ for methyl, ethyl and isopropyl axial vs equatorial a n d 4 . 8 k c a l m o l ~ ^ for tert-butylÔther references^^^'^^"^ will lead t o earlier calculations which are n o t greatly different. Various experimental measurements agree reasonably well with these^^'^^^'^'^''^. C. Polyalkylcyclohexanes

It is n o t dificult t o imagine that there is considerable scope for conformational analysis of dialkylcyclohexanes a n d polyalkylcyclohexanes, m a n y of which have been prepared in a state of high stereochemical p u r i t y I n the case of 1,3- a n d 1,4-disubstituted and 1,3,5-trisubstituted cyclohexanes, conformational effects are expected t o be nearly additive b u t there m a y be some interest in the extent to which they a r e n o t exactly so. Dialkylcyclohexanes with tert-butyl as alkyl groups have received detailed consideration as discussed in Section V.E below. I a m unaware of systematic work on 1,2-dialkycyclohexanes, although the interaction between substituents in such cases should be interesting. 1,2,3,4,5,6-Hexaalkyl cyclohexanes have received some attention, the ring inversion of the all-c/5 hexamethyl c o m p o u n d being discussed below. A crystal structure determination of all-equatorial hexaethylcyclohexane^^^ gains interest from the fact that hexaisopropylcyclohexane with all isopropyl groups equatorial is less stable t h a n its conformational isomer with all isopropyl groups axial, reflecting interactions of isopropyl g r o u p s ^ A n alkyl g r o u p flanked by four methyl groups in cyclohexane might have little reason t o prefer a n equatorial position t o a n axial one, since its interactions with methyl groups when equatorial resemble its transannular diaxial interactions when it is axial^^% t h o u g h in fact the opposite is observed with a chloro, b r o m o o r hydroxy substituent^^^. Isotope effects on conformational equilibria have been studied using cyclohexane as a test bed^^^"^"^^. In monodeuterocyclohexane^"^^^ a n d monotritiocyclohexane^"^^^ deuterium a n d tritium are m o r e stable in the equatorial position t h a n in the axial position by 8.2 a n d 1 1 . 2 c a l m o r \ respectively. D. Chair-Chair Interconversions

O n e much-studied subject is the ring inversion of cyclohexane a n d polymethylcyclohexanes, as shown in Table 8. T h e subject h a s been reviewed^^^ but, very generally, c o m p o u n d s with flattened chair conformations d u e t o m e t h y l - m e t h y l 1,3-diaxial interactions^'^^'^'^^ have lowered barriers. Simply substituted c o m p o u n d s where rotation a b o u t substituted bonds c a n take place in the b o a t - t w i s t manifold of conformations have barriers similar^^^'^"^^ t o that of cyclohexane, while m o r e highly substituted c o m p o u n d s , where rotation a b o u t substituted bonds must take place o n the way t o the transition state^'^^"^'^'^, have markedly higher barriers t h a n in cyclohexane. Various studies have been reported of cyclohexane rings with one or m o r e h y d r o c a r b o n rings attached spiro-fashion^'^'^^'^'^^"^^^ In c o m p o u n d 43^^°, there is a n equilibrium

3. C o n f o r m a t i o n a l

a n a l y s i s o f acyclic a n d alicyclic s a t u r a t e d h y d r o c a r b o n s

121

TABLE 8. Barriers (kcal mol ~ ^) to ring inversion of polymethylcyclohexanes Barrier

Substituents

10.3 10.3 10.3 9.8 9.8 8.7 11.4

[M]d

(58)

-7.4*»

(59)

expected that the hydroxy g r o u p of 58 would have little additional rotatory effect. Molecular modeling^^ gave the torsion angles shown in Table 20. The sum of the sines of these angles is —0.2944, whence the calculated rotation is [M]D = - (0.2944/sin 60°)i^(C—H)^ = - 20.4° It is noteworthy that the sum of the sines of the internal (acute) angles is almost exactly zero ( - 0 . 0 0 7 ) . The fact that the calculated rotation is larger than that observed might suggest that obtuse angles have lower rotatory power than acute angles. Since trans-decalin is achiral, the rotations of the decalols serve as a measure of the change in molecular rotation to be expected on insertion of a hydroxy group in other c o m p o u n d s containing trans-fused cyclohexane rings. The two possible equatorial TABLE 20. Torsion angles for (R, R)-( —)-trans-hydrindane

Skew unit

Torsion angle

Sine

Symmetry multiplier

0.85373

x2

6-7-8-1 = 5-4-9-3

+ 175.13

0.08490

x2

5-6-7-8 = 6-5-4-9

-55.00

-0.81915

x2

4-5-6-7

+ 54.36

+ 0.81269

6-7-8-9 = 5-4-9-8

+ 58.62°

-61.98

-0.88278

+172.28

0.13433

1-8-9-3

+ 46.54

0.72585

2-1-8-9=2-3-9-8

-37.30

-0.60599

x2

-158.30

-0.36975

x2

+14.29

0.24683

x2

7-8-9-4 7-8-9-3 = 1-8-9-4

2-1-8-7 = 2 - 3 - 9 - 4 1-2-3-4=8-1-2-3

x2

4. Chiroptical properties of alkanes and cycloalkanes

171

secondary alcohols of this series (60,61) have been prepared via resolutions expected to give optically pure materials and their configurations have been defined by their relation ships to monocyclic c o m p o u n d s T h e corresponding ketones give C o t t o n effects as expected under the O c t a n t Rule. The rotation of the trans-leq-dQca\o\ (60) ( [ M ] D + 62°) is attributable to the right-gauche conformational relationship of the hydroxy g r o u p with C(8)- The hydroxy g r o u p of the trans-2eq-dQCSi\o\ (61) is anti to b o t h C(4) and C(9) and would be expected to m a k e essentially no contribution to optical rotation ([M]DH- 1.9°; ethanol). These rotational shifts correspond well with those observed in the steroid s e r i e s ^ ( s e e 62, which is configurationally related to 60, and 63, rings A and B of which are enantiomeric to 61).

CM]D+62o

(60)

(62)

(61)

(63)

W h e n the rotational shifts of hydroxy groups in the decalols are applied to the transtransoid-trans-perhydrophensLnthrols (64-68), it becomes possible to deduce the rotatory contribution of the parent hydrocarbon ( P H P ) (69). (Note that the configuration of the ring in 67 is opposite to that in the other c o m p o u n d s of this series) G r a n t i n g that there is considerable spread a m o n g these values, the average rotation for 69 is found to be + 55.7°, which is quite close to the value [ + /c(C—H)^] expected from the simple four-atom analysis seen in 69. It might be argued that 68 contains a crowded hydroxy group and should not be included in the average; if so, the average value becomes + 62.4°. Perhydrotriphenylene 70 is of interest because it forms inclusion c o m p o u n d s ^ I t is chiral and has been obtained in nonracemic form by peroxide decarboxylation of the acid (71), which could be resolved to apparent enantiomeric purity. A sample of the ( + ) acid (40% optical purity) was degraded to the ketone (72) ([M]^^'' + 3 3 2 ° ) ^ T h i s showed a positive C o t t o n effect in the O R D , at 308-272 nm, allowing assignment of configuration by use of the O c t a n t Rule (72b). A simple four-atom analysis indicates that 70 should have a rotation of — 3/c(C—H)^ or —180°. In contrast with the value for trans-1,2-

OH(eq) OH(eq)

PHP = -58'' (65)

PHP=-8r

(64)

PHP=-51.8*' (66)

(ax)Ha

OH(eq) [M]D + 120.6 T - ^ , .

(5)

n^/T(R.)

The units of Kpj are (atm)^" where An = Y^j^j — Hiî- If species concentrations are used rather t h a n pressures, then the equilibrium constant is written K^j and it has the units of (concentration)"^", where concentration is expressed either in mol liter or mol cm The two equilibrium constants are related by the equation Kp = K,x{R'Tf^

(6)

where R' is the gas constant, but now in units of l a t m m o l " ^ K ~ ^ (0.08205) or c m ^ a t m m o r ^ K " ^ (82.05). The Gibbs free energy represents the driving force of a reaction: a large negative value for AG means a large value for or K^, which means equilibrium favors products of the reaction. A large positive value for AG means a small equilibrium constant, which means that reagents are favored. N o t e that whether a reaction will actually proceed to equilibrium or n o t — a n d at what r a t e — m a y be controlled completely by kinetics, not thermochemistry. The driving force of a reaction represents the net result of two opposing tendencies: equihbrium is favored by a lower potential energy (or enthalpy) state, b u t a higher entropy state. That is, potential energy (or enthalpy) tends to decrease while entropy tends to increase. Historically, before the principles of thermodynamics were thoroughly understood it was thought that the energy alone was the driving force of a reaction. These ideas are expressed quantitatively by the relationships G = E + PV -TS

= H-TS

(7)

where £ , H and S are energy, enthalpy (also called heat content) and entropy, respectively. (Formal derivation of the fundamental relationships of thermodynamics is outside the scope of this chapter; our purpose in this section is merely to gather all the equations necessary for an understanding of the remainder of the discussion.) F o r most practical purposes, enthalpy is more useful a concept than energy, and we will not discuss E further. Both enthalpy and entropy are related to the heat capacity of a substance by relationships such as

CT2

AHr,-AHr,=

CJT P^

(8)

C,d\nT

(9)

Here, Cp is the heat capacity at constant pressure. It is related to the heat capacity at constant volume, by C, = C, +

PV/T

= C, + R (for ideal gases)

(10)

Since equilibrium constants are related to Gibbs free energy, and the latter in turn is related to H and S, it is apparent that in some sense, heat capacities are the fundamental quantities from which all the others can be derived. Equations 8 and 9 provide recipes for calculating changes with temperature in the enthalpy and entropy of a substance. Complete evaluations still require knowing these

6. T h e thermochemistry of alkanes a n d cycloalkanes

219

properties at T = 0 (or some other base temperature) a n d what A H a n d A 5 are for each phase change, such as melting o r sublimation. The third law of thermodynamics, namely that the entropy of a pure crystalline substance approaches zero as T approaches absolute zero, anchors t h e entropy scale. Nevertheless, difficulties in measuring or calculating heat capacities at very low temperatures m a k e it particularly useful t o have in h a n d a value of the entropy at some temperature. There is n o corresponding law regarding enthalpies: i.e. even at absolute zero a substance has a residual heat (or energy) content. While there are procedures for calculating the heat capacity of a substance (and hence, changes in enthalpy o r entropy with temperature), which we will present later in this chapter, there is n o practical way t o calculate A^f/o given our current knowledge. Hence, apart from very approximate estimating schemes, o n e is forced t o rely o n experimental measurements t o anchor the enthalpy scale. Similarly, the enthalpy changes associated with phase changes must be measured experimentally (or estimated only approximately). F r o m the above relationships, it should be apparent that, if there are n o phase changes involved, we can characterize the thermochemistry of a substance if we k n o w AfH a n d S at some temperature (tables and compilations list either A^Hq, AfH2-73 o r AfH298) a n d Cp as a function of temperature. F r o m the thermodynamic quantities for the reagents and products of a reaction, it is possible t o derive the corresponding quantities for the reaction itself (i.e. the net change in properties in the course of a reaction, defined by equations of the form of equation 3). F o r the practitioner concerned with chemical processes, whether in a catalytic cracking plant o r a pharmaceutical laboratory, t h e equilibrium constants, o r K^, are t h e quantities of primary concern. If the kinetics are favorable, c a n the reaction proceed as written? W h a t is the m a x i m u m product yield? Will the yield increase if the temperature is raised? T h e equilibrium constant indicates t h e m a x i m u m possible yield, a n d its temperature dependence reveals h o w t h e yield c a n change with temperature. T h e thermodynamic quantities (G, H and S) used to calculate K relate the equilibrium constant to fundamental physical quantities. Thus, while tables of equilibrium constants m a y appear t o be arrays of arbitrary numbers, tables of thermodynamic quantities reveal structural relationships that can be used t o predict equilibrium constants for processes never previously studied. Hence, the scope of this chapter is t o provide the reader with a n appreciation for the data a n d techniques available (and their accuracy) for evaluating fundamental thermochemical quantities that a r e necessary for understanding t h e chemistry of the hydrocarbons. B. Statistical Thermodynamic Relations

Statistical thermodynamics provides exact formulas for t h e calculation of t h e fundamental quantities of heat capacities, enthalpies and entropies, provided that certain assumptions are vahd. A m o n g these assumptions are: (1) Translational, vibrational, rotational a n d electronic degrees of freedom a r e completely separable for the molecule of interest. (2) T h e rigid-rotor harmonic oscillator approximation provides a n adequate description of molecular properties. (3) T h e gaseous species obeys the ideal gas equation of state. A fundamental equation of statistical mechanics is that for the partition function, g , for a collection of identical molecules: Q = Y.Pi^xp(-eJRT)

(11)

220

N . Cohen a n d S. W. Benson

where Pi is the n u m b e r of discrete states (the degeneracy) that have energy in a system at equihbrium at temperature T. T h e various thermodynamic properties are defined in terms of the partition function. In this discussion, we are interested in only f o u r — h e a t capacity at constant volume, entropy, internal energy a n d enthalpy: CJR = (3 In Q/S In T), + (3^ In e/^(ln T)\ =

(12)

{SHnQ/3{l/T)\

S/R = \nQ-i3\nQ/S(l/T))/T

(13)

E/R=-{S\nQ/3{l/T)\

(14)

H/R=-{S\nQ/S{l/m+T

(15)

If the various degrees of freedom are separable (assumption 1 above), then the partition function can be factored into the product of partial partition functions: e=e.ra„.xnewb,.xao.xe,„,

(i6)

The factors on the right-hand side of equation 16 can be expressed in terms of various molecular properties: Q,,^^,= Vx{2nMkT/hfi^

e,i,, = ( l - e x p ( - H A T ) ) - i

(17)

(18)

for the ith vibrational mode. T h e total partition function includes one such factor for each vibrational mode. The rotational partition function (for external rotation, or rotation of the molecule as a whole) depends on whether the molecule is linear (2 degrees of freedom) or nonlinear (3 degrees of freedom): erot-2D

= (8^'^^^/^')/ê

erot-3D = {n"^lo:){^nÎJiTlh^fl^ eelec

= Z^.eXp(-£fAr)

(19) (20)

(21)

All the hnear (i.e. noncyclic) alkanes have internal rotations a b o u t the C — C bonds. F o r each internal rotation, if there is n o energy barrier to rotation, the partition function for free internal (one-dimensional) rotation is

Gf.i.r = (8^'î.r.^^/^')''>i

(22)

In equations 17-22, h is Planck's constant, k Boltzmann's constant, V the molar volume, M the molecular weight, a n d o-j are the symmetry numbers for external or internal rotation, respectively; / is the m o m e n t of inertia a n d is the p r o d u c t of principal m o m e n t s of inertia (for external, or overall, rotation), 1-^^ is the m o m e n t of inertia for internal rotation, g-^ a n d &i are the degeneracy a n d energy level of the ith electronic level. In general, hydrocarbons have n o low-lying excited electronic states, a n d t h e degeneracy of the g r o u n d state is unity; hence Q^^^^ = 1. (For alkyl free radicals it is generally assumed that the g r o u n d state has spin \ a n d hence Q e i e c = 2.) Since there are no linear (i.e. two-dimensional) alkanes or cycloalkanes, we d o n o t need equation 19 for the two-dimensional rotor. F o r computational purposes, it is m o r e convenient t o work in molar rather t h a n molecular units. I n the following expressions, we have evaluated all the numerical constants in molar units. T h e Boltzmann constant, /c, is thus replaced by the universal gas constant, R = NQ/C = 1.987calmol~ ^ where No is Avogadro's number. W e can evaluate equations 1 2 - 1 5 for the thermodynamic functions using the specific formulas of equations 17-22. T h e results are summarized below.

6. The thermochemistry of alkanes a n d cycloalkanes

221

C. Translation

Qtra„s)/^ = f

(23)

(25)

KUPT = I (^T-ôUs/^^ = f

(26)

^t°rans/^ = - 1.16 + (f) In M + (f) In T + In w = 13.08 + (f) In M + (f) In (7/298) + In n

(27)

where, in the last expressions, M is molecular weight in daltons a n d n is the number of optical isomers (discussed further below). D. External Rotation (three dimensions)

^p(e r

^ f (rigid-rotor harmonic oscillator)

ElJRT = l {H^^-HllJRT = l SIJR = - 0.034 + 1 In T + f In

(28)

(29) (30) - In

= 11.5 + f ln(T/298) + | l n ( / J a ^ 2 )

(7,

(31)

where, in the last expression, 7^, the product of principal m o m e n t s of inertia, is in units of (dalton cm^)^. The subscript 'e.r.' signifies external rotation contribution. Because the translational functions (equations 23-27) depend only on parameters that are k n o w n precisely, they can be calculated exactly. It is useful t o remember this, since the translational contribution is generally by far the largest of the several degrees of freedom. T h e m o m e n t s of inertia of the molecule depend o n its large-scale spatial configuration—whether it is approximately linear, tightly coiled or somewhere in between (i.e. the rigid-rotor assumption m a y n o t be a good one). F o r example, the difference in rotational entropy between gauche- and trans-butane is approximately 0.3 eu ( l e u = l entropy u n i t = l gibbs mol~^ = 1 c a l m o l " ^ K~^). F o r decane, the entropy difference between stretched and coiled configurations is approximately 0.7 eu. Thus, for a large alkane, there is some uncertainty in the rotational contributions to thermodynamic functions. I n principle, one would perform some sort of time-averaged calculation over the various spatial configurations. In practice, one should expect a n uncertainty on the order of 0.5 eu in the calculation. E. Internal Rotations

Internal rotations are generally treated by considering the m o d e as a free rotation (no potential energy barrier), and then by making approximate corrections for the effect of the barrier. Calculating the properties of free rotation is handicapped by the difficulty in evaluating the m o m e n t s of inertia for the internal rotation. M o s t computational schemes rely o n a n approximate procedure developed by Herschbach a n d coworkers'^. This involves calculating the moments of inertia of each of the t w o moieties attached to the b o n d that is the axis of rotation, a n d 7^. Then, l/7ir=l/7,+ l/7,

(32)

The separate m o m e n t s 7^ and 7^ are estimated by assuming that each moiety is a t o p rotating a b o u t a n axis parallel t o the b o n d joining the two moieties and passing t h r o u g h

222

N . Cohen and S. W. Benson TABLE 1. Approximate moments of inertia for some free rotors Rotor 3.0 20 28 56 80 100

CH3

C2H3 n-C3H, 1-C3H,

n-C^Hg t-C4H9

"Units are (dalton A^)^, calculated assuming the rotor is connected to an infinite mass and rotates about an axis through its own center of mass and parallel to the C — C bond connecting the rotor to that infinite mass.

its own center of gravity. In Table 1 we list approximate moments of inertia for the rotors commonly encountered in evaluating properties of alkanes. F o r a free rotor with symmetry CJ, cyR=^2 EyRT {H°^-Hl\JRT

(33)

=^

(34)

=^

(35)

S° = - 1.1 + K In ( / i ' / > i ) + ^R\nT = 4.6 + R In (Iliya;) + | K In (T/298)

(36)

In equation 36, the units of I. ^ are (dalton A^)^. Frequently in the discussion that follows we refer to the intrinsic entropy, 5°^^. This is the entropy when the effects of symmetry and optical isomerism are neglected: •^HIT = 'ÔBSERVED + ^ (CT/H), whcrc (T = 0"^ X (JJ. Thc determination of symmetry n u m b e r a n d optical isomerism is discussed further below. If there is a potential energy barrier to rotation, the rotor is hindered. If the barrier is very low, the hindrance becomes inconsequential as temperature increases. If the barrier is very high, the rotor can be treated approximately as a torsional vibration. The spectroscopic vibrational frequency of a hindered rotor is given by v(in cm-')

= 360{T/29S){l/Qf){V/RTy'^

(37)

F o r V/RT> 10, the thermodynamic functions S\ G°/T and HyT of the rotor are accurately represented (within 0.05 cal mol~ ^ K~ ^) by the functions of the vibration with frequency given by equation 37. Only the intermediate case (V/RT 1) presents problems. The principal difficulty in this case is that of ascertaining with any precision the barrier height. This is a consequence of the fact that several different factors determine the barrier height, and all are highly sensitive to the interatomic distances involved. Furthermore, while most treatments to derive thermodynamic properties assume the barriers for an n-fold rotation (e.g. 3-fold rotation for a methyl rotor) are symmetric, this is not in general true. F o r example, for rotation about the central C — C b o n d in butane, the transgauche and gauche ^cis barriers are approximately 4 a n d 6 kcal mol ~ ^ respectively^. The effect of a barrier to internal rotation is to reduce the heat capacity, a n d hence the enthalpy, energy and entropy, of the free rotor. The numerical magnitude of the


223

TABLE 2. Approximate torsional barriers to internal rotation F (kcal mol" 1)

Bond

CH3—CH3 CH3—C2H5

2.9 3.3 3.3 3.8 4.7 3.5 4.2 [6.5] [10.9] 4.3 [8.9] 7.0 9.8 [10.8]

CH3—n-C3H7

CH3—1-C3H7 CH3

t-C^Yig

C2H5

C2H5

CHs-n-CjH,

C2H5—neo-C2Hii C3H7 t-C^Jtig Z-C3H7 —I-C3H7 /-C3H7 —i-C4H9 /-C3H7 — f - Q H g f^-C4H9—t-Cîrig /-C4H9 — t-Cîi-g 2,4,4-trimethyl-2-C5Hi 1— 2,4,4-trimethyl-2-C5Hi 1

Reference Pitzer^ Chao and coworkers^ Chen and coworkers^ Chen and coworkers^ Sackwild and Richards^ Chen and coworkers^ Sackwild and Richards^ Zirnet and Sushinskii^^'' Zirnet and Sushinskii^^ Lunazzi and coworkers^ S Jaime and Osawa Zirnet and Sushinskii^^ Anderson and Pearson Jaime and Osawa Anderson and Pearson Jaime and Osawa Zirnet and Sushinskii^^

13.8

Anderson and Pearson

Jaime and Osawa

"The values deduced by Zirnet and Sushinskii are reasonable, but the procedures by which they were derived are questionable; hence they should be regarded as only approximate.

effect depends on t w o parameters: V/RT, where V is the barrier height; a n d gf, the partition function for free rotation. Some barrier heights pertinent t o alkanes are listed in Table 2. The contributions to thermodynamic functions from hindered internal rotation were worked out in a series of papers by Pitzer a n d coworkers^'^ in the 1930s, '40s a n d '50s, a n d are tabulated by Pitzer a n d Brewer^^, to which the reader is referred for further details. Here, we simply note that a n uncertainty in V/RT of 4 . 0 + 1 . 5 (corresponding t o an uncertainty of 900cal m o l " ^ at 298 K — w h i c h is similar to the uncertainty for most barriers for rotors larger t h a n CH3) produces an uncertainty in rotational entropy of approximately ± 0 . 5 eu. Since a C„ alkane without rings has n — l internal rotations, this puts a lower limit t o the uncertainty in any calculation of the entropy of a n alkane of approximately 0.5(n — 3)eu for n ^ 5. F. Vibration

F o r a h a r m o n i c oscillator, Cl/R = {H^^-HXJRT

=

(38)

uê-"/(l-e-"f ue-V{l-e-")

SyR = ue-"/{l

- e-") - l n ( l -

(39) e-")

(40)

where w = 1.438 (oJT a n d a>i is the fundamental wave n u m b e r of the h a r m o n i c oscillator in c m ~ ^ Vibrational frequencies are n o t easily deconvoluted from raw infrared spectral data, especially for a molecule with more than 4 or 5 atoms. Alkane vibrational frequencies fall into a few classes (Table 3). The high C—H stretching frequencies are inactive except at very high temperatures; they contribute httle to the Cp (and hence to other functions), a n d errors in their values are inconsequential. Only errors in low frequencies are significant. An error of 2 5 c m ~ ^

224


TABLE 3. Characteristic frequencies for vibrational modes Vibrational mode

Approximate frequency (cm ^)

C — H stretch C — C stretch H — C — H bend (CH3 deformation, CH2 scissors) CH2 twist, wag C — C — H bend (CH3 rock) C — C — H bend (CH^ rock) C — C — C bend Ring deformations (in-plane) Ring deformations (out-of-plane) CH3—CH2R torsions (internal rotations) RCH2—CH2R torsions (internal rotations)

2850-3000 900-1100 1400-1500 1200-1400 900-1300 750-800 250-500 400-600 200-400 200-225 75-100

in a 200 cm ~^ frequency contributes approximately 0.2 eu error t o t h e entropy at a n y temperature from 200 t o 1500 K. The last two entries in Table 3 cover all t h e internal rotations of alkanes, which have characteristic frequencies just as d o vibrations. T h e first of the two includes a methyl g r o u p rotating against t h e rest of the molecule (R is any alkyl group); the second includes all rotations where both moieties are ethyl groups or larger. All routine statistical mechanical calculations for hydrocarbons assume vibrations are adequately described by the harmonic oscillator approximation. W e c a n get a rough indication of the magnitude of the possible errors this approximation causes by examining the isolated C H and C2 molecules, for both of which the required spectroscopic constants are available. F o r C H , the entropy correction is 0.012 eu at 298 K and 0.05 eu at 1000 K. F o r C2, which is more nearly harmonic, the corresponding values are 0.004 and 0.02 eu. An alkane, C„H2„+2, will have 2n + 2 C — H stretches a n d n—1 C—C stretches, each of which can contribute to the anharmonicity. Bending modes are more complex, b u t we c a n assess their importance from a study of the thermodynamics of C3 by Strauss and Thiele^^. F o r this triatomic molecule, they found that detailed q u a n t u m corrections (including anharmonicity) t o the rigid-rotor harmonic oscillator ( R R H O ) approximation decreased the entropy by 0.02 and 0.002 eu at 298 and 1000 K, respectively. These results suggest that near 298 K the R R H O approximation will underestimate S by a b o u t 0.01 eu per C atom, and by about 0.1 eu per C a t o m near 1000 K. F o r most purposes these are small errors, b u t certainly n o t negligible for decanes or larger alkanes. G. Symmetry Numbers, Optical Isomers, Entropy of Mixing and Some Kinetic Considerations

If there are two or more physically distinguishable isomeric forms, the entropy of a mixture must include a term for the entropy of mixing. F o r i different species, the mole fraction of each of which is n^, the entropy of mixing (per mole of final mixture) is given by

AS„.i„,= - « I " . l n ( » . )

(41)

If the different species have different enthalpies of formation, the rii will b e temperaturedependent a n d hence so will AS^.^.^^. If the species all have the same enthalpy a n d t h e same statistical probability, theiTthe rii are all equal (and independent of temperature), and A5^.^.^g = R\nn, where n is the n u m b e r of such species. This is t h e origin of t h e final term o n the right-hand side of equation 27.

6. The thermochemistry of alkanes and cycloalkanes

225

Optical isomerism will result if there is a chiral center, when the molecule will have the property of rotating a beam of polarized light. T h e two forms, or enantiomers, are designated R and S (from the Latin rectus and sinister, signifying right and left, respectively; formely, the designations dextro- a n d levo-, depending which one rotates the hght beam clockwise and which, counterclockwise, were used). If there are n chiral centers, there can be as m a n y as 2" optical isomers. An exception occurs when there are two identical chiral centers, as in 3,4-dimethylhexane, in which case there are only three optical isomers, since one of the apparent four is its own mirror image. This latter form is the m^5o-compound. (See Example 1 in Section XIII for more details.) Optical isomerism can also result without a chiral center: the most stable configuration of cyclopentane is nonplanar, so that the molecule and its mirror image are not superposable and n = 2. The symmetry number is easiest calculated by first treating the molecule as rigid and calculating the external symmetry number, a^. F o r CH4, 0-^=12; for any other linear unbranched alkane, (j^ = 6. F o r most branched alkanes, can be 1,2,3,4 or 6. Each internal CH3 rotor contributes a factor of 3 to (7^; each t-Bu rotor contributes a factor of 3"^: 3 for each CH3 g r o u p and 3 for overall symmetry of the three CH3 groups. Accounting properly for the effects of the symmetry number on b o t h thermochemical and kinetic properties has often led to computational errors in the past, a n d practitioners need to take care in their bookkeeping. Cycloalkanes present ample opportunities for such pitfalls. The simplest ring, cyclopropane, has an unambiguous symmetry number of 6. Cyclobutane would have 0-^ = 8 if it were planar, but there is some slight deviation from planarity, and actually = 4. Since the energy barrier to ring puckering is only about 1 kcal mol ~ \ the deformation from one side of the plane to the other is very rapid, and we could consider the molecule as dynamically planar a n d compute accordingly; it would simply be a matter of adjusting our bookkeeping (namely, the ring correction of Table 13) accordingly. However, we chose to m a k e o u r calculations with the symmetry number of 4. (A precise calculation of entropy would take into account the fact that cyclobutane is a mixture of puckered and planar molecules, the former more stable by about 1 kcal mol In the limit of very low temperature, the mixture consists entirely of puckered molecules; at high temperatures, | of the molecules are planar. The entropy of an equilibrium mixture will thus include a contribution from ^'^mixing ^^^^ approaches zero at low temperatures and approximately 1.4 eu at high temperatures. But between 298 and 1500K, AS^.^.^^ varies by less than 0.1 eu, and the mixing aspect can be ignored without serious consequence.) Cyclohexane exists in several n o n p lan ar structural configurations, of which the 'chair' is the most stable. In this configuration, for which cr^ = 6, there are two different kinds of H atoms: equatorial (approximately in the plane of the skeletal ring) and axial (approximately perpendicular to the ring). A second configuration, considerably more rigid, is the 'boat' form, in which two opposite H atoms are very close to one another (the 'bowsprit-flagpole' interaction). The more stable boat form is the 'twist boat' or 'skew b o a f form, in which the boat deforms slightly to increase the separation of the bowsprit-flagpole interaction. The twist boat is a b o u t 5.5 kcal mol ~^ less stable than the chair, and the boat form is about 1.6 kcal mol ~^ less stable yet. O n e chair form converts into the other (interchanging axial and equatorial H atoms) by passing through the 'boat' and 'twist boat' forms. The energy barrier to the transition is approximately 10 kcal mol Thus, at r o o m temperature or below, > 9 9 % of the molecules are in the chair configuration—although the lifetime for a particular molecule to transform from one chair form into another, interconverting axial a n d equatorial H atoms, is on the order of microseconds. Cyclopentane, as noted above, is also nonplanar, with two different configurations more stable than the planar: an 'envelope', with a = 1 and n=l, and a 'half-chair', with

226


n = 2 and a = 2. The envelope form is the more stable. Cycloheptane has n o symmetries (a = 1), thus consisting of fourteen nonequivalent stereoisomers. (Although kinetics problems are not directly in our present purview, we cannot entirely overlook them as one important area of application of thermochemistry. In predicting rate coefficients, one needs t o k n o w the n u m b e r of reaction p a t h s — o r , what is equivalent, the change in symmetry number in a reaction. T h e fact that cycloheptane is puckered poses the interesting question of whether the different H atoms (since at any given instant they are n o t all equivalent) have different reactivities. Strictly speaking, a separate rate coefficient calculation should be m a d e for each of the 14 nonequivalent H atoms; the total rate coefficient is then the s u m of the 14 individual o n e s — e a c h for a reagent of ( 7 = 1 . In practice, the differences in reactivities of the 14 H atoms are smaUer t h a n the uncertainties in the appropriate kinetic calculations. The single calculation c a n thus be carried o u t for a single reagent with cr = 14. I n the case of cyclohexane, it is k n o w n that the preferred conformation for substituents is invariably the equatorial position. This does n o t necessarily mean that the equatorial H a t o m is more reactive, b u t only that once substitution takes place, the equatorial position is the more stable.)

H. Deviations from Ideality: Real Gases

All the statistical mechanical formulas presented so far were evaluated assuming that the gas obeyed the ideal gas law PV = RT

(42)

where V represents the volume per mole of the gas at pressure P a n d temperature T. Real gases deviate from this behavior to a slight but measurable degree, and that deviation increases as pressure increases and temperature decreases. (As P/TÔ, molecules become less a n d less sensitive t o the presence of one another, a n d the behavior of a real gas approaches very nearly that of t h e ideal gas.) T h e behavior of a real gas is often characterized by a power series in F , namely PV/RT

=1+B/V

+ C/V^ + D/V^ + . • •

(43)

Such equations (sometimes the expansion is written in powers of P) are called virial equations of state, and the coefficients B, C, D,... are the second, third, f o u r t h , . . . virial coefficients. The thermodynamic functions Cp, H a n d S of the real gas deviate from t h e expressions already presented by correction factors that are functions of t h e virial coefficients. F o r example, the deviation of Cp from the ideal gas heat capacity, C°, is 1

17

^

given by^ (Cp - Cpx = - n(3^B/dT^)P

+ (3^C/dT^)PV2

+ •••]

(44)

T o a first approximation (i.e. if the molecules behave like hard spheres with n o other intermolecular forces), the virial coefficients are simply related t o the rigid-sphere collision diameter, cr, of the molecule: B = |7RIVO6

.5 5.09

4.83

2m5 AAfH°^g

>1 >S

4.92

> 2m6 4.73

5.00

> 2m7

3m6

4.97

> 3m7

5.07

Thus, the gain from the much greater effort of using a c o m p o n e n t scheme is negligible considering the ease a n d reliability of the g r o u p additivity scheme. W h e n experimental thermochemical quantities have been measured with a n uncertainty that is consistently smaller t h a n the error in g r o u p additivity predictions, it will be a p p r o p r i a t e t o reconsider replacing g r o u p additivity with a m o r e elaborate estimation scheme. Apart from this issue, it is i m p o r t a n t t o remember that tabulated enthalpies for alkanes other t h a n those hsted in Table 18 a r e all based o n approximative calculations, a n d a r e subject t o some error. Consider for example, the following 7 branched decanes, a n d t h e values of Af//° listed by SWS a n d A G : Alkane 4ip7 3ip2m6 4e24mm6 3e234m35 3344m^6 22344m^5 22334m^5

A,H°,g(SWS)

Af//°,g(AG)

Af//°,g(Gp.Add.Rev.)

-60.02 -61.11 -60.43 -60.09 -60.37 -59.04 -59.08

-60.71 -59.25 -61.11 -57.58 -59.37 -58.77 -58.27

-60.8 -61.6 -60.1 -60.1 -60.2 -61.0 -60.5

T h e differences between the three sets of values range u p t o 2.5 kcal mol ~ \ Bearing in mind the earlier statement that experimental uncertainties are of t h e order of 0.1 kcal mol ~^ per atom, we c a n n o t expect t o measure t h e enthalpies for these decanes to better t h a n + 1 kcal m o l " ^ uncertainty. T h e differences in t h e three sets of values are thus barely large enough t o be significant, a n d the g r o u p additivity values a r e as reasonable as any. VIII. ALKYL RADICAL GROUPS A. Enthalpies

Establishing values for b o n d strengths in the alkanes is equivalent t o determining t h e heats of formation of the various alkyl radicals; for this reason we consider also radicals in a chapter that should be dealing exclusively with alkanes. In order t o apply g r o u p additivity rules t o alkyl radicals, seven new groups have t o be defined a n d assigned enthalpy values: a = AfH°[C- - ( C ) ( H ) 2 ] b = AfH°[C- -(C)2(H)] c = AfH°[C- - ( C ) 3 ] d = Af/f°[C- -(C-)(H)3] e = AfH°[C--(C)(C-XH),] f= g=

AfH°[C--(C)2(C-XH)] AfH°[C--(C)3(C)]


259

TABLE 19. Experimental radical enthalpies of formation at 298 K Radical

AfH°^g(kcalmol-i)

Notes

Methyl Ethyl n-Propyl i-Propyl s-Butyl t-Butyl i-Butyl neo-Pentyl

35.1+0.15 28.4 + 0.5 23.4 + 1.0 20.0 + 0.5 15.0+1.0 9.4 + 0.5 (16.0 + 1.0?) 8.9 + 1.0

a b c d e f 9 h

"Dobis and Benson^'' determined a value of 35.06 ± 0.1 kcal mol~^ based on the kinetics of the reaction, CI + CH4;^HC1 + CH3. Pacey and Wimalasena^^ obtained 35.1 ± 0.5 from an ethane pyrolysis experiment. A shghtly smaller value of 34.8 + 0.3 was reported by Russell and coworkers^^ based on the same technique. The latter result is in g o o d agreement with the older CH4 photoionization spectral data upon which was based the value used by Chase and collaborators^^. We accept the results of Reference 57. The uncertainty in A[H° for CH3 is now limited by the uncertainty in the corresponding quantity for CH^. ''Two recent studies^^'^^ agree on the value shown, with stated uncertainties of 0.4-0.5 kcal m o l " ^ in each case resulting from the experimental uncertainties. A third experimental study^^ reported 28.3 + 0.4 kcal m o l " ^ Additionally, the calculated enthalpy depends on the value assumed for the entropy of the radical. An uncertainty of + 0.2 gibbs m o l " ^ in S°(C2H5) produces an additional uncertainty in A(H° of ± 0 . 0 6 kcal m o l " \ with the likely direction of the uncertainty in S° such as to result in underestimating AfH°. ^Marshall and Rahman recommended 22.6 kcal m o l " ^ Castelhano and Griller^* reported 22.8, but relative to an assumed Aff/°(298) for CH3 of 34.4 kcal m o l " ^ with the recommended value for the latter of 35.1, their AfH°(298) for C3H7 becomes 23.5. McMillen and Golden^^ had recommended 21.0 in Table 2 of their review, based on experiments pubhshed prior to 1969. We prefer the value of 23.4 + 1.0 kcal m o l " ^; this makes the enthalpy contribution of the e group the same as that of the S group. ''Castelhano and Griller^* measured 19.2 kcal m o l " ^ relative to the value for CH3, which, when corrected for the latter (see preceding note), becomes 19.9, slightly larger than the value of 19.0 + 0.5 obtained by Baldwin and coworkers^^. Doering^^ had recommended 20.0, while McMillen and Golden^^ recommended 18.2 kcal mol " \ The values for AfH° of n-Pr, i-Pr, Et and s-Bu radicals reported by Castelhano and Griller are consistent with the requirement of equation 67, which the recommendations of Reference 65 are not. In a recent reevalution, Tschuikow-Roux and Chen^^ recommended 21.0 + 0.5 kcal m o l " \ consistent with a small barrier of approximately 1 kcal m o l " ^ for internal rotation. Luo and Benson^^ derived a value of 20.0 + 0.5 by linear B D E relationships involving several molecules; we accept this value. ^Castelhano and Griller^* reported 13.9 kcal m o l " ^; correcting for the better value for the AfH{CH^) gives 14.6. McMillen and Golden^^ had recommended 13.0 based on experiments pubhshed prior to 1969. T o be consistent with equation 67, we recommend 15.0 kcal mol "^ ^The enthalpy of t-butyl has been the subject of considerable controversy, as reviewed elsewhere^^'''^. Values published in the past 25 years range from 7.5 to 12.5 kcal m o l " \ and even recent studies do not seem to be converging on a consistent number. Thus, Miiller-Markgraf, Rossi and Golden^ ^ recently determined a value of 9.2 + 0.5 from rate coefficients for the reactions of f-Bu with DBr and DI, whereas in contrast, Russell and coworkers''^ had recently reported a value of 11.6 + 0.4 from measurements of the kinetics of the forward and reverse reactions ^Bu + HBr^î-C^Hio + Br. Our choice of the value of 9.4 is based on evidence presented by Benson^^ ^This quantity has not been measured. The value assumed has been chosen to make the group contribution of / the same as that of the T group, which was also the basis for the assignment of O'Neal and Benson^^. Schultz and collaborators''^ argue for a value of 15.0, based on the assumption that the primary C — H bond strength is the same as in C3H6. Fliszar and Minichino'^^ find that 14.9 gives the best consistency in their study of charge distributions and bond dissociation energies in alkanes. ''The bond dissociation energy of neopentane was determined''^ to be 3.9 ± 1 kcal mol "^ smaller than that of methane, which is now accepted to be 105.1, making the neopentane bond 101.2. With AfH°(neo-C5Hi2)= - 4 0 . 2 we obtain AfH°(neo-C5Hii) = 8.9 kcal m o l " 1. McMillen and Golden^ ^ recommended 8.7.

260

N . C o h e n a n d S. W . Benson

Finally, there is the contribution from gauche interactions involving the •CH2 g r o u p if it is off the main chain, which we d o n o t discuss further here. As O'Neal a n d Benson have pointed out^^, only six of the g r o u p values are linearly independent; one can be assigned arbitrarily. As they did, we choose t o set d = F. T h e other six terms can be calculated from experimentally determined enthalpies of formation of the radicals ethyl, n-propyl, i-propyl, t-butyl, i-butyl a n d neo-pentyl. The enthalpy of 5-butyl can be substituted for that of either n-propyl or i-propyl. T h e relationships a r e as follows: a = AfH°(Et) - P

(64)

b = Af//°(j-Pr) - 2 P

(65)

c = AfH°(t-Bu) - 3 P

(66)

e = Af//°(n-Pr) - AfH°(Et)

(67)

[or e = Af//°(s-Bu) - 2 P - b)]

(68)

/ = AfH°(i-Bu) - AfH°(Et) - P

(69)

g = Af//°(neo-Pn) - Af//°(Et) - 2 P

(70)

In order t o be consistent, the t w o relationships involving e (equations 67 a n d 68) require that Af//°(5-Bu) = Af//°(n-Pr) + Af//°(i-Pr) - AfH°(Et)

(71)

T h e values for the radical enthalpies of formation are listed in Table 19, together with references. W i t h t h e enthalpy values of Table 19, a n d using equations 4 5 - 4 8 , 50 a n d 51, we c a n derive the g r o u p values for the free radical groups as follows: a = 38.4 ± 0.5 ^ = 40.2+1.0 c = 39A ± 0.5 d=-

10.0

e = -5.0+1.5 / = - 2.4 ± 1.5 ^ = 0.5 + 1.5 T h e values given previously by Benson in Reference 34 for these seven parameters are 35.82, 37.45, 38.0, - 1 0 . 0 8 , - 4 . 9 5 , - 1 . 9 a n d 1.5 kcal m o l " \ respectively. (Earlier, O'Neal a n d Benson^^ h a d selected 37.0 for c.)

B. Entropies and Heat Capacities

O'Neal a n d B e n s o n h a v e carried o u t a detailed analysis of the entropies a n d heat capacities of alkyl free radicals, and we refer the reader to their work. It is w o r t h noting that entropies a n d heat capacities for free radicals are n o t measured directly, b u t either calculated by one of the techniques outlined earlier o r inferred from experimental kinetic measurements in conjunction with some calculations. Principal sources of uncertainty in such calculations have been, a n d continue t o be, questions of structural symmetry and barriers to internal rotations in the radicals. The calculation of S^g^ for the t-butyl radical illustrates b o t h of these uncertainties. O'Neal a n d Benson^^, and later Benson^^, assumed that the radical site in planar, a n d thus h a s a symmetry n u m b e r c = 162 (6 for


261

the overall symmetry a n d an additional factor of 3 for each of the methyl rotors). B e n s o n f u r t h e r assumed a rotational barrier of 3.0 kcal mol " \ down from 4.7 kcal mol ~ ^ in the parent alkane, neopentane. With these assumptions, he calculated a value of 72.1 eu for S^^^. Pacansky a n d Chang"^"^, on the basis of infrared matrix isolation studies, concluded that the radical has C^^ symmetry (thus (7 = 81), a n d the rotational barrier is only 0.5kcalmol~^; Pacansky a n d Yoshimine^^ later revised the latter value to 1.5 kcal mol~ ^ With these changes, S^^g is 74.6 eu. This value is compatible with a value for Af/Z^^g of 10.1 kcal m o l " ^—disconcertingly larger than the value recommended in Table 19 above. Entropies of other radicals are subject to similar uncertainties. It should be stressed that rotational barrier heights are the largest source of uncertainty in calculated entropies a n d heat capacities of free radicals—and, in some cases, of stable molecules. F o r example, if there is a high barrier to an internal rotation in a radical, it has n o effect on thermodynamic properties near r o o m temperature—where measurements are generally made. That is, a low-temperature measurement will n o t be sensitive to a high barrier. (Kinetic methods of determining a barrier height, such as N M R a n d E P R , measure the rate at which a molecule or radical undergoes transition from one conformation to another. If there are two pathways, over barriers of different heights, the path over the lower barrier will be the faster a n d will be measured. Transition over the higher barrier will n o t be seen, a n d hence that barrier height cannot be determined.) But at sufficiently high temperatures, the effects of the barrier become significant; thus the difficulty in extrapolating thermochemical properties from low to high temperatures. IX. ALKANE BOND STRENGTHS

The bond dissociation

enthalpy for the b o n d A — B is defined as A^H° for the reaction A—BÂ-fB

and is related to the bond dissociation

energy (BDE), AÊ, by the equation

A,E = E°(A) + £°(B) - E°(AB) = [AfH°(A) - i^T] + [Af//°(B) ~RT^=

[Af//°(AB) - i ? T ]

A,W-RT

F o r many years, BDEs for all primary C — H bonds were regarded as equal, a n d similarly for secondary a n d tertiary C — H bonds. T o the limits of experimental accuracy, this was generally true. According to group additivity (or component additivity) rules, this need n o t be the case. The group additivity values P , S, T a n d Q a n d a through g determine the b o n d dissociation energies (BDEs) for various C — H a n d C — C bonds in alkanes. F o r example, the P ( l ) b o n d (C2H5—H) would be predicted to be 100.6 ± 0.5; the P(2) bond ( R C H 2 C H 2 — H ) , 100.5 + 1; the P(3) bond ( R 2 C H C H 2 — H ) , 100.1 ± 1; a n d the P(4) b o n d (R3CCH2—H), 101.2 + 1 kcal m o l " ^ Unfortunately, the usefulness of these predictions is considerably reduced by the fact that the uncertainties exceed the mean differences; it is quite possible (on this information alone) that all four bond types have the same BDEs. In Table 20 we list experimental (or deduced) B D E s for several alkane C — H bonds. The bond type for a C — H bond is identified by the component classification of the C atom; for a C — C bond, by the classification of the pair of C atoms. X. GROUPS FOR LIQUIDS; GROUPS FOR AHâp

All of o u r discussion so far has been devoted to hydrocarbons in the gaseous phase. At room temperature, alkanes from C4 through Cjg are normally in the liquid phase; hence.

262

N . C o h e n a n d S. W. Benson TABLE 20. Bond dissociation energies in alkanes Bond H3C—H CH3CH2—H CH3CH2CH2—H (CH3)2CHCH2—H Neopentyl—H (CH3)2CH—H CH3CH2CH(CH3)—H C-C3H5—H C-C4H7—H C-C5H9—H c-C^Hii-H c-C,Hi3—H Spiropentyl—H t-Butyl—H H3C—CH3 H3C—CH2CH2CH3 H3CCH2—CH2CH3 C — C in C-C3H6 C — C in C-C4H8

Bond type P(0) P(l) P(2) P(3) P(4) S(ll) S(12) S(22) S(22) S(22) S(22) S(22) S(24) T(lll) P(l)-P(l) P(2)-S(12) S(12)-S(12) S(22)—S(22) S(22)—S(22)

^^êxperimental

105.1+0.2" 100.6 + 0.5" 100.5 + 1" 100.1 + V 101.2+1" 97.1 + 1" 97.1 + 1" 106.3 + V 96.5 + P 94.5 + 1' 9 5 . 5 + 1*' 92.5 + 1' [98.8 + 2f'' 93.6 + 0.5" 90.2 + 0.4" 87.9 + 1.1" 87.0 + 1" 6 5 + 2^* 6 3 + 2^*

"Derived from data in Tables 9 and 19. ''From J. A. Kerr and A. F. Trotman-Dickenson 'Strengths of Chemical Bonds', in Handbook of Chemistry and Physics, 67th edn. (Ed. R. C. Weast), CRC Press, Boca Raton, Florida, 1986, pp. F-233ff, and references cited therein. ''From Reference 65. ''From data in S. W. Benson and H. E. O'Neal, Kinetic Data on Gas Phase Unimolecular Reactions, U.S. D e p t of Commerce National Bureau of Standards (now National Institute of Standards and Technology) N S R D S - 2 1 , Washington, D.C., 1970. ^This value, taken by Kerr and Trotman-Dickenson from Reference 65, comes ultimately from a kinetic study^^ and was derived using an E v a n s - P o l a n y i activation e n e r g y - B D E relationship. In the same study, a value for the cyclopropane C — H bond of 100.7 was reported. The latter value is now k n o w n to be wrong, and we suspect the spiropentane value, which should not be very different from that for cyclopropane, is also; a value near 106 + 2 seems more reasonable.

it is often i m p o r t a n t to be able to estimate thermochemical properties for alkanes in this state. G r o u p additivities for hquid-phase enthalpies at 298 K are easy to derive from the experimental d a t a collected by P N K . Since AH^^^ = AfHnq - AfH^^^ g r o u p values for the enthalpy of vaporization follow directly from the groups for the liquids a n d gases. In Table 21 we list the experimental enthalpies for hquid alkanes, together with the values calculated with the best set of g r o u p additivity parameters (i.e. the parameters chosen to minimize the average error of calculation of the 62 measured alkanes). Alicyclic c o m p o u n d s , as noted earlier, present the difficulty that there are necessary nonsystematic corrections to be applied to the calculated thermochemical properties in order to bring the group additivity values into agreement with the measurements. In Table 22, we present a comparison of experimental hquid-phase enthalpies for cycloalkanes with values calculated by g r o u p additivity, using the g r o u p values of the preceding table. As was d o n e in the case of gas-phase enthalpies, the ring correction

6. The thermochemistry of alkanes and cycloalkanes TABLE 21. Enthalpies of formation (298 K) Alkane 4 2m3 5 2m4 22mm3 6 2m5 3m5 22mm4 23mm4 7 2m6 3m6 22mm5 23mm5 24mm5 33mm5 3e5 223mM 8 2m7 3m7 4m7 2233mM 22mm6 23mm6 24mm6 25mm6 34mm6 3e6 33mm6 3e2m5 3e3m5 223m35 224m^5 233m^5 234m35 9 223m^6 224m^6 225m^6 233m36 235m36 244m^6 334m^6 33ee5 3e22mm5 3e24mm5 2233m^5 22440-^5 2234m^5

AfH°(expr -35.04 -36.69 -41.47 -42.66 -45.46 -47.49 -48.90 -48.37 -51.10 -49.57 -53.59 -54.85 -54.11 -56.96 -55.71 -56.07 -55.98 -53.73 -56.52 -59.78 -60.95 -60.30 -60.13 -64.27 -62.60 -60.37 -61.42 -62.24 -60.18 -59.85 -61.54 -59.66 -60.42 -61.40 -61.95 -60.59 -60.95 -65.65 -67.57 -67.59 -70.10 -67.18 -67.88 -66.97 -66.32 -65.82 -65.18 -64.46 -66.52 -66.92 -66.37

of hquid

263

alkanes

AfH°(ca\cf

Error

-35.34 -36.88 -41.45 -42.44 -45.49 -47.56 -48.55 -48.00 -50.50 -48.99 -53.67 -54.66 -54.11 -56.61 -54.55 -55.65 -55.51 -53.56 -56.50 -59.78 -60.77 -60.22 -60.22 -63.46 -62.72 -60.66 -61.21 -61.76 -60.11 -59.67 -61.62 -60.11 -60.52 -62.06 -61.64 -61.51 -61.10 -65.89 -68.17 -67.20 -69.82 -67.62 -67.76 -66.65 -67.07 -65.53 -67.62 -66.66 -68.47 -67.63 -66.54

0.30 0.19 -0.02 -0.22 0.03 0.07 -0.35 -0.37 -0.60 -0.58 0.08 -0.19 0.00 -0.35 -1.16 -0.42 -0.47 -0.17 -0.02 0.00 -0.18 -0.08 0.09 -0.81 0.12 0.29 -0.21 -0.48 -0.07 -0.18 0.08 0.45 0.10 0.66 -0.31 0.92 0.15 0.24 0.60 -0.39 -0.28 0.44 -0.12 -0.32 0.75 -0.29 2.44 2.20 1.95 0.71 0.17 (continued)

264

N . C o h e n and S. W. Benson TABLE 21. Alkane 2334m^5 10 2m9 5m9 11 2255m^7 3355m'^7 22445m56 12 3366m*8 4466m^9

{continued) AfH°(EXPR

AfH°(calcf

Error

-66.42 -71.92 -74.04 -73.59 -78.20 -83.94 -77.84 -78.63 -83.87 -89.10 -88.67

-67.51 -72.00 -72.99 -72.44 -78.11 -82.89 -77.65

1.09 0.08 -1.05 -1.15 -0.09 -1.05 -0.19 0.01 0.35 -1.20 1.20

-'78.64

-84.22 -87.90 -89.87

"Experimental values from PNK^^. ^Calculated using group values P = - 1 1 . 5 6 , S = - 6.11, T = - 2.20, Q = 0.75, G = 0.55 and F = 2.07; and revised gauche counting.

terms have been chosen so as to m a k e the calculated enthalpies of the unbranched ring c o m p o u n d s equal to the experimental values; the same corrections are then assumed to apply to alkylcycloalkanes. The ortho correction for cis-1,2 substitutions on cyclopropane and cyclopentane is assumed to be the same as in the gas phase (1 kcal mol ~^). T h e average calculated error for these cycloalkanes is 0.68 kcal mol ~ ^ The errors for three compounds—methylcyclobutane, 1,1,2-trimethylcyclopropane and 1,1,2,2-tetramethylcyclopropane—are so large that the experimental values are almost surely wrong. If these problematic cycloalkanes are omitted, the average error is reduced to 0.26 kcal mol ~ ^ The ring corrections for C-C7H14, c-CgR^^ and C-C9H18 are given for comparison purposes only; they are not used to correct any other ring c o m p o u n d values. Similarly, we can derive group values for calculating the entropy of the liquid alkanes at 298 K. W e use as our database all the alkanes tabulated by SWS^^ for which experimental entropy measurements are available. The group parameters were chosen to minimize the average error between the calculated and tabulated values. T h e resulting average error is 0.34 eu. The d a t a are listed in Table 23. The one outstanding discrepancy is in the case of octadecane, and we suspect an experimental error; there is no good explanation for the near-perfect agreement for the other large hnear alkanes to be followed by such a large discrepancy. Calculations of entropies of liquid cycloalkanes require ring corrections, just as in the case of gas-phase cycloalkanes, but the corrections are numerically different. As before, we derive the corrections by comparing calculated entropies with experimental values for the unsubstituted cycloalkanes—cyclobutane, cyclopentane, cyclohexane, cycloheptane and cyclooctane. Experimental values are listed in Table 24 and c o m p a r e d with the calculated ones. The average error is 0.83 eu. The fits are not good for several of the substituted ring c o m p o u n d s . In the case of the dimethylcyclohexanes, all of which were examined in the same study^^, the discrepancy can be traced to very large differences in the enthalpies of fusion (or melting) a m o n g the compounds; this quantity makes a contribution to the experimental liquid entropy equal to AHJT^. F o r example, AHJ{\\mmC^) was measured to be 0 . 4 8 k c a l m o P ^ (at 239K), m u c h smaller t h a n the value of 2.95 kcal mol ~^ for A H „ ( t r a n s - H m m C g ) (at 236 K). T h e former contributes 2.02 eu, the latter 12.48 eu. (In addition, it appears that the evaluation of Reference 79 did not account properly for the entropy contribution of optical isomerism.) Recall t h a t

6. T h e thermochemistry of alkanes a n d cycloalkanes TABLE 22. Enthalpies of formation of liquid cycloalkanes at 298 K Alkane" mC3 llmmC3 cis-12mmC3

trans-llmmC^ 112m3C3 llmm2eC3 1122m'^C3 eC3

cis-12eeC3

trans-llQQC^ llmm2pC3

C4 mC4 eC4

C5 eC5

pCs llmmCs cis-12mmC5

trans-llmmCs trans-13mmC 5

Ce mC^ eCe llmmCg cis-12mmC6 trans-12mmC6 cis-IBmmCg trans-OmmCg cis-MmmCg trans-14mmC6 lelmCe cis-le2mC6 trans-le2mC6 cis-leSmCg cis-le4mC6 trans-le4mC5 Cv

Cs

0.41 -7.96 -6.29 -7.34 -22.99 -21.56 -28.61 -5.93 -19.10 -19.91 -27.72 0.88 -10.64 -14.10 -25.12 -39.05 -45.12 -41.11 -39.51 -40.92 -40.18 -37.38 -45.43 -50.65 -52.27 -50.62 -52.15 -53.27 -51.55 -51.53 -53.15 -57.41 -56.45 -57.41 -59.06 -57.10 -58.89 -37.43 -40.08 -43.31

AfH°(calcy

Error**

0.41 -8.20 -6.24 -7.24 -14.85 -21.41 -22.91 -5.70 -18.46 -19.46 -27.07 0.88 -6.77 -12.88 -25.12 -38.88 -44.99 -41.38 -39.42 -40.42 -40.42 -37.38 -45.03 -50.59 -52.54 -51.03 -52.13 -52.68 -51.58 -51.58 -52.68 -57.55 -56.59 -57.59 -58.24 -57.14 -58.24 -37.43 -40.08 -43.31

0.00 0.24 -0.05 -0.09 -8.14 -0.14 -5.70 -0.22 -0.63 -0.45 -0.65 0.00 -3.87 -1.23 0.00 -0.17 -0.13 0.27 -0.09 -0.50 0.24 0.00 -0.40 -0.05 0.27 0.41 -0.02 -0.59 0.03 0.05 -0.47 0.14 0.14 0.28 -0.82 0.04 -0.65 0.00 0.00 0.00

"The notation C„ designates an n-cycloalkane; the prefixes m , e and p indicate methyl, ethyl or propyl side chains, respectively. ''Experimental values from tabulation of P N K ^ ^ Table 1.1. 'Calculated by group additivity; P = - 11.5, S = - 6.11, T = - 2 . 2 , Q = 0.75, G = 0.55; ortho correction = 1.0; ring corrections; C4 = 25.32, C5 = 5.43, Cg = - 0.72, C, = 5.34, C3 = 8.8, C^ = 11.68. ''The error is the experimental value minus the calculated one. Apparent discrepancies in this column are due t o round-off error.

265

266

N . Cohen a n d S. W. Benson TABLE 23. Experimental and calculated entropies of liquid alkanes (298 K) Alkane

S(expr

5(calc)''

Error

4 2m3 5 2m4 6 2m5 7 2m6 223m34 8 224m35 234m35 9 10 2m9 3m9 4m9 5m9 11 12 13 14 15 16 18

55.20 52.09 62.78 62.24 70.76 69.45 78.53 77.28 69.85 86.23 78.40 78.71 94.09 101.79 100.40 102.10 101.70 101.30 109.49 117.26 124.97 132.74 140.41 148.09 166.50

55.66 51.99 63.36 61.87 71.06 69.57 78.76 77.27 69.92 86.46 77.62 79.25 94.16 101.86 100.37 101.75 101.75 100.37 109.56 117.26 124.96 132.66 140.36 148.06 163.46

0.46 -0.10 0.58 -0.37 0.30 0.12 0.23 -0.01 0.07 0.23 -0.78 0.54 0.07 0.07 -0.03 -0.35 0.05 -0.93 0.07 -0.00 -0.01 -0.08 -0.05 -0.03 -3.04

"Experimental values taken from the tabulation of SWS, Chapter 14. ''Calculated by group additivity using the group values P = 23.00, S = 7.7, T = - 8.28, Q = - 23.70.

the group additivity-derived gaseous entropies for these same c o m p o u n d s agreed well with experiment (see Table 15); this points o u t one of the pitfalls in a third-law entropy calculation, which requires knowing accurately the enthalpies of all phase transitions. As in t h e case of gas-phase compounds, calculating thermodynamic functions for hquid alkanes at temperatures above 298 K is greatly facilitated with polynomial expansions for heat capacities. Shaw^^ has evaluated the group contributions t o Cp at 298 K for hydrocarbons as well as other liquids; however, rather t h a n evaluate the g r o u p contributions at a series of discrete temperatures, we proceed directly t o a polynomial expansions for Cp. In Table 25 are listed the polynomial coefficients for each of the four alkane group contributions t o Cp. The polynomials agree well with experimental d a t a in the range of 100-400 K, but are probably unreliable near the boiling point or above. A. Vaporization Processes

Calculations for processes that include changes of phase (fusion, vaporization, sublimation o r their reverses) must take into account the contributions t o the t h e r m o dynamic properties associated with the phase change. Hirschfelder, Curtiss and Bird^^ have shown that Eyring's equation of state for dense

6. The thermochemistry of alkanes and cycloalkanes TABLE 24. Entropies of hquid cycloalkanes (298 K) Alkane

0

N

5(EXPR

S(calc)^

Error

C4 C5

8 10 3 3 3 18 9 18 18 3 6 3 9 9 18 9 9 9 18 3 3 3 3 3 1 3 8

1 1 1 1 1 1 1 2 2 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1

43.44 48.82 59.26 74.29 82.18 63.34 64.33 64.86 66.90 128.71 48.84 59.26 63.87 65.52 65.30 65.16 66.03 64.80 64.06 67.14 74.54 82.45 129.10 147.1 57.97 106.80 62.62

43.47 49.92 59.34 74.74 82.44 63.36 64.17 64.17 64.17 128.64 51.04 59.43 64.83 65.65 64.27 64.27 65.65 64.27 62.90 67.14 74.84 82.54 128.74 144.14 58.00 101.34 62.67

0.03 1.10 0.08 0.45 0.26 0.02 -0.16 -0.69 -2.73 -0.07 2.20 0.18 0.96 0.13 -1.03 -0.89 -0.38 -0.53 -1.16 0.0 0.30 0.09 -0.36 -2.96 0.03 -5.46 0.05

mCs

PC5 bCs llmmCs CIS-12mmC 5

TRANS-LLMMC^ traws-lSmmCs

dC5 Ce

MCE llmmCg cis-12mmC5

TRANS-LLMMC^ cis-UmmCe trans-ISmmCg cis-14mmC6 trans-14mmC6 eC, pCe

HC, DecylCe DodecylCg Cv HexylC^ Cs

"Values are based on experimental measurements as tabulated by SWS, Chapter 14. ''Calculated using group values of Table 23 and ring corrections: C4 = 16.8, C5 = 16.0, Ce = 8.4, C7 = 4.1, Cg = 5.2.

TABLE 25. Polynomial expressions for liquid phase groups"

for alkane

Group C-(C)(H)3

C-{CUHH C-(C)3(H) C-(C)4

«I

100 X ^ 2

10' X ^ 3

10' X FL4

8.459 -1.383 2.489 9.116

0.211 7.049 -4.617 -23.54

-5.61 -20.63 31.81 128.7

1.723 2.269 -4.565 -19.06

"M. Luria and S. W. Benson^^. N o t e that these a,- coefficients are related to the coefficients of equation 49 by aj = a; x Rcalmo\~^K~^.

267

268

N . Cohen a n d S. W . Benson

gases leads t o the following relationship between vapor pressure a n d AHâp= (RT/SVmAH^JRT)

- 1]^ exp [ - AH^JR^

(72)

If the factor RT/SVis approximated by a universal constant of 35 (obtained by setting the liquid molar volume t o 82 cc mol ~ ^ a n d T t o 298 K), the preceding equation c a n be solved by setting T = Tb, the normal boiling point, a n d p^^p the vapor pressure at that temperature, namely 1 atm, t o give T r o u t o n ' s rule, [ A H 3 p . b . p . / « 7 ^ b . p . ] = 10-4

(73)

And since, for a phase change, AG = 0, the above gives AS.ap,,.p./R=10.4

(74)

Chickos a n d coworkers^"^ have developed semiempirical procedures for estimating b o t h A//yap,298 ^ ^ s u b , 2 9 8 - Thc former quantity, however, is easily calculated from our g r o u p additivity values for the gas- a n d liquid-phase groups, since

AH,,p = AfH°-AfH,

a n d A5,,p = 5 ° - S ,

Thus, t h e g r o u p contributions t o AH^^p, AS^^p a n d ACp ^^p are determined simply by the differences in the corresponding quantities for the liquid a n d gas phase. C o l u m n 2 of Table 26 provides the constants that are used t o compute AH^^^ of a n alkane at 298 K. T o carry o u t the same calculation at another temperature, for example, the boiling point, one can calculate A^H^ and Af Hj by using the appropriate polynomial expansions of equation 50, or use the set of Aa^ ^^p, also tabulated in Table 26, which are the differences in the corresponding g and (The former are given in Table 7 and the latter in Table 25.) There are, however, easier ways t o estimate AH^^^ a n d AS^^^ at the boihng point. If Tb.p. is known, then Trouton's rule, equations 73 a n d 74, provides the quickest procedure. (If a n d P^, the critical temperature a n d pressure, are k n o w n in addition t o T^.p,, there are several methods for estimating AH^^p ^.p., m a n y of which have been reviewed by Reid a n d collaborators'^^.) F o r 56 alkanes from C4 through C20, equation 73 gives AHâp.b.p. with a n average error of 0.26 kcal m o l " ^ If p is n o t known, then one c a n use a g r o u p additivity approach. F o r the same 56 alkanes, the following equation gives

TABLE 26. Group contributions to AH and AS (298 K), and ACp of vaporization" Group P S T

1.56 1.11 -0.20 -0.65 0.35

Q G C4 C5 Cg C7 Cg C9

ring ring ring ring ring ring

correction correction correction correction correction correction

1.5 1.3 1.2 1.1 1.1 1.1

7.30 1.70 -4.02 -11.30 -0.47 13.1 13.3 12.4 11.8 11.3

100 X Aa2,vap

10^ X Aa3,,,p

10^ X Afl4,,3p

-8.63 1.13 -4.21 -13.19

2.23 -4.76 7.27 27.35

4.44 19.30 -33.85 -132.3

-1.701 -2.239 4.621 19.17

-14.02 -45.23 -24.94

4.49 39.88 16.97

23.63 -117.43 -28.91

8.374 -11.142 -0.316

"These coefficients are vahd for calculations below the boiling point. ''Derived from values in Table 27. Derived from values in Table 28.


AHyapbp with an average error of 0.34kcalmol~^: AH,,p,,.p. = 3.0np + 0.43ns - 2.5^^ - 5An^

269

(75)

where Up, Us, Uj a n d HQ are the numbers of primary, secondary, tertiary a n d quaternary groups. T h e method is best for larger ( > C5) alkanes; for C 7 S a n d higher, the maximum error is 0.58kcalmol~^. We can develop a rough relationship between AH^^^T a n d AHy^p ^.p. following a n argument put forth by Benson a n d Garland^ ^. They start with the general relationship

AH,,p,^ = AH,,p,,.p.+ ["^

ACp,,,p^T

(76)

The integration is approximated by making use of the following assumptions a n d relationships: (1) for many hydrocarbons (especially with branching), ACp âp.b.p. — H; (2) according t o the G u l d b e r g - G u y e r u l e ^ Tb.p./T, ^ 0.625 for most regular liquids; (3) at the critical point (and, approximately, at T^), ACp ^^p = 0; a n d (4) above the boiling point, ACp ^âp can be assumed to be a linear function of temperature. F r o m these conditions, it follows that ACp,,,p^-28.0+17.6(r/rb.p.)

(77)

whence equation 76 can be integrated to give AH^^^^

^ AH,,p,b.p. + 28.0(T - T^.p.) + 8.8[(r^ - T^.p.)/Tb.p.]

(78)

which gives the heat of vaporization at any temperature near the boiling point from its value at the boiling point. W e can then use Trouton's rule, equation 73, to give AH^^^^ ^ 2A//,,p,b.p. - 2 8 T + 170TVAH,,p,b.p.

(79)

At temperatures well below the boiling point, it is more accurate to use Table 26 t o calculate ACp as a function of temperature a n d then integrate equation 76 t o obtain

AHvap,rXI. SOLUTIONS

When two liquids are mixed, there is in general a nonzero free energy change associated with the process. This free energy change is due to contributions from both enthalpy, A H ^ i x , a n d entropy, AS^j^, of mixing. However, for a particular type of s o l u t i o n — a perfect, or ideal solution—the enthalpy of mixing is zero. An ideal solution is defined as one for which the fugacity, / , of each component is proportional t o its molar fraction: (80)

fi = f-Xi

where / ? is a constant at a given temperature a n d pressure for each substance x^. Physically, two components form a n ideal, or nearly ideal, solution when their structures are very similar or when they have very weak intermolecular forces. T h e hydrocarbons satisfy one or both of these requirements, a n d consequently form nearly ideal solutions; the enthalpies of mixing are typically only a few tens of calories per mole^^. In general, G, = G° + K T l n ( x , ) If A/f

(81)

= 0, then Hi-H°

=0

(82)

^See J. R. Partington, An Advanced Treatise on Physical Chemistry, Vol. 1, Wiley, N e w York, 1949, p. 646, for more background on this empirical rule and pertinent references.

270


and T{Si-5?)

= Gi- G° = RTlniXi)

(83)

= Xx,(5, - S°) = - Z x , In (x,)

(84)

whence AS^JR

which is analogous t o equation 41. F o r practical purposes, one is generahy concerned with entropies of mixing of given volumes of liquids rather t h a n of moles. (In the case of ideal gases, the two are identical, and in the case of equation 41 n o distinction was necessary.) Hence, we can modify t h e last equation t o express the entropy of mixing o n a volume basis: AS^JR

= - X(t;,p,/M,) In MM,)

(85)

where v,, a n d are the volume, molecular weight and density of the ith species, all in consistent units. (Liquid alkane densities are all in the range of 0.7 ± 0.1 g c c " ^ near r o o m temperature; consequently, the dependence of ASîx o n density may be insigni ficant.) XII. SUMMARY OF IMPORTANT GROUP VALUES; THEIR RELIABILITY A. Summary of Group Values

In Table 27 we summarize all the group additivity values necessary for estimating enthalpies a n d entropies of any alkane a n d cycloalkane, either in gas o r liquid phase, at 298 K. As indicated previously, for computational purposes, it is convenient t o express the group contributions to Cp as polynomials in T rather than as tabulated values. T h e values in Tables 28 and 29 are taken directly from Tables 7 a n d 25 above, except that polynomial expressions for cycloalkane corrections have been added. Because of the particular utility of Kf, the equilibrium constant for formation from the elements in their standard states, it is useful t o develop group additivity contributions that can be used t o calculate Kf directly, using equations 52-59. The necessary constants are listed in Tables 30 a n d 31. These values are calculated from the group additivity constants previously given, but incorporating contributions from H2(gas) and C(graphite), the elements in their standard states. The constants in the tables permit calculation of what we will define as Xf j^j, the intrinsic equilibrium constant, which is related t o t h e standard equilibrium constant by the relation =

^f,int X

n/a

where n a n d a are the number of optical isomers a n d symmetry number, respectively, of the c o m p o u n d whose equilibrium constant of formation is being calculated. Alter natively, S = Sint X Rln(n/(j) can be used t o give Kf directly. The use of these tables is illustrated by the Examples in Section XIII. B. Reliability of Group Additivity Schemes

T h r o u g h o u t this chapter we have argued for the use of group additivity methods for estimating thermodynamic a n d thermochemical properties for hydrocarbons when appropriate measurements are n o t available. W e maintain o u r conviction in the advis ability of this approach, even though there are more elaborate schemes that give better agreement with tabulated data, for the following reasons: (1) The simplicity of the group additivity method and its straightforward relationship


271

TABLE 27. Summary of group values (298 K) Gas

Liquid

Group

"ÎNT.L

P = C-(C)(H)3

S = C-(C)2{H), T = C-(C)3(H) Q = C-(C)4

G = gauche correction F = 1 5 correction a = [C—(C)(H)J b-iC' icum c = [C—(C)3] ^ = [C-(C-)(H)3]

c = [C-(C)(C-)(H)J /=[C-(C),(C)(H)] ^ = [C-(C)3(C-)] C3 C4 C5 Cg C7 Cg C9

ring ring ring ring ring ring ring

correction correction correction correction correction correction correction

-10.00 -5.00 -2.40 0.10 0.80 1.60

30.30 9.40 -12.30 -35.00

6.19 5.50 4.54 4.37

38.4 39.4 39.4 -10.00 -5.6 -2.4 0.5

30.7 10.7 -10.8 30.4 9.4 -12.1 -35.1

5.76 6.06 4.06 6.19 5.50 4.54 4.37

32.1 28.6 27.8 18.6 15.9 16.5

-3.05 -4.61 -6.50 -5.80

27.7 26.8 7.1 0.7 6.4 9.9 12.8

-11.56 -6.11 -2.20 0.75 0.55 2.07

25.3 5.4 -0.7 5.3 8.8 11.7

23.00 7.70 -8.28 -23.70

16.8 16.0 8.4 4.1 5.2

8.80 7.26 5.00 1.76

-2.34 -3.63 -3.80 -6.30 -7.62 -6.81

"Values from Tables 9 and 13. ^Values from Tables 11 and 13, and Table 2.14 of Reference 34. ''Values from Tables 2.14 and A.l of Reference 34, except those for a and b groups, have been recomputed using experimental vibrational frequencies reported by Pacansky and Scharder^^ and by Pacansky and Coufal^^ for ethyl and isopropyl, respectively. N o t e that CPS, for d, e,f and g are assumed equal to those for P, S, T and Q, respectively. ''Values from Tables 21 and 22. "Values from Tables 23 and 24. ^Group values from Shaw^^; ring corrections based on experimental data compiled by Domalski and coworkers

to fundamental physicochemical quantities a n d properties makes it easy to apply manually. This offers the possibility of making simple checks of suspect experimental results to determine the likehhood of their being in error. [ F o r example, the accepted experimental value for AfH°(C32H66), listed in Table 9, is in very p o o r agreement with the value predicted by g r o u p additivity, and is, we believe, almost certainly wrong.] Admittedly, the g r o u p additivity approach is a simplified description of reality: in fact, nonnearest-neighbor interactions are not completely negligible. The discussion in the text regarding the best scheme for counting the n u m b e r of gauche interactions implicitly concedes this fact. But the accuracy of the present database is insufficient to refine the group additivity method with any degree of confidence. (2) The growing use of high-speed computers a n d specialized chemical software programs m a y m a k e the application of more complex schemes, such as component additivity, equally convenient. However, there is the danger that complacent reliance on a complicated data-processing p r o g r a m will obscure the occasional generation of nonsensical results—which can happen when the inputs are nonsensical or when something happens that the software writers did not anticipate.

272

N . Cohen and S. W. Benson TABLE 28. Polynomial expressions for gas-phase C"^ for alkane and alkyl" groups^

Group C-(C)(H)3 C-(C),(H), C-(C)3(H) C-(C)4 [C—(C)(H),] [C—(C)2(H)] [C—(C)3] Cycloalkane corrections Cyclopropane (T < 1000) Cyclobutane Cyclopentane Cyclohexane

«i

10^ X a2

-0.10 -2.55 -1.72 -3.90

1.134 2.912 0.465

-6.54 -7.96 -10.97 -11.92

10' X ^3

10^ X

2.442 2.288 2.665 3.719

-1.18 -1.32 -2.05 -3.47

2.26 2.97 5.67 10.16

1.855 1.331 1.608

-1.111 -0.994 -1.453

2.695 2.754 4.341

1.70 1.38 1.85 2.29

-2.05 -0.98 -1.33 -0.89

8.42 2.53 3.77 0.246

"Values for [C—(C-)(H)3], [ C — ( C X C - X H ) ^ , [ C — ( C ) 2 ( C ) ( H ) ] and [ C ~ ( C ) 3 ( C ) ] groups are assumed the same as for C ^ ( C ) ( H ) 3 , C—(C)2(H)2, C—(C)3(H) and C—(C)^, respectively. ''Note that the a, coefficients in Tables 28 .and 29 are related'to the coefficients of equation 49 by AI = A,. X R c a l m o r ^ K " ^

TABLE 29. Polynomial expressions for liquid-phase C"^ for alkane groups

Group C-(C)(H)3 C-(C)3(H) C-(C)4 Cycloalkane corrections Cyclopropane Cyclobutane Cyclopentane Cyclohexane

ai

100 x ^2

10' x

10"^ x a^.

8.459 -1.383 2.489 9.116

0.211 7.049 -4.617 -23.54

-5.605 -20.63 31.81 128.7

1.723 2.269 -4.565 -19.06

28.469 6.060 34.261 13.021

-26.96 -3.114 -38.03 -14.68

65.34 -24.61 116.1 28.02

1.636 -8.349 11.18 0.318

TABLE 30. Gas-phase alkane group additivity contributions required to calculate In Kf^^^{T) Group P S T Q G F

-8.99 -11.66 -14.73 -18.30

-5.03 -2.52 -1.21 0.05 0.40 0.80

-4.61 -2.93 -1.94 -1.40

103Aa2

10Âa3

lO^Âa^

5.13 4.42 6.29 12.2

-0.846 -1.63 -5.24 -13.1

-3.30 1.12 15.0 40.9


273

TABLE 31. Liquid-phase alkane group additivity contributions required to calculate InKf^îiT) Group

P S T

Q G

F

ArS298/R

-12.66 -12.52 -12.71 -12.61

ArH29s/R

Afli

103Afl2

10'Aa3

10«Aa4

-5.82 -3.07 -1.11 0.38 0.28 1.04

-0.27 -3.50 0.177 5.24

-6.09 28.38 -30.28 -125.4

-2.32 -9.88 16.50 65.30

-8.8 -11.6 22.8 95.8

(3) T h e oft-touted greater accuracy of more elaborate semiempirical estimation schemes is generally illusory because of present limitations o n the accuracy of the experimental database. W e have suggested in the text that some of these limitations are not temporary, but are in fact inherent in what can physically be measured. W h a t is thus claimed as greater accuracy of such computational schemes is more appropriately described (at best) as greater precision, not accuracy. XIII. EXAMPLES OF APPLICATIONS

In the following examples, all S a n d Cp values are in c a l m o l ~ ^ K " \ while H a n d G values are in kcal mol however, H/R is in Kelvins a n d S/R is dimensionless. Thus, if H is given as 60.00, H/R will be 60,000/1.987 = 30,196. Example 1. Use group additivities to calculate (a) AfH° a n d (b) S° for the stereoisomers of 3,4-dimethylhexane (3,4-dmh) at 298 K. (c) Calculate the equilibrium distribution a n d (d) the entropy of the equilibrium mixture at 298 K. (a) F r o m an examination of the structure of 3,4-dmh we see that there are 4 primary, 2 secondary a n d 2 tertiary groups.

r-3,4-dmh:

H

H

I

I

H3C—CH2— C — C — CH2—CH3

I

I

H3C m-3,4-dmh:

(gfauc/ie interaction

CH3

H CH3 I I HjC—CHj— C—C— C H 2 — C H 3 I

I

H,C

H

{gauche interactions)

Whenever there is a tertiary group adjacent to a secondary or tertiary group, there will be some gauche interactions; from Table 9 we see that there can be either two or three such interactions between the two T groups, depending o n the spatial arrangement, a n d one between each adjacent pair of S a n d T groups. T h e meso form has the two CH3

274


side chains on opposite sides of the main chain, so it has the fewer gauche interactions. The values for AfH°(3,4-dmh) are therefore: r-3,4-dmh: P 4 X -10.00 S 2 x -5.00 T 2 x -2.4 G 5x 0.8

m-3,4-dmh: P 4 X -10.00 S 2 x -5.00 T 2 x -2.4 G 4x 0.8

= -40.00 = -10.00 = -4.80 = 4.00 -50.80

= -40.00 = -10.00 = -4.80 = 3.20 -51.60

(b) T o calculate S°, in addition to the properties already tallied, we need to k n o w the symmetry number, a, and the n u m b e r of optical isomers, n. The general rule for optical isomers is that each chiral center gives rise to n = 2 isomers; thus, two chiral centers would give 2 x 2 = 4 optical isomers. However, an exception to this simple rule occurs when there are two identical chiral centers, as in 3,4-dmh, in which case there are only three optical isomers, since one of the apparent four is its own mirror image. This latter form is the meso-compound. There are thus three forms of 3,4-dmh: the two optically active enantiomers—for convenience, label them ^-dmh and /-dmh (using an obsolescent terminology), which form a (generaUy inseparable) 50:50 racemic mixture—call it r-dmh; and the meso-form—call it m-dmh. F o r either d-dmh or /-dmh, cr = 3"^ x 2: each CH3 group contributes a factor of 3 to the total symmetry, and there is an overall symmetry of 2. In the racemic mixture the presence of the two inseparable nonsuperposable stereoisomers makes n = 2. F o r m-dmh, there is n o overall symmetry, so a = 81. Because the c o m p o u n d is its own mirror inverse, there is n o optical activity and n = 1. F o r b o t h forms, S?, is the same: '

int

p s T

4 x

30.30

2 x 9.40 2 x -12.30 5i„t

S° is given by:

121.20 18.80

115.40

S° = S°^^ +

so that and for the racemic mixture F o r the meso form,

Rln(n/a)

5°(^-dmh) = 5°(/-dmh) = 115.40 -h R In (1/162) = 105.29 5°(r-dmh) = 115.40 -\-Rln(2/162) = 106.67 S°(m-dmh) = 115.40 i^ln(l/81) = 106.67

(c) T h e equilibrium constants Kf for r-dmh and m-dmh reflect both the entropy a n d enthalpy contributions. Since InXf = S^R AfH°/RT, Xf(r-dmh)/Xf(m-dmh) = exp(A57i?) x exp( AAHyRT) = (2/162)/(l/81) X exp ( - 8 0 0 / 1 ^ T ) = 0.26 at 298 K which is also the equilibrium constant for the process m-dmh ^ r-dmh Thus, = 0.26 and the mixture will consist of 20.6mol% r-dmh (10.3% of each optically active form) and 79.4 mol% m-dmh. (d) The entropy of the mixture is the sum of the entropies of each c o m p o n e n t (multiplied by its mole fraction) plus the entropy of mixing, given by equation 41:


275

^totai = 0.103S°(rf-dmh) + 0.1035°(/-dmh) + 0.7945°(m-dmh) + AS^,,,^^ = 2 X 0.103[5i„t(dmh) + / ^ l n ( l / 1 6 2 ) ] 4- 0 . 7 9 4 K J d m h ) + K l n ( l / 8 1 ) ] -Rl.ni\n(ni)

= Si„t(dmh) + i ^ [ 0 . 2 0 6 I n ( 1 / 1 6 2 ) 4 - 0 . 7 9 4 I n ( 1 / 8 1 ) - 2 x 0.103In(0.103) - 0 . 7 9 4 In (0.794)] = 5i„t(dmh)-5.189/^ = 105.09 eu We could also have calculated 5totai by assuming we had a mixture of two components— 20.6% racemic and 79.4% meso. Example 2. According to experiments of Verma, M u r p h y and Bernstein^'^, the enthalpy difference between the trans and gauche isomers of n-butane is 960 cal mol favoring the former. Calculate the distribution of n-butane between the two isomers and the entropy of the mixture (a) at 298 K; (b) at 1000 K. (a) 298 K. The equilibrium constant for the reaction gauche-C^Yi i o ^ trans-C^Â^ o is = exp(ASIR) x e x p ( - AA^HIRT). The trans form has or = 18 and n = 1; the gauche form has o- = 18 and n = 2. (The gauche form is a racemic mixture of two optically active enantiomers.) Since S = S,^^ + R\n(n/a) and S^î for the two forms is the same, exp(AS/R) = (l/18)/(2/18) = 0.5; e x p ( - A A f / / / i ^ r ) = exp(960//^T). Hence, K^^ = ltransyigauche2^ci = 0.5 Qxp(960/RT). At 298 K, ^^^ = 2.53 and the mixture consists of 72% trans and 28% gauche (which in turn consists of an equal mixture of the two optical isomers). The entropy of the mixture is given by

^totai = Sitrans) + S(gauche) + 5î,i„g = 0.72S°{trans) -\- 0.2SS''(gauche) - RZ(ni In n,) = 0.72[Si„t + K l n ( l / 1 8 ) ] -h 0.28[5i„t -h R l n ( 2 / 1 8 ) ] - K[(0.72 In (0.72) + 0.26 In (0.26)] = S,„,-4.17 (b) 1000 K. The entropy contribution to K^^ is independent of temperature, but the enthalpy contribution is different. Following the above procedure but with T = 1000 we obtain X , , = 0.81, 5^^,^^^ = 1.34 and S,,,,, - S,^, = 3.62. [All the linear alkanes consist of mixtures of trans a n d gauche isomers, with each conformation possible a r o u n d each internal C—C bond. Thus, in w-pentane we find t - t , g-t, g-g(cis) and g-g(trans). If the alkane consisted only of the trans isomer, S would t>e S'int-hKln(l/18) = 5i„t —5.74. The above calculation appears to suggest an error of 5.74— 4.17 = 1.57 eu in the entropy calculation resulting from neglecting the various isomers. Similar calculations for n-pentane and n-hexane give corresponding values of approximately 3.3 and 4.2 eu, while in the case of p r o p a n e there would be no discrepancy. T o a good approximation, our scheme for evaluating the contributions of S groups to the entropy can take this complication into account implicitly. The errors can a m o u n t to several tenths of an eu, however, and this can be one important limitation on the accuracy of any additivity scheme.] Examples. Use g r o u p additivities to calculate Cp,5°,AfH°,AfG° and logKf for gaseous isooctane (224m^5) at 1 atm pressure (a) at 298 K and (b) at 1000 K. (a) 298 K. Procedure. First write out the structure and determine the number of different kinds of groups (P, S, T and Q), nonnearest-neighbor interactions (G and F), symmetry and optical isomers. (These are listed for isooctane in Tables 9 a n d 11). The

276

N . Cohen and S. W. Benson

contributions from each of these at 298 K to Af if °, 5° and C° are given in Table 27. T o calculate Af G° and Kf we need the entropy of reaction for the process of formation from the elements, 8C(solid) + 9H2(g)-*i-C8Hi8(g). This in turn requires the entropies of C(s) and H2(g). The enthalpy of reaction is just AfH for isooctane, since the enthalpy of formation of the elements is by definition zero. The entropy of the elements can be taken from some standard tabulation [we use SWS (Reference 22) throughout these examples for auxiliary data; for these quantities we use their Table Nos. 1 and 2]. Group

P

#ofgps.

AfH° 5° CI

S

T

Q

5

1

1

1

-10 30.3 6.19

-5 9.4 5.5

-2.4 -12.3 4.54

0.1 -35 4.37

G

F

(7

3

1

729

0.8 0 0

1.6 0 0

S°''[C(solid)]

13.0

Total

-53.30 100.50 45.36 1.36

5°(H2)

31.21

AS° = S°- 8S°(C) - 95°(H2) = 100.50 - 8 x 1.36 - 9 x 31.21 Af G° = Af//° - TAS° = - 53.30 - 298 x ( - 191.28/1000) logKf = -AfG72.303Rr= -3703/(4.575 x 298)

-191.28 3.703 -2.716

F o r comparison: SWS (Table N o . 137) gives C; = 45.14, AfJF/°(298) =-53.57, S° = 101.15, AGf(298) = 3.27 and logKf = -2.396. The error in Kf of about a factor of 2 is due primarily to the group additivity error in estimating AfH of isooctane, as Table 9 shows. (b) 1000 K. Thermodynamic properties are state properties; that means that the properties of a chemical/physical process are independent of the p a t h taken. The reaction yielding isooctane from the elements at 1000 K can be written with two separate pathways:

(8C + 9H2)iooo (8C +

9H2)„8

0-C8Hi8)iooo

^(i-C8Hi8)„8

d The entropy or enthalpy associated with the required pathway a is related to the others by

AS, = AS^ + AS, + A5b; AH, = AH^ + AH, + AH^ In part (a) we calculated the functions associated with path d; we need next to calculate the entropy/enthalpy changes associated with coohng the elements from 1000 K to 298 K (path b), and with heating the isooctane from 298 to 1000 K (path c). W e calculate Cp,5 and AfH at 1000 K by the use of equations 49-51. This requires the polynomial expansion coefficients for Cp, which are given in Table 26. Equation 49 gives Cpiooo directly. Equation 51 is applied at both 1000 and 298K; the difference gives the entropy change associated with p a t h c which is then added to the value of iS'(298) calculated in part (a). Equation 50 is similarly applied at both temperatures; the difference gives (H"^^^ — H^^g), the enthalpy change associated with p a t h c. This difference is added to the value of AfH298 calculated in part (a). We then subtract the corresponding difference for the elements C and H2 to get the contribution from p a t h b. Values of the latter are also taken from Table Nos. 1 and 2 in S W S ^ ^

6. The thermochemistry of alkanes and cycloalkanes Groups

P

#ofgps ai a2

5 -0.1679 0.02443 -1.2E-05 ^4 2.18E-09 Cl = ai + a2 X T + X S° -aj ^1000

= aix\nT-]-a2xT ~

H°-ae

S

T

Q

1 0.2554 0.02288 -1.3E-05 2.97E-09 -\- a^. X

1 -1.723 0.02654 -2.0E-05 5.64E-09

1 -4.078 0.03812 -3.6E-05 1.07E-08

+ a^x

"I" ~ ^ 7 ] l 0 0 0 "~ = ai X T + a2 x T^/2-\-a^

^298

^1 = ^1000 ~ ^298 =

T^/l + a^ x 7 ^ 3 ~

Total

-6.39 0.21 -1.3E-04 3.0E-08 105.44

@298 @ 1000

20.69 111.62 191.43 6.337 63.323 56.985

^1~\29%

x 7^3

~ ÊLIOOO ~

+

x TV4

277

@298 @ 1000

~ ^6]298

Hi = ^ 1 0 0 0 - ^ 2 9 8 for ^ 2

(from SWS)

4.942

^ 3 = ^1000 - ^298

(from SWS)

2.823 -63.376 5.846 39.704 -212.67 149.296 -32.63

Af//°,,, = AfH°,3 +

C

//,-8//3-9/f2

S° [C(solid)] S^H2) A,S° = S° (i - C g H i s ) - 8S°(C) - 95°(f/2) AfG° = A f H ° - T A 5 ° logXf=-AfG7i^T

(from SWS) (from SWS)

F o r comparison, SWS (Table N o . 137) gives C° = 103.60,5° = 189.83, AfH° = - 65.04, - H ° 9 g = 55.59, Af G° = 149.23 and logKf = - 32.613. Alternative method using Table 30: Table 30 is designed to simplify the calculation of Kf for alkanes from the elements at any temperature by automatically including the contributions from C and H2. The calculations use equations 5 2 - 5 9 . Groups

ASIJR AHIJR Aa^

AA2 Aa^, A«4

Total -8.99 -5.03 -4.61 0.00513 -8.5E-07 -3.3E-10

-11.66 -2.52 -2.93 0.00442 -1.6E-06 1.12E-10

-14.73 -1.21 -1.94 0.00629 -5.2E-06 1.50E-09

-18.30 0.05 -1.4 0.0122 -1.3E-05 4.09E-09

0 0.40

0 0.80

A = ASl^JR - Aa, x ln(298) - 298 x Aaj - 298^ x A A 3 / 2 - 298^ x A A 4 / 3 B=- AH\JR + 298Aai -h 298^ x Aa^/l -H 298^ x AFL3/3 + 298^ x AFL4/4 C = Afli

D = Afl2/2 £ = AFL3/6 F = AFL4/12

\nKf = A+BIT+C\nT logKf = lnX/2.303

+ DT + ET^-\-FT^

729

-96.23 -26,817 -29.32 4.86E-02 -2.42E-05 4.05E-09 86.70 20,030.23 -29.32 2.43E-02 -4.03E-06 3.38E-10 -75.23 -32.66

Example 4. Calculate Cp,S,AfH,AfG and Kf of liquid isooctane (224m^5) at 298 K. The procedure is the same as before, except that g r o u p values for the liquid phase are used; these are given in Table 27 together with the gas-phase values.

278

N . Cohen and S. W. Benson

Groups

p

# of gps.

5 -11.56 23.00 8.80 S° [C(sohd)]

S

T

Q

1 -6.11 7.70 7.26

1 -2.20 -8.28 5.00

1 0.75 -23.70 1.76

G

F

3 1 0.55 2.07 0 0 0 0 (from SWS) (from SWS)

a

Total

729

- Cg/Zis) - 85°(C) - 95°(H2) AfG° = A f / / ° - T A 5 ° logXf= -AfG72.303RT Ar5° = S°{i

13.0

-61.640 77.62 58.02 1.361 31.211 -214.16 2.181 -1.600

Example 5. Calculate A^H for both liquid and gaseous i-octane at the boiling point (372.4 K); calculate AH^^^ and AS^^^ at that temperature, (a) Gaseous state Groups

P

S

T

Total

# of gps. a,

^1

«4

Cp = S°-a^

1 1 -0.1679 0.2554 -1.723 0.02443 0.02288 0.02654 - 1.2E-05 -1.3E-05 -2.0E-05 2.18E-09 2.97E-09 5.64E-09 + ^2 X T + a3 X + ^4 X = a^ x l n T + a2 x T-\-a^ x T^/2-\-a^ x

•^372 "298 • L - "/ H°-fl6 = «i X T M + a2

V

TÎ2 + ^3

X

TV3 +

^4 :

1 -4.078 0.03812 -3.6E-05 1.07E-08 @372 @298 @372

: rV4

@298 @372

= "~ ^298 = ~ ^^2,12 ~ ~ '^6]298 if 2 = (//372 - ^ 2 9 8 ) ( ^ 2 ) (ôm SWS: interpolated) = (i/°,2 - ^298)(Q (fro"^ SWS: interpolated) A , H ° , , = A,H°,3 + - 8 H 3 - 9H,

f/l

-6.39 0.21 -1.3E-04 3.0E-08 55.504 20.69 31.93 111.74 6.337 10.103 3.765 0.520 0.188 -55.759

(b) Liquid state 2.489 fli 8.459 -1.383 -0.04617 ^2 0.00211 0.0749 3.2E-04 fl3 -5.6E-05 -2.1E-04 a^ 1.7E-07 2.3E-07 -4.6E-07 C° = fli + fl2 X T-hfl3 xT^-â^xT^ S°-a^ = a^ x l n T - F - a 2 x 7 + % x 7 ^ 2 + ^ 4 x 5372 = ^298 + [ ^ ° - ^ 7 ] 372 - [ ^ ° - « 7 ] 2 9 8 H° - ^6 = fli X T + fl2 X T 7 2 + ^3 X T^/3 -f ^372 - ^298 =

- ^6]372 "

fl4 X

" ^6]298 "- 9 ^ 2

^372 = ^298 + (^372 ~ ^298) ~ (c) AH,,p = A , i f ° ( g ) - A f i / ( l ) A5,,p = 5 ° ( g ) - 5 ( 1 ) = 1 1 1 . 7 4 - 9 1 . 9 3

TV4

9.116 -0.2354 1.3E-03 - 1.9E-06 @372 @29S @372 @ 298 @372

52.52 -0.20 l.lE-03 - 1.3E-06 68.769 279.17 293.47 91.93 14.294 19.083 4.788 -63.076 7.316 19.81


279

AH^^p{312)

F o r comparison, SWS gives = 7.410. N o t e that AH^^p/T^.p. = 19.67; for a phase change, AG = 0, so this quantity should equal AiS^^p- According to Trouton's rule, A5vap the boiling point is approximately 20.7calmol~ ^

6.

Example Estimate Cp for hquid hexacosane (C26H54) at the melting point, 332 K, and at 358 K. F r o m these, calculate AS and AH on heating the liquid from 332 to 358 K.

We use the coefficients listed in Table 29 to calculate Cp at the two temperatures. We then use equations 50 and 51 to calculate the enthalpy and entropy. N o t e that the coefficients in Table 29 give Cp directly, not Cp/R. Groups

P

s

Total

# of gps «i

2 8.459 0.00211 -5.605 X 10-' 1.723 X 1 0 - ^

24 1.383 0.07049 - 2 . 0 6 3 X 10"^ 2.269 X 1 0 - ^

26 -16.274 1.69598 -0.00506 5.79 X 1 0 - 6

«2 «3 ^4

C,{T) S{T) HIT H(T)

A @332K -16.27 563.39 -558.75 212.25 200.62 260.17 132.23 43901.66

@358K -16.27 608.11 -650.98 266.92 207.78 275.54 137.52 49231.63

15.38 5330.0

Andon and Martin^^ measured the heat capacity of hexacosane over the temperature range of 13 to 358 K. At 332 K they obtained 203.37 cal m o l " ^; at 358, 210.06 cal m o l " ^ The error in the group additivity calculation is 1.3% at the lower temperature and 1.1 at the higher. They also tabulated calculated thermodynamic functions over a range of temperatures. Interpolating from their tables, we find the entropy change on heating from 332 and 358 to be 15.1 cal m o l " ^ K " ^ and the enthalpy change to be 5370cal m o l " \ both in good agreement with the group additivity estimates. Example

for gaseous C2H5 at 1000 K, using the alternative method

7. Calculate

of Table 30. Groups # of gps ^S'',JR "'298/

G

0 0 -14.73 -18.30 -5.03 -2.52 -1.21 0.05 Aa, -4.61 -2.93 -1.94 -1.40 0.00513 0.00442 0.00629 0.0122 Afl2 -8.5E-07 -1.6E-06 -5.2E-06 -1.3E-05 Aa^ -3.3E-10 1.12E-10 1.50E-09 4.09E-09 Aa^. A = ASl^,,JR - Aai X In (298) - 298 x Afl2 - 298^ x Aa3/2 - 298^ x \ j R + 298Aai + 298^ x Afl2/2 + 298^ x AaJ3 + 298^* x B=-AH C = Aa, D = Aajl E = AaJ6 F = Aa4/12 In K = A + B / T + CIn T + + + FT^ logX

Example

2

-8.99

0

-11.66

0 0 0.40

Aa4/3 AaJA

n

o Total

0 18 0 0.80

-20.87 -10,060 -9.22 0.010 -1.69E-06 -6.60E-10 37.90 7751.78 -9.22 5.13E-03 -2.82E-07 -5.50E-11 -13.24 -5.75

8. (a) Calculate the gas-phase K^^ between ethane and isooctane at 1000 K.

280


(b) W h a t is the partial pressure of isooctane produced starting from ethane at a pressure of 1 atm? (c) 10 atm? The equilibrium constant is related to the various Kf values for products and reagents by equation 5. N o t e that Kf for the elements is unity at all temperatures. (a) 4 C 2 H 6 ^ C 8 H i 8 + 3H2 K,^ = KS-CsU.s) X lKf(U2)y/lUC2n,)r logKe, = logXf(i-C8Hi8)-41ogKf(C2H6)= - 3 2 . 6 3 - 4 x ( - 5 . 7 5 ) - 9 . 6 3 (b) T h e equilibrium constant (with the standard state of 1 atm) for this reaction is related to the species partial pressures at equilibrium by

'

(C.H,)-

If Pq = original C j H g pressure, then at equilibrium,

(H2) = 3x and 10-9,63

(Po-4xr whence

or x^lQ-^^'Po Thus, at an initial pressure of Pq = 1 atm, x = 10"^'^^ atm. (c) At an initial pressure of 10 atm, x = 10"^'^^ atm. Example 9. Calculate Aifgomb a n d K,^ for oxidation of gaseous i-octane to give gaseous products (a) at 1000 K; (b) at 500 K; (c) at 500 K, assuming that the water is produced in the liquid state. The heat of combustion of a c o m p o u n d is the heat of rection for the complete oxidation process. F o r any alkane, the products of combustion are CO2 a n d H2O, the latter generally assumed to be in the liquid state (However, at high temperatures thermodynamic functions for water are generally tabulated in the gaseous state.) W e start by writing the balanced equation for the reaction. (a) 1000 K. C g H i s + I2.5O2 ^ 8 C 0 2 ( g ) + 9H20(g) 1000 K C g H i s O2 C02(g) H20(g) AfH° -63.376 0 -94.320 -59.240 logKf -32.63 0 20.67 10.06

Reaction -1,224 288.53

6. T h e thermochemistry of alkanes a n d cycloalkanes (b) 5 0 0 K. C g H i s + I2.5O2 500 K CgHis

281

8C02(g) + 9H20(g) O2

C02(g)

AfH°

-59.250

0

-94.090

logXf

-18.99

0

41.25

H20(g) -58.276

Reaction -1,218

22.88

554.91

(c) 500 K, giving hquid vâter as product. C g H i s + I2.5O2 8C02(g) + 9H20(1) 500K

CgHis

O2

C02(g)

HÔO) Reaction

AfH°

-59.250

0

-94.090

-59.240

logKf

-18.99

0

41.25

10.06

-1,227 439.53

P a r t (a) a n d (b) show that the difference in energy liberated by completely burning isooctane at 1000 K is only a b o u t 6 kcal mol ~^ larger, or 0.5%, t h a n t h e corresponding value at 5 0 0 K. T h e difference in heats of combustion found in parts (b) a n d (c) should equal t o AH^^^ of water at 500 K. Most thermochemical tables list properties of gaseous water at high temperatures; the more practical calculation, involving liquid water product, can therefore be carried o u t using AHy^p at the appropriate temperature. N o t e that the tabulated values are generally at l a t m pressure, which m a y n o t correspond t o the physical case of interest. Example 10. Chickos a n d coworkers^"^ have proposed a simple empirical relationship for predicting AZ/y^p 2 9 8 for alkanes: A H , , p , 2 9 8 = 0.31nQ +

1.12nc + 0.71

(a)

where HQ is the n u m b e r of quaternary carbons a n d fie is the n u m b e r of n o n q u a t e r n a r y carbons. C o m p a r e this equation's predictions with group additivity for i-C4Hio, n-CgHig and i-CgHig. F r o m equation a above, A H , , p , 2 9 8 = 0.31nQ + 1.12nc + 0.71 = 0.31Q + 1.12(P + S + T) + 0 . 7 1

where we have substituted our usual nomenclature for the n u m b e r of primary, secondary, tertiary a n d quaternary carbons. F o r any branched alkane without rings, P = 2 + T + 2Q

(b)

whence AH,,p,298

= 2.55Q + 2.24T 4- 1.12S + 2.95

(c)

F r o m Table 26, AH,3p,298 = 1-56P + 1.11s - 0.2T - 0.65Q + 0.35G

(d)

Substituting from equation b we obtain AH,,p,298

= 2.47Q + 1.36T + l . l l S + 3.12 + 0.35G

(e)

Comprison of equations c a n d e shows that the expression of Chickos a n d coworkers is not very different from the g r o u p additivity prediction, especially if there are n o tertiary carbon atoms a n d n o gauche interactions. T h e predictions of equation a/c a n d e are compared with the experimental values (from P N K ) below:

282

N . Cohen a n d S. W. Benson Alkane

equation a/c

equation e

Af/âpCexp)

5.19 9.67 8.86

4.48 9.78 9.11

4.61 9.92 8.40

Isobutane Octane Isooctane (224m35)

Example 11. Calculate, using group additivity, AH^^^ for 1,1-dimethylcyclopentane (a) at 298 K; (b) at the boihng point, 3 6 1 K . (a) All the numerical constants needed are in Table 26. T h e constitutent groups of l l m m C s are: 2Ps, 4 Ss, 1 Q, a n d 1 C5 ring correction. F r o m the second column of the Table we find the respective contributions to AH^^^ at 298 K: P:

2x1.56

=

3.12

S:

4x1.11

=

4.44

Q:

I x -0.65=-0.65

C5 ring corr: 1 X 1.3

=

1.3 8.21 kcal m o r ^

(b) W e calculate the change in AH^^^ in going from 298 to 3 6 1 K by using equation 50 twice (first with T = 298, then with T = 361), except that instead of a, coefficients we use the Aa,- coefficients of Table 26. G r o u p contributions t o ACp needed to calculate the variation of Ai/y^p with temperature are as follows: Groups each P each S each Q C5 ring corr Total

Aai -8.63 1.13 -13.19 -45.23 -71.16

100

X

Aa2

2.23 -4.76 27.35 39.88 52.65

10^ X Afl3

4.44 19.30 -132.3 -117.4 -163.62

10^

X

Aa4

-1.701 -2.239 19.167 11.218 18.027

AAH,,p(361 - 298): Aa, x (361 - 298) + Aa^ x (361^ - 298^)72 + Aa3 X (361^ - 298^)/3 + Aa^ x (361^ - 298^)/4 = - 71.16 X 63 + 0.5265 x 20758 - 0.0016362 x 6860763 + 18.027 x 1 0 - ^ x 2.274 x 10^ = -680.2 Therefore, Aif^^p at 361 K = 8 2 1 0 - 6 8 0 = 7 5 3 0 c a l m o r ^ F r o m SWS, Table N o . 349, we see that the experimental value is 7239 cal mol Trouton's rule, equation 73, predicts a value of 7460 cal mol

XIV. APPENDIX. BIBLIOGRAPHY OF USEFUL COMPILATIONS AND REFERENCES

The following selective hst begins with three particularly useful book-length studies a n d then lists (in chronological order) significant m o n o g r a p h s a n d journal references that deal extensively with the alkanes and cycloalkanes that are the subject of this Volume.


283

D. R. Stull, E. F. Westrum, Jr. and G. C. Sinke, The Chemical Thermodynamics of Organic Compounds (SWS), Krieger Publ. Co., Malabar, Florida, 1987. T h e first 200 pages include a review of basic thermodynamic concepts a n d thermochemistry, the evaluation of entropy, the estimation of thermodynamic quantities and applications to industrial problems. The bulk of the volume consists of ideal gas tables [including C;, 5°, -(G° - H ° 9 g ) / T , H ° 9 g , A f A f G°, and logXf for 298 < T (K) < 1000] for hydrocarbons, C — H — O compounds, C — H — N — O compounds, organic halogen c o m p o u n d s a n d organic sulfur compounds. A separate table lists experimental data at 298 K. J. B. Pedley, R. D . Naylor and S. P . Kirby, Thermochemical Data of Organic Compounds (PNK), C h a p m a n a n d Hall, L o n d o n & N e w York, 1986. T h e tabulated heats of reaction and heats of formation update the tables of Cox a n d Pilcher. Introductory chapters discuss additivity schemes a n d develop a complex component additivity formalism for predicting enthalpies of organic compounds. J. D . Cox a n d G. Pilcher, Thermochemistry of Organic and Organometallic Compounds, Academic Press, L o n d o n & New York, 1970. T h e major feature is a tabulation of experimental measurements of A^H°, heats of reaction, for organic a n d organometalhc compounds. Values of AfH° are derived for each experimental result; where phase changes are involved measurements of A//°^p (heat of vaporization) are tabulated. Experimental uncertainties are assessed. Introductory chapters discuss the basics of thermochemistry, the types of experimental measurements involved, their accuracies a n d limitations. Additional chapters examine theoretical aspects of thermochemistry a n d various schemes for relating thermochemical properties to structural parameters. A. Labbauf, J. B. Greenshields a n d F . D . Rossini, 'Heats of formation, combustion, a n d vaporization of the 35 nonanes a n d 75 decanes', J . Chem. Eng. Data, 6, 261 (1961). Tabulates calculated values of AH^^^ a n d of AHf a n d AHgomb for both vapor a n d liquid phase, all at 298 K. R. C. Wilhoit, B. J. Zwolinski G. K. Estok, G. B. Mahoney, and S. M. Dregne, Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds, Thermodynamics Research Center, Dept. of Chemistry, College Station, Texas, Texas A & M University, 1971. Includes table of Aif^,p(298) a n d AHvap(b.p.) for many hydrocarbons, including alkanes a n d cycloalkanes. J. Chao, R. C. Wilhoit and B. J. Zwohnski, Tdeal gas thermodynamic properties of ethane and propane', J. Phys. Chem. Ref Data, 2, 427 (1973). Review a n d evaluation of structural parameters (including vibrational frequencies a n d internal rotation properties); tabulation of thermodynamic properties [C°, S°, {H° - H°), {H° - H^yT, -{G°-Hl)/T, AfG°,AfH°, l o g X f ] for 0 < T ( K ) < 1^00 calculated by statistical thermodynamic methods [rigid-rotor harmonic oscillator ( R R H O ) approximation]. D. W. Scott, 'Correlation of the chemical thermodynamic properties of alkane hydrocarbons', J . Chem. Phys., 60, 3144 (1974). Includes 'working formulas, tables, and equations . . . whereby thermodynamic properties for selected temperatures between 200 a n d 1500K can be calculated for any alkane hydrocarbon with a tractably small number of molecular conformations (say < 3^* = 81). . . . Values so obtained for the entropy, heat capacity, a n d enthalpy of formation at 298.15 K are tabulated for all alkanes C g - C i o - Calculated values are compared with measured ones'. The procedure is updated from the pioneering work of Pitzer^ ^ as modified by Person a n d PimenteF'^, incorporating newer experimental data a n d elaborate computational schemes for taking account explicitly of conformational isomers (e.g. trans-gauche). This paper represents perhaps the most detailed scheme for predicting alkane thermochemical properties, b u t the accompanying drawback is that it is very difficult for the reader to apply the procedures to other cases of interest.

284

N . C o h e n and S. W. Benson

S. S. Chen, R. C. Wilhoit and B. J. Zwohnski, 'Ideal gas thermodynamic properties a n d isomerization of n-butane and isobutane', J. Phys. Chem. Ref. Data, 4, 859 (1975). Review and evaluation of structural parameters (including vibrational frequencies and internal rotation properties); tabulation of thermodynamic properties [ C ° , S°, iH°-Hl)/T, ( G ° - H ° ) / T ] for 0 < T ( K ) < 1500 calculated by statisWl thermodynamic methods ( R R H O approximation). K. M . Pamidimukkala, D . Rogers and G. B. Skinner, 'Ideal gas t h e r m o d y n a m i c properties of CH3, CD3, CD4, C 2 D 2 , C2D4, C2D6, C2H6, CH3N2CH3 a n d CD3N2CD3', J. Phys. Chem. Ref Data, 11, 83 (1982). Includes ideal gas thermodynamic properties [ C ; , S°, (H° - Hl^^)/T, -(G° - Hl^^)/T, AfH\ l o g K f ] for 0 < T ( K ) < 3 0 0 0 calculated by statistical thermodynamic m e t h o d s ( R R H O approximation) for CH3, C2H6 and perdeuteriated analogs. D. F. M c M i h e n and D . M . Golden, ' H y d r o c a r b o n b o n d dissociation energies', Ann. Rev. Phys. Chem., 33, 493 (1982). A review a n d recommendation of best values of b o n d dissociation energies for various classes of h y d r o c a r b o n c o m p o u n d s . W. M . Haynes and R. D . Goodwin, Thermophysical Properties of Normal Butane from 135 to 700 K at Pressures to 70MPa, U.S. Dept. of Commerce, N a t i o n a l Bureau of Standards M o n o g r a p h 169, 1982, 192 pp. Tabulated d a t a include densities, compressibihty factors, internal energies, enthalpies, entropies, heat capacities, fugacities and more. Equations are given for calculating vapor pressures, liquid and vapor densities, ideal gas properties, second virial coefficients, heats of vaporization, hquid specific heats, enthalpies and entropies. R. D . G o o d w i n and W. M. Haynes, Thermophysical Properties of Propane from 135 to 700 K at Pressures to 70MPa, U.S. Dept. of Commerce, N a t i o n a l Bureau of Standards M o n o g r a p h 170, 1982, 244 pp. Tabulated d a t a include densities, compressibility factors, internal energies, enthalpies, entropies, heat capacities, fugacities and more. Equations are given for calculating vapor pressures, liquid a n d vapor densities, ideal gas properties, second virial coefficients, heats of vaporization, liquid specific heats, enthalpies a n d entropies. E. S. Domalski, W. H. Evans and E. D . Hearing, 'Heat Capacities and Entropies of Organic C o m p o u n d s in the Condensed Phase', J. Phys. Chem. Ref Data, 13 (1984), Supplement N o . 1, 286 pp. D a t a for over 1400 organic c o m p o u n d s are tabulated, with single-temperature (as near to 298 K as possible) values for Cp and 5, a n d AH and AS for any phase changes. Each original reference constitutes a separate entry, and while the compilers provide letter grade evaluations (A t h r o u g h D) of the estimated rehability of the work, there is n o consolidation or intercomparison of d a t a when there are more t h a n one source. R. A. Alberty and C. A. Gehrig, 'Standard chemical thermodynamic properties of alkane isomer groups', J. Phys. Chem. Ref Data, 13,1173 (1984). Tabulations of C°, 5°, Af H ° and AfG° for 0 < T ( K ) < 1500 for alkanes with 10 or fewer carbons. Also tabulated are group contributions a n d equilibrium fractions within alkane isomer groups. The values are updated from the study by D . W. Scott (1974). R. A. Alberty and Y. S. H a , 'Standard chemical thermodynamic properties of alkylcyclopentane isomer groups, alkylcyclohexane isomer groups, and combined isomer groups', J. Phys. Chem. Ref. Data, 14, 1107 (1985). Ideal gas t h e r m o d y n a m i c properties (C°, 5°, Af Af G°) for 298 < T (K) < 1000 are calculated and tabulated for alkylcyclopentanes t h r o u g h C9H18 and alkylcyclohexanes t h r o u g h C10H20. G r o u p incremental contributions for thermochemical properties are tabulated a n d g r o u p additivities used to calculate properties of individual species for which literature d a t a are not available. Equilibrium mole fractions are calculated within alkylcycloalkane isomer groups for 298 < T (K) < 1000. O. V. Dorofeeva, L. V. Gurvich and V. S. Jorish, 'Thermodynamic properties of


285

twenty-one monocychc hydrocarbons', J . Phys. Chem. Ref. Data, 15, 437 (1986). Structural p a r a m e t e r s for cycloalkanes (C3 to Cg) a n d other c o m p o u n d s are reviewed a n d evaluated; structural constants were estimated where necessary; a n d ideal gas t h e r m o d y n a m i c properties [C°, 5°, (if ° - H°), - G° - H ° / T , log K^] for 100 < T ( K ) < 1500 calculated by statistical t h e r m o d y n a m i c m e t h o d s ( R R H O approximation). E. S. D o m a l s k i a n d E. D . Hearing, 'Estimation of the t h e r m o d y n a m i c properties of h y d r o c a r b o n s at 298.15', J . Phys. Chem. Ref. Data, 17, 1637 (1988). Application of g r o u p additivity techniques to calculated t h e r m o d y n a m i c properties for liquid and solid phases at 298 K for straight chain (C1-C20) a n d branched alkanes, cycloalkanes and alkylcycloalkanes, a n d other c o m p o u n d s . G r o u p values for Afii°, a n d S° ait 298 K are tabulated for gas, liquid a n d sohd phase. Corrections for gauche interactions in gas-phase branched alkanes are reevaluated using a questionable, a n d certainly m o r e complex, scheme. Sources of 'experimental' d a t a are n o t indicated, a n d seem to include previously estimated values as well as experimentally measured ones. XV. REFERENCES 1. G. N . Lewis and M. Randall, Thermodynamics and the Free Energy of Chemical Substances, McGraw-Hill, N e w York and London, 1923. 2. G. N. Lewis and M. Randall, Reference 1, p. 13 [from Ann. Mines, 13, 157 [1888)]. 3. Cp, 5 and H are considered thermodynamic quantities; all the properties derived from them—including G and K—are thermochemical quantities. 4. D . R. Herschbach, H. S. Johnston, K. S. Pitzer and R. E. Powell, J. Chem. Phys., 25,736 (1956). 5. See A. Veillard, 'Ab initio calculations of barrier heights'. Chap. 11 in Internal Rotation in Molecules (Ed. J. Orville-Thomas), Wiley, N e w York, 1974. 6. R. M. Pitzer, Acc. Chem. Res., 16, 207 (1983). 7. J. Chao, R. C. Wilhoit and B. J. Zwohnski, J. Phys. Chem. Ref. Data, 2, 427 (1973). 8. S. S. Chen, R. C. Wilhoit and B. J. Zwohnski, J. Phys. Chem. Ref. Data, 4, 859 (1975). 9. V. Sackwild and W. G. Richards, J. Mol. Struct. (Theochem), 89, 269 (1982). 10. U. A. Zirnet and M. M. Sushinskii, Optics and Spectroscopy, 16, 489 (1964). I L L . Lunazzi, D. Macciantelh, F. Bernardi and K. U. Ingold, J. Am. Chem. Soc, 99,4573 (1977). 12. C. Jaime and E. Osawa, Tetrahedron, 39, 2769 (1983). 13. J. E. Anderson and H. Pearson, J. Am. Chem. Soc, 97, 764 (1975). 14. K. S. Pitzer, J. Chem. Phys., 5, 469 (1937); K. S. Pitzer and W. D . Gwinn, J. Chem. Phys., 10, 428 (1942); K. S. Pitzer, J. Chem. Phys., 14, 239 (1946); J. E. Kilpatrick and K. S. Pitzer, J. Chem. Phys., 17, 1064 (1949); J. C. M. Li and K. S. Pitzer, J. Phys. Chem., 60, 466 (1956). 15. G. N . Lewis and M. Randall, Thermodynamics (revised by K. S. Pitzer and L. Brewer), Chap. 27, 2nd edn., McGraw-Hill, N e w York, 1961. 16. H. L. Strauss and E. Thiele, J. Chem. Phys., 46, 2473 (1967). 17. See, for example. Reference 15, Chap. 16; or J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids, Chap. 1, Wiley, N e w York, 1954. 18. See J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, N e w York, 1954, p. 167. 19. G. Waddington, S. S. Todd and H. M. Huffman, J. Am. Chem. Soc, 69, 22 (1947). 20. Reference 22, p. 249. 21. J. D . Cox and G. Pilcher, Thermochemistry of Organic and Organometallic Compounds Chap. 7, Academic Press, London and N e w York, 1970. 22. D . R. StuU, E. F. Westrum, Jr., and G. C. Sinke, The Chemical Thermodynamics of Organic Compounds, Krieger Publ. Co., Malabar, Florida, 1987. 23. M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D . J. Frurip, R. A. McDonald and A. N . Syverud, J A N A F Thermochemical Tables, 3rd Edition, J. Phys. Chem. Ref. Data, 14, Supplement 1 (1985). 24. A. L. Verma, W. F. Murphy and H. J. Bernstein, J. Chem. Phys., 60, 1540 (1974). 25. D . A. Pittam and G. Pilcher, J. Chem. Soc, Faraday Trans 1, 68, 2224 (1972).

286

N . C o h e n and S. W. Benson

26. F. D . Rossini, J. Res. Natl. Bur. Stand., 6, 37 (1931); 7, 329 (1931); 12, 735 (1934); 15, 357 (1935); E. J. Prosen, F. W. Maron and F. D . Rossini, J. Res. Natl. Bur. Stand., 46, 106 (1951). 27. S. Gordon and B. J. McBride, 'Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks and Chapman-Jouguet Detonations', N A S A SP-273 (1971). 28. A. Burcat, Thermochemical data for combustion calculations'. Chap. 8 in Combustion Chemistry (Ed. W. C. Gardiner, Jr.), Springer-Verlag, N e w York, 1984. 29. R. A. Alberty and C. A. Gehrig, J. Phys. Chem. Ref. Data, 13, 1173 (1984). 30. K. Fajans, Chem. Ber., 53, 643 (1920); 55, 2826 (1922); M. S. Kharasch, J. Res. Natl. Bur. Stand., 2, 359 (1929). 31. S. W. Benson and J. H. Buss, J. Chem. Phys., 29, 546 (1958). 32. S. W. Benson, Thermochemical Kinetics, 2nd edn., Wiley, N e w York, 1976, p. 25. 33. Reference 21 Chap. 7 shows the equivalence of the group additivity approach and the schemes proposed by Laidler and by Allen. 34. K. J. Laidler, Can. J. Chem., 34, 626 (1956). 35. T. L. Allen, J. Chem. Phys., 31, 1039 (1959). 36. J. R. Piatt, J. Chem Phys., 15, 419 (1947); J. Phys. Chem., 56, 328 (1952). 37. J. B. Greenshields and F. D . Rossini, J. Phys. Chem., 62, 271 (1958). 38. G. R. Somayajulu and B. J. Zwolinski, Trans. Faraday Soc, 62, 2327 (1966). 39. R. M. Joshi, J. Macromol. Sci., Chem., A4, 1819 (1970). 40. Reference 37, as modified by H. A. Skinner, J. Chem. Soc, 4396 (1962). 41. J. D . Overmars and S. M. Blinder, J. Phys. Chem., 68, 1801 (1964). 42. M. Senders, Jr., C. S. Matthews and C. O. Hurd, Ind. Eng. Chem., 41, 1048 (1949). 43. V. M. Tatevskii, V. A. Benderskh and S. S. Yarovoi, Rules and Methods for Calculating the Physico-chemical Properties of Paraffinic Hydrocarbons (transl. B. P. Mulhns), Pergamon, Oxford, 1961, 44. K. K. Verma and K. K. Doraiswamy, Ind. Eng. Chem. Fundam., 4, 389 (1965). 45. R. C. Reid, J. M. Prausnitz and B. E. Pohng, The Properties of Gases and Liquids, 4th edn.. Chap. 6, McGraw-Hill, N e w York, 1987. 46. Reference 32, p. 26. 47. The contribution of the C—(C)2(H)2 group is of particular historical interest. Since the CH2 group contribution was easily derivable from the heats of formation of successive homologs in various series, it was early examined for constancy, as P. Sellers, G. Stridh and S. Sunner [J. Chem. Eng. Data, 23, 250 (1978)] have pointed out. In 1886, J. Thomsen (Thermochemische Untersuchungen, Vol. 4, Barth, Leipzig, 1886) deduced that a CH2 group added 158 kcal mol to the enthalpy of combustion of a compound, whence we derive a value of 6.15 for the contribudon to AHf. F. D . Rossini [J. Res. Natl. Bur. Stand., 13, 21(1934)], using the then-most-recent experimental data, obtained a value of 5.15 kcal mol ~S a value later refined to 4.926 [E. J. Prosen, W. H. Johnson and F. D . Rossini, J. Res. Natl. Bur. Stand., 37, 51 (1946)]. Sellers and coworkers determined separate constants for C H j increments in different homologous series. For n-alkanes, they found 4.95 ± 0 . 0 1 ; for 2-methylalkanes, 5.01 ± 0.05; for 1-cyclohexylalkanes, 4.96 ± 0.03. We discuss the question of the constancy of this 'constant' later in the text. 48. S. W. Benson, F. R. Cruickshank, D . M. Golden, G. R. Haugen, H. E. O'Neal, A. S. Rodgers, R. Shaw and R. Walsh, Chem. Rev., 69, 279 (1969). 49. It is at least of historical interest to note that M. Souders, Jr., C. S. Matthews and C. O. Hurd, Ref 42, derived group values for hydrocarbon groups which, at least in the case of enthalpies, were not very different from current best values. Their enthalpy values, corresponding to column 2 of Table 6, were - 10.05, - 4.95, - 0.88 (except for a group on the 2nd carbon, for which the value was - 1.57) and 2.45 (0.85 for the 2nd carbon). 50. M. L. Huggins, in Structural Chemistry and Molecular Biology (Eds. A. Rich and N. Davidson), W. H. Freeman, San Francisco, 1968, p. 761. 51. See the discussion in S. W. Benson and M. Luria, J. Am. Chem. Soc, 91, 704 (1975). 52. S. W. Benson, Reference 32, p. 30, presented arguments supporting the supposition that the gauche interaction is attributable to the repulsions of the 1,4 H atoms. These arguments were elaborated in S. W. Benson and M. Luria, J. Am. Chem. Soc, 91, 704 (1975). 53. J. B. Pedley, R. D . Naylor and S. P. Kirby, Thermochemical Data of Organic Compounds, 2nd edn. Chapman and Hall, London & N e w York, 1986.

6. The thermochemistry of alkanes and cycloalkanes 54. 55. 56. 57. 58. 59. 60.

61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84.

85. 86.

287

W. B. Person and G. C. Pimentel, J. Am. Chem. Soc., 75, 532 (1953). D . W. Scott, J. Chem. Phys., 60, 3144 (1974). H. E. O'Neal and S. W. Benson, Int. J. Chem. Kinet., 1, 221 (1969). O. Dobis and S. W. Benson, Int. J. Chem. Kinet., 19, 691 (1987). P. D . Pacey and J. H. Wimalasena, J. Phys. Chem., 88, 5657 (1984). J. J. Russell, J. A. Seetula, S. M. Senkan and D . Gutman, Int. J. Chem. Kinet., 20, 759 (1988). M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D . J. Frurip, R. A. McDonald and A. N. Syverud, 'JANAF Thermochemical Tables, 3rd Edition', J. Phys. Chem. Ref. Data, 14, Supplement 1 (1985). M. Brouard, P. D . Lightfoot and M. J. Pilling, J. Phys. Chem., 90, 445 (1986). S. S. Parmar and S. W. Benson, J. Am. Chem. Soc, 111, 57 (1989). R. M. Marshall and L. Rahman, Int. J. Chem. Kinet., 9, 705 (1977). A. L. Castelhano and D . Griller, J. Am. Chem. Soc, 104, 3655 (1982). D. F. McMillen and D. M. Golden, Ann. Rev. Phys. Chem., 33, 493 (1982). R. R. Baldwin, G. R. Drewery and R. W. Walker, J. Chem. Soc, Faraday Trans, i, 80,2827 (1984). W. V. E. Doering, Proc Natl. Acad Sci. U.S.A., 78, 5279 (1981). E. Tschuikow-Roux and Y. Chen. J. Am. Chem. Soc, 111, 9030 (1989). Y.-R. Luo and S. W. Benson, J. Phys. Chem., 93, 3304 (1989). J. E. Baggott and M. J. Pilling, Ann. Rep. Chem. Soc, Sect. C, 199 (1982). W. Miiller-Markgraf, M. J. Rossi and D. M. Golden, J. Am. Chem. Soc, 111, 956 (1989). J. J. Russell, J. A. Seetula, R. S. Timonen, D . Gutman and D . F. Nava, J. Am. Chem. Soc, 110, 3084 (1988). S. W. Benson, J. Chem. Soc, Faraday Trans. 2, 83, 791 (1987); T. S. A. Islam and S. W. Benson, Int. J. Chem. Kinet., 16, 995 (1984). J. C. Schultz, F. A. Houle and J. L. Beauchamp, J. Am. Chem. Soc, 106, 3917 (1984). S. Fhszar and C. Minichino, Can. J. Chem., 65, 2495 (1987). C. W. Larson, E. A. Hardwidge and B. S. Rabinovitch, J. Chem. Phys., 50, 2769 (1969). J. Pacansky and J. S. Chang, J. Chem. Phys., 74, 5539 (1981). J. Pacansky and M. Yoshimine, J. Phys. Chem., 90, 1980 (1986). S. H. Jones and E. Whittle, Int. J. Chem. Kinet., 2, 479 (1970). H. M. Huffman, S. S. Todd and G. D. Ohver, J. Am. Chem. Soc, 71, 584 (1949). R. Shaw, J. Chem. Eng. Data, 14, 461 (1969). M. Luria and S. W. Benson, J. Chem. Eng. Data, 22, 90 (1977). Reference 18, p. 283. J. S. Chickos, A. S. Hyman, L. H. Ladon and J. F. Liebman, J. Org. Chem., 46, 4294 (1981); J. S. Chickos, R. Annunziata, L. H. Ladon, A. S. Hyman and J. F. Liebman, J. Org. Chem., 51, 4311 (1986). S. W. Benson and L. J. Garland, J. Phys. Chem., 95, 4915 (1991). Data for hexane-cetane ( C i g H j J mixtures typify the magnitude of AH^^^ and illustrate its dependence on composition and temperature: T(K)

(Cetane mol%)

293

21 50 69 37 54

323

A//,3p

(calmor^) 21 31 27 7.4 8.8

(Taken from Landolt-Bornstein Numerical Data and Functional Relations in Science and New Series, Group IV, Vol. 2, Heats of Mixing and Solution, p. 492).

Technology,

87. J. Pacansky and B. Schrader, J. Chem. Phys., 78, 1033 (1983). 88. J. Pacansky and H. Coufal, J. Chem. Phys., 72, 3298 (1980). 89. E. S. Domalski, W. H. Evans and E. D . Hearing, 'Heat Capacities and Entropies of Organic Compounds in the Condensed Phase', J. Phys. Chem. Ref Data, 13, Supplement 1 (1984). 90. R. J. L. Andon and J. F. Martin, J. Chem. Thermodyn., 17, 1159 (1976). 91. K. S. Pitzer, J. Chem. Phys., 8, 711 (1940).

CHAPTER

7

The analysis of alkanes and cycloalkanes ZEEV AlZENSHTAT Department of Organic Cliemistry and Casali Institute University of Jerusalem, Jerusalem 91904, Israel

of Applied

Ctiemistry,

The Hebrew

1. I N T R O D U C T I O N IL A L K A N E S A. N o r m a l Alkanes B. Branched Alkanes C. Cycloalkanes D. Polycyclic Alkanes III. S I N G L E C O M P O U N D ANALYSIS A. Mass Spectrometry of Alkanes a n d Cycloalkanes 1. Ionization and appearance potential 2. Fragmentation patterns as related to structure 3. Cycloalkanes B. Infra-red Spectra of Alkanes C. a n d ^^C N M R IV. S E P A R A T I O N O F S A T U R A T E D H Y D R O C A R B O N S F R O M MIXTURES V. S E P A R A T I O N O F T H E S A T U R A T E D H Y D R O C A R B O N F R A C T I O N INTO H O M O L O G O U S FAMILIES VL G A S C H R O M A T O G R A P H Y , AS U S E D F O R ANALYSIS O F ALKANES A N D CYCLOALKANES VII. MASS S P E C T R O M E T E R D E T E C T O R (MSD) A. G a s C h r o m a t o g r a p h y / M a s s Spectrometry/Computerized ( G C / M S / C ) System B. Isotope Analysis of Alkanes and Cycloalkanes VIII. R E F E R E N C E S

291 291 291 292 295 296 301 302 302 303 306 314 316 318 321 322 329 330 340 346

ABBREVIATIONS

ACE CI

alternating chemical a n d electron impact ionization chemical ionization


289

290 CZE DC DCD ID-NMR 2D-NMR ECD EI eV FI FID FIMS FPD FSCOT FT FTIR GC GC-C-isoMS GC-MI GC/MS GC/MS/C GPC GTA HECTOR HRC HR-MS HPLC INEPT-INADEQUATE IP LC MI MI/IR MI/FTIR MPLC MSD NBS NOE NOESY PFK PID PTC RF RID RRF RP SCOT SEC SIM SIR TCD TG TIC TEC

Z. Aizenshtat capillary zone electrophoresis dielectric constant dielectric constant detector one-dimensional N M R (regular) two-dimensional N M R electron capture detector electron impact electron volt field ionization flame ionization detector field ionization-MS flame photometric detector fused silica-SCOT Fourier transform Fourier transform infra-red gas c h r o m a t o g r a p h y GC-combustion-isotope measurement M S GC-matrix isolation gas chromatography/mass spectrometry GC/MS/computerized gel permeation chromatography—size exclusion g r o u p type analysis heteronuclear shift-correlated-spectrum high resolution c h r o m a t o g r a p h y high resolution-MS high pressure liquid c h r o m a t o g r a p h y insensitive nuclear enhancement by polarization transfer ionization potential liquid c h r o m a t o g r a p h y matrix isolation matrix isolation/IR matrix isolation/FTIR medium pressure liquid c h r o m a t o g r a p h y mass spectrometer detector National Bureau of Standards nuclear Overhauser effect N O E a n d exchange spectrometry perfluorinated kerosene photoionization detector p r o g r a m m i n g temperature controller retention factor or response factor (as marked) refractive index detector relative retention factor reversed phase or resolution power (MS) surface coated open tubular super-critical fluid chromatography selective ion monitoring selected ion recording thermoconductivity detector thermogravimetry total ion current thin-layer c h r o m a t o g r a p h y

7. T h e analysis of alkanes a n d cycloalkanes

291

I. INTRODUCTION

In the early stages of preparation of the present manuscript I was confronted with a surprise: T h e analysis of alkanes a n d cycloalkanes' h a s never been reviewed as such. Although the C—C and C—H bonds are the most a b u n d a n t bonds in organic chemistry, the analysis of c o m p o u n d s constructed solely from these bonds cannot be found in analytical reviews of 'functional' groups. Therefore, I could n o t relate t o previous secondary o r tertiary sources of literature. Moreover, the reader of this chapter will find that, although I attempted t o stay as objective as possible in presenting the various analytical techniques, most of the advanced applications come from petroleum and other fossil fuels studies. Since the choice of analytical techniques relates t o structures of the whole alkane or cycloalkane, the various isomers, enantiomers o r conformations are discussed. In general, the scheme of the present chapter foUows the analysis of single c o m p o u n d s by the various techniques a n d then tackles the more difficult problem of the separation and chromatographic analysis of mixtures. Some basic spectral properties of alkanes and cycloalkanes are mentioned briefly a n d the reader is directed t o other chapters of this book. Most basic methods are referred t o the literature and, in cases where figures help t o demonstrate the analytical concept, they are presented. However, in more advanced instrumental analyses, much of the information is in the 'grey literature': manufacturers' information data sheets. The analysis of families of alkanes and cycloalkanes has t o take into account the fact that the homologous members may range from Ci t o C70. Hence, the petroleum industry is still using the refining of crudes t o separate it into fractions of different boihng point ranges. This separation by physical properties was foUowed by all the developed chromatography techniques. Another analytical challenge presented to the researcher involved with thermal stability and catalytic reactivity of hydrocarbons relates to cracking of heavy fractions of petroleum. Thermal analysis is n o t discussed in this chapter. However, o n e should be aware that, although paraffins are considered t o be chemically inactive, the application of certain analytical techniques m a y cause cracking, rearrangement a n d isomerization. II. ALKANES

Almost every textbook o n organic chemistry starts with a chapter o n alkanes, also called saturated hydrocarbons o r paraffins. T h e word paraffin, which comes from the Latin parum afflnis (slight affinity), indicates that, already at t h e early stages of organic chemistry, it was recognized that non-substituted paraffins are rather inert. In petroleum analysis the mixture of the higher alkanes is named wax. D u e t o the low reactivity of alkanes, their analysis by derivatization is very difficult. Moreover, most of the literature o n analysis of functional groups does n o t include analytical methods for separation a n d identification of alkanes. The diversity of alkane isomers is discussed in detail in the chapter by Kier a n d Hall in this volume. However, we should mention that the C„H2„ + 2 open-chain alkanes can have from a single structural isomer (C^—C3) u p t o 366,319 isomers for C20H42. Hence, the analysis of alkanes is more and more complicated with increasing number of C atoms. A. Normal Alkanes

N o r m a l alkanes (straight-chain alkanes o r normal paraffins) are t h e simplest homologous series of the group. The Ci—C5 n-alkanes are gases at room temperature whereas the C5—C^^^^-j are

292

Z. Aizenshtat

C i o p

=

M o l . o o

b . p .

c o

5

c

1 0 0

Q.

2

C

0

4

c

w t . 1 0 0

c l o s e

t o

l O O ^ C

/

o CD

-

1

0

0

/

|a

=

7 3 ° C

5 0 M o l e c u l a r

1

1

1 0 0

1 5 0

w e i g h t

F I G U R E 1. Boihng points of n-alkanes^

hquids a n d t h e longer ones are solids. T h e boiling points of n-alkanes from up to Cio (Figure 1)^ allow their separation by a good distillation column. T h e question of refining will be addressed when we deal with mixtures. T h e specific gravity of the n-alkanes (Table 1)^ shows considerable increases from 0.424 (liquid C H 4 ) t o 0.626 (n-pentane) a n d 0.794 for C 5 0 . B. Branched Alkanes

F o r each carbon number there is only one normal alkane, while the branched alkanes include all other isomers. T h e first branched isomer is 2-methylpropane (isobutane) (Table 2). The most important C5 unit, isoprene (alkene) and the saturated isoprane are for the most part photosynthetically produced a n d are t h e building blocks of t h e open-chain and cyclic terpenoids. The importance of the analysis of the mono-, di-, etc. cychc terpanes will be discussed in the cycloalkanes section. M o s t terpene (Cio) hydrocarbons have double bonds, hence their analysis c a n be approached as t h e analysis of cycloalkenes. However, some saturated terpanes were found in petroleum and bitumens.

293

7. T h e analysis of alkanes a n d cycloalkanes TABLE 1. Normal alkanes^ Formula, Name Methane Ethane Propane n-Butane n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Undecane n-Dodecane n-Tridecane n-Tetradecane n-Pentadecane n-Hexadecane n-Heptadecane n-Octadecane n-Nonadecane n-Eicosane n-Heneicosane n-Docosane n-Tricosane n-Tetracosane n-Pentacosane n-Triacontane n-Pentatriacontane n-Tetracontane n-Pentacontane n-Hexacontane n-Dehexacontane n-Tetrahexacontane n-Heptacontane

QH211+2

CH4 C2H6 C3H8 C4H10 C5H12 C7H16 CsHis

C9H20 C10H22 C11H24 C12H26 C13H28 C14H30 C15H32 C17H36 C18H38 C19H40 C21H44 ^22^46 C23H48 C24H5O C25H52 ^30^62 C35H72 QoH82

C50H102 ^60^122 C62H126 C64H130 ^70^142

m.p. (°C) -182.6 -172.0 -187.1 -135.0 -129.7 -94.0 -90.5 -56.8 -53.7 -29.7 -25.6 -9.6 -6 5.5 10 18.1 22.0 28.0 32 36.4 40.4 44.4 47.4 51.1 53.3 66 74.6 81 92 99 101 102 105

b.p.

CO

-161.7 -88.6 -42.2 -0.5 36.1 68.7 98.4 125.6 150.7 174.0 195.8 216.3 (230) 251 268 280 303 308 330

Sp. gr. (as liquids)" 0.4240 ^ 0.5462 I g 0.5824 a 0.5788 . 0.6264 ^ 0.6594 0.6837 0.7028 0.7179 0.7298 0.7404 . '3 7.7493 0.7568 0.7636 0.7688 0.7749 0.7767 > 0.7767 0.7776 0.7777 0.7782 0.7778 0.7797 0.7786

0.7814

' 1

0.7940

300 at 0.00001 m m

"Specific gravities reported in this table refer to the liquid state. With substances liquid at 20 °C, values for this temperature are given where available. The data given for more volatile substances are for temperatures close to the boiling point, those for less volatile compounds are for temperatures just above the melting points.

The most studied open-chain diterpenoid is phytol (C20H40O) which was isolated from chlorophyll hydrolysate by Willstatter in 1909^, a n d shown t o be a n allylic alcohol by Fischer^. Since then, both phytane (C20H42) a n d pristane (C19H40) have been identified in all fossil fuels (petroleum, coals, asphalts, bitumens, etc.). CH2OH (phytol) Phytol contains two asymmetric carbons (positions 7 a n d 11) whereas phytane (C20H42) has three such chiral centers (3,7 a n d 11). (phytane)

294

Z. Aizenshtat

D u e t o the three chiral centres, phytane has diastereoisomers with different physical properties. Fischer's suggestion that phytol is biogenically produced from geraniol a n d farnesol was followed by Burrell^'^, a n d the stereochemistry of phytol was established as trans-3J{R),n(R). Formerly, it was suggested that the isopranes found in petroleum are synthesized by n a t u r e as isoprenoids. During the early p a r t of the 1960s a very intensive effort was m a d e to isolate the isoprane, which appears close t o the n-Ci7 hydrocarbon. F o r reference, 2,6,10,14-tetramethylpentadecane (C19H40 pristane) was analysed. Spectro scopic m e t h o d s (IR, N M R a n d MS) showed very close similarity of the isolated fraction to synthetic pristane. The physical properties compared were boiling point, freezing point, specific gravity a n d refractive index. Since the pioneering studies by Erdman"^ a n d Bendoraitis a n d coworkers^, single alkanes are still identified by the same methods; the isolation m e t h o d is n o longer used. C a r b o n s 6 a n d 10 in pristane can have stereoisomeric ROT S configuration. Determination of the stereochemistry can support or disprove the suggestion that some of the acychc isopranes Cjg, C15, C14 derive from the phytol structure. The stereochemical determination of alkanes a n d cycloalkanes is always m o r e difficult t h a n that of 'functionalized' organic molecules. F o r most methods, such as optical rotation measurements or X-ray crystahography, a n isolated adequate a m o u n t of a single c o m p o u n d is required. It was also shown that for acyclic isopranes (terpanes) the specific optical rotation values^ are very low, virtually invalidating the use of polarimetry. F o r the stereochemical determination, it seemed theoretically that the most efficient m e t h o d of separation for the three pristane isomers A, B a n d C would be direct gas c h r o m a t o g r a p h y on an optically active stationary phase. Such a m e t h o d was successfully employed for a m i n o acids a n d amine enantiomers^. However, this m e t h o d was found ineffective for pristane, a n d hence various gas-chromatographic 'inactive' stationary phases were employed^ for the separation of the diastereoisomers. T h e relative stereo chemistry could be determined, provided standards with k n o w n respective stereo chemistry are available.

(A)

(B)

(C)

Since pristane is a n 'inactive' alkane, the direct analysis will yield two peaks a n d n o t three; the 6(jR),10(5) = 6(S),10{R) [ A ] is symmetric a n d 6(R),10(R) will n o t separate from 6(iS'),10(iS) [B + C ] . Hence two isomers can be separated. If the examined sample is the meso form 6(/?),10(5) then the absolute stereochemistry of the alkane can be determined

7. The analysis of alkanes a n d cycloalkanes

295

Another alternative is t o functionalize the alkane and form diastereoisomeric derivatives of the functional group (e.g. after oxidation t o acids), which are easier t o separate. Since 1971 Maxwell's group at Bristol used these methods t o separate a n d identify the stereochemistry of isoprenoidic acyclic a l k a n e s W h e r e a s most acyclic isoprenoids in nature appear functionalized (alcohols, acids, alkenes, etc.), they are found in the geoenvironment as fossil alkanes. Hence it is important not only t o analyse the structural isomers, b u t also t o determine the stereochemistry. Isoprenoids (terpanes), with a longer chain than pristane, have been detected in fossil fuels (see below the discussion o n the analysis of petroleum). C25—C30 isoprane hydro carbons were analysed in a number of methanogenic bacteria T h e C40 isoalkane, which was isolated from the saturated fraction of the bitumen of the Green River Shale (USA), is claimed t o be the product of total saturation of carotenoids. The analysis of these polyhydrogenated carotenes (PHC) requires special G C high-temperature inert columns (see G C of high carbon number wax hydrocarbons). C. Cycloalkanes

The monocyclic hydrocarbons (C„H2„) found in nature contain from 3 t o 30 carbons, although in principle there is n o limit to the ring size. Even so, cyclopentanes a n d cyclohexanes are the most a b u n d a n t in nature. T h e analysis of single c o m p o u n d monocyclic alkanes is in many respects similar t o the analysis of the open-chain alkanes. However, for small rings (cyclopropane, cyclobutane) some added methods can be employed because of their higher chemical activity, due to the distortion of the C — C — C angles. The olefmic properties of cyclopropanes were reviewed by Charton^^. The stereochemistry of cycloalkanes is discussed extensively in the chapter by Anderson, a n d it is important for a n understanding of the analyses offered for these compounds t o distinguish between isomers and conformers. Because of the low energetic barrier for equilibration between axial and equatorial conformers, only low-temperature ^ H N M R or ^ ^ C N M R as weU as IR wih freeze the equilibration and allow the spectral analysis of the conformers. However, disubstituted cycloalkanes will exhibit, in addition to structural isomerism, also cis, trans isomerism. Both cis a n d trans isomers of 1,4-dimethylcyclohexane undergo, at room temperature, a conformer equilibration. In the case of the trans isomer the conformer with two equatorial CH3 groups is more stable, while for the cis isomer both conformers are equally stable a n d cannot be separated. In general the boiling points of the cycloalkanes are slightly higher than those of the corresponding alkanes and this is also true for the freezing point (see Tables 2a and 2b)^ ^. Monocycloalkanes and their alkylated derivatives are n a m e d in the petroleum industry naphthenes. Most of them distil between 50-120 °C, a n d so these c o m p o u n d s are a n important part of the n a p h t h a fraction. F o r example, in the monocyclic terpane, pmenthane, the cis and trans isomers are assigned arbitrarily. As will be discussed later, only at low temperatures could the bandwidth of the Matrix Isolation F T / I R = MI/FT/IR^"^ analyse the differences. T h e M S of the two isomers (Figure 2) are essentially the same (the N B S hbrary for p-menthane indicates the same spectrum for both). Figure 3 shows the fingerprint region, which is dominated by the C — H bending absorption (see IR of alkanes), a n d here the t w o isomers show different characteristics. T h e gem-dimethyl group absorptions are located a r o u n d 1 3 8 7 - 1 3 6 9 c m " ^ (a a n d b . Figure 3). However, one can see the differences which allow isomer assignment. All the above is true only if one has authentic isolated isomers, hence quantification of a mixture might be problematic. These results are claimed t o be comparable t o ^ ^ C N M R with the advantage of the use of nanograms vs miligrams needed for NMR^"^. Since o n e would expect such isomers to be also separable by high-quality G C (capillary columns), t h e use of G C / M I / F T / I R

296

Z. Aizenshtat

is possible. This of course will require fast cryogenic t r a p p i n g a n d flush heat release (see Section VI). It is also possible t o identify isomers by X-ray analysis of t h e solid.

p-menthane (b.p. 1 7 2 X )

D. Polycyclic Alkanes T h e analytical challenge for structure d e t e r m i n a t i o n is increased with t h e n u m b e r of rings in t h e cycloalkanes studied. Classification of the polycyclic alkanes c a n be s u p p o r t e d by t h e general formulae C„H2„ for monocyclics, C„H2„-2 for t h e dicyclics, C „ H 2 „ - 4 for tricyclics, etc. L a t e r in

TABLE 2a. Paraffin hydrocarbons

Name Methane Ethane Propane Butanes n-Butane Isobutane Pentanes n-Pentane Isopentane (2-methylbutane) 2,2-Dimethylpropane Hexanes n-Hexane Isohexane (2-methylpentane) 3-Methylpentane 2,2-Dimethylbutane 2,3-Dimethylbutane Heptanes n-Heptane Isoheptane (2-methylhexane) 3-Methylhexane 3-Ethylpentane 2,2-Dimethylpentane 2,3-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,2,3-Trimethylbutane

Mehing point (X)

Formula

CF)

CH4 C^H, C3H8

-300 -278 - 309.8

-184 -172 - 189.9

C4H10 C4H10

-211.8 -229

C5H12 C5H12

Boihng point"

CF)

CQ

-258.5 - 126.4 -48.1

- 161.4 -88.3 -44.5

-135 -145

31 13.6

-0.6 -10.2

0.60(0) 0.559(20)

-201.7 -254.8

- 129.9 - 159.7

96.8 87.8

36 28

0.626(20) 0.619(20)

C5H12

- 4

-20

49.1

9.5

0.613(0)

C6H14 C6Hi4

-139.5 - 244.6

-95.3 - 153.7

155.7 140.4

68.7 60.2

0.660(20) 0.654(20)

C5H14 C6H14 C6H14

- 180.4 -144.8 -211.2

-118 -98.2 -135.1

145.8 121.5 136.6

63.2 49.7 58.1

0.668(20) 0.649(20) 0.662(20)

C7H16 C7H16

- 130.9 -182.4

-90.5 -119.1

209.1 194

98.4 90

0.684(20) 0.679(20)

C7H16 C7H16 C7H16 C7H16 C7H16 C7H16 C7H,,

-182.9 -181.8 -194.1

-119.4 -118.8 -125.6

- 182.9 -211 -13

-119.4 -135 -25

197.2 199.9 174 193.5 177.4 186.8 177.6

91.8 93.3 78.9 89.7 80.8 86 80.9

0.687(20) 0.698(20) 0.674(20) 0.695(20) 0.675(20) 0.693(20) 0.690(20)

Sp. gr. (at °C) 0.415(liq.-164) 0.446 (hq. 0) 0.536 (liq. 0)

297

7. T h e analysis of alkanes a n d cycloalkanes TABLE 2a (continued)

Name Octanes n-Octane Isooctane (2-methylheptane) 2,2,4-Trimethylpentane'' n-Nonane n-Decane n-Undecane n-Dodecane n-Tridecane n-Tetradecane n-Pentadecane n-Hexadecane (cetane) n-Heptadecane n-Octadecane n-Nonadecane n-Eicosane

Formula

Melting point

Boiling point''

CF) CQ

CF) CQ

-70.4 -168.3

-56.9 -111.3

258.1 243

125.6 117.2

C19H40 C20H42

-160.3 -64.7 -21.5 -14.3 14.4 21.2 41.9 50 64.4 72.5 82.4 89.6 97.7

-107.4 -53.7 -29.7 -25.7 -9.7 -6 5.5 10 18 22.5 28 32 36.5

210.7 303.3 345.2 384.4 420.6 453.2 486.5 518.9 549.5 577.4 602.6 626 401

n-Heneicosane

C21II44

104.9

40.5

419

n-Docosane

C22H46

111.9

44.4

436.1

n-Tricosane

C23H48

117.8

47.7

453.2

n-Tetracosane n-Pentacosane n-Hexacosane n-Heptacosane

C24H50 C25H52 C27II56

123.8 129.2 134.6 139.1

51 54 57 59.5

615.2 761 784.4 518

n-Octacosane n-Nonacosane n-Triacontane n-Hentriacontane

C28II58 C29II6O C30II62 C31H54

143.6 146.3 150.8 154.6

62 63.5 66 68.1

834.8 896 861.8 575.6

n-Dotriacontane (dicetyl)

C32II66

158

70

590

n-Tritriacontane

C33H68

161.6

72

622.4

n-Tetratriacontane n-Pentatriacontane

C34II7O C35H72

163.4 166.5

73 74.7

908.6 627.8

n-Hexatriacontane

^36^74

168.8

76

509

n-Tetracontane

C40II82

177.8

81

465.8

n-Pentacontane

C50H102

199.4

93

789.8

99.3 150.7 174 195.8 216.2 234 252.5 270.5 287.5 303 317 330 205 (15 mm) 215 (15 mm) 224.5 (15 mm) 234 (15 mm) 324 405 418 270 (15 mm) 446 480 461 302 (15 mm) 310 (15 mm) 328 (15 mm) 487 331 (15 mm) 265 (1.0 mm) 241 (0.3 mm) 421 (15 mm)

nHexacontane n-Dohexacontane n-Tetrahexacontane n-Heptacontane

^60^122

210.2 213.8 215.6 221

99 101 102 105

C9H20 C10H22 C11H21 C12II26 C13H28 C14H30 C15II32 C16II34 C17H36

^26^54

^62^126 ^64^130

C70H142

"At 760 m m mercury, unless otherwise specified. ''This chemical is used as standard in octane rating.

Sp. gr. (at °C)

0.703(20) 0.698(20) 0.692(20) 0.718(20) 0.730(20) 0.740(20) 0.749(20) 0.772(0) 0.774 (at m.p.) 0.776 (at m.p.) 0.775 (at m.p.) 0.777 (at m.p.) 0.777 (at m.p.) 0.777 (at m.p.) 0.778 (at m.p.) 0.778 (at m.p.) 0.778 (at m.p.) 0.778 (at m.p.) 0.779 (at m.p.) 0.779(20) 0.779(20) 0.780 (at m.p.) 0.779(20) 0.780(20) 0.780(20) 0.781 (at m.p.) 0.773(80) 0.780 (at m.p.) 0.780 (at m.p.) 0.782 (at m.p.) 0.782 (at m.p.)

0.794 (at m.p.)

298

"c5 ON O O O A ^ -h B • radical

^C"^ + D neutral

M ' -> Rearranged M"^ + (neutral fragment)

F r a g m e n t a t i o n could h a p p e n also directly from M . T h e lowest energy for which the ionization occurs is the ionization potential of M , whereas the electron beam energy necessary t o cause a particular fragment t o appear is the appearance potential. Table 3 gives I P values and heats of formation^ ^ for selected alkanes and cycloalkanes. It is clear that the I P differences are n o t large enough t o render these as diagnostic tools for the analysis of alkanes a n d cycloalkanes. Since the I P measures the energy needed TABLE 3. Gas-phase ion and neutral theromochemistry^^

Ion/neutral

CH4+/CH4 C2H6VC2H6 C3H6 "^/Cyclopropane CH3CH=CH2 C3H8^/C3H8

C4H8 "^/Cyclobutane C H 2 = C H C H 2 C H 3 £ or Z C 4 H i o ^ / n-C4Hio iso-C4Hio

C5H10 ^ /Cyclopentane CsHi^Vn-CsHi^ iso-C5Hi2 Neopentane CgH 12 ^ /Cyclohexane

Ionization ential (IP) (eV)

Af/f(ion) (kcal m o l - 1 )

Afff (neutral) (kcal m o l - 1 )

12.51 11.52 9.86 9.73 10.97 (9.92) 9.1

271.0 245.6 240 229 227 (235) 207-208''

10.53 10.57 10.51 10.35 < 10.22 < 10.21 9.86 10.13-10.1

213 212 224 204-211" 199-207'' 195-203'' 198 188-194"

-17.8 -20.1 -hl2.7 -F4.8 -25.0 ( + 6.8) -1.9 -2.9 -30.0 -32.1 -18.7 -35.0 -27.3" -36.7-28.4" -40.0-32.4" -29.5 -43.0-31.0"

9.65

163

-40-50"

iso-C6Hi4^ all isomers

CioH22"^/n-CioH22 "Range of several experimentally determined values.

7. The analysis of alkanes and cycloalkanes

303

for the expulsion of an electron from the alkane molecular orbitals, it does not change with the expected isomeric structure-stability of the carbocation (see C5H12 isomers Table 3). However, the information is valid for an understanding of ionization processes such as photoionization (see Section VI, P I D — p h o t o i o n i z a t i o n detector). Different appearance potentials can be recorded for different fragment ions of the same molecule. The energy required for fragmentation may originate in the electron beam. Since M S are usuahy obtained at 70 eV (EI), considerable excess energy is imparted to the initially formed ion, causing fragmentations and rearrangements, depending on the alkane or cycloalkane structure. The connection between fragmentation patterns and the formation of carbocation structures can be related to their heat of formation (see Table 3). The heat of formation of —C4 alkylcarbonium ions was calculated in good agreement with the experimental values^^'^^. The most stable forms of C3H7^, C4H9^ and C s H ^ ^ ions are predicted to have a bridged protonated cyclopropane structure:

This stability of the 'non-classical carbonium ion' or its open C3H7'^ fragment makes the m/z 43 fragment the base peak even for higher normal or branched alkanes. The assumption that alkanes, which are the simplest of all organic compounds, wih hence produce easy-to-interpret M S was proved erroneous^^. 2. Fragmentation

patterns

as related

to

structure

Saturated hydrocarbons produce fragmentation patterns which could be correlated with their structures only with some difficulty. A frequently cited example is the generation of the ethyl ion from isobutane [CH3CH(CH3)2]; the C H 3 C H 2 ^ ion cannot be formed by simple b o n d cleavage but must involve one or more rearrangements^^. At high energies ( > 70 eV), various theories were proposed to explain such drastic cleavage of bonds or even milder rearrangements. N o r m a l mass spectra of alkanes obtained in the EI m o d e (70 eV, and heated source) exhibit a characteristic and seemingly simple profile. The fragmentation pattern shows groups of peaks (m/z) spaced by 14 mass units corresponding to the CH2 group. The fragments formed will be C„H2„ + i ions having increasing a b u n d a n c e with decreasing carbon number (see Figure 4). The molecular M ^ ion under these conditions is quite low, and in most n-alkanes C3 is the base peak. Unfortunately, most papers do not show the C3 peak, which may be four to five times higher than, e.g., the '100%' C4 peaks shown in Figures 4a and b (see also the chapter on M S by T. G a u m a n n in this volume). F o r long-chain normal alkanes the C g H n and lower fragments are the highest ( 2 0 - 2 5 % relative intensity to the C3H7 ^ = 100%). The use of these fragments in mass fragmentometry in computerized gas c h r o m a t o g r a p h M S ( G C / M S / C ) will be discussed later in this review. In the case of M S study of n-alkanes, very little use has been m a d e of other modes of ionization such as chemical ionization (CI) or photoionization (PI), field ionization (FI) and others. This is because the sensitivity of these methods and the quantity of the produced ions are very low and the molecular information is minimal. The M S of branched alkanes is more structure-dependent, and the fragmentation pattern follows the position of branching. The abundance of C„H2„ + i fragments can be related to the

304

Z. Aizenshtat C4

C5

100-1 CH3(CH2)I5CH3 0, O C O

8 0

§

6 0

O

•i

4 0 -

2 0 -

C7

'17 ^ 9 •III

6 0

8 0

1 0 0

1 2 0

^10

C,2 lU T 1 6 0

;LI 1 4 0

J

0^4 J1 8 0

CI5

^

2 4 0 ( M + ) J.

1

2 0 0

2 2 0

2 4 0

M / E

LOON C H 3 — ( C H 2 ) 5 — C H — ( C H 2 ) 5 — C H 3

C H 3

8 0 O C O C

B 6 0 -

O A>

^>

4 0 -

O

2 0 '14 C 9

C10

C12

C I 3

1 9 8 ( M + )

—H— 6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

M / E

F I G U R E 4. (a) Mass spectrum of n-C,,U^^ (MW = 240). (b) M S of 7-methyltridecane (branched C 1 4 H 3 0 , M W = 198). N o t e the m/z 14 units fragmentation for the normal alkane in comparison to the domination of Cg, C 5 in (b)^

relative stability of the carbocation. [ R 3 C - C R 3 ] ^

. R 3 C ^ +

C R 3

R = H, or alkyl stability: tertiary > secondary > primary Hence, branching changes the pattern of fragmentation favouring the tertiary ions (or quaternary ions from neoalkanes) in accordance with the stability of the carbocation


305

A/\A/\A/\A

150

100

250

, . II,,,III. . , 1 1 , ,

f-r50

200

150

200

250

F I G U R E 5. (a) Mass spectra of 2,6,10,14-tetramethylpentadecane (pristane), M W = 268, and (b) 2,6,10,14-Tetramethylhexadecane (phytane), M W = 282. Both spectra were taken under 70 eV E P ^

formed. It is thus possible to deduce the position of branching from different fragmentation distributions from different structural isomers of the same molecular weight. An apparent exception are the 2-methylalkanes (iso-branched), which show

306

Z. Aizenshtat

preferred loss of a n isopropyl fragment a n d retain the charge o n the formally primary ion^"^: CH3

/-= ^RFLLN + 1 ~

CH2CH^

> ^N^LN + 1^^2 ^ + C3H7 *

CH3 However, in the case of ante-iso c o m p o u n d s (branching o n carbon 3 rather t h a n o n carbon 2) the fragmentation pattern again follows the general rules. P h y t a n e a n d pristane (Section H.B a n d Figure 5)^^ belong t o the multibranched isoalkanes a n d hence show a small [ M — 1 5 ] ^ a n d a strong [ M — 4 3 ] ^ peak: [M-15f

[M-43]^

ante-lso [M-29]"*"

Since phytane (C20H42) has at o n e end an iso a n d at the other a n ante-iso structure, its fragmentation pattern is different from pristane (C19H40). Below mass (m/z) 113 b o t h fragmentation patterns seem very similar.

Pristane

M=268

[M-15J [ M - 4 3 ] [M-29]

4

Phytane M = 2 8 2

A very detailed discussion of branched alkanes M S appears in the literature reviews of 'biomarkers'^^'^^. M o s t of the c o m p o u n d s were analysed by combined G C / M S . A more detailed examination of the use of fragmentation profiles will be given in o u r discussion of separation methods a n d petroleum analysis (Section VH. A). 3.

Cycloalkanes

T h e analysis of cycloalkanes by M S gives information n o t only about the n u m b e r of rings b u t also relates to the m o d e of connection (fused or isolated) a n d stereochemistry. T h e structure of cyclic alkanes cannot be derived based solely o n t h e fragmentograms (m/z profile) without consideration of eliminations a n d rearrangements. Even when we consider monocyclics such as c y c l o p e n t a n e ^ o r cyclohexane^^, the complexity of the


307

M S fragmentation becomes evident. In order to be able to understand the fragmentation, ^^C and D labelling of these cycloalkanes was investigated. Also, low eV spectra were taken and alkyl derivatives measured. It is therefore suggested that the loss of ethylene is not directly from the cycloalkane but rather an elimination from the open-ring radical ion formed (M '^), so that only 6% of the ethylene is formed by the external C H 3 group^^. This suggested model would also explain the various migrations of hydrogen (or D, if labelled).

2^0^

2 1 %

1 4 %

m e t h y l c y c l o h e x a n e

14%

The same phenomenon was studied also in alkylated (R = Me, Et) cyclopentanes and 80% of the ethylene formed was found to originate in the ring carbons. However, in the case of long-chain alkylated cyclopentanes, the chain fission dominates the spectra. In fossil fuels the monoalkylated cyclohexanes are characterized by the m/z 83 fragment^ ^. O n e should be aware of the problem that fragmentation of alkylated cycloalkanes could be followed by rearrangement of the ions formed; hence m/z 83 could also be formed from the methylcyclopentyl ion^^. Of course we must bear in mind the fact that the molecular weight of monocychc alkanes is the same as for mono-unsaturated alkenes and, when investigating mixtures, this point is of importance (see also the discussion on fossil fuels. Section VILA). Cis, trans isomers of disubstituted monocyclics generally exhibit similar M S profiles. However, subtle differences in fragmentation (relative abundance) profiles were found, e.g. in cis- and trans-1,2-dimethylcyclohexane^^. Bicyclic and higher polycyclic alkanes exhibit much more complex M S fragmentation. Budzikiewic and coworkers^^ caution that great prudence, even in the use of published spectra, must be exercised for comparison and identification purposes of polycychc alkanes. As examples they show the mass spectrum of cis-hydrindane, in which m/e 95,96,81 are major fragments which can be assigned only in retrospect to the structure once known. However, given only the M S it wiU be impossible to reconstruct the structure of the molecule.

In Section II.D we discussed the decalines. T h o u g h the cis and trans isomers show quite similar M S , there are very noticeable quantitative differences in abundances^^ (Figure 6). The M S becomes still less characteristic in more complex structures, such as terpanes (Figure 7a,b^°, Figure 8^^). All three sesquiterpanes shown have molecular weights of 208 but the fragmentation profile is quite different, e.g. the base peaks are m/z 109, 123 and 193, respectively. The mass spectrum of a d a m a n t a n e is unlike most saturated hydrocarbons; the base peak at m/z 136 is the molecular peak. This reflects the inherent rigidity of the interlocking rings, where effective fragmentation of the M ' ^

308

Z. Aizenshtat

(a)

C10H18

9

1

-

1

7

-

8

N a p h t h a l e n e , decahydro —

1 0 0 8 0 6 0 4 0 2 0 -

1 0

2

0

3

0

4

0

5 0

6

0

7 0

(b)

8

0

9

0

1 0 0

1 1 0

1 2 0

1 3 0

4

C i n H 10*^18

9

1 4 0

3

-

0

1 5 0

2

-

7

Naphthalene, decahydro—,//'j/7S—

-I—'—I—^*^T 1 0

2

0

3 0

— 4

0

\ 5 0

^

— 6

I 0

— 7

— 0

1' " " ' 8

0

9

0

I

1 0 0

4 1 1 0

\

1

1 2 0

1 3 0

r 1 4 0

1 5 0

F I G U R E 6. Mass spectra of probably cis (a) [Chemical Abstract Search number 91-17-8] and trans (b) [CAS 493-02-7] decahydronaphthalene (decaline), as available in the M S Library (NBS)^ ^

requires that three C — C bonds be cleaved. Hence, the M — 15 a n d M — 28(29) which would have been a b u n d a n t in acyclic or monocyclic alkanes are not preferred. Figure 9^^ presents the M S of a d a m a n t a n e showing C 3 and C4 losses as the favoured pathways^^'^"^. It is n o t easy to explain the fragmentation patterns of a d a m a n t a n e . However, in 1-hydroxyadamantane the key t o the fragmentation mechanism is the formation of a protonated phenol^^. A more direct suggestion for understanding the influence of structure on M S fragmentation was given for diamantane, C19H20. This c o m p o u n d is pentacyclic with m.p. 244-245 °C (see Figure 9^^). T h e proposed fragmentation pathway^^ shows that m/z 173, 146, 106, 105 a n d 91 are ah fragments containing a benzene ring. This aromatization during fragmentation is suggested for all diamonoids^^^. The mass spectra of 4-, 3- a n d 1-methyl-diamantanes, which were found a n d identified in petroleum, exhibit the M ' ^ m/z 202 molecular ion t o be strongest for the 3-methyl. However, for ah three isomers the [ M — 1 5 ] ^ m/z 187 is the base peak^^. T h e C20H36 tricyclic diterpanes are also called diterpane resins, derived from the abietane skeleton. Fichtelite ( C 1 9 H 3 4 ) , which belongs to the same family, is presumed to be the result of decarboxylation of the abietic acid. The M S of these relate t o individual structures'^ (see Figure 1 0 a - e ' ^ ~ ' ^ ) .

309


CO

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 6 0

1 8 0

2 0 0

2 2 0

c D

Si

F I G U R E 7. Mass spectra of two bicyclic sesquiterpanes ( C 1 5 H 2 8 ) , (a) 8j5(//)-Drimane (MW = 208) with base peak m/z 123 and (b) 4i5(//)-eudesmane (MW = 208) with base peak m/z 1 0 9 3 0 ' 2 6

The mass spectra of tricyclic alkanes relate to the basic structure of the biogenic precursor. The abietane fragmentation shows both m/z 191 and 163 fragments as well as the cleaving of the isopropyl group [ M — 15] and [ M — 43] (m/z 261 and 233) whereas the norpimarane shows the base peak at m/z 233 [ M - 29] due to ethyl g r o u p cleavage (Figure 10c). The formation of the m/z 123 and m/z 109 fragments is enhanced for

310

Z. Aizenshtat m / z 191

m / z 191

m/z 1 6 3 I

^

m/z123^

11

1, \

M-43

R

R

M W = 2 7 6 , C20- a b i e t a n e

MW = 2 7 6 , C 2 o - t r i c y c l i c t e r p a n e

r = r1 = r 2 = c H 3

R = CH3

des-4-methyl c o m p o u n d s (Figure 10b). In contrast, the C2o-tricychc terpanes show the m/z 191 fragment as the base peak. This m/z 191 fragment is used as a mass spectra m a r k e r for such structures a n d hence is diagnostic to tri-, tetra- a n d pentacyclic terpanes (see also discussion o n hopanes in petroleum. Section VILA). Tetracychc a n d pentacyclic terpanes are found to be ubiquitously distributed in crude oils, a n d the use of the m/z 191 fragment as diagnostic parameter can be complemented by b o t h the molecular weight M a n d other mass fragments. Since these c o m p o u n d s have several chiral centers (see Section VILA) they have diastereoisomers that can be chromatographicaUy separated. However, these stereoisomers show similar fragmenta tion patterns (see also Figure 29). An example which we choose to discuss is cholestane, which is the fuUy hydrogenated (non-functionalized) cholesterol. Being a tetracychc alkane, it is obvious that its base peak is not formed by cleaving the alkyl group. T h e M ' ^ a n d [ M — C H 3 ] ^ are almost equal in abundance. However, the m/z 218 a n d 217 fragments are the most a b u n d a n t (see Figure 29). T h e ratio of m/z 218 a n d 217 apparently

— reversed flow during backflush^^

elute as a 'group' some 1 to 1.5 min (at the given conditions) before the n-C^, and the first is the one substituted closest to the middle of the chain (7,6,5,.. .y^. We should note that the last conclusion is true for all positions from 4 on. However, 3-methyl isomers appear after the 2-methyl alkanes. Detailed investigation of alkanes was carried out on specific sub-families, a m o n g which the analysis of the saturated hydrocarbon fraction of petroleum, bitumen or extracted coals is the most demanding. This is due to possible co-elution of various isomers even if high-resolution capillary G C ( H R C GC) is used. The alkane-cycloalkane fraction of petroleum contains gas, liquid and wax; some groups used for the separation one column with p r o g r a m m e d temperature from — 20 °C u p to 325 °C, and others a combination of two columns in sequence. The two columns could be placed either in one oven, the first as a concentrator to a cold t r a p and the second for the detailed chromatography, or in two ovens, allowing better temperature control on each column. M o s t information is contained in commercial d a t a bulletins and instrumentation guides, since several companies offer various G C , F S C O T capillary columns (15 m u p to 100 m in length) with different internal diameters, with different thicknesses of coat and a variety of liquid phases. Prospective users should take into consideration that for the analysis of alkanes and cycloalkanes, the choice of the proper column is the heart of the G C procedure. Until two or three years ago, the G C of hydrocarbons was restricted by the highest temperature at which the liquid phase did not 'bleed'. Hence with the exception of an inorganic salt 'Eutectic' packed column"^^ (which could be used up to 400 °C), all s t a n d a r d columns were restricted to 325-350 °C maximum temperature. This temperature limit

327


Pristane

n-Ci8

10 minutes lOminutes

20

20

F I G U R E 23. Gas chromatograms of (a) a whole crude oil from the Altamont BluebeU Field, Unita Basin, and (b) saturated hydrocarbons from a Canadian Arctic Island sedimentary rock, G C on 'eutectic' column'^^

Att.32IAtt.16

n - C 2 o added Steranes and triterpanes

100

150

200

250

300

F I G U R E 24. G a s chromatogram of branched and cychc saturated hydrocarbons from the Green River oil shale. Same column as in Figure 23''^

328

Z. Aizenshtat

did n o t permit the analysis of waxy fractions (C33—C35). T h e use of the 'eutectic' column with rapid programming ( 1 0 ° C m i n ~ ^ u p to 400 °C) aUowed analyses of crude oils for major saturated hydrocarbons to be conducted in about 30 min (see Figures 23 a n d 24^^). Despite the claim that the separation of steranes a n d hopanes gives a resolution in the C27-C30 fraction comparable to a 15 m S C O T capihary column (coated with SE30), it is of course inferior to longer columns. Moreover, the column is highly hygroscopic a n d if impure carrier gas is used it leads to high-temperature oxidations. The introduction of the bonded high-temperature (420-425 °C) F S C O T capihary columns using super pure H e or H2 as carrier gas brought about the possibility t o study

C30

C50

yj o CVJ

in c\j Time

o ro (min)

Time (min) CANADIAN WAX Column

S U P E R C A P 'High Temperature', AI clad Fused Silica Bonded Methyl 5% Phenyl Silicone 15 Meter x 0.25 mm id, 0.1 fxm film 400-2HT-15-0.1F

Press: Temp: Injection: Sample Detector: Chart: Flow Rate:

lOp.s.i. Helium 60-400°C at 1 0 ° C m i n - ^ then hold at 400 °C Perkin-Elmer PTV lnjector-60-400 °C; 1.0/^1 Spht 50:1 20 mg dissolved in 1ml of 1:1 CS2: isooctane 420 °C F I D Attn: X32 60cmh~^ He © 1.5 ml/min

F I G U R E 25. G C obtained for Canadian wax using a Supercap high temperature column, injected on 6 0 - 4 0 0 "C programmed PTV, program 6 0 - 4 0 0 °C at 10 °C min"^ and holds at 400 °C (oven temperature)

7. T h e analysis of alkanes and cycloalkanes

329

waxes. Figure 25 shows hydrocarbons u p to C^qI Such analyses of waxes focus o u r attention on the mode of introduction of the sample into the column. Various injection methods were employed, such as simple injection ports (separate temperature control), programmed injection units (PTC) and on-column, all glass injectors. F o r low temperatures the use of a septum presents n o problem, but at temperatures over 400 °C the bleed from the septa used is problematic. Again, the main sources of information about injectors are the commercial catalogues. Whereas the power of resolution depends on the quality of the column, quantification and identification of the separated compounds is a function of the detector. The oldest G C detector, still used for hydrocarbon gases, is the T C D (Thermal Conductivity Detector). The T C D response is proportional to the molar fraction and the specific heat of the c o m p o u n d detected"^^. Its sensitivity is in the fig (10"^ g) range, but even for the same homologous family, this changes with molecular weight'^'^'^^. The F I D (flame ionization detector) is ideal for hydrocarbon analysis. It is very sensitive (10~^-10~^^g range) a n d responds in direct proportion to the a m o u n t of carbon c o m b u s t e d ^ I t is possible to bring the end of the separatory column very close to the flame, thus avoiding 'dead volume' a n d loss of resolution. T h e F I D is simple to construct a n d operate, but has one major fault: the destruction of the sample. This can be overcome by splitting the eluent at the end of the column, using only part in the F I D for detection a n d quantitation, a n d collecting the rest for further analyses. The technique is reported extensively in the literature, especiaUy for the characterization of n-alkanes in petroleum fractions^^. Lately, some companies have introduced a capillary column and quantified standard (?^150 compounds), using the same F I D conditions a n d integration mode which enables characterization of petroleum. O n e such application for cycloalkanes in petroleum was recently demonstrated^ ^ M S wih be discussed in Section VILA. Other detectors for G C which have been used for the analysis of hydrocarbons are usually more specific for molecules containing heteroatoms (e.g. B C D , F P D , etc.)"^^. Similarly, the use of F T I R as a G C detector, though used also for hydrocarbons, is applied more for functionalized compounds. T h e high-resolution gas chromatography using matrix isolation F T I R needs a very elaborate interface"^^ whereas a 'normal' F T I R ceU can be employed as detector for thermogravimetric (TG) analysis. The application of T G - F T I R for the study of hydrocarbon structure is also utilized for hydrocarbon analysis to characterize solid fossil fuels^^. Quantification or integration of the data obtained relates to specific regions of the spectra (see also Section III.B). VII. MASS SPECTROMETER DETECTOR (MSD)

The use of M S as a detector for both H P L C a n d G C added a new dimension to the analysis of alkanes, a n d even more so to the identification of complex cycloalkanes. The basic concepts have already been presented in this review. However, the study of single c o m p o u n d s does not require an interface between the chromatographic unit and the M S . The analysis of mixtures by M S relates not only t o G C / M S or HPLC/MS^"^. The popularity of G C / M S systems can be examined by the number of relevant publications. These were less than 100 in 1968, rose to a peak of 2000 papers in 1979, dropped to ^ 1 5 0 0 - 1 7 5 0 yearly until 1988, when they rose again to 2000. The use of M S D for H P L C (also caUed L C / M S ) also rose from a few publications in 1975 to a few hundred in 1988. A method, less used for hydrocarbon analysis, S F C (Super-critical Fluid Chromatography)/MS, was initiated only in 1985 a n d is gaining interest slowly. These data are given by Evershed^^. Obviously it will be impossible to review all these developments in the use of MSD^"^, even for the analysis of alkanes a n d cycloalkanes. In the analysis of mixtures, it is possible to use one mass spectrometer as the separator and use a second as a M S D ( M S / M S system). This method is very quick a n d dispenses

330

Z. Aizenshtat

with the need for long chromatographic columns. However, the instrumentation is expensive a n d for many cases, such as separation of isomers (see Figure 30), it cannot be used. The use of M S in addition t o G C / M S includes methods such as capillary zone electro phoresis (CZE/MS), thin layer c h r o m a t o g r a p h y (TLC/MS) a n d others. T h e major problem in employing these separation-MSD methods is the interface. T h e very high vacuum required for M S operation requires complete removal of the carrier gas o r liquid^^. Since the present review treats specifically the use of the M S D for the analysis of alkanes a n d cycloalkanes, we concentrate on the G C / M S D / C (gas c h r o m a t o g r a p h y / mass spectrometry/computerized) method. T h e M S used can be quadrupole or magnetic and its configuration wih, of course, control the power of resolution (PR), the mass range, etc. T h e ionization m o d e is also important, e.g. whether EI o r C I (see Sections, III.A.l and ni.A.2). A. Gas Chromatography/Mass Spectrometry/Computerized (GC/MS/C) System

The independent development of b o t h G C a n d M S t o a high degree of sophistication led t o their combination in one instrument, a n d the need t o process vast a m o u n t s of d a t a required computerization of the system. T h e applications of G C / M S in organic geochemistry were reviewed by Burlingame a n d Schnoes^^. Obviously, in fossil fuels the main effort is on the analysis of hydrocarbons. As a n example, we can employ pioneering work using a capillary column t o analyse alkanes u p to C ^ by MS^^, applying conventional M S as a detector for G C . I n the early days of G C / M S apphcation t o t h e analysis of alkanes a n d cycloalkanes, quantitation of the MS-identified c o m p o u n d s was carried o u t by F I D (see the previous discussion o n GC). It took twenty-five years t o substantiate the statement: ' G C / M S has been widely accepted for quantitative analysis of individual target compounds in organic mixtures because of its sensitivity a n d specificity'^"^. T h e capability of monitoring o n e o r several selected ions characteristic of branched or cyclic n-alkanes allows analyses which are free of interference from chromatographic co-elutes. In general, the use of internal standards in quantitative M S is ideal, b u t this standard should have the same M S behaviour as the mixture t o be analysed. Hence, reliable G C / M S quantitation is best performed by isotope-labelled c o m p o u n d s of the same structure^ ^. The main reason for the need for an internal standard is t h e reliability a n d reproducibility of the M S response, which depends heavily o n specific instrumental factors. These performance criteria, which need t o be controlled, are different for different M S devices, a n d include, just t o mention a few, the filament condition, electron beam energy, repeller voltage a n d so on. The quantitative response factors (RF) of 14 long-chain n-alkanes, using the EI mode a n d C I , were determined showing that R F / m o l ratio is similar t o T I C (total ion current)^^. The author's group in Jerusalem is involved in both G C a n d G C / M S / C of fossil fuels. The availability of M S (VG ZABIIF) linked t o a G C allowed various operation modes. Some of the data presented in this review have n o t been published previously, except in industrial reports. T h e main advantage in the use of G C / M S / C for saturated hydro carbons lies in the ability t o identify the branched a n d cyclic 'bio'-alkanes, also called 'biomarkers'. T h e basic analytical approach t o the study of these c o m p o u n d s was discussed in Section III.A.3. However, the G C / M S / C method provides the possibility t o work o n the whole saturated hydrocarbon fraction, without employing extensive F I G U R E 26. G C profiles of (a) bitumen of the Green River formation sample as extracted, (PHC) denotes perhydrogenated carotene and (b) hydrocarbons formed by pyrolysis at high temperature, in the presence of H2O. Both were analysed on the same column (30m SE 30 FSCOT)

7. T h e analysis of alkanes and cycloalkanes

331

n - C i 7 0)

P r i s t a n e

c o Q. O) 4)

/ n-C28

Hl

I I I I I I I I 1 I I I t I 1 I I I • I I I I I I 1 » I I 1 I I I « 1 I » t I I I I I i 1 I I I I 1 T I M E

F I G U R E 26. {caption

opposite)

332

Z. Aizenshtat

separation methods. The mass spectrometry of phytane a n d pristane, as discussed before, revealed very characteristic fragmentation patterns, typical for isoprane units. This knowledge was employed in the identification of the homologous C5- t o C4o-perhydrogenated carotenes ( P H C ) (see also Figure 26a). Figure 26b shows the whole range of hydrocarbons thermahy produced and, by comparison, one can see that the 'biomarkers' that dominate the bitumen as well as the P H C (Figure 26a) appear above the n-C28 range. Both bitumen a n d the hydrous pyrolysis products (Figures 26a a n d 26b), respectively) are of a Green River formation sample. T h e mass spectra (MS) of these cychc alkanes are more complex than the acyclic compounds. W e have chosen t o show first the G C profile of this boiling range to emphasize complexity due also to various isomers, enantiomers a n d structural changes. T h e early identification of steranes a n d hopanes was very t e d i o u s h e n c e the very early application of G C / M S / C t o the study of 'biological markers'. Each research group has its own instrumentation a n d its o w n technique of G C / M S / C . While some groups study whole crude oils, most prefer t o separate the petroleum prior to G C / M S by LC. T h e utilization of the G C / M S / C system for natural products includes steroids a n d other terpenoids (mostly functionalized by double bonds and other functional groups). However, in geochemistry we regard 'biological markers' as organic c o m p o u n d s maintaining the skeleton of the original molecule. T h u s to become a 'chemical fossil' it has to become chemicahy inactive, by hydrogenation of the double bonds and loss of the oxygen-containing functional groups. Low molecular weight branched alkanes a n d monocyclic alkanes in petroleum can be explained by the thermally-controlled 'depolymerization' (named catagenesis) of the sedimentary kerogen. Hence, we will expect the thermodynamicahy stable isomers t o dominate. Analyses of single alkanes a n d cycloalkanes by M S were discussed in Section nLA.2, but the complex mixtures have to be examined by G C / M S utilizing the computerized treatment of the data^^. Isoprenoids-isopranes in petroleum a n d other fossil fuels as studied by G C / M S / C are divided into three large groups: (C10-C40) aliphatic isopranes, alicyclic isopranes a n d isoprenoids containing a n aromatic ring or rings (moieties). In the present review we wih n o t deal with the latter. T w o groups of tetracyclic a n d pentacyclic alkanes, steranes a n d hopanes, respectively, are presented schematically in Figures 27 a n d 28. T h e analysis of these 'biomarkers' requires the optimal combined techniques of G C a n d M S , as well as a large memory and fast computers. T h e application of the G C / M S / C analysis of steranes a n d hopanes in petroleum geochemistry was extensively studied a n d r e v i e w e d ^ M o s t of the

10 5

A 5

F I G U R E 27. Schematic stereostructure of the sterane tetracyclic skeleton. N o t e that positions 5,8,9,10,13,14,17 are asymmetric carbons. Bond cleavage and change of 5a to 5p wih cause the A and B rings to be in the cis form (see also Figure 9 and Table 6 below)

7. The analysis of alkanes and cycloalkanes OH

333

OH

R=H,CH3

F I G U R E 28. Structure and numerical assignment of hopanes (pentacyclic C35 terpanes). Compound I (tetrahydroxybacteriohopane), T H B H is suggested as the precursor of all hopanes in the geoenvironment. Compounds II represent structures of the derived hopanes (see also Table 5 below)

modifications introduced in the G C section for the analysis of higher-boiling-point compounds and for the enhancement of the resolution at elevated temperatures were discussed previously. However, the mode of injection is important in order to obtain reliable results. The three accepted methods (splitless, split and cooled on column) were investigated by KiUops^^ and by the author's groups leading to the conclusion that the on-column injection is superior to the other two, providing very small quantities are injected. The optimization of the M S sectors and the selection of the most suitable operational mode for the G C / M S / C of 'biomarkers' depend on the type of instrument and computerizing system. Specific detection of certain fragments and pattern recognition relate to the resolution power (RP) of the mass spectrometer and the computer's capability to match the reference file with the analysed mixture. Hence the identification of a given c o m p o u n d or isomer could be performed by comparison with a synthetic standard or by M S statistical analogy. The statistical approach allows G T A either by selection of typical groups of fragments or by statistical whole M S soft independent modehng of class analogy (SIMCA)^^'^^ The use of capiUary columns in the G C / M S / C method produced a new challenge to the operation of the M S arising from the need for the short interval of time {ca 7 s at half height of the peak). Hence the M S data have to be produced and collected in 0.5-1.2 s to produce a true TIC. This, in turn, requires either fast scanning of the M S or preselection of one or several m/z ions (fragmentometry). Most of the information relating to technical changes in the hardware and software was published in the data sheets of the various G C / M S / C manufacturers. The most popular M S operation mode is the EI (see Section III.A) and the most popular G C / M S / C recording mode is selective ion monitoring (SIM). The latter mode can be operated for low, medium or high resolution M S , in various combinations of factors. All SIM modes are simUar to those described in 1967 by Gallegos and coUaborators^^. This method in practice requires a very large d a t a storage memory and pushes the magnetic sector to its 'speed limit'^'^. Therefore, it was suggested that, for comparative runs, restricted information should be monitored, stiU using high resolution

334

Z. Aizenshtat

and accurate mass (AM). F o r this selected ion recording (SIR) one has to predetermine the ions to be recorded and, instead of scanning, the magnet is 'parked' on a k n o w n accurate mass and the accelerating voltage j u m p s from this selected mass to the reference file and back. This method of operating a double focussing M S has also the advantage that the real time for each scan is very short for each ion mass selected^^. In G C / M S / C , the CI m o d e is used much less t h a n other methods for a n u m b e r of reasons, such as the need for an active gas atmosphere, and lower sensitivity. Some M S instruments allow alternating EI, CI, A C E giving, for the same run, the benefit of molecular weight determination and fragmentation pattern recognition. Some of the early m e t h o d s used for G C / M S ^ ^ in the analysis of complex hydrocarbon mixtures have changed names, but are still effective. Whereas low voltage (EI) could be applied to the analysis of aromatics, 7 0 - 8 0 eV is used for saturated hydrocarbons.

1500 39.07

2000 51-.28

F I G U R E 29. {caption on p. 336)

2500 1.03.50

i.i6:i2

7. T h e analysis of alkanes a n d cycloalkanes I00n

/n/z

191.178

^

335 ^

75-

5 0 -

2 5 -

K

5 0 0

1 0 0 0

14:23

/n/z

100-1

1 5 0 0

26:95

39:07

217.196

2 0 0 0 5i:28

g

2500

3000

i:o3:5o

i:i6:i2

SCAN TIME

h

75-

50-

)

25-

5 0 0 14:23

1000

1500

2 0 0 0

2 6 : 4 5

39:07

5i:28

F I G U R E 29.

(continued)

2 5 0 0

3 0 0 0

SCAN TIME

i : o 3 ; 5 0

i:i6:i2

336

Z. Aizenshtat

100m/z

218.203

75-

50-

25-

500

1000

1500

14:23

26:45

39.07

2500 1:03:50

SCAN 3000

TIME

i:i6:i2

F I G U R E 29. The G C / M S / C analysis of the saturated hydrocarbon fraction of an Israeh crude oil: (a) total ion current (TIC); (b) trace of fragment m/z 133.133, typical of open-chain alkanes; (c) trace of fragment (mass fragmentogram) m/z 133.133, typical for most tri-, tetra- and pentacyclic terpanes, dominated by the hopanes: (d) the m/z 217.196 mass fragmentogram, steranes, and (e) the m/z 218.203 fragmentogram, also s t e r a n e s ^ T r a c e s b - e are SIM of accurate mass (AM) with R P of 5000

Figures 2 9 a - e a n d 30a,b show the analyses by various G C / M S / C a n d M S - M S techniques, as employed for a n Israeli oil (coastal plain, Heletz), using R P ca 5000 as described before^^"^^^ T h e results brought in Figure 2 9 a - e show that the T I C profile is obviously interfered with d u e t o the reference file 'background'; P F K is constantly introduced for mass reference (Figure 29a). However, the mass fragmentogram for m/z 133.133 (saturated hydrocarbons) shows the domination of the n-alkanes (Figure 29b). The hopanes dominate the m/z 191.178 mass fragmentogram (Figure 29c). In Figure 30a the same distribution of hopanes is shown for the same oil using the SIR mode rather than the S I M method which produced the Figure 29c profile. The m/z 217.196 a n d m/z 218.204 peaks monitored in Figures 29d a n d e show the steranes with high selectivity. The m/z 218 fragment is much more a b u n d a n t for the 14j9(H) a n d 17j?(H) isomers (see also Table 6 a n d Figure 27). As was described before, the SIR mode provides very fast scan time and very accurate profiles, which can be stored and compared. Hence this method is recommended if large numbers of samples have t o be studied^^. T h e M S - M S method shown in comparison to the SIR monitoring (same sample) in Figure 30b does n o t require the use of a G C separation, hence the whole analysis is completed within ca 10 minutes. I n this case the same M S apparatus can be used for H R SIR (Figure 30a) a n d M S - M S by the C A D (collision activated dissociation) m e t h o d (Figure 30b) demonstrating the advantages a n d disadvantages for both methods. T h e direct introduction by C A D M S - M S is rapid, handles mixtures a n d has n o molecular weight restriction, b u t it gives n o separation of

7. T h e analysis of alkanes a n d cycloalkanes 191 Triterpane

m/z 100-| 9590858075706560555045403530252015105-

337

chromatogram

HELEZ 1 M

(coastal plain)

A

•ll ll

4

0-^ "^0-00

45:00

50:00

55':oo

1:06:00

1:05.00

Averaged mass spectra of parents of

100 95 90858075 7065605550 45403530252015105-

m/z

191 by CAD MS — M S

412.3

390.3

482.6

440.3 426.3

468.4 370.3 HELEZ 1

454.4

(coastal plain) 315.3 330.3 345.3 357.3

385.4

496.5

I

0-P

.

.

.

.

300

320

340

360

380

fl^li^^

400

,

.

420

440

1 1 1 , ill

""'^ 460

480

500

H^* ^^Tuf^^lî^^ ^"If ^" '^"^P^^ (^^^ ^^"^^ as in Figure 29) by GC/MS/C(a) SIR mode and (b) C A D (collision activated dissociation) M S - M S . The SIR for m/z 191 (hopanes)

"'^'.o^' ^'f'' ^^^"''"^ ^^^^^^ ^'^'^''^ monitoring: m/z 1 7 7 % i 217, 218, 231 and 259. (see text for SIR mode), (b) was run under the following conditions: collision between ml llo^ selected by voltage switching, parent ion by quadropole scanning between m/z 150-800, 1 s per scan, probe programme 5 0 - 3 2 0 °C at 60°C/min

338

Z. Aizenshtat

structural isomers a n d requires expensive M S - M S hardware. T h e G C / M S / C m e t h o d is better in separation of individual components a n d in relative quantification of isomers, but it is time-consuming (1.5-2 h), requires d a t a manipulation a n d high-resolution G C , which also limits the molecular range t o C^s max. Tables 5 a n d 6 must be considered together with Figures 27 a n d 28, which show the chiral centers. T h e triterpanes of the h o p a n e family have the m/z 191 fragment a n d thermal structural changes occur at carbon positions 17,21 (rings) a n d 22 (side chain). The natural tetrahydroxyhopane (see Figure 28) has the conformation 17j5(H), 21j5(H) and 22R. With increase in temperature the 22R 22S isomerization occurs, as well as changes in the E ring fohowing the stability: 17j?(H), 21i8(H) < 11 m i 21a(H) < 17a(H) 21j5(H). Hence in the more mature samples, e.g. petroleum, the 17a(H), 21j5(H) conformer dominates. In the sterane structure (Figure 27) carbons 5,14,17 as well as 20 are sensitive to thermal changes a n d hence the natural 5a(H), 14a(H), 17a(H) a n d 201^ (abbreviated conformation gives the isomer a b u n d a n c e shown below:

ocaocR)

aaai^

:

1

:

aaa5 1

: :

aPPR 3

:

: 3

a^pS

structure

abundance

These trends of thermal isomerization of polycyclic terpanes are utilized analytically in oil-oil correlations a n d for the determination of maturation trends for oil exploration in sedimentary basins. Another a p p r o a c h for t h e determination of petroleum steranes by M S of selected metastable ions^^^ utilizes the spontaneous unimolecular fragmentation of sterane parent ions, occurring in the first field-free region of a double focusing M S . T h e sterane

TABLE 5. Triterpane identification and structures'^

Compound A B C D E F G H X I J K L M

18a(H)-trisnorneohopane 17a(H)-trisnorhopane 17a(H)-norhopane normoretane 17a(H)-hopane moretane 17a(H)-homohopane (225) 17a(H)-homohopane {22R) + gammacerane? unknown triterpane homomoretane 17a(H)-bishomohopane (225 and 22R) 17a(H)-trishomohopane (225 and 22R) 17a(H)-tetrakishomohopane (225 and 22R) 17a(H)-pentakishomohopane (225 and 22R)

Elemental composition

C27H46 C27H46 C29H50 C29H50 C30H52 C30H52 C31H54 C31H54 C30H52 C31H54 C32H56 C33H58 C34H60 C35H62

Structure I II, R = H

II, R - C2H5 III, R = C2H5 II, R = CH(CH3)2 III, R = CH(CH3)2 II, R - CH(CH3)C2H5 II, R = CH(CH3)C2H5 IV

III, R = CH(CH3)C2H5 II, R = CH(CH3)C3H7 II, R = CH(CH3)C4H9 II, R-CH(CH3)C5Hii I I , R = CH(CH3)C6Hi3

(IV)


339

TABLE 6. Sterane identification and structures'^ Elemental composition

Compound a b c d e f

g h i

jk 1 m n

0

P q r s t

^ 2 7 ^ 4 8

13jS(H), 17a(H)-diacholestane (205) 13j9(H), 17a(H)-diacholestane (20R) 13a(H), 17i5(H)-diacholestane (205) 13a(H), 17i5(H)-diacholestane (20/?) 24-methyl-13i5(H), 17a(H)-diacholestane (205) 24-methyl-13j5(H), 17a(H)-diacholestane (lOR) 24-methyl-13a(H), 17i5(H)-diacholestane (205) + 14a(H), 17a(H)-cholestane (205) 24-ethyl-13i?(H), 17a(H)-diacholestane (205) + 14j8(H), 17i?(H)-cholestane {20R) 14i9(H), 17j8(H)-cholestane (205) + 24-methyl-13a(H), 17j5(H)-diacholestane {20R) 14a(H), 17a(H)-cholestane (20R)

C 2 7 H 4 8 C 2 7 H 4 8 ^ 2 8 ^ 5 0 ^ 2 8 ^ 5 0 C 2 7 H 4 8 C 2 9 H 5 2 C 2 7 H 4 8 ^ ^ 2 7 ^ 4 8 ^ 2 8 ^ 5 0 C 2 7 H 4 8 C 2 9 H 5 2 C 2 9 H 5 2 C 2 8 5 IIO C 2 9 H 5 2 ^ 2 8 ^ 5 0 ( ^ 2 8 ^ 5 0 ^ 2 8 ^ 5 0 C 2 9 H 5 2 C 2 9 H 5 2 ( ^ 2 9 ^ 5 2 C 2 9 H 5 2

24-ethyl-13i5(H), 17jg(H)-diacholestane 17a(H)-diacholestane (20jR) 24-ethyl-13a(H), (205) 24-methyl-14a(H), 17a(H)-cholestane (205) 24-ethyl-13a(H), 17i5(H)-diacholestane (20K) + 24-methyl-14j5(H), 17i9(H)-cholestane {20R) 24-methyl-14j5(H), 17i5(H)-cholestane (205) 24-methyl-14a(H), 17a(H)-cholestane {20R) 24-ethyl-14a(H), 17a(H)-cholestane (205) 24.ethyl-14jS(H), 17jg(H)-cholestane (20/?) 24-ethyl-14i3(H), 17i9(H)-cholestane (205) 24-ethyl-14a(H), 17a(H)-cholestane (20/?)

Structure I, R = H I, R = H II, R = H II, R = H

CH3 CH3 CH3

I, R = I, R = II, III, RR== H I, R ^ C ^ H s IV, R = H IV, R = H

CH3

II, III, RR== H

I, R = C 2 H 5 II, R = C 2 H 5 III, R = C H3 II, R = C 2 H 5 IV, R = C H3 IV, R = C H3 III, R = C H3 III, R = C 2 H 5 IV, R = C 2 H 5 IV, R = C 2 H 5 III, R = C 2 H 5

(III) metastable parent ion transitions, corresponding to 372"^ ^ 2 1 7 ^ , 386"^-•217^ and 400^ ^ 2 1 7 ^ , can be observed separately during a single G C / M S run. The authors claim that this method is superior to the SIM (3000 RP) for the nominal 217 m/z fragmentogram since it separates much more clearly the C 2 7 isomer from the C 2 8 isomers^^^. A year later the same method was employed to extract by means of factor analysis information on various hopanes and steranes^^^. In Figure 31 the use of M I M (metastable ion monitoring) is demonstrated for the C 3 0 series of steranes and hopanes. T o some extent the SIM for m/z 191,217,231 nominal masses or SIR might give similar profiles. However, since C 3 0 steranes relate to marine sources, the exact profile restricted to these is of importance. A restricting factor in G C / M S / C analysis of alkanes and cycloalkanes is the scanning time, which is much shorter for quadrupole than for magnetic M S , a n d the mass range scanned. Q u a d r u p o l e M S was restricted in the past to m/z 600, but in the last few years the range reached m/z 1200 at low resolution. In magnetic sector M S , fast scanning for large range (m/z 50-1000) causes magnetic hysteresis. F o r heavy bitumens and waxy

340

Z. Aizenshtat

Relative

17a-Hopane

intensity 100

m/z

C30 Terpanes

412—-191

GC Time direction

F I G U R E 31. Daughter-ion scans for C30 steranes in Sadlerochit, Alaska (marine) crude' ( 5 / £ linked scan: M S is scanned in such a mode that the ratio of magnetic {&) to electric (£) selector fields is maintained constant as both are scanned, with accelerating voltage held constant

matter another problem is the volatilization of the introduced compounds, hence the adoption of the GC-field ionization M S (GC-FIMS)^^'^. This method was employed by using packed G C columns connected through a separator to F I modified M S and mass range scan m/z 80-800 5 s per decade, giving a total scan time of only U s . This m e t h o d allowed the identification of n-alkanes u p t o C40, although with m u c h lower G C resolution than capihary G C / M S . T h e authors^^"^ predicted that G C - F I M S has the 'potential of being one of the most powerful a n d valuable tools available for research in this field', b u t actuahy the major effort in G C / M S / C did n o t shift in this direction. B. Isotope Analysis of Allcanes and Cycloallcanes

Both carbon a n d hydrogen have stable isotopes a n d the isotopic composition is measured as i.e. the ratio of the heavier isotope t o the lighter one for t h e measured sample compared with a n elected standard compound: (^^C/^^C) sample

-1

X

1000

_ ( i ' C / ^ ' C ) standard The same basic formula is used for ^ D and results are given in %o values. Since saturated hydrocarbons appear in nature in mixtures with other c o m p o u n d s , in order to otain their b^^C and (5D values one has to separate them from the mixture. It is beyond the scope of the present review t o discuss the use of stable carbon a n d hydrogen isotopes, even as used on whole f r a c t i o n s ^ T h e point of interest is that the saturated hydrocarbon fraction, for all oils examined, shows a n enrichment of ^^C as compared with aromatics, resins a n d asphaltenes^^^. Already in 1939 it was weh


341

estabhshed^^^ that carbon c o m p o u n d s of biological pedigree are markedly enriched in the light isotope, while most carbonates are relatively enriched in ^^C. Within the hydrocarbons, in liquid petroleum, S^^C values range a r o u n d — 28%o ± 3%o, while for methane S^^C values were from — 21%o to — 75%o. There are deviations from these ranges in specific cases. The genetic characterization of natural gases, mostly C^-C^. hydrocarbons, is usually based on concentration of the homologues and on carbon and hydrogen isotope v a r i a t i o n s T h e natural gases studied (ca 5 0 0 ) show methane of biogenic, thermogenic and mixed sources. The possibility to determine ^^^C and SD separately for each hydrocarbon became possible by the use of G C separation. Analyticahy, the separated gases have to be combusted to form CO2 for ^^^C measurements and the H2O formed is turned into H2, which is measured for ^ D . The standard for carbon isotopes is usually P D B (Peedee Belemnite, a carbonate) though the oil industry also uses the NBS22 (an oil fraction), whereas the ST> standard is S M O W (Standard M e a n Ocean Water). A vast a m o u n t of d^^C a n d 3D information was collected on various petroleum fractions and on general concepts relating to the isotopic signature. Also, much effort was invested to minimize the a m o u n t of CO2 needed and the possibihty to interface the GC-isoMS. This method, allowing direct connection of the separating analytical method with the isotope M S , expanded the possibility to determine ^^^C for single compounds. Matthews and Hayes investigated the possibility to improve the technique of continuous isotopic analysis of the effluent of a gas c h r o m a t o g r a p h y U n t i l 19S1^^^, the isotopic carbon composition was still given for fractions isolated and sealed in quartz tubes to produce C O 2 (see Table 7 ) ^ ^ ^ Within the last two years, two new analytical approaches to the compound-specific isotope analyses were suggested, both based on the early work by Sano and coworkers ^y^, recognizing the importance of interposing a combustion furnace between the G C and the M S in order to determine isotopic abundance data from smaU quantities of G C effluents. Thus studies of ^^^C of n-alkanes were performed by Gilmour and collaborators^^^. This still requires trapping of the CO2 formed in the furnace and its transfer to the M S , but the reproducibility of the method was very good and S^^C of n-alkanes could be determined with ± 0 . 2 % o precision. F o r better separation and more universal use a G C / I R M S instrument interface (Isochrom H), VG-Isogas Co., was introduced. F r o m the applications of this system we TABLE 7. Isotopic compositions of carbon fractions in the Messel shaleîi"

Sample identification Total carbonate Total organic carbon, kerogen Total extractable organic material'' Total extract fractionated on S i 0 2 column^ Hexane eluent Toluene eluent Methanol eluent Alkyl porphyrin fraction (Strasbourg) Total porphyrins (Bloomington) Acid prophyrin fraction (Strasbourg)

o !>; O Nv q ^ ^^< ^

Tl-

N O s < N < N O N T H T H O O ^ r -V O < N m r ( O 'V O T ^ tO O -( V O rn < •ro în H orN vN dvC d-^ uT S^ o roT o-^ 'n d co o or N T ^T N rn ro nc S rn jd T trv ro ro rn nr otrr-n tN cO nrT nN rn

^

< L ) W j < U o o

H i l l

« O « O W

4H

o

c

I o

«

,§6 Si in-

0 3

IS IS I < N T' '4 '7' K T' o nKQ alkyl ion + alkyl radical > alkene ion -f- alkane > lower alkyl ion + alkene > alkenyl ion + alkane > alkene ion -I- alkyl radical > alkene ion -h alkene > alkenyl ion + alkyl radical > alkyne ion -h alkane > alkenyl ion + alkene

molecular ions alkyl ions

alkene ions

alkenyl ions

>C3H3^ -hCH4

> alkyl ion + C2H2 C„H,

'alkyne' ions IONS

. C „ _ i H 2 „ - 5 ^ ions + C H 3

>loss of C2H2

[20] [13] [29] [11] [1] [8] [13] [5] [5] [5] [9] [8] [14]

(8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)

The reactions corresponding to a loss of a hydrogen a t o m or molecule are not included. The numbers in brackets are the n u m b e r of times the metastable reaction was observed by the authors^^, by Schug^^ and by Meyerson^^. These numbers have n o meaning as to the relative importance of the different competing fragmentation reactions, since m a n y of these reactions are only observed on smah fragments present in all mass spectra. Reactions 8 and 9 are the main reactions to be observed in the mass spectrum of an alkane. In both cases the neutral fragment contains generally not more t h a n half of the n u m b e r of carbon atoms originally present. This rule seems to be true for most of the fragmentation reactions, thus reactions 11 and 12 correspond mostly only to an elimination of CH4 or C H 3 . In addition to these reactions a loss of one or several molecules of hydrogen is often observed. In order to illustrate this reaction scheme a fragmentation diagram for n-hexane is given in Scheme 1 as proposed by Liardon a n d G a u m a n n ^ ^ It is based on metastable and high resolution measurements with a series of hexanes labeled with D in different positions. It is divided into two parts, the left side

9. T h e mass spectra of alkanes

401

0,17.

SCHEME 1 corresponding t o reaction 8 a n d the right side to reaction 9 as primary fragmentations. The abundance of each ion is given as % of the total ion current (TIC) for the source spectrum. N u m b e r s above arrows of some reactions represent a n estimate of their relative contributions t o the T I C . These estimates are based on quite a few assumptions a n d should be considered as approximate indications of their importance. However, this diagram illustrates the relative importance t o be expected for reactions 8 - 2 0 in the fragmentation of an alkane. Only in the metastable decays can the proportion of a reaction p a t h be assessed with some precision. However, it is n o t always easy to determine quantitatively the importance of a type of reaction in the metastable decay for instrumental reasons: the limited mass resolution when labelling is used, a n d contributions by C A D due t o coUisions with the residual gases. The formation of the ions H ^ , H 2 ^ a n d H g ^ is energeticaUy n o t favoured. It has been observed in ethane a n d p r o p a n e b u t its importance seems to diminish with increasing chain length. Since these ions are in a mass range that is seldom scanned, it could also be that they are often overlooked. In the next sections a few typical examples were selected in order to demonstrate some of the problems encountered in mass spectrometry of alkanes. They should be considered as typical for their class a n d stand for many similar samples that could not be mentioned within this review. They cover the topics that are best k n o w n in this field. II. METHANE—THE ISOTOPE EFFECT

Methane has the electronic structure (lai)^(2fli)^(lt2)^, the last orbital being triply degenerate. Its mass spectrum is given in Table 2. T h e ionization a n d appearance energies for electron impact have been determined a n d reviewed by Plessis, M a r m e t a n d DutiP^. To a first approximation, it looks very simple. However, it should n o t be forgotten that superexcited states a n d their fragmentation (see above) seem t o play an important role^.

402

T. G a u m a n n TABLE 2. The mass spectrum of methane Ion

CH4+ CH3 + CH2 + CH + C+

Neutrals

AE^'CeV)

— H

H2 H +H2(?) — CH3

12.51 14.3; 1 3 . 5 ^ 15.2 22.4 ^25.2 22.3^22.7^

Ticcrj 51/49(53) 38/40(39) 6.7/7.7(5.0) 2.8/2.9(2.4) 0.64/1.0(0.7) 2.7/?^

"Appearance energy^. ''Total ion current: Quadrupole mass spectrometer at 50eV^^/FT/ICR at 70 eV for CH^ (% for CD^)^*. ^Reference 35. ''Threshold for ion-pair formation. Electron affinity of H is 0.75 eV^^. ^Reference 37. in a quadrupole mass spectrometer is 0.48% TIC.

By impact of low energy electrons on CH4, protons of high translational energy are produced. They arise from the dissociation of the first excited state of C H 4 ' ^ , which results from the removal of the 2aelectron from methane^^. The appearance energy of the p r o t o n coincides with that of the emission of jS-Balmer radiation of the neutral hydrogen atom, indicating that both species originate from the same superexcited state^. Some emission from excited carbon-containing fragments has also been observed, but only little work is being done in this difficult field. Since methane contains only C—H bonds, it has been the molecule of choice for studying the primary H / D isotope effect in the fragmentation of ions. This isotope effect has been defined by Evans and coUeagues^^. T w o fragmentations can be easily defined, viz. the loss of a H or D atom and the loss of the hydrogen molecules H2, H D and D2 under the condition that we assume a simple one-step elimination. Although this must be true for energetic reasons near the appearance energy, its validity has not been proven for higher energies of the ionizing electrons. If we define P(X) as the probability for the loss of X in a given isotopicahy substituted methane, corrected for its statistical probability within this molecule, a factor nf(D/H) can be defined as in equation 21. n,(D/H) ^ P(D)/P(H)

for CD,H4_,

(21)

This factor defines the (smaller) probability for a D a t o m to be lost as neutral fragment compared to an H atom within the same molecule. Another factor (equation 22) r,(H) ^ [P(H) in CD,H4_ J / [ P ( H ) in CH4]

(22)

shows the (increased) probability to lose an H a t o m in an isotopicahy substituted methane compared to the same reaction in CH4. An analogous probability can be defined for a D - a t o m elimination (equation 23): r,(D) = [P(D) in CD,H4_ J / [ P ( D ) in CD4]

(23)

Several similar definitions are possible for the loss of a hydrogen molecule. Some of them are given in equations 24-26. n,(HD/H2) = P(HD)/P(H2)

in CDiH4 _,

(24)

r,(H2) ^ [P(H2) in CD,H4-J/[F(H2) in CH4]

i^ 2

(25)

in CD,H4_ J / [ P ( D 2 ) in CD4]

i> 2

(26)

nî)

= IPiî)

9. The mass spectra of alkanes

403

TABLE 3. The isotope effect in the fragmentation of methane

r(H)

MS" ^Jt

QET^

CH,

CH3D

CH2D2

CHD3

1 1 1

L13 1.24 1.14

1.51 1.58 1.32

2.17 2.17 1.65

0.36 0.52 0.62

0.54 0.70 0.70 4.1 1.4 1.55 1

0.75 0.73 0.80

1 1 1

0.62 0.61 0.78

0.71 0.82 0.75 0.91

1 1 1

0.36 0.34 0.49

F(D)

MS FT QET

m i )

MS FT QET

r(HD)

FT

r(D2)

MS FT QET

n(D/H)

MS FT QET

0.31 0.41 0.56

0.37 0.38 0.54

nCHD/HJ

MS FT QET

0.20 0.50 0.69

0.20 0.25 0.66

1 1 1

2.4 1.11 1.15 1.60

CD,

"Measured with a double-focusing instrument*^. ''Measured with a FT/ICR instrument^*. "Calculation based on the quasi-equihbrium theory*^.

In Table 3 values are presented for the isotope effect. O n e set of d a t a has been obtained by Futrell and collaborators'^^ with a high-resolution double-focusing two-sector instrument. A second set was determined with a F T / I C R mass spectrometer. The double-focusing instrument integrates over a time scale ranging from very short times to microseconds. Thus the ions must have some excess internal energy in order to be able to fragment in a sufficiently short time. In the F T / I C R , the integration extends into the millisecond range, including also the metastable range. It will be shown below that metastable fragmentations are not very important in methane, so the two instruments should not give very different results. But in addition, precise high-resolution measurements always suffer from the problem of discrimination within a mass doublet, an effect that is difficult to check. A third set of values is calculated by means of the quasi-equilibrium theory (QET). In this case some assumptions h a d to be made^"^. The data of Table 3 demonstrate a rather good agreement between the three sets. It can be seen that the relative probability to lose an H a t o m increases with a decrease in the number of H atoms within the molecule. This is even more pronounced for the loss of H2. The contrary is true for the loss of D or D2. This is true whether one compares with the loss within the molecule (H-effect) or with CH4 and CD4 respectively (F-effect). The overall fragmentation of methane shows also some isotope effect: the molecular ion is a little more stable when fully deuterated, the formation of the methyl ion goes through a maximum (43%) for CHD^^ and the loss of molecular hydrogen is steadily decreasing^"^. A decrease of 20% in the dissociative fragmentation of superexcited states is observed for CD4 compared with C H , ^. This is explained by the smaller zero-point energy of the C — D vibrations'^^. Very often H / D substitution is used to elucidate a particular fragmentation mechanism. However, an isotope effect of this order is often large enough to favour another mechanism, thus favouring a reaction p a t h with a smaher

404

T. G a u m a n n

probability in the reaction scheme of the unlabelled ion. This is particularly true in the metastable range, where the excess energy of the ion a n d the difference in zero-point energies of the vibration are often of the same order of magnitude. The similarity in the fragmentation patterns of low-molecular-weight alkanes led Lenz a n d Conner'*^ t o construct a general p r o g r a m m e for calculating fragmentation patterns of deuterated m e t h a n e a n d ethane, using a single adjustable parameter. It uses a statistical approxi m a t i o n a n d can be used for analyses of deuterated mixtures. However, it is based on an empirical a p p r o a c h a n d gives n o insight into the fragmentation mechanisms. The temperature dependence of the fragmentation of C H 4 and C D 4 has been determined by K o m a r o v and Tikhomirov"^^. In the temperature range of 200 to 800 °C the relative intensity of the molecular ion decreases by only 12% and 18% for C H 4 " ^ ' and C D 4 " ^ ' , respectively; the methyl ions increase by a b o u t 20%, CH"^ a n d C D ^ by 20% a n d 40%, respectively; C^" shows also increase of 40%. T h e change corresponds again to the prediction of the Q E T . All possible fragment ions are formed in the decom position of C H 4 " ^ ' . This does not m e a n that all possible reactions leading to the products are important. T w o kinds of experiment lend themselves to unravel the reaction paths: photoionization a n d the metastable decay. The former has the advantage of a very high energy resolution and elaborate setups such as p h o t o e l e c t r o n - p h o t o i o n coincidence ( P E P I C O ) and p h o t o e l e c t r o n - p h o t o i o n - p h o t o i o n coincidences ( P E P I P I C O , for doubly charged ions"^^) are feasible. The study of the metastable decay has the advantage that a given ion can be isolated and its fragmentation examined under the condition of small internal excess energy; the limited mass resolution is a definite disadvantage. P h o t o ionization experiments by Chupka^^, Brehm'^'^ and by Dibeler a n d coworkers^^ disclose that the onset of ionization of the molecular ion has a complicated structure that originates from vibrational fine structure (hot bands) a n d a very low transition probability to the g r o u n d state of the molecular ion. Calculations by R a d o m a n d coworkers'^^ indicate that the most stable structure of C H 4 ^' has a C2V symmetry with a pair of long C • • • H b o n d s due to a strong J a h n - T e l l e r distortion. This could explain the hot bands. The C2v(^5i) g r o u n d state structure of the methane cation has been experimentally proven for C H 4 + - a n d C H 2 D 2 ^ ' by ESR in a solid N e matrix at 4K'^\ The process with the lowest energy requirement for C H g ^ is the ion-pair formation (equation 27). CH4-H/ZV-^CH3^ -hH"

(27)

The analogous production of H ~ by photoionization in ethane, p r o p a n e a n d n-butane has also been observed'*^. The above process is lower in energy by the electron affinity of H (0.75 eV) t h a n that in equation 28. CH4 + /iv^CH3+ - h H + e "

(28)

The corresponding photoionization yield curve shows a p r o n o u n c e d curvature that C h u p k a explains by the thermal rotational energy of CH4^^. Chesnavich^^ summarized the different calculations for the transition state leading to this reaction. The alternative reaction (equation 29) CH4 + e - ^ C H 3 + H ^

+2e-

(29)

is less i m p o r t a n t a n d has been discussed above^^. The methylene cation can have two precursors (equations 30 a n d 31). CH4 + ^ C H 2 ^ CH3^^CH2^

H-H2

(30)

+H

(31)

Again some curvature, explainable by the rotational energy of methane, is observed. The hydrogen molecule produced in reaction (30) must be in the g r o u n d state, at least at the threshold. Photoionization measurements give accurate threshold energies; the


405

structure of the cross section as a function of p h o t o n energy sometimes aUows one to discern the onset of reactions with higher energy requirement, but it does not allow one to draw a reaction scheme for ionization by electrons of higher kinetic energies. Cross sections for the different fragments in methane as a function of the electron energy have been determined by Mackenzie Peers and Milhaud^^ and extended to higher energies by C h a t h a m and c o w o r k e r s b u t these measurements do not reveal reaction paths either. Metastable fragmentations have the advantage that the relation between parent and fragment ion are defined and t h a t — t o a certain limit—the kinetic energy released can be determined. Rosenstock and coworkers, after an unsuccessful attempt^ \ could only find a weak metastable reaction in C D , ^ ^ (equation 32). C D , + • -> CD3 + + D-

(0.080%)

(32)

The intensity of the metastable transitions in CH4^" is apparently several orders of magnitude weaker than in the higher alkane ions. By a careful extrapolation to low pressures, Ottinger^^ was able to find the corresponding reactions of the other isotopomers (equations 33-35). CH3D ^ ^ C H 2 D + + H

(0.099%)

(33)

CH2D2^^CHD2^+H

(0.133%)

(34)

CHD3 + - ^ C D 3 + + H '

(0.184%)

(35)

With the exception of reaction (35) no deuterium loss was ever found. H e was also unable to detect the reaction shown in equation 36. CH4+-^CH3++H

(0.061%)

(36)

This reaction was detected by Futreh and coworkers"^^. The numbers given in parentheses are the values determined by these authors in % of the total ion current for the time interval from 1.8/is to 3 m s , i.e. the total part of CH4'^" ions that fragment after 1.8 fis^"^. The fraction is very small indeed, but Futrell and coworkers^"^ were able to show that with a few reasonable assumptions such low figures could be explained by the quasi-equilibrium theory. They also proposed a breakdown graph for C H 2 D 2 ^ . By extrapolation to zero pressure they observed also a hydrogen molecule loss from methylene ion, but the values are very small and especiahy with isotopically substituted ions the low mass resolution of the metastable spectra poses a problem. Cooks and c o w o r k e r s m e a s u r e d a very small translational energy release for reaction 36 and its temperature effect. It correlates well with the variation in centrifugal barrier height with rotational energy derived from a simple form of the Langevin collision theory. However, it is also in very good agreement with the more rigourous treatment of Klots^^'^^ which ahows tunnelling through the centrifugal barrier. In conclusion, it can be said that the metastable fragmentation and the photoionization studies reveal very detailed information about reaction 36 and indicate the presence of molecular hydrogen loss from the molecular and of atomic hydrogen from the methyl ion (reactions 30 and 31). VestaP^ constructed a fragmentation scheme, based on the information available in 1968. It is astonishing that the fragmentation reactions for such a simple molecule are not better understood. The fragmentation of methane can also be studied by allowing collisions between the ions and a cohiding target gas. This technique, the cohision-activated dissociation (CAD), is very popular in mass spectrometry in order to be able to differentiate a m o n g different isomeric metastable or stable ions. A detailed study of the C A D of methane has been undertaken by Ouwerkerk and c o l l e a g u e s u s i n g ions with a kinetic energy of several keV and He, Ar and Xe as target gases. The authors measured the decomposition as a

406

T. G a u m a n n

function of pressure, i.e. the n u m b e r of cohisions per unit time. C o n t r a r y to the fragmentation of a molecule ionized a n d excited by an electron or a photon, C A D is a rather brutal fragmentation method where higher electronically excited states can be occupied and, e.g., any number of hydrogens can be lost. T h e authors m a d e this assumption a n d calculated by a least-squares procedure a fragmentation probabihty per cohision for all ten possible reactions for hydrogen loss in methane a n d its fragments (4 in CH4+ , 3 in CH3+, 2 in CH2^ a n d 1 in C H + ) as a function of the n u m b e r of cohisions. T h e method has the disadvantage that it is very difficult to assess any systematic errors in the results, but at least it gives some idea of the weight of the different reactions possible. T h e d a t a a r e — a s expected—rather similar for H e a n d Ar as target gas. T h e most important reactions are given in equations 3 7 - 4 3 together with the relative probability of this reaction to take place in one collision. T h e first n u m b e r refers to a cohision in He, the second in Xe. It is evident that the simplest reaction, the loss of hydrogen from the molecular ion, is also the most important one. Its significance increases with the difference in relative molecular weight between the ion a n d the target gas. T h e loss of two hydrogens from the molecular ion is more important t h a n the simplest reaction from the methyl ion. T h e probability for losing several hydrogen a t o m s in a cohision decreases with the n u m b e r of hydrogens lost in one cohision a n d the atomic weight of the target gas. Although such measurements give n o clue to the primary fragmentation of an ion after electron impact, it very often allows one to get i m p o r t a n t conclusions about the structure(s) of the ion in the m o m e n t of the collision, since this process is t o o fast ( ' ^ 1 0 ~ ^ ^ s ) to allow rearrangements. However, it should be remembered that it will be the structure(s) that resists fragmentation in the ^s time scale. They d o not always correspond to the initial structure of the ion, since it h a d sufficient time to rearrange to the most stable ionic structure, if it can be attained with an activation energy smaller t h a n the difference between the ionization energy a n d the appearance energy of the first fragment ion. CH4+- + M ^ C H 3 + + H - + M

25%/47%

(37)

CH4-^- + M ^ C H 2 ' - - + (H,H) + M

18%/14%

(38)

CH4+• + M ^ C H + + (H,H,H) + M

8%/4%

(39)

C H 3 - ' + M ^ C H 2 " ' - + H- + M

16%/12%

(40)

C H 3 ^ - h M ^ C H - ^ -f (H,H)-f M

9%/4%

(41)

CH2 ^ • + M ^ C H + -F H- + M C H ^ - h M ^ C - ^ - + H- + M

8%/6% 5%/7%

(42) (43)

The doubly charged ion C H 4 ^ ^ , the determination of its ionization energy a n d its decomposition have been described by Stahl a n d coworkers^^ a n d by H a n n e r a n d M o r a n ^ ^ Extended molecular orbital calculations were in agreement with their experimental finding a n d confirmed the ground state structure for C H 4 ^ (C2v) a n d CH4^'^ (D4h). W o n g a n d Radom^^ calculated that the dication is planar, b u t not square. Hatherly a n d coworkers"^^ reviewed the doubly charged ion a n d added kinetic d a t a obtained by a triple coincidence technique, using the high-energy p h o t o n flux of a synchrotron. Only five exit channels were found: C H j ^ - h H ^ ; CH2^ +H2^;

CH2+ - h H + ; C H + - h H ^ ; C+ + H + . CH4'^" a n d CH3'^ have been the ions of choice to study ion/molecule reactions. A description of these results would n o t only exceed the framework of this review, but it is not even possible to cite all relevant publications^^'^^"^^ It is evident that also the isotope effect of these reactions has received much attention^^'^^"^^. T h e charge transfer

9. T h e mass spectra of alkanes

407

to atoms a n d smaU molecules has also been investigated^ as weU as the neutralization/re-ionization behaviour^^. It should be mentioned that ions also play a n imporant role in radiation chemistry a n d quite a few good ideas have been transferred from irradiation experiments t o mass spectrometry^^'^^"^^. The methane ion and its fragments have been test substances for many experimental a n d theoretical ideas in mass spectrometry. III. BUTANE—THE STRUCTURE OF THE MOLECULAR ION

Butane is the shortest n-alkane that can isomerize (to 2-methylpropane). In a molecule, the activation barrier for a n isomerization is usually rather high. In the molecular ion, where one bonding electron is missing, this barrier might be lower. Further, the appearance energy for the first fragment is often one or several eV, i.e. a couple of l O O k J m o l " \ above the first ionization energy. Therefore an isomerization can probably take place easily before fragmentation a n d some examples are known (see e.g. Lorquet^^). The question is h o w to prove the structure of the cation. This is a question that is often a topic of heated discussion, not only because it is a difficult subject, b u t also because the problem is badly defined. It is general chemical knowledge that two stable structures are known for the formula C^HIQ: n-butane a n d isobutane. They correspond to two minima in the hyperplane defined by the coordinates of the nuclei, the transition from one minimum to the other requiring an activation energy that is large compared to the thermal energy. T h e ionization process results in a change of the structure of these molecules, since photoionization measurements d o not ahow one t o determine the adiabatic ionization energy (see Section IV); from the photoelectron spectrum Heilbronner a n d coUaborators^"^ estimated it to be below 10.6 eV a n d Meot-Ner, Sieck a n d Ausloos^^ obtained from equilibrium measurements a value of 10.35 eV. Thus in such a process some additional energy is given to the ion; it might be little in mass spectrometric terms, but it is easily forgotten that an excess of 0.1 eV corresponds t o an equilibrium temperature of ~ 1000 °C. In terms of the quasi-equilibrium theory the excess energy is distributed randomly a m o n g the available degrees of freedom; at a given m o m e n t sufficient energy might concentrate on a given bond to dissociate it. Only a few organic molecules survive a temperature of 1000 °C! The temperature of the molecules within the ion source wih be in most cases above 100 °C. T h e fragmentation of butane has been used by Amorebieta a n d Colussi^^'^^ t o determine the temperature of butane molecules after collision with a h o t surface. T h e calibration curves given by these authors can be used t o estimate the effective temperature of the neutrals within the ion source. Small molecules have relatively little internal energy, but also a small number of degrees of freedom, whereas the internal thermal energy in large molecules may attain rather high values, distributed a m o n g many degrees of freedom. T h e first question is whether n-butane, when ionized, will form one (and only one) ionic structure, a n d if so, the second question will be whether such a structure is different from the one formed from isobutane. These questions can only be answered correctly with thermodynamic equilibrium measurements, since ions are unstable a n d spectroscopic measurements, particularly at low temperatures, are difficult, albeit not impossible. However, this would not solve the problem in mass spectrometry. If there are activation barriers between different ionic structures, are they lower t h a n the lowest barrier for dissociation or does an isomerization take place in the fragmenting transition state? Beside the question of the activation barrier between different ionic structures it should be remembered that these ions can easily be produced—especiaUy by electrons of 70 e V — i n an excited electronic state. According t o the forbiddenness of a state, its lifetime can vary between 10ns a n d I s , but the fragmentations in mass spectrometry are measured between 10 ps a n d 1 s. Thus it is by n o means astonishing that different

408

T. G a u m a n n

experimental techniques may give different answers. M a n y of them are correct, but they are answers to different questions! C o m m o n l y the 'standard' mass spectrometric conditions are assumed, i.e. 70 V electrons, a temperature of the ion source somewhere between 100 and 200 °C, and a residence time in the ion source of fis. T h u s the question boils d o w n to two parts: firstly, the structure of decomposing ions within the ion source, and secondly, the structure of the ions that survived a few jis and that are either in the electronic ground state or in a metastable excited state. The research concentrates mainly on these ions in spite of the fact that they represent rarely more t h a n one or two percent of the ions initially formed (for a review see Reference 98). The reason is that the states involved and their energies are much better defined. However, it should not be overlooked that the conclusions are only valid for a few percent of the reacting ions! Ab initio calculations have been a considerable help in determining the different minima of the energy surface. The impact of new, calculated structures of cations in organic chemistry cannot be overestimated^^. However, for the moment, the proof for a given structure or a mixture of different isomeric ions must be undertaken experimentally. T h e heat of formation of n-butane is 8 kJ m o l " ^ higher than that of 2-methylpropane; the latter has a somewhat higher ionization energy (10.57 vs 10.53 eV)^, thus the difference in stability in favour of the cation of 2-methylpropane that VestaF^ estimated to be 1 4 k J m o l ~ ^ is probably t o o high by l O k J m o l " ^ and the smah difference of 4 k J m o l " ^ is more realistic^. Bouma, Poppinger and Radom"^^ m a d e a detailed analysis of the possible structures of the ions of n- and isobutane (among other hydrocarbons) using ab initio calculations of different levels. They reviewed also older calculations. The H O M O orbital of n-butane is the 7ag[C2h] orbital. It is sufficiently separated from the next lower M O , such that one can assume that the electron is eliminated from the H O M O . The corresponding ionized state does not correspond to a minimum and the a u t h o r s calculate a difference between the vertical and the adiabatic ionization energy of 1.0 eV, compared with an experimentahy determined value of 0.7 eV^'^'^^^'^^^ The H O M O of n-butane includes the central C — C and two C — H bonds. Therefore the authors tried to find the m i n i m u m of a structure with an elongated 2 - 3 bond. Accidentally this turned out to be the structure with the lowest minimum with a b o n d length of 2.02 A. The proposal of a complex between an ion and radical made by Bowen and Wihiams^^^"^^^ finds some confirmation in this structure, but the calculated structure is more strongly bound. However, R a d o m and collaborators found within a few tenths of an eV a few other minima with other bonds lengthened that are well within the excess energy furnished by the vertical ionization process. The ion has therefore to chose between several possible geometries. In isobutane the two highest orbitals are rather close, ahowing an ionization from two different orbitals. Again several minima were found, allowing a facile interchange a m o n g the three methyl groups. N o structure was proposed that would permit a facile isomeriza tion between the two butane ions. Takeuchi and coworkers^^^'^^^ repeated some of the calculations of R a d o m and extended them to larger values of the dissociating C — C bond. They demonstrate that for the loss of M e a barrier has to be crossed formed by a 1,2-hydrogen shift leading to the isopropyl ion, but that this barrier is lower t h a n the energy needed to dissociate the b o n d leading to the formation of the Et"^. The main ions in the mass spectrum of n-butane are given in Table 4. This is p r o b a b l y the most often measured substance in mass spectrometry, but the relative values vary according to the type of instrument and the instrumental conditions. The loss of methyl is the most important reaction; CaHg"^ results from a consecutive fragmentation, C2H5"^ can be either a direct loss of C2H5" or the result of consecutive reactions. It should be noted that in the metastable time range the loss of CH4 and CHg' are not just the only reactions observable, but they have similar probabihties. The photofragmentation of butane as a function of the p h o t o n energy has been determined by Steiner, Giese a n d


409

TABLE 4. Major ions in the mass spectrum of butane in % TIC Metastable Ion

m/z

C4H/ C3H/ C3H5 + C2H4"

"In ''In 'In ''In

the the the the

58 57 56 43 42 41 29 28 27

Probable neutral fragments

H H,

CH3 CH, H , CH,; (CH„ H )

C2H5; ( H , C^H,) C2H6 —

FT/ICR a

Source b

5.9 1.0 0.3 40.9 6.0 12.9 9.6 7.0 9.0

3.5 0.8 0.2 29.9 3.8 9.5 13.2 10.1 12.8

c

d

3 37 60

55 45

0 - 1 0 ms time range^*. 0 - 2 /is range. ~ 10 fis to ~ 20 fis time range^^^. 5 /is to 4 ms time range

1/ ^ 1/

o

X

28

\

r 13

I

11 photon

12 energy

/

(eVj

F I G U R E 3. The photofragmentation of n-butane as a function of the photon energy (after Chupka and Berkowitz"^^. Reproduced with permission)

Inghram^^ and C h u p k a and Berkowitz"^^ and is shown in Figure 3. The ionizationefficiency curve for mass 57 indicates the occurrence of the ion-pair formation (equation 4) beside the (higher energy) process of splitting off a hydrogen atom. The threshold for the formation of C3H7 corresponds to the energy of the secondary propyl (see later). The threshold for formation of C^He^ is, within the limits of error, identical to C3H7'^. The curve for C2H5'^ approaches the energy axis asymptotically, typical for a process that must compete with several others. A reliable threshold cannot be determined. The apparent threshold for C2H4'^' is 11.65eV, higher than the calculated value of 10.45 eV. The difference may be due either to excess kinetic shift caused by competing

410

T. G a u m a n n

processes of lower energy or to excess activation energy which is often required for fragmentation with rearrangement"^^. T h e ions produced in the primary fragmentation (the ions of the T I M S ' as they are called by MaccoU^^^) are probably the following: C^H^^ ( + H), C 4 H 8 ^ ( + H2), C 3 H / ( + CH3), C 3 H 6 ^ ( + CH4), C ^ H s ^ ( + C2H5), € 2 1 1 4 ^ ( + C2H6) and correspond to the general fragmentation scheme cited in Section I. Flesch a n d Svec^^^ arrive at a slightly different classification. Isobutane has a similar spectrum, but with reduced intensities of C 2 H 5 ^ and C 2 H 4 ^ " in favour of C^Re^ • This seems to reflect the different structures of the molecular ions. T h e question is whether, and if so at which moment in the time scale of fragmentation, can there or must there be a n isomerization of the molecular ion. This depends critically o n the distribution of the internal energy at the m o m e n t of ionization. Since n-butane has been the workhorse for the evolution a n d tests of the quasi-equilibrium theory, this point is discussed in numerous publications that have become classical papers in the field (see e.g. References 58, 112-114) a n d h a s sometimes advanced the experimental confirmations. In Scheme 2 a n energy diagram is shown for different fragments in the mass spectrum of butane. It is based o n the data given in References 115-117. The results of an attempt to determine the contribution of the different mechanisms involved are presented in Tables 5 a n d 6. T h e data were obtained by using a least-squares procedure containing reasonable possible reaction paths for the fragmentations under study and, as input, the spectra of 23 differently D and/or ^^C labehed butanes. T h e reactions that gave a non-significant contribution are n o t mentioned. H is mainly eliminated from secondary positions, as would be expected for energetic reasons, b u t a small a m o u n t stems from terminal positions; it cannot be decided if there is some H / D scrambling or if some n-Bu^ is formed as a n intermediate ion. It might well be that, e.g., n-Bu"^ is being formed with more internal energy than 5 - B u ^ , thus the larger part of it could have fragmented further (see later). The isotope effect of 0.5 is a time-averaged value! The loss of molecular hydrogen is unimportant; the ratio of l-butene'^72-butene'^' formed is about 1:4. F o r

1 0 . 5 eV

CH3CH2CH2* + CH3

1 0 . 0 eV —

S-C3H7* + CHS

cyc/o-CGHE 9.5 eV — F-C4H9* + H

CHSCHRCHZ* 9.0 eV

CH3CH2CH2CH3

—

CH3CH=CHCH3* + H2

SCHEME 2


411

TABLE 5. The selective loss of hydrogen from molecular ion of n-butane (in %, source spectra, FT/ICR, 70 eV)^'^ Reaction -(H,D) -(H,D)/ - ( H , D ) 3 = [M - ( H , D ) ] + - ( H , D ) 2 M+ - ( H , D ) 5 = [ M - ( H , D ) - ( H , D y ^ - ( H , D ) 2

Position"

Probabihty

Isotope effect^

1 2 1,2 2,3 random** random

6 94 20 80

0.5 0.48

0.96 0.92

"}i,D from this position lost to the neutral. ^Weak signal. ''All positions have the same probabihty. TABLE 6. Results from the fragmentation of labehed n-butane (in % contribution for the reaction at 70 eV; 12 eV similar) Position of the label lost to the neutral fragment Reaction

-CH3

-CH4

1 2 2 2 1 1 1 2 2 2

-[CH5] M+ - C 2 H 5

D

FT/ICR^^ (see also Reference 116)

1,1,1 1,2,2 2,2,3 2,2,4 1,1,1,2 or 3

93 2 2 3 47

1,1,1,4 1,2,2,4

41 3

2,2,3,4 H,CH4(rnd)'' CH3, H2(rnd)^

9 20 80 80 10 3 7 85^

Metastable^^^ 92 8

87

13

1,2 1,3 1,4 2,3 1,2

"Loss of H according to Table 5, random loss of CH4. ''Loss of CH3 according to this Table, random loss of H 2 . ''Other reactions unknown.

the further loss of molecular hydrogen no specific reaction can be recognized, and a r a n d o m process must be assumed as is often observed in the fragmentation of secondary fragments in hydrocarbons. Several authors have realized that M e is not only lost from terminal positions^^^'^^^'î^'ii'-i^^ although different interpretations are offered. 7% of M e lost originates from a position within the chain. The ratio of internal to terminal loss does not seem to depend on time, but in the metastable range the relative importance of the two sources of the additional hydrogen a t o m for the internal loss seems to change, since in the metastable decay of l , 4 - D 6 - b u t a n e no loss of CH2D" could be o b s e r v e d ^ T h e reaction proceeds within 0.05 eV of the calculated threshold of the most stable product, the 2-propyl ion^^^. An analogous situation is seen with higher alkane ions, showing

412

T. G a u m a n n

that either prior to or simultaneously with the fragmentation, a 1,2-hydrogen shift has to take place, at least for the low-energy metastable fragmentation. Coggeshah^^^ claimed that the metastable decay can be split-off in three processes with different htetimes, but Schug^^^ demonstrated that the same experimental d a t a can be represented as well with only two lifetimes. O n e might question the validity of results of this kind that have been obtained with relatively simple instrumentation, although there is n o a priori reason that the fragmentation scheme can be due to populations with different lifetimes as has been demonstrated by elaborated photoionization experiments, e.g. by Brand and Baer^^^. The M e loss has been discussed in detail and an explanation by an isomerization process has been proposed by Wendelboe, Bowen and WiUiams^^^ but it does not predict the observed isotope distribution. The loss of methane can again be divided into an internal and a terminal loss that does not seem to depend upon time. In the latter reaction the additional hydrogen can be abstracted from position 2,3 or 4. The origin of the additional D has been determined by different authors over different time scales. Some data are collected in Table 7. T h e d a t a are remarkably similar, since the metastable d a t a are from measurements where an error due to a superposition with the M e loss cannot be separated rigourously a n d no correction was applied for an internal loss. The results are equal within a reasonable error limit and do not seem to depend on the time scale of the experiment. If one assumes an equal isotope effect of 1.3 for the internal and terminal abstraction, a probability of 5 3 % is obtained for an abstraction of a hydrogen in a primary position. It is not quite evident that the probability be divided for an internal loss between positions 2 a n d 3, but it seems that both positions have an equal participation of 24%. If a r a n d o m distribution is assumed, the participation should be 42.8% and 28.6% for a terminal a n d an internal position. These values seem to be outside the error hmit; a r a n d o m scrambling of the seven hydrogen atoms is not observed. W h a t is the structure of the resulting C g H e ^ ' ion, propene or cyclopropane? Appearance energy measurements indicate that sufficient energy is available for either isomer (0.69 and 0.28 eV, respectively)^ The activation energy for isomerization has been determined to be 1.4 eV above cyclo propane^ ^''^ and the two structures are indistinguishable by their metastable fragmenta tions. Also their C A D spectra are very similar, but Bowen, McLafferty and coUaborators^^^ were to distinguish the molecular ions of propene and cyclopropane over the fragmentation of the doubly charged ions. By comparing the CÛe^ ion originating from butane, these authors concluded that this ion must have the propene structure. W h e n measuring the released translational energy for the loss of C H , from butane and assuming the vahdity of the H a n e y - F r a n k l i n e q u a t i o n ^ t h a t relates the internal energy of a fragmenting ion with its translational energy, Wendelboe, Bowen and Williams arrive at the conclusion that the formation of cyclopropane is more probable. The two-step reaction C4Hio"^' - ^ C 4 H 9 ^ -^C^H^^ can probably be excluded as a source of'internal' loss, since the latter reaction has not been observed as a metastable fragmentation of C4H9'^ (see later). CgHs"^ is one of the major ions in the mass spectrum of butane, but it is a tertiary ion. Loss of CH4 from C 4 H 9 ^ , H2 from C3H7+ and H from C s H ^ ^ are ah c o m m o n fragmentations. If Bu"^ would be the major precursor, the probability for the loss of the labels, in particular ^^C, should be r a n d o m , i.e. 25%, independent of its initial position (see later). In the other cases the distribution should be the same as in the C3 ion, i.e. ~ 4 5 % for a ^^C in position 1 of b u t a n e and ~ 5 % for position 2, nearly identical for C3H7^ and C^HeThe latter is the case; it can thus be concluded that C4H9"^ is not an important ion for the formation of C3H5 *; it follows that B u ^ cannot be an i m p o r t a n t primary fragment in the mass spectrometric fragmentation of butane. C2H5 ^ and C 2 H 4 ^ ' could be primary as weU as secondary fragment ions, since ^ 80% seem to come from a 1,2-loss to the neutral, without or with a hydrogen transfer, respectively. The reaction p a t h appears evident, but it turns out that in the scission of

413

5 t2

s Ig

5

1 O

•5b

5J

o

uuu

'5b

I O (u

Q ffi ffi

uuu 03

VO

PQ

Tt

999 "4

CO 1,2-Pr » 1,2-Me. His proposals d o not correspond to the k n o w n data. Considering all arguments, it seems to be sure that molecular ions of n-alkanes with more t h a n six carbon atoms do not isomerize. T h e same may be true for n-pentane a n d n-hexane. The terminal hydrogen atoms d o not scramble, since they keep their identity even in the fragmentation of the secondary alkyl fragments (see Section VI). It is not evident that one can exclude mixing of the hydrogen atoms within the chain. T h e study of the metastable loss of, e.g., the C2 fragments in n-nonanes, labelled with D in different positions, is indicative of a n o n - m i x i n g ^ b u t metastable studies with labelled molecular ions are not easy because of the superposition of the labelled fragments and the isotope effects (see Table 8). H e p t a n e is taken as a case study for understanding the fragmentation of the higher alkanes. In Table 9 the relative contributions of different fragments in the source spectrum of heptane are given. It is a typical mass spectrum of an n-alkane, where TABLE 9. The most important peaks" in the source spectrum of n-heptane and the probabihties (in %) of a given position to be lost to the neutral Position of ^^C Neutral lost''

% TIC

1

2

3

4

rnd'^

CsHii^

C2H5

CsHio^

QH^

C4H9" C4H8" C3H7"

C3H7 C3H8 C4H9 C4H10 C4H11 C5H11

12 6 10 7 21 5 9 6

46 43 49 49 65 66 77 78

44 42 47 46 62 56 71 73

7 10 49 48 46 43 77 58

7 10 10 14 54 69 59 80

28.6 28.6 42.9 42.9 57.1 57.1 714 714

Ion

C3H5" C2H5"

r 102% 111% 105% 115% 99% 120% 99% 108%

"Only fragments that contribute ^ 5% to the total ionization are given. ''The 'neutral lost' may (or has to) correspond to several species, lost either in one step or in consecutive reactions. 'Corresponding to a random distributions of all positions. ''Sum of the probabilities of all positions divided by the number of carbon atoms lost to the neutral.


419

alkyls and alkenes form the majority of the ions in a ratio of a b o u t 2:1. In the same table the probability of a given position to be lost to the neutral is also given as they were determined by Lavanchy, Houriet and G a u m a n n T w o things can be seen: every position has a non-zero probability to be lost to the neutral fragment and this probability corresponds in no case to a r a n d o m distribution. The last column gives the sum of all probabilities divided by the number of carbon atoms for the neutral. Neglecting an isotope effect, it should be 100%; the deviations give some indication of the reliabhity of the results. The general rule, that the fragment with the largest n u m b e r of hydrogen atoms within a group (the alkyl ion) yields the most precise results, can be well seen. The authors used these (and other) data to construct a fragmentation scheme for the alkyl ions. They m a d e the assumption that an alkyl ion can be formed either by direct fragmentation of the molecular ion (equation 46),

^RFILN + L^ -^^RJ^2M+L^ or by an olefin loss from an alkyl ion with n^l>m

^N-NFLLIN-M)+I

(46)

+ I (equation 47)

Q^2L + 1 ^ ^ ^RJ^LM + 1 ^ +

_ RJI2(L - M)

They m a d e two hypotheses for the fragmentations: (i) reactions of the type shown in equation 46 involve only the loss of terminal positions (they call these reactions type A reactions); (ii) the formation an alkyl ion by reaction (47) (type B) involve all positions in a r a n d o m manner. Using the d a t a from many ^^C-labelled n-heptanes, they were able to calculate the probabhities for the two types of reactions that are given in Scheme 3. It can be seen that according to this scheme the fragmentations yielding alkyl ions containing more than n/2 atoms are mainly ( 8 5 % ) formed by direct cleavage, where the contrary is true for smaher alkyl ions. Since the higher-molecular-weight alkyl ions wih fragment further, such a fragmentation scheme allows one also to estimate the relative importance of the primary fragmentations. The authors were also able to show that the figures of Scheme 3 do not depend strongly on the energy of the ionizing electrons, as would be expected for such an overall scheme. W h a t is the value of such a scheme? The d a t a were obtained from unit resolution spectra by the usual arithmetic procedures. Such calculations are difficult to check for their internal consistency. This, together with an insufficient knowledge of the fragmenta tions of olefins, precluded a simhar calculation for the olefins. The second hypothesis (random fragmentation of alkyl ions) is shown to be true only for the lower alkyl ions (which works in this case). The postulated loss of CgHg from hexyl ions is not observed in the metastable fragmentation of hexane (but it is not forbidden neither; see Reference 150). The importance of the [ M — 1 ] ^ ion is astonishing. It was assumed to account for the observation of an internal loss of C2H5'. However, this reaction, which also h a d been observed for the metastable decay (see Table 8), must be explained by other mechanisms. The weakness of such calculations is that they can furnish figures only for reactions that were put into the calculations; thus they depend on the knowledge of possible reaction schemes. The inclusion of many reactions asks for more data than are possibly available and has the danger that it whl yield for every reaction included some smah probabihty. In summary, it can be said that such schemes may give a reasonable semi-quantitative picture of the fragmentation that can be used as a basis for discussion, the figures for the main reactions being relatively reliable; the contributions for minor reactions must be considered with caution and are subject to later modifications when improved experimental techniques are avahable. The d a t a of Table 10 indicate the importance of the loss of neutral fragments from within the chain for all n-alkanes. Although in higher alkanes the metastable loss of larger fragments can be observed, this type of internal loss is only seen for neutral fragments containing less than five carbon atoms. However, it must be admitted that

(47)

T. G a u m a n n

420

- C2H5

86%

14%

.H ^

n

i

5

• C3H7

87%

C 7 H 1 6 *

7

•

13%

- CHa*

+

Ll

• C2H4

-C4H9

2 2 %

6%

^

- CH3

^

u

+

- C3H6

+

•C2H4

C 7 H 1 6 *

7 2 % • CzHs-

^ C 5 H 1 1

C5H1

14%

C 2 H 5 *

C 7 H 1 6

86%

- C3H7

+

- C2H4

U 4 M 9

SCHEME 3

reliable metastable measurements on higher-molecular-weight alkanes are difficult to perform. The fact that the internal loss is a generahy observed p h e n o m e n o n led Lavanchy and c o w o r k e r s ^ t o extend their measurements and calculations to higher alkanes, using the same assumptions. In Section VI it will be shown that these assumptions are only approximately valid. Their principal results are shown in Table 11. T h e same picture is seen: the fragments with less than one-half of the carbon atoms of the molecular ion include in 8 1 % (s = ± 8%) of the cases the terminal positions, the others in 15% (s = ± 4%). This seems to be a general picture for the fragmentation of n-alkanes within the ion source. 2-Methylhexane, an isomer of n-heptane, may serve as an ihustration of the difficulty in interpreting labelled data. The most important products of primary fragmentations are C g H i s ^ ( — C H 3 ) , C4H9"' (—C3H7) and perhaps C3H7+ (—C4H9), the latter being a possible counterpart of C 4 H 9 ^ . T h e first two ions are also the important ions in the metastable decay beside the loss of CH4, C2H6 and C3H6, which gain in importance in the metastable range. In the ion source fragmentation the main ion C 4 H 9 ^ can be

421

13

M

10 ns), where the M e groups originate from the ring; the authors assumed for this second path that ring opening precedes the M e loss. Hirota and Niwa^"^^ calculated scission probabhities of skeletal C — C bonds for the monocyclic unsubstituted alkanes containing five to eight carbon atoms. The cations of two isomeric hydrocarbons may isomerize and form a mixture of two (or more) structures, separated by barriers of different heights, but lower than the energy needed for the appearance of the first fragment. K o m a r o v and cohaborators^"^^ demonstrated that in these cases the spectra of two isomeric neutrals may be the same if they are measured at different temperatures in order to compensate for the difference in internal energy of the ions when formed by electron impact, e.g. 500 °C for toluene and 220 °C for cycloheptatriene. F o r cyclopentane and 2-pentene, a mutual approach of the intensities in the two spectra is not observed with an increase in temperature up to even 1000 °C. T h e authors conclude that the structures of the two molecular ions must therefore be different. Brand a n d Baer^^^ used the photoelectron photoion coincidence technique ( P E P I C O ) to study the fragmentation of the different isomers of C5H10. They were able to show that all isomers, with the exception of 2-methyl-2-butene, exhibited a two-component decay as a function of time, indicating that dissociation occurs from at least two distinct forms of the molecular ion. The assumption of more than two forms improved somewhat the fitting of the results at the expense of additional parameters. Only 2-methyl-2-butene, the ion with the lowest heat of formation, shows a single exponential decay. T h e authors propose that every molecular ion isomerizes partiahy to the lowest-energy ion 2-methyl-2-butene before fragmentation. Ausloos and collaborators ^'^^ show for cyclopentane and different alkylclopentane cations that the degree of ring opening observed depends on the internal energy of the molecular ion. It can thus be assumed that cyclic cations wih undergo ring opening before fragmentation, but only to an extent that is determined by the internal energy of the ion. This is not an encouraging fact for the study of the fragmenta tion of these ions. Even-electron cyclic alkyl cations have received much attention, in particular carbonium ions and p r o t o n a t e d cyclopropanes^'^'^^'^'^'^'^'^'^^. The general experience is that the cyclic ion is often the most stable form and thus is preferentiahy formed. H o w ever, an important skeletal isomerization is always observed with a corresponding

426

T. G a u m a n n

randomization of the labels in given initial positions, indicating the ease with which the structures interconvert. As an example the study by Schwarz a n d colleagues^'^^ with C^Hg^ ions may be mentioned. The authors synthesized several C s H g B r compounds, doubly labelled with ^^€2 in such a way that the two labels were separated by at least one unlabelled carbon atom. They studied the metastable loss of C2H4 from C^Hg^ for bromocyclopentane and 5-bromo-l-pentane as precursors and observed for ah isomers that the probability of losing a label to the neutral fragment corresponded exactly to a r a n d o m loss of two ^^C a m o n g five carbon atoms. Methylcyclohexane ( M C H ) is taken as an example to demonstrate the possibhities and fallacies of the use of isotopic labels. The M e group in M C H has the advantage of fixing the positions within the ring and offering a favourable location on position 1 for localizing the charge. The relative importance of the different fragments in the mass spec t r u m of M C H for ionization with 70 eV electrons is given in Table 13 for the source spectrum in a F T / I C R instrument and the metastable M I K E spectrum in a Z A B - 2 F double-focussing mass spectrometer, operated with an ion energy of 8 keV. The loss of a CH3 group yields the most important ion, in particular in the metastable spectrum. This is somewhat astonishing, since the loss of a M e group corresponds to a simple C — C b o n d breaking and more complicated rearrangement processes usually prevail in the metastable time range of several tens of ps. The loss of a propyl group as neutral fragment is of equal importance. The difference with the spectra of C7H16 alkanes is apparent: the contributions to the total ionization by the molecular ion and by fragments with four to six carbon atoms is much more important; low-molecular-weight C 1 - C 3 ions are nearly missing. This may reflect the fact that for fragmentations an additional step is needed, thus decreasing the time avahable for consecutive fragmentations. As in the case of alkanes of the same size, the loss of a hydrogen atom from the molecular ion is a minor reaction, unless the further fragmentation is so fast that the intermediate ion cannot be seen. This is very improbable since the fragmentation of the (M — 1) ^ cycloalkyl ions can be observed in the metastable spectrum. Meyerson and cohaborators^^^ labelled different positions with one D a t o m a n d measured the probability of losing the label to the neutral fragment. Amir-Ebrahimi and Gault^'^'^ prepared ^^C monolabelled M C H where every position was labelled. The results of the two studies are collected in Table 14. All these d a t a present source spectra results obtained with unit resolution. In parentheses are the results obtained with a TABLE 13. The main fragments in the mass spectrum of methylcyclohexane m/z

Ion

98 97 83 82 70 69 68 56 55 54 42 41 40

C7H14"

Neutral lost

C7Hi3^ CeHji CeHio CsHio^

H

CH3 CH4 C2H4

C5H/ CsHg

C4H8" C4H7 + C4H6" C3H6" C3H5" C3H4"

"In % of the total ion current.

C2H5 C3H, C3H7 C3H8 C4H3 C4H9 C4H10

Source'' 15 0.6 24 5 6 5 2 5 22 1 5 8 —

Metastable"

Reaction in Scheme 4

a 61 13 5.6 4.0 3.6 4.0 8.3

b,c d

h

427

[XI

OO^

o of O

»N O OO ^

On

O^ OO

OO

IN

^

Ii

RN'OO'

C S S

if

S^

ÔO"

0^ O

^

88

1 3

o

OO

On O

O On

OO (N ^

S ^

M

OO OS 0^

R-

^

o M

T — (

"SO

OO

=3

^

a^

On

ON VO

43

I II

^

VO ^

CNI

oq

B o

VD VO

o

o O

PQ

250,000) to resolve all possible multiplets containing ^^C and D^"^^. The possibilities and the performance of the m e t h o d have been d e m o n s t r a t e d I t can be seen that the results agree fairly well. Some differences may be expected, since in a sector instrument the ion intensity is integrated over ~ 2 /xs and in a F T / I C R over a few ms, including the metastable range. T h e formation of the C ^ H i 1 ^ and CgHio ^' ions corresponds to the loss from the methyl group, although a very small participation of other positions seems to be real. This is rather different from methylcyclopentane (see above). F o r all other fragment ions ah positions contribute to the neutral in different amounts. This is particularly true for D atoms: if a scrambling should take place, it is by n o means complete! This somewhat contradicts theoretical predictions'^^. A check of the quality of the results is obtained by adding the p r o b a b h i t y of losing a position to the neutral over all positions. The sum, divided by the n u m b e r of carbon (or deuterium) atoms lost to the neutral fragment, should give 100%, aside from a possible isotope effect. These figures are also given in Table 14. Even for D atoms, where an isotope effect could be more important, satisfactory agreement is observed, demonstrating the quality of the measurements. Amir-Ebrahimi and Gault used the d a t a to construct a fragmentation scheme for M C H . They defined a number of possible reactions and used the label distribution to calculate the contribution of a given reaction to yield a given ion. W h e n the n u m b e r of d a t a exceeded the number of equations, they did not use a least-squares calculation, but used the additional d a t a to check the validity of their assumptions. If the number of equations exceeded the n u m b e r of data, they also used the d a t a for D-labelling in order to obtain enough equations. They had to m a k e a choice for the fragmentation reactions assumed. Firstly they had to limit the number of different fragmentations to a reasonable figure. The choice of such reactions is by n o means evident, since very little is k n o w n about fragmentation of rings a n d the predictive power of theoretical calculations is in such systems rather ml. They further assumed that only neighbouring C atoms within the ring are lost to the neutral fragment. With these hypotheses they were able to obtain a fragmentation diagram whose main features are shown in Scheme 4. The following

-C3H6

f

e

• i

8*

12*

el

24

15*

C3H5* 25*

24

24

SCHEME 4

5

15

14


429

TABLE 15. The importance of the different primary fragmentation in the mass spectrum of methylcyclohexane (see Scheme 4)^'^'' Reaction a b c d e f 9 h Sum

Neutral lost

Positions lost

CH3 C2H4 C2H4

Me 3,4 2,3 Me,l 3,4,5 Me,l,2 2,3,4 Me,l,2,6

C3H6 C3H6 C3H6 C4H9

% Total ion 30 2 24 11 4 9 7 4 91

conventions are used in this scheme: (i) Italic letters mean a primary fragmentation path. They are summarized in Tables 13 and 15. (ii) XI (xij) means a secondary (tertiary) fragmentation of the ion formed in the primary fragmentation x; i and j are the number of carbon atoms lost in the secondary and tertiary fragmentation, respectively. (hi) The number below an ion is its intensity compared to that of C^H^^^ which is taken equal to 100, (As an indication, the sum of all ions is roughly 400.) An asterisk corresponds to an odd-electron radical ion. (iv) A solid line corresponds to a reaction that was also observed in the metastable spectrum of the unlabelled ion. F o r obvious reasons one cannot distinguish between isobaric ions of different origin. Hashed lines correspond to reactions that are not observed in the metastable range, either because they were too fast or because the assump tion of a one-step fragmentation is not valid in this case. The percentage that can be attributed to the different primary fragmentations is given in Table 15. M o r e than 90% of the observed ions is explained by this scheme. The loss of C H j ' or C2H4 makes up for more than 50% of the ions. The main contribution to the latter is from positions 2, 3, possibly in a concerted reaction. C2H5' originates from positions Me, 1. The elimination of C3H7' in a one-step reaction from weh-defmed positions is not observed, in spite of the fact that the corresponding metastable decay is seen and C4H7 is a main ion in the spectrum. C3H6 comes in roughly equal a m o u n t s from the positions Me, 1,2, 2 - 4 and 3 - 5 , the only reaction paths admitted by the authors for this elimination. The elimination of C4H9' as a neutral fragment in a one-step reaction, although not very important, is a rather surprising proposal. The elimination of atomic hydrogen in reactions of the type xO and xiO makes up for about one-third of the ions observed. This is very astonishing, as it is rarely observed in a metastable decay and is usuahy energetically not favoured. This may be one of the weaknesses of the proposed scheme. W h a t is the value of such a scheme? T o the best of our knowledge it is the only complete fragmentation scheme proposed for a cyclic hydrocarbon ion. A citation by Benson ^"^^ is particularly appropriate for such a case: Tt is an unwritten law of chemical kinetics that ah proposed mechanisms are inherently suspect, so that detailed d a t a derived from proposed mechanisms always have somewhat of a tentative quahty'. Mass spectro metrists have a tendency to concentrate on specific mechanisms, i.e. they prefer the trees to the forest. It is evidently not reasonable to try to m a k e a complete fragmentation scheme without at least some knowledge of the detailed reactions possible in the system

430

T. G a u m a n n

under study. O n the other hand, such fragmentation schemes have the advantage of stimulating the directions of further research a n d they are finally one of the ultimate goals of mass spectrometry. There is no d o u b t that the quantitative statements of the scheme are at the best very approximate, because with the small n u m b e r of labelled c o m p o u n d s available and the m e t h o d of calculation used, the errors have a tendency to accumulate the further one proceeds d o w n the scheme. W h a t a b o u t the qualitative aspects of such an attempt? The o u t p u t can only reflect the reactions the authors put in their calculations and this corresponds to the knowledge of such systems fifteen years ago. This is particularly true for the consecutive reactions. The cyclohexyl cation, a main ion in this system, may serve as an example. Its stability has been studied by Schwarz and coworkers F r o m measurements of the kinetic energy release in the metastable decay and C A D spectra they concluded that the cyclohexyl cation isomerizes immediately to 1-Me-cyclopentyl. Cacace a n d coheagues^ tried to measure quantitatively the conversion of the cyclohexyl cation to the methylcyclo pentyl cation using radiation chemical techniques in the gas phase. They found a preexponential factor of 10^^s " ^ and an activation energy of 31 ± 4 kJ m o l " ^ The latter value is very small for mass-spectrometric systems and confirms the conclusion by Schwarz. The conversion is well k n o w n in the liquid state from N M R studies. O l a h a n d Lukas^^^ observed the spontaneous transformation of cyclohexyl cation into methylcyclopentyl cation even at — 110°C, whereas Saunders and Rosenfeld^^^ showed that the label of the Me-labelled methylcyclopentyl cation equilibrates at — 25 °C over cyclohexyl cation into the five-membered ring. The conformation of the ring also has i n f l u e n c e ^ T h i s seems to be the general behaviour, as has been demonstrated in N M R studies of Kirchen and Sorensen^^^ for cycloalkyl cations with 8, 9 and 11 carbon a t o m s that convert immediately to the corresponding l-methyl-7-, 8- and 10-carbon tertiary rings. The ten-membered ring forms an exception, as is often observed, since in this case the decalyl cation is formed. In an attempt to be in a better position to judge the validity of Scheme 4, several labehed M C H have been synthesized and measured with high r e s o l u t i o n ^ T h e results for the methyl and 1 positions are resumed in Table 16 (several d a t a are averages obtained for different labehed compounds). These d a t a ahow one to check to which extent the loss of a D a t o m in a given position is coupled with the loss of a ^^C in the same or another position. The fohowing observations can be made. C ^ H n ^ : M o s t of the M e eliminated consists of the M e g r o u p of the neutral, but a small a m o u n t stems from positions within the ring. In this case one hydrogen of the methyl group will participate in 14% of the cases (excluding an isotope effect). C^H^q^: The CH4 comes exclusively from the M e group. Position 1 participates with 10% to the additional hydrogen a t o m needed, the rest being furnished mainly by positions 2 and 6. C^H^q^ : The ethylene eliminated originates in 10% of the cases from positions 1 and M e together. U p to two hydrogen atoms in the M e position are exchanged before the elimination, demonstrating the complexity of this reaction. C^Hg^: In two-thirds of the eliminations C2H5" comes from positions 1 and M e together. Little exchange of the hydrogen from the methyl group, but a large exchange from position 1, is observed. The rest stems mainly from positions 2 - 6 with a limited participation of a hydrogen from positions 1 and methyl. Cg/Zg^ • The majority of C2H6 originates from positions 1 and M e together, coupled with some hydrogen exchange from the methyl g r o u p and a large exchange from position 1. C^Hq^ : The loss of CgHg is again a reaction where positions 1 and M e are either eliminated together (40%) or not at all. Again, little scrambling from the methyl g r o u p and m u c h exchange from the position 1 is observed. The formation of this ion must be a mixture of different processes, contrary to the prediction of Scheme 4. T h e elimination of positions 1 and M e and their hydrogen atoms together, as is proposed, corresponds to 2 5 % or less. In 50% the M e g r o u p with ah of its hydrogen a t o m s is lost, but with little contribution from position 1. It is fair t o assume that this reaction

C^.H-j^:

431

^^^^^^^

I

! if .a

i

+

I 5 8

S

2

§

U

1

m C3H5 + -h H X (X = CI of Br)

(51)

as was realized by Harrison and coworkers'^^. The C A D spectra of Bu ions of different precursors may vary, as has been shown by Maquestiau, F l a m m a n g and Meyrant'^^. The authors explain the difference by a ratio of s-Bu"^/t-Bu^ that changes according to the precursor ion. This finding was put in quantitative form by Shold and Ausloos^ who used C H 3 C O O H as a p r o t o n acceptor for s-Bu"^. By assuming that only s-Bu^ and t-Bu^ are present in the millisecond and second time range, they were able to measure this ratio as a function of different alkanes as the precursor ion and its internal energy at pressures of about 1 0 " ^ t o r r . In n-alkanes, 2-methylbutane, 3-methylpentane, n-butyl halides and s-butyl halides, both s-Bu"^ and t-Bu"^ ions are observed, the s-Bu^ surviving without rearrangement for at least 0.1s, the measuring time in a I C R / M S . Isobutane, neopentane, 2,2-dimethylbutane, isobutyl halides and t-butyl halides form uniquely t-Bu^. They confirmed their findings by radiolytic measurements at different pressures. It is evident from these experiments that the percentage of t-Bu^ from n-hexane is becoming substantially smaller with increasing pressure, whereas the i-Bu"^ from isobutyl bromide rearranges to t-Bu^ even at atmospheric pressures. The authors propose that about 90% of the i-Bu"^ ions can rearrange to t-Bu"^ ions by simple 1,2-hydride shift. Using deuterated compounds, they were also able to determine isotope effects. Howe^^^ showed that the heat of formation data are consistent with the formation of the t-Bu^ when n-Pr is eliminated from the molecular ion of 2-methylhexane. The 1,2-hydrogen shift that must accompany this reaction is confirmed via a deuterium isotope effect u p o n the metastable decomposition. M e o t - N e r m e a s u r e d and discussed the secondary isotope effect for t-Bu due to hyperconjugation by the CD3 groups. The fact that B u ^ ion fragments from electron impact do not necessarily isomerize was also shown by Stahl and cohaborators^"^^''^^, who showed that t-butyl chloride labelled in central position by ^^C lost 10% of the label in the source, 16% in the C A D and 2 5 % in the metastable spectrum. They also made the interesting observation that the induction

436

T. G a u m a n n

time for fragmentation induced by p h o t o n s of l O ^ m wavelength in a F T / I C R ^ w a s significantly longer for t-Bu^ t h a n for 5 - B u ^ , indicating that either more p h o t o n s are needed t o reach the transition state or the emission probabhity for IR p h o t o n s is larger for r-Bu + . In conclusion it can be said that in fragmentations of a l k a n e s — a t least in t h e time scale observable by these instruments—t-Bu"^ as weh as s-Bu^ c a n be formed. s-Bu^ can exchange t h e charge between positions 2 a n d 3 by a hydride shift that h a s a small activation energy leading t o a H / D scrambling without changing its structure. Ottinger showed^ ^^'^^^ that they fragment with different kinetic energies if their precursor is n-butane or n-heptane. This fact m a y well explain the sometimes different results obtained by different authors, b u t it may also be that the choice of precursors is n o t of general validity, since Stahl, G a u m a n n and coworkers ^"^^ measured a large n u m b e r of metastable B u ^ fragmentations originating from n-alkanes with 7 - 1 2 c a r b o n atoms, labehed in different positions with ^^C. F o r monolabelled B u ^ they determined a p r o b a b i h t y of 23.8 + 0.2%, a n d for doubly labelled Bu+ 48.5 + 0.1%, t o be lost t o the neutral. Thus, beside a small isotope effect, all positions in B u ^ formed as a fragment in n-alkanes are equivalent. It is n o t a n easy task t o determine which Bu ion(s) is formed in a fragmentation, since neither the time n o r the energy scale can be changed continuously. O n e has the impression that even a given structure, such as t-Bu^, has several pathways for fragmentation. Labels within t h e fragment can be exchanged, its rate constant d e p e n d i n g — a m o n g other variables—on the internal energy of the ion. This means that it is generally n o t feasible t o draw conclusions a b o u t consecutive fragmentations from labehing experiments.

B. Heptyl Ions

Beside Bu"^, heptyl ions a r e the alkyl ions that were studied the most, in particular by labelling with D a n d ^^C. W h e n trying t o explain the fragmentation mechanism of this ion, t w o questions come t o mind: (i) Where is the charge localized? (ii) H o w can heptyl ions in defined states be produced? It is reasonable t o assume that t h e localization of the charge in a primary position of a heptyl ion corresponds t o a n unstable form as in B u ^ . By a 1,2-hydride shift the charge wih be moved immediately t o a secondary, energetically more favourable, position. This reaction is probably very fast, b u t n o measurements of its rate constant in the gas phase are known. The charge can be easily shifted over all secondary positions in the ion, thus causing a scrambling of the hydrogens in secondary positions, whereas the a t o m s in a primary position will remain untouched. A rate constant of 4 x l 0 ^ s ~ ^ h a s been estimated for the migration frequency of h y d r o g e n A s in B u ^ , there is the possibhity of skeletal rearrangements of the carbon atoms. Among t h e m a n y different isomers possible, ^Bu-dimethylcarbenium ions have been shown by N M R measurements t o be the most stable form in the liquid phase 212 ^^^^ ^^^^ ^^^Q metastable spectra only o n e neutral fragment is lost (CgHg) is a n additional argument in favour of t h e formation of this structure. This is probably also true in t h e gas phase. It is reasonable to assume that the energy needed t o interconvert the different structures is smaller t h a n the activation energy needed for further fragmentation. However, these processes take time a n d perhaps m a y n o t compete with the fast dissociation of a n ion with a large a m o u n t of excess energy. Thus the time scale a n d the excess energy of the ion m a y be important. In alkanes, the fragmentation of a n alkyl ion is a secondary o r tertiary reaction, where it may be expected that the ion has already lost a large part of its excess energy. The fragmentation of alkanes produces alkyl ions in different, u n k n o w n states. I n


437

order to study the reactions of a heptyl ion, it should be generated in a better-defined state. Little study has been conducted on ionization of heptyl radicals. D e a r d e n and B e a u c h a m p ' ^ ^ studied the isomerization and decomposition of 1-pentyl, 1-hexyl and 1-heptyl radicals by photoelectron spectroscopy. The results are consistent with a mechanism involving isomerization via an intramolecular hydrogen shift to produce sec-alkyl radicals whose isomers could not be distinguished in the spectra. Further, the adiabatic and vertical ionization potentials were determined. The most often used method is to start with a functional g r o u p in a defined position that is eashy lost upon ionization. Halogen atoms are mostly used; for the production of heptyl ions, the iodides are particularly useful since the intensity of the molecular ion is weak, the heptyl parent ion is relatively a b u n d a n t a n d the ions with iodine or fragments thereof contribute to less t h a n 1% of the total ion current'^'*. They can be considered a clean source of heptyl (or any alkyl) ions. Another possibility are ion/molecule reactions occurring in chemical ionization, either by adding a p r o t o n to an olefin, by hydride (or another anion) abstraction with, e.g., E t ^ , or by p r o t o n transfer, e.g., by CH^^ to an alkane to form an unstable p r o t o n a t e d alkane ion (equations 52-56). AH^ +C7Hi4Â4-C7Hi5+ C2H5 ^ + C7H16 -

+ C7H, 5 ^

CH5 ^ + C 7 H 1 , ^ CH4 + [ C 7 H 1 7 ] ^

(52) (53) (54)

lC,U,,r-^C,U,,^+U,

(55)

[C7H,7]^-C7_„H,5-2.^+C^H2^^2

(56)

In reaction 52 the difference in p r o t o n affinity can be changed. The fragmentation spectrum is very simple (mainly m/z 57 and 99) when water is used as reagent for chemical ionization; more fragments are observed with methane (m/z 57, 55, 97)"^^. The hydride transfer reaction in alkanes has been very extensively studied by Lias, Eyler a n d Ausloos'^^ and, for labehed alkanes, by Houriet and G a u m a n n B y using selectively deuterated compounds, these authors determined a ratio of kjkp, i.e. the probabhity to transfer a hydrogen from a secondary or a primary position, of 3.3 for n-hexane, 1.7 for n-pentane a n d 1.9 for propane, respectively, and for the first substance an isotope effect of 1.14 that seems to affect equally the primary and the secondary position. All secondary positions seem to be equivalent for the hydride transfer. Chemical ionization analogous to reaction 53 has also been used as a convenient way to produce heptyl ions from heptyl halides^^^ Reaction 54 is of a m o r e complex nature, since the intermediate heptonium is not known. F o r lower alkanes Hiraoka and Kebarle'^^ were able to demonstrate the existence of two species, one corresponding probably to a complex between an alkyl ion a n d a H2 molecule, the other to a C — C protonated alkane. Different mechanisms have been discussed by Houriet, Parisod a n d G a u m a n n ^ ^. In trying to rationalize the observations, the authors were led to propose two paths for the formation of heptyl ion"^"^. Reaction 56 is particularly intriguing, since it is the only case where they observed a clean C — C b o n d split without a prior positional scrambling (vide supra). Unfortunately, it cannot be decided if this elimination of an H2 and an olefin is so fast that there is n o time for a skeletal randomization, or if the loss of an alkane neutral moiety is a rather clean, u n k n o w n elimination. The spectrum of the heptyl ion is given in Table 18. The results for the source spectra are obtained from the spectrum of 1-iodo-n-heptane after correction for the fragments containing iodine. Bu"^ is by far the most a b u n d a n t ion. The formation of propyl ion in the source might be astonishing, since it does not correspond to Stevenson's rule^^; it could be formed by successive eliminations of two ethylenes, but we will show later

438

T. G a u m a n n

TABLE 18. The fragmentation spectrum of C7Hi5^^^'^''

Source'' Metastable'

0.1 = Al7;

cpj=

f

A,L\j=

k= 1

f

A,L,,

(33)

k= 1

It is evident that all this is formahy identical to the E B O treatment discussed in Section II.B, the matrix F ^ playing the role of H;^ (e.g. matrix 19), and L"^ the role of C in transformation 22. If one computes the matrices L, A and F ^ for a series of saturated hydrocarbon molecules, starting with the C M O s from an ab initio S C F calculation, one can m a k e the following very general observations: (a) The L M O s A^ are in an obvious one-to-one correspondence to the chemical valence hnes in the structural formulae. Labeling the C C and C H bonds in the formula of a hydrocarbon molecule labels the corresponding L M O s A^. (b) Two L M O s of same type and surrounded by simhar bonds, but located in two different molecules, are practically identical, which means a m o n g other things that their self-energies Fj^jj = Aj can be transferred quantitatively, almost without change, from the H a r t r e e - F o c k matrix of one molecule to that of the other. (c) The crossterms F^^-^ = < A y | ^ | A ^ ) in the H a r t r e e - F o c k matrices F ^ of two different molecules are almost identical, if the environment and the relative geometrical arrangement of the two bonds carrying the L M O s Aj and A^ are a b o u t the same in both molecules.

2. Rules governing

the elements

of the matrix

for saturated

hydrocarbons

Examination of the matrix elements Aj, B^j, Y^j, etc. of the F ^ matrices computed for a series of saturated hydrocarbons^'^ has led to the following observations (cf. also References 13 and 18): (1) F o r standard interatomic distances ( K c c = 154 pm, RCH = 109 pm) and for saturated, unstrained hydrocarbons, i.e. hydrocarbons in which all C C C bond angles are close to tetrahedral, the diagonal terms F^jj, i.e. the self-energies Aj of the L M O s A c c or ^ C H J span very narrow ranges. F o r example, based on a STO-3G treatment, the self-energies of the L M O s A c c of all open-chain hydrocarbons from methane to neopentane are found to lie within the interval —17.84 eV < ^ c c — 17.73 eV, and those of the L M O s ACH within -16.97 eV < ^ C H < - 1 6 . 9 2 e V ^ ^ Although the difference ^ c c — ^ c H ~ 0.8 eV is significant, it is small enough to suggest as a first approximation that ylcc ^ c H are about equal, independent of the size and structure of the mole cule: AQQ ^ y4cH

(2) F o r tetrahedral bond angles

(Oij

109.5°) the crossterms

(34) Bij between two geminal

L M O s Aj, Aj of a saturated, unstrained hydrocarbon are quite independent of the nature

10. The photoelectron spectra of saturated hydrocarbons of the two molecule. treatment - 2.88 eV

467

L M O s involved, and independent of the size and structure of the hydrocarbon Thus, one finds for the above set of molecules (using again a n S T O - 3 G for a start), - 2.98 eV < 5cc,cc < - 2 . 9 4 e V ; - 2.92 eV < B C C C H < - 2 . 9 1 e V ; < 5cH,cH < - 2.86 eV. It fohows that: ^CC,CC ~ ^CC,CH ~ ^CH,CH

(35)

(3) The crossterms Tu between t w o vicinal L M O s Aj, A^ in a saturated, unstrained hydrocarbon (all bond angles close to tetrahedral) are again independent of the nature of the two L M O s involved, and independent of the size a n d structure of the molecule, if the torsion angle defining the relative, local conformation of the two L M O s A^, Aîs the same. Using the same set of molecules and the same treatment as above, one finds for Tij=m° (anti-planar conformation) -h 0.94 eV < r^/180°) \r;;\>\A;;\. The important conclusion t o be drawn from these observations is that the assumption of equivalent b o n d orbitals as used in a n E B O treatment c a n be validated by the properties of L M O s A^- derived from ab initio calculations. The mathematical formahsm for handling L M O s according t o equations, 32 and 33 is exactly the same as that of a n E B O model, which implies that this Hiickel-type treatment is capable of yielding excehent approximations t o the S C F orbital energies Sj a n d the corresponding C M O s cpj of saturated hydrocarbons.

3. Derivation

of EBOs

from

LMOs

Acceptance of the approximations expressed by approximations 34,35 and 36 leads to the conclusion that ah these matrix elements can be cahbrated through multhinear regression treatments, with reference t o observed ionization energies of a calibration set of hydrocarbons^'^, if we wish t o obtain a treatment appropriate for the prediction of such quantities. W e shall explore this in more detail in Section V. Assuming the validity of K o o p m a n s ' theorem (cf. Section III.A) one obtains adjusted parameters Aqq, ^ C H » ^ C C C C ? ^cc,cH» ^cH,cH5 rcc,cc('^)» rcc,cH(^) ^tc. Thus one is led back t o a n E B O formahsm, having replaced implicitly the L M O s by EBOs, A ^ » A^, for which the calibrated matrix elements (collected in H;^) are valid. As we are going t o use the E B O s 2.j as basis functions, we shall index them with greek letters, e.g. A^, etc., the indices p, v referring t o the bonds in question. a. The AB-model. The s i m p l e ^ E B O model that can be derived in this fashion consists in taking only geminal interactions into account, neglecting all others. I n addition, o n the basis of approximations 34 and 35 we make the simplifying assumptions A ^ ^ = A^î = A for the self-energies, and Bcccc = ^ C C C H = ^ C H , C H = B for the crossterms. U n d e r these conditions the model is described by only two parameters, namely A and B, so that the matrix H;^ is defined—in complete analogy t o the standard H M O treatment of n systems—by

H;, = Al-\- BA

(37)

468

E. Heilbronner

where 1 = (S^^) is the unit matrix, and A = (a^^) the adjacency matrix of the graph representing the geminal interaction pattern of the hydrocarbon. This is shown in Figure 4 for the example of p r o p a n e CgHg, whose structural formula (a) includes the labelling of the EBOs A^. In the graph ^ (b) each vertex p stands for the E B O A^, and each edge e^^ for a geminal interaction B^^. It is amusing to note that a three-dimensional representation of this graph resembles the van't Hoff model of the corresponding hydrocarbon, i.e. in case of propane, three tetrahedra joined by their vertices, as shown in Figure 4c. As in standard Huckel treatments, it is of advantage to introduce an abbreviation -x

= {A-8)/B

(38)

which reduces the eigenvalue problem det(H^ — gl) = 0 connected with H;^ (definition 37) to the diagonalization of the adjacency matrix A: det(A-xl) = 0

(39)

The result for p r o p a n e is shown in Figure 5. The ten eigenvalues XJ are those of the adjacency matrix A underlying the matrix H;^ shown in Figure 4, and the corresponding C M O diagrams are based on graph (b) of Figure 4. Each circle refers to the coefficient c^J of the E B O in the linear combination CPJ (cf equation 21). The radius of the circles is proportional to the absolute value |c^^|, and full or open circles correspond to coefficients c^J of opposite sign. The labels of the C M O s refer to the point group of p r o p a n e in its lowest-energy conformation, and the numbering takes only the valence orbitals into account. This AB-modd suffers from quite a few defects, some of which are already apparent from the results for propane, shown in Figure 5. The neglect of vicinal (and higher) interaction terms leads necessarily to a model which is conformation-independent. Furthermore, the ^ B - m o d e l yields large sets of accidentally degenerate orbitals, e.g. orbitals CP^ to CPG in the case of propane. This wih prove to be a very p o o r approximation for interpreting the low-energy part of the P E spectra of hydrocarbons, as we shall see in Section V. O n the other hand, the lowest n orbital energies £J of the C M O s (PJ, j = 1 to n, obtained through an AB-mode\ for a saturated hydrocarbon C„H^, wih turn out to yield a very satisfactory interpretation of the high-energy part of its P E spectrum. b. The AT-model. The above E B O ylB-model can be vastly improved by including vicinal interaction terms F^^, which leads to the AF-model. Because the matrix elements r^y(T^y) depend on the local twist angles T^^, their inclusion will m a k e the model conformation-dependent. This will also lift most of the accidental degeneracies, as can be deduced by inspecting the orbital diagrams of Figure 5. N o t e that the interactions would correspond to additional edges in the graph ^ (Figure 4b) between vertices separated by two consecutive edges.

Â graph ^ is a set of N vertices (points) {•••/i, v, •••} joined by edges (lines) e^^, e.g. in Figure 4 the graph (a) represenhng the structure of propane, or the graph (b) depicting the geminal interactions between the 10 EBOs in the same molecule. Such a graph ^ can be characterized by a AT x AT adjacency matrix A = (a^J whose matrix elements are a^^=\, if the vertices p and v are joined by an edge, and zero otherwise. For example, the adjacency matrix A of the graph ^ of the methane EBO model depicted in drawing 18 is /O

1

1

1 0

1\ 1 1

" ^ ^ 1 1 0 1

Vi

1

1

0/

3 A 5 6 7 8 9

1

i ^

31 2 ^

< 1

(

5

8 7

6

10

^,

9

^

(a)

10

(b)

(c)

F I G U R E 4. The structure of the H;^ matrix for the A5-model of propane. The black squares are the self-energies A for the CC and CH EBOs, assumed to be equal. The geminal crossterms B are the same for C H / C H , C H / C C and CC/CC interactions. All other crossterms are set equal to zero. Graph (a) shows the numbering of the bonds in propane. In graph ^ (b), each vertex (point) refers to an EBO, and each edge (line) to a geminal interaction. Graph (c) is a three-dimensional representation of (b)

-1.791 -1.477 -1.000 -1.000 -1.000 -1.000 -1.000

1.552

^ 3

= 2a,

2.791

3.925

cp, = â,

F I G U R E 5. Scheme of the valence orbitals of propane obtained by diagonalizing the matrix shown in Figure 4. The orbital energies Sj are given in terms of the parameter Xj, i.e. 8j = A + XjB (cf equation 38) and the orbitals (pj as hnear combinations (pj = Hn^fiC^j of the EBOs /L^ with reference to graph (b) of Figure 4. The orbital labels refer to the point group €2^. N o t e that the orbitals (/>4 to cp^, which are accidentally degenerate, are given in one of the many possible symmetry adapted, real representations

10. T h e photoelectron spectra of saturated hydrocarbons

471

In its simplest form the ^ r - m o d e l makes use of the observations expressed in approximations 35 a n d 36, by postulating ^CCCC = ^CCCH = ^CH,CH = ^

TccccC^) = ^cccniT^)

= rcH.cHl-^) = To COS(T)

(40)

where FQ is a negative energy parameter. Accordingly, the vicinal crossterms roCOs(T) are negative for a local syn-periplanar a n d positive for a n antZ-periplanar conformation of the two vicinal bonds. A simple mnemonic for the sign of FQ COS(T) is given by the following two diagrams, which show a positive, bonding overlap, a n d hence a negative crossterm for the s};n-periplanar arrangement, a n d a negative, antibonding overlap associated with a positive crossterm for the anti-periplanar one.

syn

anti

Q

As before, the approximation in equation 40 is acceptable under the implicit assumption of (approximately) tetrahedral bond angles. T h e self-energies (equation 34) can be treated as either independent, T I C C ^ ^ C H ^ or as identical, A ^ ^ ^ Aq^ = A , depending o n the required precision. We shall discuss this model in more detail in Section V. (Concerning the inclusion of higher interaction matrix elements, the reader is referred t o References 13 a n d 14.)

III. PHOTOELECTRON (PE) SPECTROSCOPY

A. General Remarks

7. P E spectrum

and ionization

energies

The theoretical a n d experimental principles of P E spectroscopy have been reviewed e x t e n s i v e l y I n particular, the book by Eland^^ provides a n elegant a n d compact introduction. I n this section we summarize only the essentials necessary t o fohow t h e arguments presented in Section V. As far as the present review is concerned, we shah only be concerned with the primary process consisting in the ejection, by a p h o t o n of energy hv, of a n electron e~ from a closed-shell hydrocarbon C„H^ in hs electronic ground state (cf conhguration 15). The product is a hydrocarbon radical ion C„H^+ in one of its doublet electronic states (In the context of P E spectroscopy it is customary t o write C „ H ^ ^ for the open-shell, radical cation, rather t h a n C,,!!,^"^). W e shall n o t be concerned with subsequent rearrangements a n d / o r fragmentation reactions of the radical cation C „ H ^ ^ , in contrast to its geometric relaxations which conserve the original connectivity of the parent hydrocarbon C„H^. Typical p h o t o n sources used in standard P E spectroscopy are h e h u m atoms, He(I), or helium ions, He(II), undergoing the following transitions shown in display 4 1 .

472

E. Heilbronner He(Ia):(ls)^(2s)^ - >(lsf; He(IIa):(2p)^ >iUy;

/l = 58.4nm;

/zv = 21.2eV

/l = 30.4nm;

/iv = 40.8eV

(41)

If these p h o t o n energies a r e j a r g e r t h a n the ionization energies Ij needed to reach the radical ion doublet states ^"^j in which we are interested, the excess energy is carried off by the photoelectron e~ as kinetic energy Tj = hv — Ij. Accordingly the primary process can be written as

QHJiô) + hv-.C„U;ê^'j)

+ e-{Tj)

(42)

The quantity measured by the P E spectrometer is the n u m b e r Z(e~) of electrons ejected per unit time from a gaseous sample of fixed volume (measured in cps = counts per second) as a function of the kinetic energy T of the ejected electrons. The result is presented as a plot of Z ( e " ) vs ionization energies / = /iv — T, as shown in Figure 6 for a hypothetical molecule, not necessarily a hydrocarbon. The low-energy part of this P E spectrum consists of four bands, numbered ® to @ with increasing ionization energy, which—for simplicity—we assume not to overlap. The bands ® and © exhibit resolved vibrational fine structure, which is rather the exception in the case of P E spectra of saturated hydrocarbons. In contrast, the fine structure of (D and ® is unresolved, which could be due to the limited resolution of the recording (which is of the order of AI/I ^ 1/200 in standard P E spectrometers), to r a n d o m noise a n d / o r to intrinsic line broadening, which would prevent a resolution even in the absence of the other factors. The latter effect is by far the most i m p o r t a n t cause for the occurrence of wide, unresolved bands in the P E spectra of saturated hydrocarbons.

Cfcps) /a

®

rvu^N

J

® \ J

F I G U R E 6. Schematic representation of the PE spectrum of a hypothetical molecule. Abscissa: Ionization energy / in eV. Ordinate: Intensity C in counts per second (cps). = adiabatic ionization energy, / } = vertical ionization energy. If = ionization energy corresponding to the maximum of the band

10. The photoelectron spectra of saturated hydrocarbons

473

The position of a b a n d ® on the abscissa / (eV) of a P E spectrum can be characterized by: (1) 7^, corresponding to the maximum of the contour of b a n d ® . F o r our purposes 7™ is usuahy a sufficiently close approximation for the so-called vertical ionization energy 7^ (see below) in which we are interested primarily. As 7^ is b o t h easier to measure and much better defined from an experimental point of view, we shall use the approximation 7™ ^ II throughout this chapter. (2) II, the adiabatic ionization energy, corresponds to the position of the first vibrational component of a P E b a n d (disregarding possible hot bands). This quantity is usually not accessible with the desired precision, because of the lack of fine structure (e.g. bands (D and ® of Figure 6), and because of strongly overlapping bands. In a crude approximation one may assume that 7^ coincides with the onset of the b a n d ® , a quantity usually uncertain by about 0.2 eV. 2. Interpretation

of the PE

spectrum

With regard to the M O models discussed in Section II, the ionization process (reaction 42) can be visualized as the ejection of an electron from one of the C M O s of the neutral hydrocarbon C„H,„, say from the C M O cpj. This point of view is especially appropriate for independent electron models, such as the standard H M O treatment of n systems, or the E B O .4B-model of hydrocarbons. Both are two-parameter models, in which the orbital energies 8j = (x + Pxj or £j = A + Bxj are given with respect to the edge of the continuum, ficontinuum = 0, corresponding to a free electron of zero kinetic energy, T = 0. Within such an independent electron approximation, the ionization energy needed to remove an electron from orbital cpj is therefore i]= — The situation is more involved if we use a many-electron treatment. M a k i n g the crude (and in fact unreasonable) assumption that the removal of an electron from the C M O (Pj whl not affect its shape, nor the shapes of the other C M O s cp^, j, used for the description (determinant 15) of the electronic ground state ^^ô of the hydrocarbon C„H^, the resulting electronic state of the radical cation C „ H ^ ^ can be written as

\\\^lî---^j-l'n-flwti-Tetracyclo[7.1.0.02'^.0^''']decane anfi-flnti-Tetracyclo[7.1.0.0^'^.0^''^]decane 2,4-Dehydroadamantane l,l'-Bi(bicyclo[l.l.l]pentane) Dispiro [cyclopropane-1,2'-bicyclo [2.2.1 ] heptane3',1 "-cyclopropane] 2,4-Dehydrohomoadamantane Tetracyclo[4.2.2.22'^0i'^]dodecane Tetracyclo[5.2.1.02'^23'^]dodecane Tetracyclo[5.2.1.02'^23'^]dodecane Dispiro[cyclopropane-l,2'-bicyclo[2.2.2]octane3', 1 "-cyclopropane]

3',r'-cyclopropane] 10

14

11

16

12

18

13 15 16 19

20 24 26 32

Polycyclic 8

8

9

10

10

10

10

12

11

12

11

14

References

Name

No.

m, n

479

100 58 28 29 32 36 63 46 47 48

Tetracyclo[5.2.2.02^2^'5]tridecane Hexamethyl-c/s,rrans-trihomobenzene Hexadecahydropyrene 5a-Androstane 5a, 14a-Androstane, Etioahocholane

Hydrocarbons

80 70 71 82 65 84 72 56 57 83 64 73 34 98

107 29, 108 109, 110, 111 112 107 33 33 113 85 114 115 107 116 93 117 117 117 33 67 94 33 118 119 120 94 119 113 80, 74 121 122

with more than Four Rings

Cubane Cuneane Pentacyclo[4.3.0.03'^.03'^0^'^]nonane Homo-cubane Diademane Pentaprismane Pentacyclo[4.4.0.02'''.03'^0''']decane Pentacyclo[5.3.0.02'^0^'^0«'i^]decane Pentacyclo[5.3.0.02'^0^'^0«'i°]decane Basketane Decahydrotricyclopropa[crf,/,/zi]indene Octahydrospiro [cyclopropane-1,3'- [ 1,2] methanodicyclopropa [cd,gh'] pentalene Pentacyclo[3.3.3.0^^0^'^0^'ii]undecane 2,4-Methano-2,4-dehydroadamantane

109, 123, 124 109 110, 111 33 74 123 110, 111 125 125 33 74 126 127 128 (continued)

480

E. Heilbronner

TABLE 1. m, n

(continued) No.

12

14

13

16

78 114 93

14 15

20 14

120 87 101 75

15

18

94

20

30

102

Name

References

Hexacyclo[6.4.0.02'^.03'1 ^.0^'Ô*^'11 jdodecane [4]Rotane Trispiro[cyclopropane-(l,3')-tricyclo[2.2.1.0^'^]heptane-(5',r')-cyclopropane-(7',r')-cyclopropane] Trishomotriquinacene Trishomobullvalene Congressane Dispiro[tetracyclo[3.2.0.0^'^.0^'^]heptane3,1 '-cyclopropane-2',3"-tetracyclo[3.2.0.02'^.0^'^]heptane] Trispiro[cyclopropane-(l,3')-tetracyclo[3.3.1.02'^0'*'^]nonane-(7',l")-cyclopropane(!', 1 "')-cyclopropane] 1,1'-Diadamantane

116 115 129 33 33 79

130

129 79

Concerning Table 1, the following remarks are in order: (1) The list of references is not complete. In particular, some of the early work on ionization energies of hydrocarbons is not mentioned. However, it can easily be traced through the leading references given in the Table. (2) Table 1 is subdivided into linear, mono-, bi-, tri-, tetra- and higher cyclic hydro carbons C„H^, arranged according to n, m within each group. Deuteriated and Protiated derivatives appear together. The reader is reminded that in a saturated h y d r o c a r b o n C „ H ^ the number c of cycles is given by c = n + 1 — m/2. (3) Although the names given are unambiguous, they do not always satisfy the l U P A C rules. We have used trivial names whenever convenient. (4) The arrangement according to n,m necessarily separates the parent c o m p o u n d s from their alkyl-substituted derivatives. T o compensate for this shortcoming, related molecules have been grouped together in the scheme of structural formulae. T h e bold numbers (in the column headed No.) refer to this formula scheme, where the hydrocarbons have been grouped according to either a c o m m o n parent hydrocarbon (e.g. a given bicyclo [/i./c./] alkane), or their belonging to the same category (e.g. highly symmetrical hydrocarbons). However, it should be borne in mind that such groupings are largely subjective.

Me

(1 )

Me

(2)

^

^

(3) /-Bu


(12)

(14)

(13)

481

(15)

Me Me Me

Me

(17)

(16)

(19)

(23)

(26)

(20)

(24)

(27)

(18)

(22)

(21)

(25)

(28)

482

(34)

(33)

(35)

(37)

(36)

(39)

(38)

Me Me

Me

(40)

(41)

(42)

(43)

(44)

Me

(45)

(46)

(47)

(48)


483

(49) (50) (52)

(51)

(53)

(55)

(54)

Me Me

> (61)

(62)

Me

Me

(63)

(66)

Me

Y Me

(65)

(60)

(59)

(58)

(57)

(56)

(67)

(6 4)

(68)

484

E. H e i l b r o n n e r

(69)

(70)

(71)

(72)

(74)

(73)

(75)

(76)

(77) (78)

/-Bu

^

^—

7^

/-Bu (79)

(84)

(80)

(85)

(81)

(86)

(82)

(87)

(83)

(88)

10. The photoelectron spectra of saturated hydrocarbons Me

Me

(69)

(90)

(91)

(93)

(92)

(94)

Me

(95)

(96)

(97)

(98)

(99)

(100)

(101)

(102)

485

486


(103)

(104)

(105)

(108)

(106)

(109)

(111)

(112)

(115)

(118)

(110)

(113)

(116)

(107)

(114)

(117)

(119) (120)

10. T h e photoelectron spectra of saturated hydrocarbons

487

V. DISCUSSION OF PE SPECTRA

A. Methane and Ethane

The P E spectra of methane a n d ethane are rather special cases, because of their high symmetry. T h e point groups of methane a n d of ethane, the latter in its staggered conformation, are a n d D^d respectively, with the consequence that some of their valence shell orbitals are degenerate. They are indicated in bold type in the following list:

CH4 :lt2,2ai

[la,)

C2U,:3a,^,

(l«2u)(lîg)

le^, le,, la^^, 2a,^

(45)

Descending order of orbital energy The numbering of the orbitals (of 45) includes those of carbon Is origin, given in parentheses. T h e corresponding peaks can only be observed in the E S C A spectra^ ^, a n d are found at /(IflJ = 290.8 eV for C H ^ , a n d at / ( l a ) = 290.7eV for C2H6. The P E spectra of methane a n d ethane are redrawn in Figure 8 from the He(IIa) spectra recorded by Bieri a n d Asbrink^^ (cf also Figure 7). They present some special features, which are due t o the J a h n - T e h e r d i s t o r t i o n ^ o f the radical cation when the photoelectron has been ejected from one of the degenerate orbitals. Although the P E spectra of methane a n d ethane have been m u c h studied, b o t h experimentally a n d theoretically, fohowing the pioneering work by Al-Joboury a n d T u r n e r ^ w e shah restrict o u r discussion t o only a few points, relevant for the ensuing discussion of the P E spectra of higher alkanes. 1. The PE spectrum

of

methane

The ionization energies^ ^ of methane a n d the corresponding assignments are presented in Table 2. Ejection of a n electron from the triply degenerate H O M O It2 of methane gives rise in its P E spectrum t o the complicated feature between 13 a n d 16eV (see Figure 8), rather than the simple, single b a n d o n e might have expected naively, by applying K o o p m a n s ' theorem (equation 44) t o either the naive E B O results shown in Figure 2, or t o those obtained by any other S C F M O treatment. This is a consequence of the J a h n - T e h e r instabhity of the orbitally degenerate methane radical cation CH4"^ of T^ symmetry, reached verticahy by removal of a n electron from o n e of the It2 H O M O s of CH4. T h e radical cation C H 4 ^ can lower its total energy by undergoing a T-type distortion, whereby one of the H C H b o n d angles opens u p a n d the opposite H C H b o n d angle closes down, so that the geometrically relaxed radical cation assumes a C2V structure, as shown qualitatively in the diagrams 46.

H

H

\ '

/7

K CH4:

(46)

CH/:C2

Both semi-classical a n d quantum-mechanical calculations show^^^'^^"^ that the resulting F r a n c k - C o n d o n envelope of the b a n d system ® , (D, (D should consist of three (overlapping) maxima. T h e position of the second m a x i m u m is predicted t o be close

488


cps

CH,

\J cps

~'—\—I

25

20

10 / ( e V )

15

@

©©® A

A C 2 H 6

R

cps

10

/(eV)

cps

/ 7 - C 4 H 1 0

1

I

25

r

—

'

'

I

20

'

I

^—>—1

15

1—'

I

I

I—R

10 /(eV)

F I G U R E 8. He(IIa) PE spectra of methane, ethane, propane and butane, redrawn from Reference 28


489

TABLE 2. Valence ionization energies of methane and ethane Ethane

Methane

/;^(eVf

Orb.«

/;(evr

ri3.6

12.7

LA.

14.4 U5.0 22.9

22.4

S.U.'^ S.U.''

28 31

1^2

Orb.

lû 2«2u 2^1.

/-(eVf 12.0 rl2.7 M3.5 rl5.0 M5.8 20.4 23.9

/;(eVr 11.6

202

"Orb. = Vacated orbital. ÎJ = position of band maximum, in eV. Î] = adiabatic ionization energy, in eV. ''The two bands of methods labelled 'S.U.' are so-called 'shake-up' bands; cf text.

to the true vertical ionization energy, r^Î"^, which corresponds to the creation of the radical cation CH4'^ having exactly the same structure as the parent hydrocarbon CH4. The two side bands ® and (D should be placed symmetrically with respect to the central b a n d (2). This prediction is in reasonable agreement with observation (cf Figure 8), especiahy if one considers that changes in the F r a n c k - C o n d o n envelope due to the neglected vibronic interactions are presumably important in this case^^ A more detahed discussion can be found in References 20, 21, 133 and 134. The b a n d at 22.9 eV, labeled ® in Figure 8, corresponds to electron ejection from orbital 2a^, its vibrational fine structure, with a spacing of 2 1 9 0 c m " ^ being due to the breathing vibration of the radical cation. Band @ is followed at higher ionization energies by two 'shake-up' bands at 28 and 31 eV, not shown in Figure 8. They are due to a ' n o n - K o o p m a n s ' ionization process, i.e. one in which an electron is ejected from the 2a^ orbital, and one of the remaining electrons of CU^^ is p r o m o t e d simultaneously to a higher, antibonding (i.e. previously unoccupied) o r b i t a l ^ ( T h e dependence of the intensities of the methane U2 and 2^1 P E bands on p h o t o n energy^^^'^^'^, and the angular distribution of the corresponding photoelectrons^^"^'^^^, have been studied.) With reference to the results of the naive, two-parameter E B O model of methane shown in Figure 2, we are now in a position to reach a first (crude) estimate of the self-energy A ^ ^ of an E B O /I^H and the geminal crossterm BCH,CH between two such EBOs, using K o o p m a n s ' theorem (equation 44), i.e. £(1^2) = ^ C H — ^ C H CH = — ^''(1^2) ^ -/-(lr2)= - 1 4 . 4 e V , and £(2ai) = ^ C H + 35CH,CH = - ^ 2 ^ 1 ) ^ -^"(2ai) = - 2 2 . 9 e V . This yields Methane EBO:

Acn = - 16.5 eV,

J5CH,CH = - 2.1 eV

(47)

However, it should be remembered that methane is a rather special case, because of its high symmetry. 2. The PE spectrum

of

ethane

The assignment of the P E spectrum of ethane, given in list 45 and in Table 2, is due to Richartz and his c o w o r k e r s ^ i n particular as far as the first three maxima are concerned. It differs from the assignments given in, e.g., References 32 and 140, where the first two maxima have been assigned to the LE^ orbitals. The problem associated with the interpretation of the low-energy part of the ethane

490

E. Heilbronner

P E spectrum stems from the extreme closeness, i.e. the (almost) accidental degeneracy of the l^g and 3aig C M O energies, and their dependence o n small changes of molecular geometry, which affect their relative sequence. I n addition, it should be remembered that in such cases t h e sequence predicted, by applying K o o p m a n s ' theorem t o the C M O sequence of the parent molecule, does n o t necessarily reflect the state sequence of the radical cation. T o illustrate the first part of the problem, we use again simple E B O models. T h e two-parameter AB-model yields the Sîg as H O M O at e(3a^^) = A - 1.65R This C M O is dominated by Acc- The two C M O pairs l^g a n d are accidentahy degenerate with £(l^g) = 8{\e^ = A — B, a n d entirely centred o n the ACH- This suggests that lowering t h e self-energy ^cc of the E B O Acc will lower e(3flig), and that introducing vicinal interactions FcH.cH between the E B O s ACH will move £{\e^ towards higher energies, thereby closing u p the g a p between these two orbital energies. As an example we n o w use parameters that have been chosen t o mimic a n S T O - 3 G calculation^"^, i.e. ^ C H = — l ^ - ^ e V , ^cc = — 17.5 eV, BcH.cH = ^ C H , C C = — 2.9 eV a n d rcH,cHW = EQ cos T = (— 1.0 eV) cos T, which yields rcH,cH(60°)= — 0.5eY for t w o C H bonds in gauche conformation a n d rcH,cH(180°) = + 1.0 eV for two antiplanar ones. Diagonalization of the resulting 7 x 7 matrix leads t o 8{\e^ = — 12.60eV and £(3flig) = —12.57eV, two values which are identical within the significance of the E B O approximation, b u t well separated from t h e next ones, e.g. £(1^^)= — 15.60eV. Simharly close values are obtained by other, m u c h m o r e sophisticated S C F models. It follows that the assignment of the first three m a x i m a can only be obtained by taking into account geometric changes in the radical cation, electron relaxation a n d electron correlation e f f e c t s a n d also vibronic mixing. E t h a n e is an instructive example of the inherent limitations of o u r E B O approach, which this simple model shares with more realistic S C F procedures, e.g. the calculation of ethane C M O s by extensively parametrized semi-empirical models^^, or by ah initio procedures, such as the floating Gaussian orbital model^^^ Obviously, as shown by Richartz and his c o w o r k e r s ^ c o n f i g u r a t i o n interaction methods yielding rehable cation state energies, including their dependence o n the cation geometry, are required. The vibrational fine structure of the P E bands in the spectrum of ethane h a s been analysed by Rabalais a n d Katrib^"^^. B. The C2s Manifold 1. Preliminary

comments

There are good reasons for starting a discussion of t h e P E spectra of saturated hydrocarbons C „ H ^ with the C2s bands found above 15eV. This part of the spectrum consists—at least for the smaher h y d r o c a r b o n s — o f only n weh-spaced bands, whereas the C2p system contains n + m/2 overlapping b a n d s within a narrow range of ca 5 eV, as can be seen in Figures 7 a n d 8. This suggests that the C2s bands should be m u c h simpler t o analyse a n d assign t h a n the C 2 p manifold, at least if we want t o think in terms of simple M O models a n d K o o p m a n s ' theorem. As we shah see, this is indeed the case. The reader should be warned that this seeming simplicky of the C2s b a n d system of h y d r o c a r b o n P E spectra is spurious, and largely a consequence of the low (inherent and instrumental) resolution of the experiment. Theoretical treatments including the effects of electronic relaxation a n d electron c o r r e l a t i o n ^ s h o w that the observed shapes of the individual C2s bands are the result of the superposition of a whole series of F r a n c k C o n d o n envelopes, each corresponding to one of m a n y cation states involving multiply excited configurations. However, the positions of these individual bands tend t o cluster a r o u n d the o n e b a n d (dominantly) associated with the K o o p m a n s ' state d u e t o simple


491

electron ejection from a C2s C M O . Thus, from a naive point of view, one can discuss the C2s part of the P E spectrum of a saturated hydrocarbon C„H^, as if it corresponded to simple K o o p m a n s ' states of the radical cation C „ H ^ ^ . Within the framework of an E B O model, the essential difference between the two parts of a hydrocarbon P E spectrum can be eashy rationalized, e.g. with reference to the results stemming from an ^ 5 - m o d e l . Taking propane, CgHg, as an example, we draw from Figure 5 the following conclusions, which prove to be generally valid for all saturated hydrocarbons: (a) The three C2s-type C M O s (pj{j=l, 2,3) are bonding with respect to the self-energies = ^ c H = A. As we shall show in the next section, both the shape of these C2s orbitals (pj and their orbital energies Sj change very little if higher crossterms (F^^, A^^) are included in their calculation, e.g. if we implement the ^ 5 - m o d e l to obtain an ^ F - m o d e l . (b) The seven C2p-type C M O s (pj {j = 4 to 10) are antibonding with respect to the self-energies Acc = ^ C H = A. N o t only do their orbital energies Sj fall into a small range, but five of the C M O s (pj {j = 4 to 8) are accidentahy degenerate with orbital energies £j = A — B (j = 4 to 8). In contrast to the C2s manifold, the introduction of higher crossterms (F^^, A ^ J has a profound effect on ah the C2p orbital energies Sj, and it whl lead—symmetry a h o w i n g — t o considerable mixing of the corresponding C M O s (pj. In particular, the crossterms yield first-order splits between the formerly degenerate orbitals, with the result that the C M O sequence will depend criticahy on the size and sign of these crossterms. However, the resulting C2p-type C M O s will still be close in energy, with the usual consequence that inclusion of electronic reorganization and electron correlation into the calculation can (and often does) change the predicted order of the close-lying C2p states. Finahy, vibronic mixing could further invalidate an assignment derived from many-electron S C F treatments, and a fortiori from a naive E B O model. We conclude that an adequate and heuristically useful discussion of the C2s part of the P E spectra of saturated hydrocarbons should be possible with reference to simple E B O models, in contrast to the C2p part where the applicability of such models will presumably be limited to only the simplest cases.

2. Linear

and monocyclic

hydrocarbons

The top row of the correlation diagrams of Figure 9^^'^^ show the observed P E b a n d positions {j = 1,2,...,n) for the lower members of the homologous series of linear and branched hydrocarbons C„H2„ + 2» and of the monocyclic hydrocarbons C„H2„. The b o t t o m row of the correlation diagrams refers similarly to the eigenvalues Xj—defined in equation 38—of the adjacency matrix A of the graph of the particular hydrocarbon, which defines the corresponding eigenvalue problem (equation 39). As an example, the graph ^ was given in Figure 4b for propane. The similarity between the two sets of correlation diagrams, showing either the dependence of the ionization energies / J " or of the eigenvalues Xj on the size n and the topography of the hydrocarbons, is rather striking. Obviously the simple v4B-model accounts surprisingly well for even fine details in the relative spacings of the observed 7™ values. This suggests that a parametrization of the matrix elements of the matrices H;^ (shown in Figure 4 for the particular example of propane), i.e. of the self-energy Acc = ^ c H = A and the geminal interaction parameter ^^ccc = ^ C C C H = ^ C H , C H = B by a simple linear regression calculation of / J " on Xj, should yield excellent quantitative agreement. Using 58 paired data, If,Xj stemming from a calibration set consisting of the saturated linear and branched hydrocarbons C„H^ with n^5 and the monocyclic ones with n ^ 8, one obtains the parameters 48^^. The errors quoted for A and B are

492

O OH

O

^1^

C/)

<
-

OR

u

o

CO

u o —I 00

R— O CM

—1—

55 UJ Z < ^

^

^

C> II

Q UJ

< TR CD —R-

£

S

S

A

H

O

S

^ S o

5 • > RV^ -22 3

II

^ T/) UJ

^

-1 C

I

(D

,(2s) = ( A i + A 2 + 4 + ^4)/2

CT>,{2S) = (X^ + X, + K + Î)L^ ,(2s) =

( / L 7 - f / L 8 + 29 +

(53)

/lio)/2

E B O s and of the carbon centres refers to structure 50. The bonding C M O s CP^, (p2, (P^ shown in Figure 5 can now be written to a good approximation as where—for the

(P, = A4)J2S) + H(T)^{2S) + A<J) X2S) cp2 = M2S)-CL>A2S))/^2

(54)

(P3 = ca(2s) - ^(/)b(2s) + C(/>,(2S)

F I G U R E 10. Linear regressions of the ionization energies If of the C2s bands in the He(IIa) spectra of linear, branched (top) and monocyclic (bottom) hydrocarbons on the lowest eigenvalues XJ (equation 38) obtained by diagonalizing the adjacency matrix A of the corresponding AB-mode\s (cf equation 39)^^ Linear and branched hydrocarbons: / J ' = [(16.10 + 0.08) + ( 2 1 1 ± 0.03)xJ eV, r = 0.9980. Monocyclic hydrocarbons: If = [(15.67 ± 0.09) (2.19 ± 0.03)xJ eV, r = 0.9970

496

E. Heilbronner

m o m e n t — t h e only restriction governing the coefficients a, b, c a n d d is that of the ortho gonality of the C M O s (Pi. T o calculate the orbital energies corresponding t o the C M O s 54 a n d the values of the coefficients a,b,c a n d d, one must first compute the necessary matrix elements. It follows from definitions 53 that the pseudo-2s orbitals (/>^(2s) d o not form a n orthogonal set (cf equations 55). If A are the self-energies a n d B the geminal crossterms

5 , , = = l/4 5 , , = ,(2s)> = l / 4

(55)

5 , , = ,(2s)|(/>,(2s)>=0 for the EBOs of the XF-model underlying t h e matrix 51, then t h e self-energies a^(2s) a n d the crossterms j5^v(2s) for the 'pseudo-2s' orbitals (definition 54) are given by equations 56. a,(2s) = < (/>,(2s) I je 10,(2s) > = ^ + 3B, P,,{2s) = ,(2s)|

p = a,b,c

|(/>,(2s)> = 3B/2 + A/4

= ,(2s)|^|(/>,(2s)> = 3B/2 + A/4

^^

i5,,(2s) = ,(2s)|^|(/>,(2s)> =B/4 The important point is that j5^b(2s), Pbd'^s) a n d PacC^^) d o not depend o n t h e vicinal crossterms r(T), because 2F(60°) + r(180°) = 0, assuming tetrahedral b o n d angles throughout. (This can be verified by inspection of matrix 51, where the elements of the submatrices referring t o vicinal interactions, e.g. the submatrix consisting of t h e intersection of rows 1,2,3 with columns 5,6,7, a d d u p to zero.) U n d e r these conditions one has obtained for the C2s manifold of C M O s a n independent electron model with fixed overlap S = 1/4 between bonded basis functions qc^. = - 1 6 . 8 8

m M HP H

V"f~pn V^ '— ' pi V^!^^ V^r-p^ Vdll » CH,CH -0.40

^CH,CH -0.24

^

CH,CH + 0.02

CH,CC -2.48

'

CH,CC

+ 0.62

"CH,CC -0.04

Li ^CC,CC -3.38

' CC,CC

' CC,CC

^CC,CC

-1.94

+ 0.25

-0.21

F I G U R E 23. Pictorial representation of the matrix elements (in eV) of the Hartree-Fock matrix of cubane 80 in a localized basis. The values have been obtained by subjecting the STO-3G ah initio results to a Foster-Boys localization procedure^^. The crossterms refer to the L M O s indicated by bold lines and to the symmetry-equivalent pairs


-16.994

-16.758

-2.15A

-0.910

0.508

0.517

519

-2.885

-3.A12

-2.830

-1.857

-2.088

0.137

0.375

0.674

-0.660

-0.360

-17.209

F I G U R E 24. Pictorial representahon of the matrix elements (in eV) of the Hartree-Fock matrix of pentaprismane 84 in a localized basis. See legend to Figure 23

of F c c c c if the vicinal E B O s XQC belong to two different rings. This is illustrated by the matrix elements for L M O s stemming from an S T O - 3 G calculation of cubane 80^^"^ (Figure 23) and of pentaprismane 84^^^ (Figure 24). The consequences of introducing vicinal interactions F^^ into the AB-model, to yield the ^ F - m o d e l , are shown in Figure 25 for the particular example of the orbital energies of cubane 80. The net separation in energy of the two sets of triply degenerate orbitals and from the remaining C M O s ^ g j ^ i u , « 2 u and flig of the C2p manifold has interesting consequences for the hyperconjugative properties of the cubyl group^^^. 2.

[1.1.1]Propellane

Because of the extreme deviation from a tetrahedral situation of the bridge-head atoms in [ l . l . l ] p r o p e h a n e 49, ab initio treatments using an extended polarized basis, e.g. an extended, polarized 6-3IG b a s i s o r treatments of D Z + P quality, such as a floating Gaussian basis^^^, must be used to obtain reliable results. The P E spectrum of 49^^, shown in Figure 26, agrees qualitatively and quantitatively with the orbital sequence H O M O = 3 a j , le", 3e', la^, 2e', predicted by such treatments. However, the resulting C M O s can again be expressed in terms of EBOs as shown at the b o t t o m of Figure 26. Ejection of an electron from the H O M O 3a[ of CgHg, 49, yields the radical cation CsHg"^ in its electronic ground, state Â\, to which corresponds b a n d © in the P E spectrum of 49 shown in Figure 26. The F r a n c k - C o n d o n shape of this hrst band, and in particular its very narrow width at half-height, indicate that both the parent molecule 49 and the radical cation 49"*" in its electronic ground state Â'^ differ very little in geometry. This can be interpreted in qualitative orbital language as a strong indication that the H O M O 3a\ of 49 is essentially non-bonding^^. The rather peculiar electronic structure of 49, as compared to cyclopropane and bicycio [1.1.0] butane 1, is strongly reflected in the correlation diagram of Figure 27, in particular by the fact that the first ionization energy of 49 cannot be obtained by a linear extrapolation of the first ionization energies of cyclopropane and of 1.

520

E. Heilbronner

F I G U R E 25. Schematic representation of the C M O s (pj of cubane 80, obtained by an EBO AB-model (left) and an AF-model (right), to demonstrate the important influence of the vicinal crossterms in this case

3. Bicyclo[1.1.1

Ipentane and di-bicyclo[1.1.1 ]pe

Figure 28 presents the P E spectra^^ of b i c y c l o [ l . l . l ] p e n t a n e 10 and of di-bicyclo[ l . l . l ] p e n t y l 11, the latter in its conformation. These molecules are again examples of the fact that vicinal interaction terms must be included in an E B O model, for even a qualitative discussion of their electronic structure, and thus of their P E spectra. This

10. T h e photoelectron spectra of saturated h y d r o c a r b o n s

9

10

11

12

13

14

15

16

17

/(eV)

le 3a;

3e'

102

2e'

F I G U R E 26. Top: The P E spectrum of [ l . l . l ] p r o p e h a n e 49. Bottom: Valence-sheh C M O s cpj of 49 in a qualitative EBO representation. The C M O s (pj given correspond to the first five bands in the spectrum of 49:

Band

®

(D (D @

(D

77 (eV)

CMO

9.74 11.35 12.6 (I3.45) 15.7(16.1)

3a\ le" 3e' la'^ 2e'

The diagrams show qualitatively the phase relationship between the EBOs A^

521

E. Heilbronner

522

-€y

(eV)

9 •• HOMO

10 •• 11 •12--

13 ••

15-3(7'

161 SbF3 + 2 F -

R—H-2e

.R++H+

(11)

(12)

The evolution of almost quantitative a m o u n t s of hydrogen in the reaction of Bronsted acids with an alkane have also been reported r e c e n t l y / n , O M r - b i c y c l o [ 4 . 4 . 4 ] t e t r a decane 16 in trifluoromethanesulphonic acid at 0 ° C was converted to the /«-bicyclo[4.4.4]-1-tetradecyl cation 17 in one h o u r with more t h a n 90% of the theoretical

CF3SO3H

(16)

(17)

a m o u n t of hydrogen cohected (equation 13). Deuterium labelling of the trifluoromethane sulphonic acid and of the two bridgehead hydrogens (separately) gave kinetic isotope effects /CH^/CD of 7 with labelled solvent, 1.9 when the out hydrogen was labelled and 1.0 with the in hydrogen labelled. These isotope effects are consistent with a rate-determining step in which O H and C — H out bonds are being broken, but with n o participation from the in hydrogen, i.e. formation of the symmetric /^-hydrido-bridged ion 17 is not concerted. The kinetic d a t a are consistent with a rate-determining p r o t o n a t i o n of the C — H b o n d fohowed by rapid loss of H2. The very stable cation 17 has a strong b a n d in the infrared at 2 1 1 3 c m " ^ attributed to asymmetric stretch of C — H — C . Ab initio molecular orbital calculations at the 6-3IG

540

A. C. H o p k i n s o n

level show the 3-centre 2-electron b o n d in 17 t o be linear (the ion has D3 symmetry)"^^. This contrasts with the C — H — C b o n d i n g in the m o r e flexible C H 3 — H — C H 3 ' ^ (angle 126°)^^ b u t the C — H distance of 1.251 A for 17 is close to that from the higher-level calculations o n C 2 H / (1.239 A)^^

F. Basicities Towards Transition-metal Ions

Like protons, transition-metal ions are strongly acidic and they can, in principle, a d d to b o t h the C — H a n d C — C b o n d s of alkanes. As already noted in the section o n p r o t o n affinities (Table 1) strained cycloalkanes are intrinsically m o r e basic t h a n open-chain alkanes, and the reaction of cyclopropane with Pt((II) t o form a platinacyclob u t a n e (equation 14) was the first reaction of a formally saturated h y d r o c a r b o n with a transition-metal ion"^^"^^. The driving force in this reaction is relief of the strain associated with the small ring. T h e resulting metallacyclobutane is essentially free of ring strain. M a n y low-valent transition-metal complexes have been found t o react with cycloalkanes. Metal ions convet the strained hydrocarbons quadricyclane^^'^^, c u b a n e ^ b i c y c l o [2.1.0]pentanes^^'^^ bicyclo[3.1.0]hexanes^^ bicyclo[4.1.0]heptanes^^ a n d bicyclobutanes^^'^^ into less strained isomers (usually cyclohexanes). CI Pyr

^ + ptc,2

. O"^'""'

^ / I' ' O Pyr

^^"^^

CI

The initial indication that open-chain alkanes can also be activated by transition-metal ions came in 1969 when P t C ^ ^ " was found t o catalyse the deuteration of alkanes in CH3COOD/D20^^. This observation stimulated a search for complexes containing simultaneously M — R and M — H bonds, but initial fahures t o observe such c o m p o u n d s a n d the observation that C — M b o n d s in transition-metal complexes have low dissociation energies (ca 2 0 - 3 0 kcal m o l " ^^^) led t o the belief that equilibria 15 a n d 16 were so strongly t o the left that isolation of the oxidative addition products would be impossible^^. R

(15)

(16)

Stable alkyl hydride complexes of the type shown in equation 15 were eventually synthesized by photolysis of hydride^^ a n d carbonyl^^ complexes of iridium in h y d r o c a r b o n solvents. These alkyl hydride complexes are surprisingly stable (alkane is eliminated at 110°C). (c-C5Me5)Ir(PMe3)H2 ^ ( c - C 5 M e 5 ) I r ( P M e 3 ) ( R ) ( H ) + H2

(17)

The reaction in equation 17 shows little selectivhy. T h e 16-electron intermediate

541

11. Acidity a n d basicity

produced by elimination of H2 in the photolysis is very reactive a n d attacks all C — H bonds b u t with a slight preference for primary carbons, probably due t o steric effects. The CH4 complex has been formed in a matrix at 1 2 K showing that there is essentially no barrier for addition to C—H^^. The gas-phase addition of monopositive transition-metal ions t o both C — H a n d C — C bonds of alkanes is currently a very active area of research^'*" I n the gas-phase ions M R ^ , the alkyl groups assist in delocalizing the positive charge^^^-^^^ a n d the M — R bond energy is considerably larger than in the valence saturated L„M(R)(H)^ ions where steric interactions with the ligands L weaken the M — R bond^^'^^^. Accurate 'intrinsic' b o n d energies are n o w avahable for many M — R bonds ^^^'^^^ in gas-phase ions, a n d the reactions of transition-metal ions with alkanes as a function of the kinetic energy of the ions have been studied extensively. W h h methane, transition-metal ions undergo oxidative addition to give the methyl hydride. T h e subsequent chemistry depends upon the initial energy of the ion. At low energies H2 is eliminated through a 4-centre reaction (equation 18a) while at higher energies homolytic b o n d fission occurs a n d H or, more commonly, CH3 is lost (equation 18b). H

M;

;H

-*•

M'''=CH2

+

H2

(18a) CH,

high energy..

-H+

4- CH3

(18b) -CH,

-h H

W h h larger alkanes the metal ion can interact with either a C — H bond or with C — C bond. Insertion into a C — H bond of ethane forms the ethyl hydride which, at high energies, loses an ethyl radical. At lower energies a j5-hydrogen shift occurs a n d the ethylene-coordinated dihydride is formed. This complex then eliminates H2 o r C2H4(equations 19a a n d 19b). + Ho

C2H4

(19a) M"^ +

CgHg

MCH, high energy

MH"^

+

C2H5

(19b)

542


Addition to the C — C b o n d resuUs in ehmination of methane through a 4-centre reaction. At higher energies the — C H 3 b o n d is broken (equation 20a and 20b).

CH3

=CH2 + CH4 ( 2 0 a )

CH,

-CH3 + CH3

(20b)

Higher alkanes undergo exothermic gas-phase reactions with some transition-metal ions. C o ^ and N i ^ insert into the C — C and C — H bonds of p r o p a n e t o give oxidative addition products which eliminate CH4 a n d H2, respectively. T h e relative a m o u n t of methane formed increases with the a m o u n t of branching in the alkane^^^. L a F e ^ reacts with alkanes (except methane) giving mainly dehydrogenation products, b u t with some C — C cleavage, particularly in reactions w h h cyclopropane and cyclobutane III. ACIDITY A. General

Alkanes are extremely weak acids. They are saturated molecules and, since in the case of first-row elements, t o possess more than a n octet of electrons occurs only in very unusual circumstances, they are n o t prone t o nucleophilic attack by even the strongest of bases, i.e. they d o n o t function as Lewis acids. They d o function as Bronsted acids, but only under extreme conditions. The non-polarity of the C — H b o n d makes alkanes very ineffective at hydrogen bonding a n d loss of the proton leaves a carbanion which is unable t o delocalize the excess negative charge. I n the gas phase this instability results in m a n y of the smaher alkyl anions spontaneously losing a n electron t o form alkyl r a d i c a l s T h e extremely short lifetimes of these anions in the gas phase makes measurement of proton-transfer equhibria impossible and accurate assessment of acidities becomes difficult. B. Acidities of Alkanes in Solution

Metal salts of alkanes, e.g. RLi, have long been used as sources of carbanions R~ in synthetic organic chemistry^ ^"^"^^^ and metalation of a carbon acid R'H by a n o r g a n o lithium c o m p o u n d RLi gives a measure of the relative acidities of alkanes R H a n d R H ' (equation 21). Unfortunately this metalation reaction is not quite so simple because b o t h RLi a n d R'Li usuahy exist as aggregates, even in coordinating s o l v e n t s ^ a n d in the gas phase RLi + R H

. R H + R'Li

(21)

11. Acidity a n d basicity

543

Relative stabilities of carbanions can be assessed from exchange reactions of organo metallic compounds containing these anions^^'^'^^^. F r o m N M R measurements of equilibria involving R2Mg and R^Hg and from the polarographic reduction of mercury alkyls^^^, it has been deduced that the stability of the carbanion increases with the a m o u n t of s-character in the orbital formally holding the lone pair, i.e. sp > sp^ > sp^. F o r ions in which the carbanionic carbon is formally sp^ a n d sp^ hybridized, the order of stabhity is phenyl ^ vinyl > cyclopropyl > methyl > ethyl > isopropyl > r-butyl order of stabihty is ihustrated by the basicity of the butyllithiums^^^. 5^c-Butyllithium removes a p r o t o n from ahyl ethers whereas n-butyhithium does not^^^; a n d r-butyllithium is even more basic a n d whl remove a proton from methyl vinyl ether There are two solvent systems commonly used in measuring the relative acidities of weak acids, leading to two acidity scales. In cyclohexylamine cesium salts R ' C s " ^ exist as contact ion pairs of the type usually used in organic reactions a n d the transmetalation reaction in equation 21 (using cesium as the metal rather t h a n lithium) is used to measure an ion-pair acidity scale^^^ In D M SO there is httle or n o ion pairing a n d equhibria measured in this solvent lead to an ionic acidity scale^^^"^^^. Unfortunately the pJ^^ values of cyclohexylamine (41.6) a n d D M S O (35) are much lower t h a n the pK^ values of alkanes (estimated to be ca 50) a n d direct measurements of equilibria involving alkanes are not possible. Differences in gas-phase acidities are similar to those in D M S O and, by comparing the gas-phase acidities of CH„(CN)^, where m-\-n = 4 a n d m takes values from 0 to 2, the pK^ of methane has been estimated to be 56^^^. Aqueous pK^ values of methane a n d ethane have been estimated to have values ranging from 40 to ^Qi 14,135-137 using ab initio molecular orbital calculations to calculate the deprotonation energy a n d calculating solvation energies from M o n t e Carlo statistical mechanics or molecular dynamic simulations, Jorgensen a n d coworkers^^^'^^^ have calculated the aqueous pK^ of ethane to be 50.6 ± 0.2 and, in a different study, 52 ± 2.

117,127,128

j^^^

C. Gas-phase Acidities

It is customary to characterize the acidities of molecules in the gas phase by using enthalpies, AH^^^^, rather than free energies or pK^ values. The acidity of an acid R H is given by equation 22 where A//,,id(RH) = AH,{R-) + A//f(H+) - AHf(RH). D a t a for many organic acids have recently been tabulated^^'^^^'^"^^ b u t there are few data for the unsubstituted alkanes. Standard methods of generating anions, dissociative electron attachment a n d chemical ionization reactions involving deprotonation, substhution a n d elimination are useful in generating delocalized c a r b a n i o n s b u t in general produce little (with CH4) or no alkyl a n i o n s T h i s stems in part from the difficulty of finding bases sufficiently strong to remove a p r o t o n from an unactivated C — H bond^^"^ a n d in part from the instability of the alkyl anions towards loss of an electron (equation 23). The ethyl, isopropyl, isobutyl, t-butyl, cyclobutyl, cyclopentyl a n d cyclohexyl anions are ah believed to be produced by collision-induced decarboxylation of R C O O ~ However, these anions were not detected and, on the basis of calculated flight times for an ion to the ion multiplier, an upper limit of 25 ps has been set for the lifetimes of these carbanions^^^'^^^ RH

.R

+H+

R-

>R + e

(22) (23)

The methyl radical has a smah electron affinity (1.8 ± 0.7 kcal mol ~^ ^'^^) a n d this has been combined with the b o n d dissociation energy (BDE) of methane a n d the ionization potential of H atoms to give the enthalpy for the deprotonation of methane using the thermochemical cycle (equation 24). F o r most alkyl radicals the electron affinities are


544

probably negative and are not known, and the thermochemical cycle a p p r o a c h cannot be used. CH4

>CH3 +

CH3

+ e ^CH3^H+ + e

H CH4

>Cn^-

H

B D E = 105 kcal m o l - 1 -EA= -2kcalmor' IP = 3 1 4 k c a l m o r i A//,,ID = 417kcal m o l - 1

(24)

Alkyl anions have been implicated as intermediates stabilized by a neutral molecule. Alkoxide ions when photolysed in a pulsed I C R spectrometer dissociate into alkanes and enolate anions^"^^. The intermediate 19 in equation 25 can be represented by two possible extremes. In 19a the alkyl anion R - is 'solvated' by a ketone and inl9b the radical anion of the ketone is solvated by the radical R. The structure of this intermediate wih then depend on the relative electron affinities of the alkyl group R and the ketone. B r a u m a n and cohaborators^"^^'^"^^ photolysed a series of 2-substituted-2-propoxides (18 with R' = C H 3 , R" = H and R varied). F o r substituents R = C F 3 , H, P h and H 2 C = C H , the C — R b o n d dissociation energies for homolytic fission are larger than the C — C H 3 b o n d energy, i.e. if the intermediate complex has the structure 19b then methane would be expected to be produced. Conversely, since these R groups form more stable anions t h a n C H 3 , decomposition via 19a should result in R H . The experimental observation that only R H is formed led to the conclusion that 19 is best described by the solvated alkyl anion structure 19a.

0"

I -C-

R" -CH2R"

CH2R (19A)

R'^ ;C=CHR"

(25)

0" R' (18)

(20) p//

"^CHaR"

+ RH

(19B)

The relative leaving abhities as determined by the decomposition of alkoxides are C F 3 > P h > H > t-Bu > M e > i-Pr > Et. Assuming that the intermediate has structure 19a, this order reflects the relative stabhhies of the ( R - - k e t o n e ) complexes and provides an estimate of the relative acidities of the alkanes. D e P u y and coworkers^^^'^"^^ have established the same order of acidity for alkanes by examining the preferred modes of decomposition of the 5-coordinate silicon anions^^^'^^^ formed by the reaction of O H " with ( C H 3 ) 3 S i R . By analogy with the reaction of F " the initial step is believed to be formation of the complex 21 which can either expel C H 3 - or R " . The exothermicity of the initial addition reaction is insufficient to allow expulsion of an alkyl anion and heterolysis of an S i — C b o n d results in the solvated ion 22a or 22b (Scheme 1). Rapid p r o t o n transfer within this ion-molecule complex leads to the irreversible formation of R H or C H 4 . Molecular orbital calculations^^^'^^^ show the five-coordinate silicon anion 21 (R = C H 3 ) to be at a minimum and the transition structure for decomposhion of 21 has C H 3 - almost completely removed while the p r o t o n of the O H group is only slightly perturbed. The branching ratios found for the decomposition of the five-coordinate anions provide a kinetic method for estimating alkane acidities. In principle this method can be applied

11. Acidity and basicity

545

(HjOsSiR OH-

OH

(HxOo

Si

CH,

R

(21)

OH

OH

I

SI

(H3C)2^

{H^C){ ^ C H j

CH3-

R"

(22b) (22a)

(HjOjSIO" + RH

(H3C)2RSiO

+

CH4

SCHEME 1

to any hydrogen in a hydrocarbon, providing the appropriately substituted R S i M e 3 can be synthesized, although several assumptions have to be m a d e in the analysis. The decomposition of 21 into 22 can be considered as a two-step reaction, homolytic bond dissociation followed by electron transfer to R or CH3. Assuming that the neutral fragments M e 3 S i O H and M e 2 R S i O H have the same electron affinhies, then the difference in enthalpies AA/f^^g by the two pathways is given by equation 26. The branching ratio for formation of R H and CH4 is then assumed to be related to AA//^_^g by a linear free energy relationship, ln(/ci//c2)oc AA//^_^g. AA//,

= [ B D E ( R — S i ) - B D E ( M e — S i ) ] - [EA(R) - EA(CH3)]

(26)

The difference in acidities AA//^^.^, taken from the thermochemical cycle in equation 24, is given by difference in C H 3 — H and R — H b o n d dissociation energies and the difference in the electron affmities. Equations 26 and 27 are similar and, assuming that C — S i dissociation energies very in a simhar way to C — H dissociation energies, then AA//^^gOcAA//^^.^, and \n{kJk2) = pAAH^^.^, i.e. log(RH/CH4) can be used to calculate the relative acidities. The proportionality constant, j5, was calculated from the branching ratio from M e 3 S i P h and from independent acidity measurements on methane and benzene. The kinetic acidities calculated using the value of j5 are listed in Table 2. These whl be discussed shortly after describing a third gas-phase technique in which free alkyl anions are generated^ ^^âcid = [ B D E ( R — H ) - B D E ( M e — H ) ] - [EA(R) - EA(CH3)]

(27)

546


Alkyl anions in the gas phase have been generated by collision-induced decarboxylation of carboxylate anions.

RCO2

>R +CO2

(28)

M a n y of the alkyl anions are not detected as they immediately lose an electron. In fact these ions m a y never exist; the electron may be lost as the CO2 is breaking away from the hydrocarbon fragment. M a n y carbanions have been detected from reaction 28 but most of them are stabilized by substituents a n d whl not be considered here^^^ A m o n g the saturated carbanions detected were the fragile methyl anion, and primary alkvl anions:

CH3CH2CH(CH3)CH2", (CH3)2CHCH2CH2-

and (CU^)^CCU2-

Cyclopropyl,

methylcyclopropyl a n d bridgehead [l.l.l]bicyclopentyl anions were also observed. Acidities of the hydrocarbons can be calculated from threshold energies (Ej), assuming there is essentially no barrier to the dissociation a n d using the following thermochemical cycle:

RC02~

>R +CO2

RCOOH R H -h CO2 RH

>

AHÊj

RCO2 + H + > RCOOH

> R- + H +

A//,,id(RCOOH) AH = A/ff(RCOOH) - A/f^(RH) - A//f(C02) A//^,id(RH) = sum of terms from above

(29)

It is only possible to carry out a limited comparison between the two sets of experi mental acidities in Table 2. F o r the less acidic hydrocarbons the radicals, R, have negative electron affinities and the anions, R " , are not observed in the decarboxylation experiments. F o r deprotonation of cyclopropane, neopentane a n d methylcyclopropane (secondary H) agreement is within experimental error, but for removal of the methyl p r o t o n of methylcyclopropane there is a large disagreement. P r o t o n affinities calculated from ab initio molecular orbital c a l c u l a t i o n s u s i n g the isodesmic reaction in equation 30 a n d assuming the p r o t o n affinity of C H 3 - to be 416.6 kcal m o l " ^ are generally in good agreement with the experimental values a n d are closer to those from the silicon anion work. RH + CH3-

.R

+CH4

(30)

The overah order of alkane acidities deduced from the decomposition of shicon anions is the same as that obtained from the decomposition of alkoxides ^^^'^"^^. T h e ethyl anion has the highest p r o t o n affinity, i.e., ethane is the weakest acid. T h e acidities of p r o p a n e (secondary hydrogen) a n d of cyclobutane are both lower than that of methane, b u t all other alkanes are more acidic. T h e acidity of methane is particularly enhanced by a cyclopropyl substituent a n d by a t-butyl group. It is interesting to examine the effect of a- a n d j5-methyl substitution on the acidity of methane. O n e a-methyl group decreases the acidity of methane, two a-methyl groups also decrease the acidity but by a smaher a m o u n t and the three a-methyl groups of the isobutane actually increase the acidity. (This last result is at odds with the theoretical results.) The effects of j5-methyl groups are more systematic. Ethane has the largest AH^^.^ value (420.1 kcal m o l " ^) and introduction of successive j5-methyl groups decrease this value by decrements of 4.5, 2.7 a n d 4.0 kcal m o l " ^ Alcohols are intrinsically much more acidic than the alkanes, but their acidities fohow a simhar pattern on j^-substitution by methyl groups. AH^^.^ values (in kcal m o l - ^ ) are methanol 380.6, ethanol 377.4, isopropanol 375.4 and t-butanol 374.6^^, i.e. each j5-methyl group decreases AH^^.^ by approximately 2 kcal mol " ^ The effect of jS-methyl groups is larger in the carbanions

547

11. Acidity and basicity TABLE 2.

AH^.id

values for alkanes" Experimental AH ^,,(RH) from

Anion generated Ethyl Isopropyl Cyclobutyl Methyl Cyclopentyl sec-Butyl n-Propyl t-Butyl ISO-Butyl

Cyclopropyl [l.l.lJBicyclopentyl Cyclopropylmethyl 1 -Methylcyclopropyl 2-Methylcyclopropyl Neopentyl Phenyl

Calculated proton affinities"

silicon anion''

carboxylate anion''

420.1 419.4 417.4 (416.6)'* 416.1 415.7 415.6 413.1 412.9 411.5

no anion no anion other products 418 + 3.5 no anion

422.2 422.5 421.2 417.8-^, 418.5^

—

421.9 419.3 419.6

— 410.5 409.2

— 408.9 (400.7)^*

no anion no anion no anion 408 + 5 411 + 3.5 391 + 6 413 + 3.5 411 + 5 411 + 10 401 + 10

412.6

— 413.9

— — — —

"All values in kcal mol ''Reference 113; errors are + 1 kcal m o l " ^ 'Reference 112. ''Used as reference acids in constructing acidity scale. "Reference 109. ^Reference 33. ^Reference 153.

due to the greater inability of C H 2 " to carry the negative charge, and there is more delocalization by negative hyperconjugation^^"^ onto the j5-methyl groups. Finahy, h is necessary to assess the validity of the theoretical acidities. In order to describe the loosely b o u n d outer electrons of carbanions correctly, it is necessary to augment the usual gaussian basis sets with additional s and p functions on carbon^ The 4-31 + G basis set used to calculate the p r o t o n affinities in Table 2 is then about the minimum acceptable by today's standards. Theory agrees with experiment in predicting that ethane and cyclobutane are the two least acidic alkanes. However, theory also predicts all the open-chain alkyl anions to have higher p r o t o n affinities than C H 3 " , in disagreement with experiment^ One possible reason for this difference is that, in the experimental work, anions R~ are never generated as free ions but exist only in ion-molecule complexes and that their complexed ions have different relative stabhities than the free ions. If this is the situation, then it is not clear why 'solvation' of the more substituted ions is more exothermic than solvation of the unhindered parent ion C H j " . Furthermore, the qualitative agreement between the relative acidities from decomposition of very different classes of anions a m o n g alkoxide ions^""^ and shicon a n i o n s ^ l e n d s credence to the conclusion on relative acidities. The HF/4-31 + G level of theory is small and extension of the basis set and inclusion of correlation energy, which supposedly cancels in isodesmic reactions like equation 30, may significantly change the overall conclusion. Also, some of the larger carbanions examined theoreticahy have negative electron a f f i n i t i e s ^ a n d adequate theoretical description of these u n b o u n d

548


anions may be difficult, if not impossible. The theoretical results should then be treated with some caution. IV. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30 31. 32. 33. 34. 35. 36. 37. 38. 39. 40 41. 42. 43. 44. 45. 46. 47.

REFERENCES

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11. Acidity and basicity 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93.

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P. Vogel, Carbocation Chemistry, Elsevier, Amsterdam, 1985. W. Koch, B. Liu and P. v. R. Schleyer, J. Am. Chem. Soc, 111, 3479 (1989). H. Lischka and H. J. Kohler, J. Am. Chem. Soc, 100, 5297 (1978). W. Hehre, L. Radom, P. v. R. Schleyer and J. A. Pople, Ab Initio Molecular Orbital Theory, Whey-Interscience, N e w York, 1986. M. J. S. Dewar, E. A. Healy and J. M. Ruiz, J. Chem. Soc, Chem. Commun., 943 (1987). N. G. Adams, D. Smith, M. Tichy, G. Javahery, N. D. Twiddy and E. E. Ferguson, J. Chem. Phys., 91, 4037 (1989). M. Tichy, G. Javahery, N. D. Twiddy and E. E. Ferguson, Int. J. Mass. Spectrom. Ion Phys., 93, 165 (1989). D. K. Bohme, G. I. Mackay and H. I. Schiff, J. Chem. Phys., 73, 4976 (1980). S. G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D . Levin and G. W. Mahard, J. Phys. Chem. Ref. Data, 17, Suppl. 1 (1988). T. B. McMahon and P. Kebarle, J. Am. Chem. Soc, 107, 2612 (1985). I. Santos, D. M. Balogh, C. W. Doecke, A. G. Marshah and L. Paquette, J. Am. Chem. Soc, 108, 8183 (1986). D . A. Dixon and S. G. Lias, in Molecular Structure and Energetics (Eds. J. F. Liebman and A. Greenberg), Vol. 2, Chap. 7, VCH Publishers, Inc., N e w York, 1987. O. Aschan, Justus Liebigs Ann. Chem., 1, 324 (1902). A M. McAffee, Ind Eng. Chem., 1, 131 (1915). P. L. Fabre, J. Devynck and B. Tremihon, Chem. Rev., 82, 591 (1982). J. C. Culmann and J. Sommer, J. Am. Chem. Soc, 111, 4057 (1990). The widely accepted definition of a superacid is an acid system that is stronger than 100% H2SO4. R. J. Gillespie and T. E. Peel, Adv. Phys. Org. Chem., 9, 1 (1972). H. Hogeveen and C. J. Gaasbeek, Reel. Trav. Chim. Pays-Bas, SI, 319 (1969). J. W. Otvos, D. P. Stevenson, C. D. Wagner and O. Beeck, J. Am. Chem. Soc, 73,5741 (1951). D. P. Stevenson, C. D. Wagner, O. Beeck and J. W. Otvos, J. Am. Chem. Soc, 74,3269 (1952). J. W. Larsen, J. Am. Chem. Soc, 99, 4379 (1977). T. H. Ledford, J. Org. Chem., 44, 23 (1979). R. J. Gillespie and G. P. Pez, Inorg. Chem., 8, 1233 (1969). H. Hogeveen, C. J. Gaasbeek and A. F. Bickel, Reel. Trav. Chim. Pays-Bas, 88, 703 (1969). J. W. Larsen, P. A. Buis, C. R. Watson Jr. and R. M. Pagni, J. Am. Chem. Soc, 96,2284 (1974). J. E. McMurry and T. Leckta, J. Am. Chem. Soc, 112, 869 (1990). J. E. McMurry, T. Leckta and C. N. Hodge, J. Am. Chem. Soc, 111, 8867 (1989). Calculations by E. R. Vorpagel, reported in Reference 74. C. F. H. Tipper, J. Chem. Soc, 2043 (1955). D. M. Adams, J. Chatt, R. Guy and N. Sheppard, J. Chem. Soc, 738 (1961). M. Keeton, R. Mason and D. R. Russeh, J. Organomet. Chem., 33, 259 (1961). H. Hogeveen and R. J. Nusse, Tetrahedron Lett., 159 (1974). L. Cassar and J. Halpern, J. Chem. Soc, Chem. Commun., 1082 (1971). L. Cassar, P. E. Eaton and J. Halpern, J. Am. Chem. Soc, 92, 3315 (1970); 92, 6366 (1970). L. A. Paquette, R. A. Boggs, W. B. Farnham and R. S. Beckley, J. Am. Chem. Soc, 97, 1112 (1975). P. G. Gassman, T. J. Atkins and J. T. Lumb, J. Am. Chem. Soc, 94, 7757 (1972). K. B. Wiberg and R. C. Bishop, Tetrahedron Lett., 2727 (1973). K. C. Bishop, Chem. Rev., 76, 461 (1976). M. Sakai and S. Masamune, J. Am. Chem. Soc, 93, 4610 (1971). L. A. Paquette and G. Zon, J. Am. Chem. Soc, 96, 203 (1974). N. F. Goldschleger, M. B. Tyabin, A. E. Shhov and A. A. Shteinman, Zh. Fiz. Khim., 43, 2147 (1969). J. Halpern, Acc Chem. Res., 15, 238 (1982) and references cited therein; J. Halpern, Inorg. Chim. Acta, 100, 41 (1985). For an excellent review see R. H. Crabtree, Chem. Rev., 85, 245 (1985). A. H. Janowicz and R. G. Bergman, J. Am. Chem. Soc, 104, 352 (1982); 105, 3929 (1983). J. K. Hoyano and W. A. G. Graham, J. Am. Chem. Soc, 104, 3273 (1982). A. J. Rest, I. Whitwell, W. A. G. Graham, J. K. Hoyano and A. D . McMaster, J. Chem. Soc, Chem. Commun., 624 (1984).

550 94. 95. 96. 97. 98. 99. lOO 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143.

A. C. H o p k i n s o n M. A. Tolbert and J. L. Beauchamp, J. Am. Chem. Soc., 106, 8117 (1984). L. S. Sunderhn and P. B. Armentrout, J. Phys. Chem., 92, 1209 (1988). L. S. Sunderlin, N. Aristor and P. B. Armentrout, J. Am. Chem. Soc, 109, 78 (1987). Y. Huang, M. B. Wise, D. B. Jacobson and B. S. Frieser, Organometallics, 6, 346 (1987). N. Aristor and P. B. Armentrout, J. Phys. Chem., 91, 6178 (1987). R. Georgiadis and P. B. Armentrout, J. Phys. Chem., 92, 7060 (1988). R. H. Schuhz, J. L. Elkind and P. B. Armentrout, J. Am. Chem. Soc, 110, 411 (1988). J. B. Schhhng and J. L. Beauchamp, J. Am. Chem. Soc, 110, 15 (1988). L. S. Sunderhn and P. B. Armentrout, J. Am. Chem. Soc, 111, 3845 (1989). R. Georgiadis, E. R. Fisher and P. B. Armentrout, J. Am. Chem. Soc, 111, 4251 (1989). Y. Huang and B. S. Freiser, J. Am. Chem. Soc, 110, 387 (1988). P. Armentrout and J. L. Beauchamp, J. Am. Chem. Soc, 103, 784 (1981). M. L. Mandich, L. F. Hahe and J. L. Beauchamp, J. Am. Chem. Soc, 106, 4403 (1984). F. T. T. Ng, G. L. Rempel and J. Halpern, Inorg. Chim. Acta, 11, L165 (1983). P. B. Armentrout and J. L. Beauchamp, Acc. Chem. Res., 22, 315 (1989). P. V. R. Schleyer, G. W. Spitznagel and J. Chandrasekhar, Tetrahedron Lett., 27,4411 (1986). S. T. Graul and R. R. Squires, J. Am. Chem. Soc, 110, 607 (1988). S. T. Graul and R. R. Squires, J. Am. Chem. Soc, 112, 2506 (1990). S. T. Graul and R. R. Squires, J. Am. Chem. Soc, 112, 2517 (1990). C. H. DePuy, S. Gronert, S. E. Barlow, V. M. Bierbaum and R. Damrauer, J. Am. Chem. Soc, 111, 1968 (1989). D. J. Cram, Fundamentals of Carbanion Chemistry, Academic Press, N e w York, 1965. E. Buncel, Carbanions: Mechanistic and Isotopic Aspects, Elsevier, Amsterdam, 1975. E. Buncel and T. Durst (Eds.), Comprehensive Carbanion Chemistry, Part A, Structure and Reactivity, Elsevier, Amsterdam, 1980. R. B. Bates and C. A. Ogle, Carbanion Chemistry, Springer-Verlag, Berhn, 1983. J. C. Stoweh, Carbanions in Organic Synthesis, Wiley-Interscience, N e w York, 1979. F. Hartley and S. Patai (Eds.), The Chemistry of the Carbon-Metal Bond, Wiley-Interscience, Chichester, 1985, Vols. 1 and 2. B. J. Wakefield, The Chemistry of Organolithium Compounds, Pergamon, Oxford, 1974. P. West and R. Waack, J. Am. Chem. Soc, 89, 4395 (1967). L. M. Seitz and T. L. Brown, J. Am. Chem. Soc, 88, 2174 (1966). K. C. Wihiams and T. L. Brown, J. Am. Chem. Soc, 88, 4134 (1966). L. D . McKeever, R. Waack, M. A. Doran and E. B. Baker, J. Am. Chem. Soc, 91,1057 (1969). E. Kaufmann, K. Raghavachari, A. E. Reed and P. v. R. Schleyer, Organometallics, 1, 1597 (1988). J. Berkowitz, D. A. Bafus and T. L. Brown, J. Phys. Chem., 65, 1380 (1961). R. E. Dessy, W. Kitching, T. Psarras, R. Salinger, A. Chen and T. Chi vers, J. Am. Chem. Soc, 88, 460 (1966). D . E. Applequist and D. F. O'Brien, J. Am. Chem. Soc, 85, 743 (1963). D. A. Evans, G. C. Andrews and B. Buckwalter, J. Am. Chem. Soc, 96, 5560 (1974). J. E. Baldwin, G. A. Hofle and O. W. Lever, Jr., J. Am. Chem. Soc, 96, 7125 (1974). A. Streitwieser, Jr., E. Juaristi and L. L. Nebenzahl, in Reference 116. F. G. Bordwell, Acc Chem. Res., 21, 456 (1988). R. W. Taft and F. G. Bordwell, Acc Chem. Res., 21, 463 (1988). F. G. Bordweh and D . J. Algrim, J. Am. Chem. Soc, 110, 2964 (1988). R. Stewart, The Proton: Applications to Organic Chemistry, Academic Press, N e w York, 1985. B. Juan, J. Schwarz and R. Breslow, J. Am. Chem. Soc, 102, 5741 (1980). K. P. Butin, I. P. Beletskaya, A. N. Kashin and O. A. Reutov, J. Organomet. Chem., 10, 197 (1967). W. L. Jorgensen, J. M. Briggs and J. Gao, J. Am. Chem. Soc, 109, 6857 (1987). W. L. Jorgensen and J. M. Briggs, J. Am. Chem. Soc, 111, 4190 (1989). J. E. Bartmess and R. T. Mclver, in Gas Phase Ion Chemistry (Ed. M. T. Bowers), Vol. 2, Chap. 11, Academic Press, New York, 1979. G. Boand, R. Houriet and T. Gaumann, J. Am. Chem. Soc, 105, 2203 (1983). C. H. DePuy and V. M. Bierbaum, Acc Chem. Res., 14, 146 (1981). J. G. Dillard, Chem. Rev., 73, 589 (1973).

11. Acidity and basicity 144. 145. 146. 147. 148. 149. 150 151. 152. 153. 154. 155. 156.

551

D. K. Bohme, E. Lee-Ruff and L. B. Young, J. Am. Chem. Soc, 94, 5153 (1972). G. B. Ehison, P. C. Engelking and W. C. Lineberger, J. Am. Chem. Soc, 100, 2556 (1978). E. M. Arnett, L. E. Smah, R. T. Mclver and J. S. Miher, J. Org. Chem., 43, 815 (1978). W. Tumas, R. F. Foster, M. J. Peherite and J. I. Brauman, J. Am. Chem. Soc, 105,7464 (1983). W. Tumas, R. F. Foster and J. I. Brauman, J. Am. Chem. Soc, 106, 4053 (1984). C. H. DePuy, V. M. Bierbaum and R. Damrauer, J. Am. Chem. Soc, 106, 4051 (1984). J. C. Sheldon, R. N. Hayes, J. H. Bowie and C. H. DePuy, J. Chem. Soc, Perkin Trans. 2, 275 (1987). L. P. Davis, L. W. Burggraf and M. S. Gordon, J. Am. Chem. Soc, 110, 3056 (1988). C. H. DePuy, V. M. Bierbaum, R. Damrauer and J. A. Soderquist, J. Am. Chem. Soc, 107, 3385 (1985). M. R. F. Siggel, T. D. Thomas and L. J. Saethre, J. Am. Chem. Soc, 110, 91 (1988). P. V. R. Schleyer and A. J. Kos, Tetrahedron, 39, 1141 (1983). J. Chandrasekhar, J. G. Andrade and P. v. R. Schleyer, J. Am. Chem. Soc, 103, 5609 (1981). G. W. Spitznagel, T. Clark, J. Chandrasekhar and P. v. R. Schleyer, J. Comput. Chem., 3, 363 (1982).

CHAPTER

12

Alkanes: modern synthetic methods GOVERDHAN MEHTA School of Chemistry, University of Hyderabad, Hyderabad-500 134, India and Jawaharlal Nehru Centre for Advanced Scientific Research, Indian Institute of Science Campus, Bangalore-560012, India

AND H. S U R Y A P R A K A S H R A O Department

of Chemistry,

Pondicherry-605014,

Pondicherry

University,

India

L INTRODUCTION II. F U N C T I O N A L G R O U P T R A N S F O R M A T I O N S A. Alkenes, Arenes, Alkynes and Strained Molecules 1. General aspects 2. Catalytic hydrogenation a. Hydrogenation under heterogeneous conditions b. Hydrogenation under homogeneous conditions 3. Transfer hydrogenation 4. Ionic hydrogenation 5. H y d r o b o r a t i o n - p r o t o n o l y s i s 6. Borides and aluminides 7. Chemical reduction 8. Hydrogenolysis of cyclopropanes and other strained molecules 9. Oligomerization B. Alcohols and Related Derivatives 1. Direct reduction 2. Indirect reduction a. Sulphonate esters b. Intermediate iodides c. Carboxylic acid esters

554 555 555 555 555 555 557 558 559 559 559 560 561 562 562 562 562 562 563 564


553

554

HI.

IV.

V. VI. VII. VHI. IX.

G. M e h t a a n d H. S. P. R a o d. Thiocarbonates ( B a r t o n - M c C o m b i e reaction) and phosphate esters 3. Sulphur c o m p o u n d s 4. Selenium c o m p o u n d s C. Alkyl Halides 1. General aspects 2. Hydrogenolysis 3. Low-valent metals 4. Metal hydrides 5. Electrochemical methods 6. Organometallics a n d miscellaneous reagents D. Aldehydes, Ketones a n d Related C o m p o u n d s 1. General aspects 2. Direct reduction 3. Reduction of hydrazones (Wolff-Kishner a n d Caghoti reductions). 4. Thioacetalization-desulphurization (Mozingo reaction) . . . . 5. Reductive alkylation E. Carboxylic Acids a n d Related C o m p o u n d s 1. Indirect method 2. Thermal decarboxylation 3. Photodecarboxylation F. Miscehaneous 1. Amines a n d isocyanides 2. Nitrhes 3. N i t r o c o m p o u n d s COUPLING REACTIONS A. Alkali Metals (Wurtz Coupling) B. Grignard and Related Reagents C. Transition Metal Reagents D. O r g a n o b o r a n e s a n d Organoalanes E. Kolbe Electrolysis F. Photochemical Reaction CYCLIZATIONS A. Radical Cyclization B. Organometallic Reagents C. Solvolytic Rearrangement D. Photocyclization E. Dehydrocyclization CARBENE INSERTION REACTIONS MOLECULAR EXTRUSION REACTIONS REARRANGEMENTS ACKNOWLEDGEMENTS REFERENCES

565 567 568 568 568 569 569 570 571 572 572 572 573 574 576 577 578 578 578 580 581 581 582 582 583 583 584 585 587 587 588 588 588 589 590 590 592 593 594 597 599 600

I. INTRODUCTION

Alkanes were the favoured targets of synthesis during the early phase of the evolution of synthetic organic chemistry, as they were considered to be the simplest organic molecules. Indeed, many of the classical reactions in organic chemistry, discovered during the last century a n d early part of this century, dealt with alkane syntheses. However, as synthetic organic chemistry developed, alkanes as target structures for synthesis lost

12. Alkanes: modern synthetic methods

555

their appeal a n d their preparation began t o be motivated more a n d more for testing new reactions a n d reagents for functional group transformations rather than due t o any intrinsic interest in them. This situation began t o change in the 1950s as complex alkanes, particularly polycycloalkanes h k e tetrahedrane, cubane, dodecahedrane etc., were predicted as realizable targets by theoreticians a n d thus caught the imagination of m a n y contemporary synthetic chemists. Syntheses of cubane a n d a d a m a n t a n e in the 1960s, during the exploding phase of m o d e r n organic synthesis, helped t o rekindle interest in polycycloalkanes. This interest in polycycloalkanes has persisted ever since a n d is in the forefront of synthetic activity at present. There is a vast hterature available on alkane syntheses, particularly with regard t o functional group transformations leading t o a l k a n e s I n d e e d , almost any functional group can be transformed to an alkane with the presently avahable repertoire of synthetic methods. However, emphasis in this chapter will be on methods that directly lead t o an alkane from a given functional group. F o r the most part, only one-step transformations leading t o alkanes will be described. Thus, in the case of cycloalkanes, the last key step leading t o the target hydrocarbon a n d not the framework construction whl be the focus of attention. In the various equations a n d tables that follow, only such examples a n d reactions whl be cited, wherein the end product is a n alkane. T o duly recognize the importance of polycycloalkanes a n d t o reflect the growing interest in their syntheses, the overah account is biased in their favour. Most of the examples have been drawn from the literature that appeared in the 1975-1990 period. II. FUNCTIONAL GROUP TRANSFORMATIONS A. Alkenes, Arenes, Alkynes and Strained Molecules 1. General

aspects

Direct a n d ready access to alkanes is through chemical a n d catalytic reduction of alkenes, arenes, alkynes, cyclopropanes a n d strained polycycloalkanes. Among them alkenes a n d particularly cycloalkenes are available through a wide variety of general synthetic procedures, e.g. Diels-Alder reactions, thermal a n d photochemical electrocyclizations, etc., a n d are therefore considered as versathe precursors of the corresponding alkanes. Addhionally, alkenes are readily accessible from synthons containing functional groups hke hydroxyl, carbonyl, hahde, or alkyne which can be easily transformed into alkanes. Arenes are avahable quite abundantly from various organo-chemical feedstocks and they serve as extremely useful precursors of cycloalkanes. 2. Catalytic

hydrogenation

The most convenient a n d widely applied method for the preparation of alkanes from alkenes is catalytic hydrogenation, which can be carried o u t in either heterogeneous o r homogeneous media, with a wide choice of catalysts ranging from finely divided noble metals t o transition metal complexes. The variation in the choice of solvent, temperature, pressure a n d time provides additional latitude for dealing with structurally diverse alkenes a n d for achieving selectivity. T h e general area of catalytic hydrogenation h a s been extensively reviewed a n d updated^ ^ a. Hydrogenation under heterogeneous conditions. F o r heterogeneous hydrogenations of alkenes, catalysts based o n palladium, platinum, nickel, rhodium a n d ruthenium have been traditionally used as finely divided metals directly o r o n supports like charcoal, alumina, shica gel, norit, graphite, barium sulphate, calcium a n d strontium carbonate

G. M e h t a and H. S. P. R a o

556

a m o n g others In addition, metal oxides serve as excellent catalysts through in situ reduction to active metals during hydrogenation and platinum oxide (Adams Catalyst), palladium on charcoal and Raney nickel are some of the popular catalysts that find extensive use even in modern syntheses of alkanes. Catalytic activity of rhodium, iridium and ruthenium catalysts is considered higher t h a n that of platinum and palladium, a n d the former are used in the hydrogenation of alkenes when the latter d o not work weh^^. Table 1 presents examples of several interesting polycychc alkanes that have been synthesized by the catalytic reduction of the corresponding alkenes^^. In the preparation TABLE 1. Alkanes from the catalytic hydrogenation of alkenes Starting alkene

C104II194

Product

Reference

C104H210 (tetrahectane)

13a

13b

13c

13d

13e

13f

13f

13g

13h (continued)

12. A l k a n e s : m o d e r n s y n t h e t i c m e t h o d s

557

TABLE 1. {continued) Starting alkene

Product

Reference

13h

13i

13i

13j

of c o m p l e x p o l y c y c l o a l k a n e s , c a t a l y t i c r e d u c t i o n is u s u a l l y t h e final s t e p i n t h e s y n t h e s i s . R e c e n t l y , a n o v e l m e t h o d for t h e r e d u c t i o n o f a l k e n e s w h h p a l l a d i u m d i s p e r s e d o v e r a s i l o x a n e m a t r i x h a s b e e n r e p o r t e d I n t e r e s t i n g l y , t h e r e a c t i o n is d o n e i n a q u e o u s T H F w h e r e w a t e r m a y b e t h e s o u r c e o f h y d r o g e n ( e q u a t i o n 1).

CH3(CH2)3CH=CH(CH2)3

PD(OAC)2(ETO)3SiH

CH3COCOOCH3

n-CoH^

(1)

THF-H2O100%

b. Hydrogenation under homogeneous conditions. T h e discovery of chlorotris(triphenylphosphine)rhodium by Wilkinson heralded the era of h o m o g e n e o u s hydrogenations. Reduction of alkenes in h o m o g e n e o u s media c a n be generally accomplished under a m b i e n t c o n d i t i o n s a n d i n a variety o f o r g a n i c s o l v e n t s . B e s i d e s t e m p e r a t e c o n d i t i o n s , the m a i n virtue o f h o m o g e n e o u s r e d u c t i o n s resides i n t h e r e a l i z a t i o n o f h i g h d e g r e e s o f regio- and chemoselectivity. F o r example, terminal alkenes a n d c/5-alkenes exhibit higher rates o f r e d u c t i o n c o m p a r e d t o internal a l k e n e s a n d traws-alkenes, respectively. W h h e W i l k i n s o n ' s c a t a l y s t h a s b e e n u s e d very frequently^ ^"""^ for a l k e n e r e d u c t i o n s , m a n y c a t a l y s t s like ( P P h 3 ) 3 R u C l 2 ' ' , ( P P h 3 ) 3 l r H 2 C l ^ ^ a n d ( P P h 3 ) 3 0 s H C l ^ ' ' h a v e a l s o f o u n d useful a p p l i c a t i o n s . A s a n e x t e n s i o n o f t h e utility o f t h e s e c a t a l y s t s , it h a s b e e n o b s e r v e d t h a t h o m o g e n e o u s c a t a l y s t s , e.g. ( P P h 3 ) 3 R h - X ( w h e r e X = C1, HCI2, H2CI, CI3), ( P P h 3 ) 3 N i C l 2 , (PPh3)2PdCl2 a n d (PPh3)2NiBr2, i m m o b h i z e d o r a n c h o r e d o n silica, are m o r e effective for h y d r o g e n a t i o n o f a l k e n e s a n d arenes^^. T h u s , R h C l ( N O R ) 2 o n phosphinhated polystyrene or shica reduces benzene, toluene a n d t-butylbenzene t o the c o r r e s p o n d i n g a l k a n e i n q u a n t i t a t i v e yield ( e q u a t i o n 2)^^. T h e n i c k e l o c e n e - L i A l H 4 c o m b i n a t i o n h a s p r o v e d q u i t e useful a s a h o m o g e n e o u s h y d r o g e n a t i o n c a t a l y s t for t h e r e d u c t i o n o f a l k e n e s t o a l k a n e s ( e q u a t i o n 3)^^. I r i d i u m a n d r h o d i u m b a s e d c a t a l y s t s , e.g. [ I r ( C O D ) ( P y ) ( P C y 3 ) ] P F 6 2 ^ a n d [Rh(NOR)Ph2P(CH2)4PPh2]BF42^ h a v e p r o v e d very efficacious i n t h e d i r e c t e d s t e r e o s e l e c t i v e delivery o f h y d r o g e n t o a l k e n e s a n d f o u n d m a n y a p p l i c a t i o n s i n n a t u r a l p r o d u c t s y n t h e s e s ^ ^. A significant d e v e l o p m e n t o f far-reaching c o n s e q u e n c e is t h e d e v e l o p m e n t o f several c a t a l y s t s b a s e d o n R h a n d R u

558

G. M e h t a a n d H . S. P . R a o CH3

CH3 H2,[RhCI(N0R)]2

(2)

solid s u p p o r t , 1 0 0 %

H2, nickelocene

(3) LiAIH4,85%

for enantioselective hydrogenation of alkenes^"^. T h e most notable of them is Noyori's Ru(OAc)2(BINAP) catalyst^^ 3. Transfer

hydrogenation

In this method of hydrogenation, t h e hydrogen molecule is transferred t o a n alkene from a hydrogen d o n o r in t h e presence of catalysts like platinum, palladium o r Raney Nickel (equation 4)^^. T h e methodology a n d mechanism involved in this reaction have been reviewed recently with extensive coverage^ Reduction of hindered double b o n d s CH3(CH2)5CH=CH2

d-Limonene, 10% Pd-C

n-CH3(CH2)6CH3

(4)

with diimide (N2H2) c a n be viewed as a type of transfer hydrogenation^ The reaction of diimide with alkenes results in syn addition of hydrogen across t h e double bond. Diimide is generated in situ via decomposition of potassium azodicarboxylate, anthracene-9,10-diimine a n d hydrazine a n d its d e r i v a t i v e s ^ E x a m p l e s of polycyclic alkanes synthesized from the corresponding alkene precursors by diimide reductions are gathered in Table 2 ^ ^ TABLE 2. Alkanes from the reduction of alkenes with diimide Starting alkene

Product

Reference

28a

28b

28c

12. Alkanes: modern synthetic methods 4. Ionic

559

hydrogenation

1,1-Di-, tri- a n d tetrasubstituted alkenes can be conveniently reduced by ionic hydrogenation p r o c e d u r e s ^ ^ - ^ \ which involve the sequential delivery of a p r o t o n a n d a hydride ion. T h e p r o t o n source is usually trifluoroacetic acid or trifluromethanesulphonic acid a n d the hydride source is a trialkylshyl hydride. Thus, 3-methyl-3-hexene is quantitatively a n d rapidly reduced in high yield at — 7 8 ° C (equation 5f^. A limiting aspect of ionic reductions is that they are non-stereoselective. Reduction of 1,2-dimethylcyclohexene with EtgSiH a n d C F 3 C O O H leads t o a mixture of cis- a n d tr^w5-l,2-dimethylcyclohexanes^^. However, an advantage is that hindered a n d tetraalkyl substituted double bonds can be preferentially reduced through ionic hydrogenations^^. H3CH2C

CH3

\

/ >

/

H

=

H3CH2C CF3C00H,Et3SiH — • quant.

< \

/ ;CH—CH

/

(5) \

H

CH2CH3

5. Hydroboration-

CH3 \

CH2CH3

protonolysis

Conversion of alkenes to^ trialkylboranes a n d subsequent protonolysis by a n organic acid affords alkanes in good yields^^. Hexene could be converted t o n-hexane as shown in equation 6. However, this reaction is n o t very effective for hindered alkenes like 2,2,4,4-tetramethylpentene which furnishes only 5% of alkane o n protonolysis. B2H6,CH3CH2COOH

> n-CÛ,^

CH3(CH2)3CH=CH2

6. Borides

and

(6)

aluminides

M a n y combinations of transition metal salts with sodium borohydride o r lithium aluminium hydride p r o m o t e the reduction of alkenes a n d alkynes t o alkanes. While the exact nature of the catalytic species involved a n d the mechanism of the reduction is shrouded in uncertainty, the procedure has found m a n y useful applications in alkane synthesis^"^. F o r example, mono-, di- a n d trisubstituted alkenes are quantitatively reduced by an equimolar mixture of lithium aluminium hydride a n d transition metal hahdes^^"^^. Some of the transition metal halides which have been found t o effect the conversion of alkenes to alkanes are T i C l 3 , TiCU, VCI3, ZrCU, CrCl3, FeCl2, FeCl3, C0CI2 a n d NiCl2 (equation 7). It has been further observed that C0CI2, NiCl2 a n d TiCl3 can also be used in catalytic quantities with L A H . Alkynes can also be reduced directly t o alkanes by this procedure. T h e best reagent combination is LAH-NiCl2 from the point of view of product selectivity^^.

^'^^^^ > n-C^H^^

CH3CH2CH=CHCH2CH3

(7)

TiCl4 or ZrCl4 96%

Nickel boride (P — 2) generated from nickel acetate a n d N a B H 4 in ethanol exhibits notable selectivity in reduction depending on the substitution pattern of the alkene^"^. Sodium borohydride with Co(II) has also proved to be of general utihty for the reduction of various alkenes a n d alkynes (equation 8)^^'^^.

NoBH4,CoC[2-6H20 Et0H,987o

^

/

^

(8)

560 7. Chemical

G. M e h t a a n d H . S. P . R a o reduction

Alkenes can be reduced t o alkanes by dissolving metal reductions. S o d i u m / ^ B u O H reduces terminal alkenes t o alkanes in fairly good yield in t h e presence of iV,Ar-diethylacetamide (DEA) (equation 9)"^^, o r hexamethylphosphoric triamide'^^ Di- a n d trisubstituted olefins are resistant t o reduction under these conditions. NAA-BUOH

CH3(CH2)3CH=CH2 D E A OR H M P T , 9

n-CeH,4

(9)

Tetrasubstituted alkenes c a n be reductively alkylated with tetramethylshane o r tetramethylstannane and trifluoroacetic acid in the presence of Lewis acids, e.g. AlBr3'^^. Thus, alkanes with quaternary carbon centres can be generated by this procedure in moderate yields (equation 10).

CH3 Me4Si

or

Me4Sn

(10)

C F 3 C O O H , AIBr3,35%

Alkynes can be directly reduced t o alkanes by the treatment of terminal alkynes with dhsobutylaluminium hydride (DIBALH) in the presence of metahocenes like Cl2TiCp2 or Cl2ZrCp2. O n quenching the 1,1-dimetahoalkane intermediates with D2O, terminally deuteriated alkanes are obtained (equation 11)"^^. DIBALH, CKTICP,

CH3(CH2)4C=CH

^^J^^

' ) n-C5HIICH2CHD2

TABLE 3. Reductive opening of cyclopropanes to sterically crowded alkanes and polycycloalkanes Starting alkane

Product

Reference

44a

44b

44b

44c

44d

(11)

12. Alkanes: modern synthetic methods 8. Hydrogenolysis

of cyclopropanes

and other

strained

561

molecules

The strain release associated with cleavage of cyclopropanes a n d cyclobutanes offers the possibility of construction of many theoretically interesting alkanes. I n this context, reductive opening of cyclopropanes is a frequently used protocol for assembhng diverse polycyclic alkanes. Syntheses of a few sterically crowded alkanes from their cyclopropane precursors are shown in Table 3^"^. Hydrogenolysis of spiro-fused cyclopropane rings constitutes a simple procedure for the generation of cycloalkanes with a g m - d i m e t h y l group (equation 12). Hydrogenolysis of strained polycycloalkanes with multiple cyclobutane rings, viz. cubane, homocubane, basketane, lead t o m a n y interesting polycyclic alkanes. A few examples are shown in Table 4"^^. H2,Pd—C (CH2)„

(CH2)„

quant.

(12)

TABLE 4. Alkanes through hydrogenolysis of strained C — C bonds Products

Starting alkane

Reference

R7

V

Pd(dba)2—(/-Pr)3P R T , quant-

y4

(13) Pd(dba)2 RT, 1 2 %

d b a = d i b e n z y i i d e n e acetone

562 9.

G. M e h t a a n d H . S. P . R a o Oligomerization

Structurahy novel cyclopropane-fused cycloalkanes c a n be constructed by oligomerization of cyclopropenes. Cycloaddition across the double b o n d reduces ring strain in cyclopropenes enormously. W h e n catalysed by transition metals, dimethylcyclopropene tri- or tetramerizes stereoselectively t o novel polycycloalkanes (equation 1 3 f ^'^^ B. Alcohols and Related Derivatives 1. Direct

reduction

Direct reduction of alcohols t o alkanes is difficult to accomplish since the hydroxyl group is a p o o r leaving group. However, in selected cases this can be accomplished through the activation of the hydroxyl g r o u p by protonation o r complexation with Lewis acids. F o r example, ionic hydrogenation conditions have been found t o be effective for the direct conversion of alcohols t o alkanes. Thus, E t g S i H - C F a C O O H combination has been used for the reduction of tertiary alcohols'*^. Use of b o r o n trifluoride in t h e reaction medium even permits reduction of secondary aliphatic alcohols as, e.g., of 2-octanol t o n-octane a n d of 2-adamantanol to a d a m a n t a n e (equation 14)"^^. Tertiary ahphatic alcohols can also be hydrogenated t o alkanes in the presence of trifluoroacetic acid, b u t the reaction perhaps proceeds through prior dehydration t o form alkenes'^^.

Et3SiH,BF3

(14)

86%

Raney N i h a s been successfully employed for t h e direct deoxygenation of tertiary alcohols t o alkanes (equation 15). U n d e r the reaction conditions other sensitive functionalities like t-butyldimethylsilyl ethers, acetates and alkyl chlorides are stable^^.

OH Raney Ni

n-C4H 4"9~

•n-C6Hi3 CH,

2. Indirect

80%

n - C ^4H" 9 -

-C —

I

reduction

a. Sulphonate esters. T h e commonly employed method for the reduction of primary and secondary alcohols consists of their conversion t o p-toluenesulphonate or methanesulphonate derivatives a n d subsequent treatment with a reducing agent. Lithium aluminium hydride has been extensively used for the reductive elimination of tosylates as shown in Table 5 ^ ^ However, other hydrides, e.g. sodium borohydride a n d sodium cyanoborohydride in H M P A , have also been used for this purpose^^. Brown's lithium triethylborohydride (superhydride) is a particularly effective reagent for this purpose^^^. F o r example, cyclooctyl mesylate could be reduced to cyclooctane with L i E t s B H in high yield as compared to the p o o r yield obtained with LiAlH4 (equation 16)^^. This


563

TABLE 5. Alkanes through the reduction of p-toluenesulphonate esters Starting tosylate

Product

Reference

51a

51b

CH2OTS

13g

OMs LiEtsBH

(16)

93%

time-tested method continues t o be routinely used for the two-step deoxygenation of alcohols. Another convenient procedure for the reductive removal of the mesylate or tosylate group is through reaction with a N a l / Z n system^"^. T h e iodide intermediate which is formed in the reaction is reduced to the alkane with zinc powder. Following this procedure 2-octyl tosylate could be reduced t o n-octane in high yield (equation 17)^^^. OTs CH3CH(CH2)5CH3

CH3(CH2)6CH3

(17)

glyme, 89%

b. Intermediate iodides. A one-pot method for the reductive deoxygenation of hydroxy and ether functionalities is via in situ generated iodides. The reagent system involved is chlorotrimethylshane/sodium iodide (trimethylshyl iodide, T M S I ) a n d subsequent treatment with zinc a n d acetic acid^^. This method is applicable t o a wide variety of primary and secondary alcohols, methyl ethers and trimethylshyl ethers. Thus, n-decanol could be readhy converted to n-decane fohowing this method (equation 18)^^. Me3SiCl-NaI,CH3CN CH3(CH2)8CH20H

CH3(CH2)8CH3

(18)

Z n A c O H , 80%

Tertiary alcohols are seldom amenable t o direct deoxygenation. However, sodium cyanoborohydride in the presence of zinc iodide reduces tertiary alcohols t o the corresponding alkanes in high yields^^. Primary and secondary alcohols are not reduced whh this reduction reagent a n d thus a very desirable chemoselectivity in deoxygenation is attainable.

564

G. M e h t a and H. S. P. R a o

c. Carboxylic acid esters. Acetates generated from primary, secondary and tertiary alcohols serve as good intermediates for deoxygenation reactions. Several preparative methods for this one-step transformation, generally involving radical intermediates, are available. A method that has been used with considerable success is the reductive deacetoxylation under photochemical conditions. Irradiation of acetates is usually carried out in aq. H M P A and yields, particularly in the case of polycycloalkanes, are quite satisfactory. Several examples are shown in Table 6^^. Acetates derived from tertiary and sterically hindered alcohols can be reduced to alkanes by treatment with lithium in ethylamine or potassium in r-butylamine in the presence of [18]-crown-6^^. Thus, a bridgehead acetate derived from natural product caryophyllene was transformed to the corresponding alkane in high yield (equation 19)^^^.

3

•H,C

Li — E t N H o

(19)

18-crown-6 90%

Reductive elimination of acetates from secondary alcohols has been shown to proceed in good yield, employing s o d i u m - p o t a s s i u m ahoy and tris(3,6-dioxaheptyl)amine (TDA), with the latter also functioning as an effective phase transfer catalyst (equation 20)^^.

TDA No-K,

THF,

(20) 62%

AcO

A simhar reduction of acetates with sodium in hexamethylphosphoric triamide ( H M P A ) has been reported^^. Fohowing this procedure, acetates of primary a n d TABLE 6. Alkanes through photochemical reductive deacetoxylation Starting acetate

Product

Reference

57a

57b

57b


565

secondary alcohols can be converted to the corresponding alkanes in m o d e r a t e yields. Preparation of the parent hydrocarbon (laurenane) from the diterpene natural product laurenene is one such example (equation 21)^^ In the case of highly hindered acetates alkane yields can be near-quantitative.

Na — H M P A

(21) /-BuOH,

70%

Reduction of primary, secondary a n d tertiary acetates can also be conveniently performed by reaction with triphenylsilyl hydride or p-(/?is-diphenylhydroshyl)benzene^^ under radical conditions with the latter reagent being m o r e effective (equations 22 a n d 23). It is to be noted that A I B N a n d benzoyl peroxide are n o t effective as radical initiators in this reduction^^.

PhgHSi—(O)—SiHPhg

n-C^lHgsCHgOAc /-BuOOBu-/,

95%

n-Ci2H26

(22)

JOCOCH3

PhsSiH /-BuOOBu-/,

(23)

82%

Deoxygenation of primary alcohols can also be performed by treating chloroformate esters with tripropylshane in the presence of di-t-butyl peroxide (equation 24)^^. O PrgSiH

n-C7Hi5CH20—CCl f-BuOOBu-^85%

n-CgHjg

(24)

d. Thiocarbonates (Barton-McCombie reactionf^ and phosphate esters. Barton a n d his group have invented a very versathe methodology for the deoxygenation of alcohols through radical intermediates^^. This approach essentially involves the treatment of derived iS-methyldithiocarbonates^"^'^^^'^, thionobenzoates^^^, thiocarbonylimidazohdes^^"", N,N-dialkylaminothiocarbonates^^*^, thionoformic acid esters^^^, phenylthiocarbonate^^^ etc., with tri-n-butyltin hydride (TBTH) in the presence of the radical

566

G. M e h t a a n d H . S. P . R a o TABLE 7. Alkanes through Barton-McCombie-type radical deoxygenations Radical precursor

I H3(CH2)i6

C

0

Product

C-

CH3(CH2)i6

(

C C

Reference

H

66e

CH,

c;

66f

64,66a, b MeS

C

0

66a

66c

II

generator azobisisobutyronitrile (AIBN). T h r o u g h judicious selection of the thioester or thiocarbonate moiety a n d reaction conditions, efficient reduction of either the primary or secondary alcohol can be achieved. Several examples of this deoxygenation methodology are summarized in Table 7. A recent modification of this popular procedure includes the use of triethyl boride as radical initiator (equation 25)^^. Alternatively, S-methyldithiocarbonates derived from primary a n d secondary alcohols can be converted to alkanes using EtjSiH with di-r-butyl peroxide a n d dodecanethiol in good yields (equation 26)^^.

0 — C

SMe

CeH6,93%

EtsSiH, /-BuOOBu-/ Ci2H25SH,89%

MeSC

0

(25)

(26)


567

Tertiary alcohols can be conveniently deoxygenated in high yields t h r o u g h thiohydroxamic-O-esters. In practice, an oxalic acid half ester is prepared a n d decomposed in the presence of r-butylthiol or 1,1-diethylpropanethiol under radical conditions (equation 27)^^. Diethyl phosphates a n d Ar,N,N',Ar'-tetramethylphosphorodiamidates of alcohols are readily reduced by lithium-ethylamine solutions. The m e t h o d works well with b o t h secondary and tertiary alcohols, the latter shown by the conversion of 1-adamantanol t o a d a m a n t a n e (equation 28)^°.

EtjCSH

(27) C6Hg,80%

/=

NMe2 (0Et)2 NMea

Li — E t N H a

Li—EtNHa

/-Bu0H,82%

/-Bu0H,92%

(28) 3. Sulphur

compounds

Thiols a n d thioethers a r e the most commonly encountered sulphur derivatives which can be directly reduced t o alkanes. F o r this purpose, Raney N i has been traditionally used. An example of its use is the synthesis of 7a- a n d 7j5-eremophhanes from a tricyclic thiophene precursor (equation 29)"^ ^ However, more recently nickel complex reducing agents ("NiCRA") have been profitably and effectively used for this purpose, as indicated by the reduction of dodecanethiol to dodecane (equation 30)"^^. Similarly, nickelocene in the presence of L A H has been used to effect desulphurization of t h i o l s A combination of N a E t j B H a n d FeCl2 also achieves the thiol-to-alkane transformation quite satisfactorhy"^^. T h e increasing uthity of nickel boride has also been exploited for the transformation of sulphides t o alkanes as indicated in equation 31*^^.

Raney

Ni ( W — 7 )

(29)

87%

Ni(OAc)2, NaH, ÂmONa

n-Ci,H„SH

. n-C,,H,, NiCl, 6H20,NaBH4

(30)

568

G. M e h t a a n d H. S. P. R a o

An extremely pleasing example of reductive desulphurization is the synthesis of [2]-staffane, wherein hthium in ethylamine is employed as the reducing agent (equation 32)'^^. Finally, a n example of the use of radical chemistry for the conversion of an alcohol t o an alkane via a sulphide intermediate has been reported (equation 33)^^.

PhS-

n-BusP

(33) ^

4. Selenium

^

^

BujSnH, A I B N , 9 0 %

^

^

^

compounds

Increasing use of selenium reagents in organic synthesis in recent years has rendered the selenide-to-alkane conversion an important synthetic transformation. Radical chemistry has been successfully used for this purpose and both n-tributylstannane a n d triphenylstannane reduce phenyl selenides to alkanes (equation 34)*^^. T h e same procedure is also applicable for tellurides (equation 35)^^. P h ^ S n H , toluene

n-Ci^H^SePh ^ ^ ^ ^ ^

^n-Ci^H,,

(34)

P h o S n H , toluene

C10H21-CHCH3

>n-Ci2H26

(35)

I TePh Nickel boride has also been found to be effective for reductive deselenation. T h e method is convenient for the preparation of mono-deuteriated alkanes (equation 36)"^^. NiCl2,NaBD4

n-CiiH23CH2SePh ^

-

-

MeOD,98%

> n-CiiH23CH2D H

23

2

(36) V

;

C. Alkyl Halides 1. General

aspects

Alkyl hahdes can be transformed into alkanes through two-step procedures involving dehydrohalogenation to a n alkene fohowed by reduction. However, we wih only discuss those methodologies that directly dehver alkanes from organic halides through reductive dehalogenations or hydrogenolyses^^°\ F o r the purpose of dehalogenations, either chlorides, bromides or iodides can be employed b u t the last two are generahy preferred because of greater ease of reduction. Alkyl fluorides are usually resistant to reductive dehalogenation b u t a few reagent systems are avahable for the conversion of primary alkyl fluorides to alkanes (equations 37 a n d 38)^ ^


No —K

569

(37)

dicyclohexyl-18-crown-6 87%

^

LiAlH.-CeCla C H 3 ( C H 2 ) i o C H 2 F

2.

>

C H 3 ( C H 2 ) i o C H 3

(38)

Hydrogenolysis

Catalytic hydrogenolysis of alkyl halides is one of the classical methods of alkane syntheses. Among other catalysts, Raney N i has proved t o be quite effective for the hydrogenolysis of iodides (equation 39)^^. A relatively recent discovery is the reductive dehalogenation of alkyl halides under the conditions of ionic hydrogenation. C H 3 ( C H 2 ) 4 C H 2 l

"^•^;"'""»

C H 3 ( C H 2 ) 4 C H 3

(39)

Alkyl halides can be reduced conveniently by trialkylsilanes in the presence of catalytic amounts of BF3 or A l C l 3 ^ ^ . H y d r o g e n - h a l o g e n exchange reaction of primary, secondary and tertiary chlorides or bromides is quite efficient under these conditions (equation 40). Br I

BugSiH.AlCU

C H 3 ( C H , ) , C H C H 3

•

CH3(CH,)ioCH3

(40)

Triethylsilane reduction of alkyl halides is even better in the presence of thiols, which act as polarity reversal catalysts for hydrogen a t o m transfer from shane t o alkyl groups (equation 41)^"^. This reagent in the presence of AICI3 reduces even gfem-dichlorides t o alkanes (equation 42)^^. T h e powerful hydrogen d o n o r reagent rr/s-(trimethylshyl)shane has been introduced as a superior alternative t o triethylshane for the hydrogenolysis of EtaSiH C H 3 ( C H 2 ) 6 C H 2 B r

CH3(CH,)6CH3

(41)

di-^butylhyponitîte dodecanethiol, 99% EtaSiH.AICl, C H 3 ( C H 2 ) 2 C C l 2 C H 3

—

^

C H 3 ( C H 2 ) 3 C H 3

(42)

organic halides. T h e reaction is initiated by light a n d proceeds through a free radical mechanism (equation 43)^^. C H 3 ( C H 2 ) i 6 C H 2 C l

3. Low-valent

^^^^5^

C H 3 ( C H 2 ) i 6 C H 3

(43)

metals

Dissolved alkali metals have been traditionally used for the dehalogenation of alkyl halides. T h e zinc-acetic acid system a n d m e t a l - a m m o n i a solutions were the oldest methods used for this purpose. They sthl constitute a n efficient medium for dehalogenations a n d several convenient procedures have been introduced. Sodium in

570

G. M e h t a and H. S. P. R a o TABLE 8. Alkanes through dissolved metal reduchons Starting halide

Product

Reference

87b

88b

88c

88d

89

90

ethanol^"^, lithium in t-butanol and THF^^'^^, N a - K in r-butanoP^ are the more commonly used recipes and work weh with bridgehead substituted halides. Some examples are displayed in Table 8^^~^°. In addition alkah metals in hq. N H 3 or alkylamines constitute an effective medium for dehalogenations. Samarium iodide (Sml2) has been introduced as an efficient reducing agent for alkyl bromides and iodides in the presence of a p r o t o n source (alcohol)^ ^ Alkyl chlorides are not reduced by this reagent. It has been further observed that the Sml2 reductions proceed exceedingly well in the presence of H M P A ^ ^ . Thus, primary, secondary and tertiary halides are reduced to alkanes under mild conditions and in very high yields (equation 44)^^. Sml2, H M P A , T H F

CH3(CH2)8CH2Br

CH3(CH2)8CH3

(44)

i-PrOH,99%

4. Metal

hydrides

A variety of metal hydrides reduce alkyl halides to alkanes. Sodium borohydride has been extensively used in aprotic solvents hke D M S G , D M F , diglyme a n d sulpholane. Reduction with this hydride in the presence of phase transfer catalysts is even more advantageous^^. Sodium borohydride in the presence of nickel boride (Ni2B) has been


571

used for the reduction of polychlorinated insecticides^"^. Lithium aluminium hydride has also been employed with varying degrees of success. An example is t h e last step in t h e synthesis of iceane (equation 45)^"^. L A H in combination with C0CI2 h a s found application in the reduction of secondary b r o m i d e s S o d i u m cyanoborohydride in H M P A is a particularly effective system for the reduction of bromides a n d iodides^^. Lithium triethylborohydride reduces a variety of alkyl halides every efficiently and rapidly to alkanes (equation 46)^^. Lithium triethylborodeuteride c a n be employed for deuteriolysis with stereochemical inversion at the stereogenic centre. Copper hydride has been used for the reduction of b r o m o - and iodoalkanes t o alkanes^^. Magnesium hydride reduces alkyl iodides selectively t o alkanes in the presence of bromides a n d chlorides (equation 47)^^

LiAIH4

(45)

quant.

CH3(CH2)6CH2C1

ITfZ'

CH3(CH2)6CH3

(46)

T H F , 100% MgH2

CH3(CH2)8CH3

CH3(CH2)8CH2l

(47)

T H F , 100%

Organotin hydrides have proved t o be very effective reagents for t h e reduction of alkyl hahdes under homolytic conditions in the presence of radical initiators like A I B N or benzoyl peroxide. Tributyltin hydride (TBTH) is the most commonly employed reagent (equation 48)^^, b u t others like Bu2SnH2 have found utility (equation 49)^^°.

(48)

(49)

5. Electrochemical

methods

Alkyl hahdes, excepting alkyl fluorides, can be reduced under electrochemical conditions in aprotic solvents. F o r example, 1-adamantyl bromide can be reduced t o

e l e c t r o l y s i s , Hg cathode

-Br MeOH, B u 4 N B r , 7 7 %

(50)

572

G. M e h t a a n d H . S. P . R a o

a d a m a n t a n e in good yield (equation 5 0 ) ^ I t has been further reported that electro chemical hydrogenolysis of alkyl halides can be effected in the presence of aromatic hydrocarbons like naphthalene which act as electron-transfer reagents (equation 51)^°^. naphthalene

CH3(CH2)4CH2C1

^

6. Organometallics

-

> CH3(CH2)4CH3

-

electrochemical, 8 0 - 1 0 0 %

and miscellaneous

i\

(51)

i

reagents

Several organometallic reagents have surfaced in recent years for the reduction of the c a r b o n - h a l o g e n bond. A titanocene dichloride-magnesium system reduces alkyl halides to alkanes under m h d conditions a n d in good yield (equation 52)^^^. N e w reagents based o n 9-borabicyclo[3.3.1]nonane ("9-BBN") 'ate' complexes have been used for the efficient reduction of tertiary halides (equation 53)^°"^. CH3(CH2)7CH2Br

> CH3(CH2)7CH3

(52)

Mg,H20,87%

Br I

n-C^Hg—C—C2H5

I

H 9 - B B N , n-BuLi

'^'^

I

> n-C^Hg—C—C2H5

CH3

I

(53)

CH3

Lastly, metallation of alkyl halides a n d p r o t o n a t i o n has been a frequently employed m e t h o d for the preparation of alkanes. Examples of alkane synthesis via conversion t o the Grignard reagent a n d p r o t o n a t i o n are legion. However, t w o pleasing examples have been recently reported (equations 54 a n d 55)^

/-BuLi 62%

(55) D. Aldehydes, Ketones and Related Compounds 1. General

aspects

Deoxygenation of aldehydes a n d ketones is a step frequently encountered in organic synthesis. Its importance emanates from the fact that the carbonyl g r o u p is a very versathe handle for the purpose of key organic transformations, e.g. homologations, annulations, alkylations, etc., a n d is therefore present in almost every complex synthetic venture. A large n u m b e r of c o m m o n ring forming reactions, like D i e c k m a n n cyclization, T h o r p e - Z i e g l e r cyclization, acyloin condensation, involve a carbonyl functionality which needs t o be disposed of, once it has served its purpose, t o gain access t o alkanes. W h h e


573

the carbonyl g r o u p can be transformed to the corresponding alkane via the hydroxyl group or an alkene, the concern here will be only with methods that transform a carbonyl group to a methylene g r o u p without mediation by other functional groups. 2. Direct

reduction

Catalytic hydrogenation of carbonyl c o m p o u n d s to alkanes is a difficult proposition under normal conditions, although limited success is attainable with aromatic ketones. However, certain enolates derived from ketones have been shown to undergo catalytic reduction to alkanes quite efficiently. F o r example, enol triflates of ketones are reduced over platinum oxide catalyst to alkanes (equation 56)^^^. Simharly, enol phosphates, conveniently prepared from ketones, can be quantitatively hydrogenated to alkanes (equation 57y^\

2. H j , P t O j , 7 0 %

(56)

H2,Pt-C

.0_p_(0Et)3

(57)

The remarkable reducing abihty of systems containing an organoshicon hydride a n d gaseous b o r o n trifluoride has been exploited for the direct conversion of ketones to alkanes^ Thus, 2-methylcyclohexanone a n d 2 - a d a m a n t a n o n e are efficiently transformed to methylcyclohexane a n d a d a m a n t a n e , respectively (equation 58). T h e procedure is general enough to be of preparative value, although it works better with aryl carbonyl c o m p o u n d s D i b o r a n e in the presence of BF3 is able to deoxygenate cyclopropyl ketones (equation 59)^^^.

Et3SiH,BF3-Et20 100%

(58)

BgHe —BF3 ^ 8 0 %

(59)

G. M e h t a a n d H . S. P . R a o

574

Clemmensen reduction involving reaction of ketones with amalgamated zinc in the presence of hydrochloric acid is one of the classical methods of deoxygenation^ It works well with aromatic ketones b u t its applicability to alicyclic systems is severely limited. T h e strongly acidic conditions a n d high temperature m a k e this procedure t o o stringent, especially if other functional groups are present. Quite often side reactions are observed a n d complex mixtures of products are obtained. Nonetheless, the m e t h o d h a s found favour in many cases (equation 60)^

Zn-HCI

(60)

benzene,89%

3. Reduction

of liydrazones

(WoIff-Kisfiner

and Caglioti

reductions)

A m e t h o d of almost universal applicability for the deoxygenation of carbonyl c o m p o u n d s is the Wolff-Kishner r e d u c t i o n ^ W h i l e the earlier reductions were carried o u t in t w o steps o n the derived hydrazone or semicarbazone derivatives, the H u a n g - M i n i o n modification is a single-pot operation. In this procedure, the carbonyl c o m p o u n d and hydrazine (hydrate or anhydrous) are heated (180-220 °C) in the presence of a base a n d a p r o t o n source. Sodium or potassium hydroxide, potassium-t-butoxide and other alkoxides are the frequently used bases a n d ethylene glycol or its oligomers are used as the solvent a n d p r o t o n source. Over the years, several modifications of this procedure have been used to cater t o the specific needs of a given substrate. T h e Wolff-Kishner reaction works well with both aldehydes a n d ketones a n d remains the most routinely used procedure for the preparation of alkanes from carbonyl c o m p o u n d s (Table 9)^^^. This method is equahy suitable for the synthesis of polycyclic a n d hindered alkanes. TABLE 9. Alkanes via Wolff-Kishner reduction Starting ketone

Product

Reference

113a

H3CH,C-

113b,c

113d

113e

{continued)

575

12. Alkanes: modern synthetic methods TABLE 9. {continued) Product

Starting ketone

Reference

113f

llBg

113h

113i

113j

113k

1131

A very useful variant of the hydrazone reduction is the deoxygenation of aldehydes and ketones via the hydride reduction of tosylhydrazones (Caghoti reaction)^ The method is mild, convenient a n d widely applicable. While sodium borohydride was used in the earlier procedures, considerable improvements have been achieved through the uses of sodium cyanoborohydride^^^, catecholborane^^^, diborane^^^, ^fs-benzoyloxy borane^ and copper borohydride^ as reducing agents a n d H M P A , D M F , sulpholane, etc. as solvents. Use of the sterically crowded 2,4,6-triisopropyl tosylhydrazone derivative has greatly fachitated the reduction in some cases (equations 61-64)^^^.

1. p - T s N H N H g 2.

NaCNBH3,DMF,93%

(61)

576

G. M e h t a a n d H . S. P. R a o 1.

p-TsNHNHg

CH3(CH2)5C0CH3

CH3(CH2)6CH3

(62)

2. [0}^%—H,86% \

/

\

/

\

/

l.p-TsNHNHz ^ ^

X

2.(PhC02)2BH,82%

1. 2 , 4 , 6 -

^

/

/

\

\

/

(/-PrJaCgHgSOgNHNHg ^

(63)

(64)

2.CuBH4(PPh3)2,70%

4. Thioacetalization-desulphurization

(Mozingo

reaction)

A popular two-step protocol for the deoxygenation of carbonyl c o m p o u n d s is the Mozingo reaction in which the aldehyde or ketone is transformed to a dithioacetal in the presence of a Lewis acid a n d then reductive desulphurization is carried o u t with Raney Ni^^^. T h e reaction is mild, efficient a n d particularly convenient for smah-scale preparations. Ethanedithiol, propanedithiol a n d benzene-1,2-dithiol are employed for the preparation of dithioacetals. Some of the polycycloalkanes m a d e by this procedure are shown in Table 10^

TABLE 10. Alkanes through dithioacetal desulphurization Starting ketone

Product

Reference

121a

121b

121c

577


Dithioacetals can also be desulphurized under radical conditions using tributyltin hydride (TBTH) (equation 65)^^^ or by using m e t a l - a m m o n i a solutions (equation 66)^^^. Lithium aluminium hydride has also been used in some cases for reductive desulphuriza tion. In a manner analogous to the preparation of dithioacetals, ketones can be trans formed to diselenoacetals w h h aryl or alkyl selenol. These in turn have been reduced with Raney Ni^^^ or L i - E T N H 2 ^ ^ ' ^ and under radical conditions with T B T H or triphenyltin hydride to furnish the corresponding alkanes (equation 67)^^.

BugSnH,AIBN

(65)

quant-

1. ' @ ^ s H »P T S

H,C(CHp)7C0CH, 3

2 7

3

• 2.Na—NH3,quant-

CH3(CH2)8CH3 ^

D H

(66)

6

SePh SePh PhgSnH,AIBN

(67) 91%

5. Reductive

alkylation

Reductive alkylation of aldehydes a n d ketones essentially involves replacement of oxygen with two alkyl groups to furnish alkanes. T h e procedure can be employed advantageously for the conversion of ketones into êm-dimethylated alkanes, a structural feature present in many natural products. Thus, several cyclic ketones have been transformed into êm-dimethylated alkanes, employing mild conditions, with dimethyltitanium dichloride (equation 68)^^^. ^^m-Dimethylation of ketones has also been achieved by heating them with (CH3)3 Al in the presence of AICI3 (equations 69 and 70)^^^.

MegTiClg

(68)

73%

CH3

578

G . M e h t a a n d H . S. P . R a o

MejAI isopentane, 6 0 %

CH3(CH2)5CHO

— • CH3(CH2)5CHMe2

(69)

(70)

major product

E. Carboxylic Acids and Related Compounds ) . Indirect

method

Decarbox^ylation of unactivated carboxyhc acids t o alkanes is n o t always easy t o accomplish a n d therefore indirect methods are more often employed for this purpose^ W h e n direct transformation t o alkanes is t o be carried out, suitable activation t h r o u g h derivatization becomes a pre-requisite in most cases. The indirect conversion of carboxylic acids t o alkanes is generally mediated through alkyl halides a n d olefins. T h e most commonly employed procedure for this purpose is the classical Hunsdiecker reaction^^^ and several of its modifications in which Hg(II)^^^^, lead(IV)^^^^ a n d Tl(I)^^^'^ sahs have been used t o transform the carboxyhc acid functionahty t o the corresponding alkyl halide. An alternate process for the Hunsdiecker reaction involves decarboxylative halogenation of iV-hydroxypyridine-3-thione esters in the presence of trichloromethyl r a d i c a l s T h e procedure can also be carried o u t in a single-pot operation, without the isolation of the ester. Iodoform o r iodine c a n be used in place of t h e trichloromethyl radical for obtaining iodoalkanes. M o r e recently, decarboxylative iodinations have been carried o u t employing r-butyl hypoiodide^^^ a n d hypervalent i o d i n e ^ b a s e d reagents. T h e most celebrated example in this context is the transformation of cubane carboxylic acids to iodocubanes^^^'^^^. Indirect conversion of carboxylic acids t o alkanes with the same number of carbon atoms can be achieved through 1,3-benzodithiohum tetrafluoroborate s a l t s W h i l e these indirect methods are extremely important, they whl n o t be dealt with here. 2. Thermal

decarboxylation

Direct decarboxylations t o alkanes are accomplished o n activated carboxylic acid derivatives either thermally or photochemicahy in the presence of a hydrogen donor. O n e of the early reagents used for this purpose was lead tetraacetate While primary a n d secondary carboxylic acids could be readily decarboxylated with moderate success with this reagent, results with tertiary carboxylic acids were unsatisfactory. The synthesis of cubane highlighted t h e utility of t-butyl peresters for effecting decarboxylations, particularly of bridgehead a n d tertiary carboxylic a c i d s T h i s method has been successfuhy used in m a n y polycycloalkane syntheses (Table 1 1 ) i 3 3 b , i 3 4 Several radical intermediate-based methodologies have been introduced for decarboxylations as a n extension of earlier efforts o n the deoxygenation of alcohols. O n e of the early approaches involved the T B T H reduction of the dihydrophenanthrene derivative of carboxylic acids (equation 71)^^^. However, the difficulties associated with the preparation of the phenanthrene ester derivatives a n d lack of success with tertiary carboxylic acids proved t o be disadvantageous. A more notable discovery in this context is the demonstration that esters derived from C O O H groups attached t o primary, secondary a n d tertiary carbons a n d N-hydroxypyridine-2-thione undergo efficient reductive decarboxylation in the presence of T B T H in refluxing benzene o r toluene

579

12. Alkanes: m o d e r n synthetic m e t h o d s TABLE 11. Alkanes through decomposition of peresters Starting t-butyl perester

Product

Reference

134a C

OOBu-/

134b

133b

134c

134d

COOR Bu3SnH,AIBN 72%

{

(71)

^

PhS

CH3(CH2)i6

I

C

0

/

\

N

/

BujShH.AIBN 95%

CHjCCHgJisCHj

(72)

580

G. M e h t a a n d H. S. P . R a o

(equation J2Y^^^'^^^. This methodology is convenient a n d gaining wide acceptance. Reduction of acid chlorides with tripropyltin hydride in the presence of the radical initiator di-t-butyl peroxide h a s also been shown t o furnish alkanes in m o d e r a t e yield (equation 73)^^^. Carboxylic acids can also be decarboxylated via carboselenoic acid esters with T B T H in the presence of of A I B N

PrjSiH,

/-BuOOBu-/

An alternative procedure for reductive decarboxylation without the use of trialkyltin hydrides as hydrogen a t o m d o n o r s has been d e v e l o p e d ^ A l k a n e carboxylic acid esters derived from Ar-hydroxypyridine-2-thione decomposed t o alkyl radical, which can readily accept a hydrogen a t o m from t-BuSH (equation 74) t o give alkanes. This reaction c a n be conveniently performed as a one-pot experiment wherein the acid chloride of a n alkane carboxylic acid, the sodium salt of thiohydroxamic acid, t-BuSH a n d 4-dimethylaminopyridine ( D M A P ) in benzene solution are heated t o reflux. This procedure w o r k s well for C O O H groups attached t o primary a n d secondary carbon atoms. Instead of Ar-hydroxypyridine-2-thione, o n e can use other thiohydroxamic acids, viz. iV-hydroxyA^-methylthiobenzamide^^^, 3-hydroxy-4-methylthiazole-2(3/f)-thione (equation 7 5 ) i 3 9 , i 4 o and l-Ar-hydroxy-3-N-methylbenzoylenethiourea^^^ for decarboxylation reactions.

1. c i c o c o c i CH3(CH2),4C00H

,

2.

^

,/.-BB„uSSHH.,DDM AP MAP

'

CHjCCH^j^jCH,

(74)

,N—0Na,72%

,COOH 1.

3-hydroxy-4-methylthiazole

2(3H)thione,DMAP,N,N-dicycIohexylcarbodiimide 2.

3.

Bu3SnH,23%

Photodecarboxylation

Aliphatic carboxyhc acids can be photodecarboxylated t o alkanes in t h e presence of heteroaromatic c o m p o u n d s like acridine, phenanthridine, phenazine, quinoline etc. a n d r-BuSH (equation 16^^^. T h e latter serves as the hydrogen donor. T h e reaction proceeds well with 1°-, 2°- a n d 3°-carboxylic acids. Photodecarboxylation can also be achieved via AT-acyloxyphthalimides in the presence of l,6-bis-(dimethylamino)pyrene ( B D M A P ) a n d r-BuSH in good yield (equation 11^^^. This method is also suited for 1°-, 2°- a n d 3°-carboxylic acids. In a related procedure, benzophenone oxime esters of carboxylic acids have also been shown t o undergo photochemical decarboxylation in the presence of t-BuSH (equation 78)^^^ hv, acridine

CH3(CH2).^COOH — — C H 3 ( C H 2 ) i 3 C H 3 f-BuSH, 72/o

(76)


581

0 Au, B D M A P /-BuSH,98%

hv,

S 0 2 + H 3 0 + - H H F - h S O g F SbF3 + H2 —> SbF2 + 2 H F

A H = - 3 3 kcal m o l " ^ AH = - 4 9 kcal m o l " ^

The direct reduction of SbFg in the absence of hydrocarbons by molecular hydrogen necessitates, however, more forcing conditions (50 atm, high temperature) which suggests that the protolytic ionization of alkanes proceeds probably via solvation of protonated alkane by SbFs a n d concurrent ionization-reduction (equation 14)^"^. Culman a n d Sommer have r e i n v e s t i g a t e d t h e mechanism of ShF^ oxidation of saturated hydrocarbons. They found efficient oxidation of isobutane to t-butyl cation by neat SbFg free of protic acid, at — 80 °C in the presence of a p r o t o n trap hke acetone

G. A. O l a h a n d G. K. Surya P r a k a s h

614

(equation 15). They consequently concluded that p r o t o n is not essential for the C — H b o n d oxidation by SbFg, contrary to what was previously suggested. R R —

c

,H--F —c;

(R3)C^+

)sbF3

2HF +

(14)

SbF3

SbFfi" SbFc ( C H 3 ) 3 C — H + 3SbF5 + ( C H 3 ) 2 C = 0

> ( C H 3 ) 2 C S b F 6 + ( C H 3 ) 2 C = O H S b F 6 + SbF3

(15) It must be pointed out, however, that the significant demonstration of the oxidizing abhity of pure SbF^ towards C — H bonds sthl produces protic acid in the system. In the absence of a p r o t o n trap, after the initial stage of the reaction, the in situ formed S b F j i K F conjugate superacid whl itself act as a protolytic ionizing agent. T h e situation is thus simhar t o the question of the acidic initiator in the polymerization of isobutylene. Even if Lewis acids themselves could initiate the reaction, protic acid formed in the system wih provide after the initial stage conjugate Bronsted-Lewis acid t o p r o m o t e protic initiation. Regardless, the study of S b F j free of protic acid in initiating carbocationic reactions of alkanes, such as isobutane, much furthered o u r knowledge of the field. In studies involving solid acid-catalyzed hydrocarbons cracking reactions using H Z S M - 5 zeolite, H a a g a n d Dessau^^ were able t o account nearly quantitatively for H2 formed in the protolysis ionization step of the reaction. This is a consequence of the solid acid zeolite catalyst which is n o t eashy reduced by the hydrogen gas evolved. It must also be pointed out, however, that initiation of acid-catalyzed alkane transformations under oxidative conditions (chemical or electrochemical) can also involve radical cations or radical paths leading to the initial carbenium ions. In the context of our present discussion we shah n o t elaborate on this interesting chemistry further a n d limit o u r treatment to purely protolytic reactions. U n d e r strongly acidic conditions C — H b o n d protolysis is not the only pathway by which hydrocarbons are heterolytically cleaved. C a r b o n - c a r b o n bonds can also be cleaved by protolysis^'^^ involving pentacoordinate intermediates (equation 16). H

C+

-h

I

-C

H

/ (16)

Simharly, many c a r b o n - h e t e r o a t o m bonds are also cleaved^^'^^'^^ under strong acid catalysis involving pentacoordinate carbon intermediates. III. ALKANE CONVERSION BY ELECTROCHEMICAL OXIDATION IN SUPERACIDS

In 1973, Fleischmann, Plechter a n d coworkers^^ showed that the anodic oxidation potential of several alkanes in H S O 3 F was dependent on the p r o t o n d o n o r abhity of the medium. This acidity dependence shows that there is a rapid p r o t o n a t i o n equhibrium

13. Electrophilic reactions o n alkanes

615

before the electron transfer step and it is the protonated alkane that undergoes oxidation (equation 17). ' RH ^ i i ^

R H /

•

-4-^

Pt anode

\

CHxCOO" ^

-

-

Oligomers Acids

•

(17)

Esters

M o r e recently, the electrochemical oxidation of lower alkanes in the H E solvent system has been investigated by Devynck a n d coworkers over the entire p H range^'^. Classical and cyclic voltammetry show that the oxidation process depends largely o n the acidity level. Isopentane (2-methylbutane, M2BH), for example, undergoes two-electron oxidation in H F r S b F s a n d H F i T a F s solutions (equation 18)^^ M2BH-2e- -^M2B^ +H+

(18)

In the higher-acidity region, the intensity-potential curve shows two peaks (at 0.9 V and 1.7 V, respectively, vs the Ag/Ag-h system). T h e first peak corresponds t o the oxidation of the protonated alkane and the second to the oxidation of the alkane itself. The chemical oxidation process in the acidic solution (equation 19) can be considered as a sum of two electrochemical reactions (equations 20 a n d 21).

RH + H+;=:^R^-hH2 2H -I- 2 e -

(19)

H2(E^ for H VH2)

R H ^ = : ^ R^ -h H ^ -h 2e-(E« for H+/H2)

(20)

(21)

The oxidation of the alkane (M2BH) by H"^ gives the carbocation only at p H values below 5.7. In the stronger acids it is the protonated alkane which is oxidized. At p H values higher than 5.7, oxidation of isopentane gives the alkane radical which dimerizes or oxidized in a pH-independent process (Scheme 1). M2BH ^

M2BH- +

M2B- -H H +

2M2B--^(M2B)2 M2B-^M2B + SCHEME 1 Commeyras a n d coworkers^^'^^ have also electrochemically oxidized alkanes (anodic oxidation). However, the reaction results in condensation a n d cracking of alkanes. T h e results are in agreement with the alkane behavior in superacid media a n d indicate the ease of oxidation of tertiary alkanes. However, high acidity levels are necessary for the oxidation of alkanes possessing only primary C — H bonds. Once the alkane has been partly converted into the corresponding carbenium ion, then typical rearrangement, fragmentation, hydrogen transfer as well as alkylation reactions will occur. IV. ISOMERIZATION OF ALKANES

Acid-catalyzed isomerization of saturated hydrocarbons was first reported in 1933 by Nenitzescu a n d Dragan^^. They found that when n-hexane was refluxed with aluminum chloride, it was converted into its branched isomers. This reaction is of major economic importance as the straight-chain C^-Cg alkanes are the main constituents of gasoline obtained by refining of the crude oil. Because the branched alkanes have a considerably

G. A. Olah and G. K. Surya P r a k a s h

616

higher octane number t h a n their linear counterparts, the combustion properties of gasoline can be substantially improved by isomerization. T h e isomerization of n-butane to isobutane is of substantial importance because isobutane reacts under m h d acidic conditions with olefins to give highly branched hydrocarbons in the gasoline range. A variety of useful products can be obtained from isobutane: isobutylene, t-butyl alcohol, methyl t-butyl ether and t-butyl hydroperoxide^^. A n u m b e r of methods involving solution as well as solid acid catalysts^^ have been developed to achieve isomerization of n-butane as weh as other linear higher alkanes to branched isomers. A substantial number of investigations have been devoted to this isomerization reaction and a n u m b e r of reviews are avahable^ ^"^^ The isomerization is an equihbrium reaction that can be catalyzed by various strong acids. In the industrial processes, a l u m i n u m chloride and chlorinated alumina are the most widely used catalysts. Whereas these catalysts become active only at temperatures above 80-100 °C, superacids are capable of isomerizing alkanes at r o o m temperature and below. The advantage is that lower temperatures thermodynamically favor the most branched isomers. The electron d o n o r character of C — H and C — C single bonds that leads to pentacoordinated carbonium ions explains the mechanism of acid-catalyzed isomerization of n-butane, as shown in Scheme 2. C a r b o n - c a r b o n b o n d protolysis, however, can also take place giving methane, ethane and propane. Related alkanes such as pentanes, hexanes and heptanes isomerize by simhar pathways with increasing tendency towards cracking (i.e. C — C bond cleavage).

H,C

CH,

CH,

H,C

CH

CHp

CH

CH3 HpC

CH

CH,

CH, HoC

CH

CH,

CH, H,C

SCHEME 2

C

CH,

CH:,

617

13. Electrophilic reactions on alkanes

During the isomerization process of pentanes, hexanes and heptanes, cracking of the hydrocarbon is an undesirable side reaction. The discovery that cracking can be substantially suppressed by hydrogen gas under pressure was of significant importance. In our present-day understanding, the effect of hydrogen is to quench carbocationic sites through five-coordinate carbocations to the related hydrocarbons, thus decreasing the possibihty of C — C b o n d cleavage reactions responsible for the acid-catalyzed cracking. Isomerization of n-hexane is superacids can be depicted by the three steps shown in Scheme 3. Step 1. F o r m a t i o n of the Carbenium ion: +

Ho

Step 2. Isomerization of the Carbenium ion via Hydride Shifts, Alkide Shifts and Protonated Cyclopropane (for the Branching Step): Isomers

Step 3. Hydride transfer from the Alkane to the Incipient Carbenium ion: /so-R

+

+

/so-RH

SCHEME 3 Whereas step 1 is stoichiometric, steps 2 and 3 form a catalytic cycle involving the continuous generation of carbenium ions via hydride transfer from a new hydrocarbon molecule (step 3) and isomerization of the corresponding carbenium ion (step 2). This catalytic cycle is controlled by two kinetic and two thermodynamic parameters that can help orient the isomer distribution depending on the reaction conditions. Step 2 is kinetically controlled by the relative rates of hydrogen shifts, alkyl shifts and p r o t o n a t e d cyclopropane formation and it is thermodynamicahy controlled by the relative stabhities of the secondary and tertiary ions. Step 3, however, is kinetically controlled by the hydride transfer from excess of the starting hydrocarbon and by the relative thermo dynamic stabhity of the various hydrocarbon isomers. F o r these reasons, the outcome of the reaction wih be very different depending on which thermodynamic or kinetic factor will be favored. In the presence of excess hydrocarbon in equilibrium with the catalytic phase and long contact times, the thermodynamic hydrocarbon isomer distribution is attained. However, in the presence of a large excess of acid, the product whl reflect the thermodynamic stabhity of the intermediate carbenium ions (which, of course, is different from that of hydrocarbons) if rapid hydride transfer or quenching can be achieved. Torek and coworkers^^'^^ have shown that the limiting step, in the isomerization of n-hexane and n-pentane with the H F : S b F 5 acid catalyst, is the hydride transfer with sufficient contact in a batch reactor, as indicated by the thermodynamic isomer distribution of Cg isomers. The isomerization of n-pentane in superacids of the type R F S 0 3 H : S b F 5 ( R p = C^F2^^^) has been investigated by Commeyras and coworkers^^. The influence

618


of parameters such as acidity, h y d r o c a r b o n concentration, nature of the perfluoroalkyl group, total pressure, hydrogen pressure, temperature and agitation has been studied. In weaker superacids such as neat CF3SO3H, alkanes that have n o tertiary hydrogen are isomerized only very slowly, as the acid is not strong enough to abstract hydride to form the initial carbocation. This lack of reactivity can be overcome by introducing initiator carbenium ions in the medium to start the catalytic process. F o r this purpose, alkenes m a y be added, which are directly converted into their corresponding carbenium ions by p r o t o n a t i o n , or alternatively the alkane may be electrochemically oxidized (anodic oxidation) (equation 22). Both m e t h o d s are useful to initiate isomerization a n d cracking reactions. The latter m e t h o d has been studied by Commeyras a n d coworkers^ R H ^ R H +- ^ R - ^ R +

(22)

Recently, Olah^'^ has developed a m e t h o d wherein natural gas liquids containing saturated straight-chain h y d r o c a r b o n s can be conveniently upgraded to highly branched h y d r o c a r b o n s (gasoline upgrading) using H F : B F 3 catalyst. The addition of a small a m o u n t of olefins, preferably butenes, increased the reaction rate. This can be readily explained by the formation of alkyl fluorides ( H F addition to olefins), whereby an equilibrium concentration of cations is maintained in the system during the upgrading reaction. T h e gasoline upgrading process is also improved in the presence of hydrogen gas, which helps to suppress side reactions such as cracking a n d disproportionation a n d minimize the a m o u n t of h y d r o c a r b o n products entering the catalyst phase of the reaction mixture. The advantage of the above m e t h o d is that the catalysts H F : B F 3 (being gases at ambient temperatures) can easily be recovered and recycled. Olah has also found HSO3F a n d related superacids as efficient catalysts for the isomerization of n-butane to isobutane^^. T h e difficulties encountered in handling liquid superacids a n d the need for p r o d u c t separation from catalyst in batch processes have stimulated research in the isomerization of alkanes over solid superacids. The isomerization of 2-methyl- a n d 3-methylpentane and 2,3-dimethylbutane, using SbFg-intercalated graphite as a catalyst, has been studied in a continuous flow system^^. The isomerization of cycloalkanes with acid catalysts is also well known. Over SbFs-intercalated graphite it can be achieved at r o o m temperature without the usual ring opening a n d cracking reactions which occur at higher temperatures a n d lower acidities^^. In the presence of excess h y d r o c a r b o n after several hours, the t h e r m o d y n a m i c equilibrium is reached for the isomers (Scheme 4). Interconversion between cyclohexane and methylcyclopentane yields the t h e r m o d y n a m i c equhibrium mixture. It should be mentioned, however, that the t h e r m o d y n a m i c ratio for the neutral h y d r o c a r b o n isomerization is very different as c o m p a r e d with the isomerization of the corresponding ions. The large energy difference ( > 10 kcal mol ~^) between the secondary cyclohexyl cation and the tertiary methylcyclopentyl ion means that in solution chemistry in the presence of excess superacid only the latter can be observed^. Whereas the cyclohexane-methylcyclopentane isomerization involves initial formation of the cyclohexyl (methylcyclopentyl) cation (i.e. via protolysis of a C — H bond) it should be mentioned that in the acid-catalyzed isomerization of cyclohexane up to 10% hexanes are also formed and this is indicative of C — C b o n d protolysis. The potential of other solid superacid catalysts, such as Lewis acid-treated metal oxides for the skeletal isomerization of hydrocarbons, has been studied in a n u m b e r of cases. The reaction of b u t a n e with S b F 5 : S i 0 2 : T i 0 2 gave the highest conversion forming C3, /S0-C4, iso-Cs, a n d traces of higher alkanes. T i 0 2 : S b F 5 , on the other hand, gave the highest selectivity for skeletal isomerization of butane. With S b F 5 : A l 2 0 3 , however, the conversions were very low^^'^^.

13. Electrophilic reactions o n alkanes +

619

H +)

H

+

Hp

H-cyclohexonium ion H

H

y

-H

H—/

11 .

C - c y c l o h e x o n i u m ion

Hexane isomers

; ^ = : ^ [CH3(CH2)4CH2]

H

CH,

SCHEME 4 Simharly, isomerization of pentane a n d 2-methylbutane over a n u m b e r of S b F 5-treated metal oxides has been investigated. The T i 0 2 : Z r 0 2 : S b F 5 system was the most reactive and, at the maximum conversion, the selectivity for skeletal isomerization was found t o be ca 100%^^ A comparison of the reactivity of S b F 5-treated metal oxides with that of HSOaF-treated catalysts showed that the former is by far the better catalyst for reaction of alkanes at r o o m temperature, although the H S O g F - t r e a t e d catalyst showed some potential for isomerization of 1-butane"^ ^ S b F 5 : S i 0 2 : A l 2 0 3 h a s been used t o isomerize a series of alkanes at or below r o o m temperature. Methylcyclopentane, cyclohexane, propane, butane, 2-methylpropane and pentane all reacted at r o o m temperature, whereas methane, ethane a n d 2,2dimethylpropane could n o t be activated"^ ^ The isomerization of a large number of C^^ hydrocarbons under strongly acidic conditions gives the unusually stable isomer a d a m a n t a n e . T h e first such isomerization was reported by Schleyer in 1957"^^^. During a study of the facile aluminum chloride-catalyzed endo:exo isomerization of tetrahydrodicyclopentadiene, difficulty was encountered with a highly crystalline material that often clogged distillation heads. This crystalline material was found to be a d a m a n t a n e . A d a m a n t a n e c a n be prepared from a variety of C^^ precursors a n d involves a series of hydride a n d alkyde shifts. T h e mechanism of the reaction h a s been reviewed in detail"^^^. F l u o r o a n t i m o n i c acid ( H F i S b F s ) very effectively isomerizes tetrahydrodicyclopentadiene into adamantane'^^'^. The work has been extended to other conjugate superacids'^^, wherein a d a m a n t a n e is obtained in quantitative yields (equation 23). M o r e recently"^"^* isomerization of polycyclic hydrocarbons C^^^^H^^^^^ 3) led t o a d a m a n t a n e , d i a m a n t a n e a n d triamantane, respectively, using new generation acid systems such as B ( O S 0 2 C F 3 ) 3 , B ( O S 0 2 C F 3 ) 3 + CF3SO3H a n d S b F 5 : C F 3 S 0 3 H (equation 24). T h e yields of these cage c o m p o u n d s substantially improved u p o n addition

620


of catalytic a m o u n t of 1-bromo (chloro, fluoro)-adamantane as a source of 1-adamantyl cation. These reactions were further p r o m o t e d by sonication (ultrasound treatment).

(23)

Superacid

(24)

4/7 + 6 ^ 4 / 7 + 1 2

/7 = 2

/7=1

/7

= 3

Sodium borohydride in excess of triflic acid at low temperature provides"^"^^ a highly efficient reductive superacid system, which was found effective for the reductive superacid isomerization of unsaturated polycyclic precursers to cage h y d r o c a r b o n s in high yields (equation 25). T h e key to the success of the ionic hydrogenation system appears t o be due to the in situ formation of b o r o n tris(triflate), a highly superacidic Lewis acid.

NaBH4 CF,S0,H

(25)

NaBH^ CF3SO3H

Vol'pin a n d coworkers have developed significant new chemistry "^^^ with R C O X - 2 A I X 3 complexes (R = alkyl, aryl; X = CI, Br) as efficient aprotic superacids for isomerizations a n d transformation of alkanes a n d cycloalkanes. T h e systems also p r o m o t e cleavage of C — C a n d C — H cr-bonds. These aprotic superacid systems were reported to be frequently m o r e convenient a n d superior to protic a n d Lewis acid systems in their activity. A good example of superacid catalyzed isomerization is the fascinating synthesis of 1,16-dimethyldodecahedrane from the seco-dimethyldodecahedrene (equation 26)"^^*^. A novel a p p r o a c h to highly symmetrical pentagonal dodecahedrane which involved gas phase isomerization of [ l . l . l . l ] p a g o d a n e over 0 . 1 % P t / A l 2 0 3 under a n a t m o s phere of H2 at 360 °C was provided by Prinzbach, Schleyer, R o t h a n d coworkers"^^^. D o d e c a h e d r a n e was obtained in 8% yield (equation 27). T h e isomerization probably involves carbocationic intermediates.

621


(26)

(27)

V. ACID-CATALYZED CLEAVAGE (CRACKING) REACTIONS OF ALKANES (p-CLEAVAGE vs C — C BOND PROTOLYSIS)

The reduction in molecular weight of various fractions of crude oh is an important operation in petroleum chemistry. The process is called cracking. Catalytic cracking is usually achieved by passing the hydrocarbons over a metallic or acidic catalyst, such as crystalline zeolites at a b o u t 400-600 °C. The molecular-weight reduction involves carbocationic intermediates a n d the mechanism is based on the ^-scission of carbenium ions (equation 28). R'

(28)

The main goal of catalytic cracking is to upgrade higher bohing oils which, through this process, yield lower hydrocarbons in the gasoline range''"^''^^. Historically, the first cracking catalyst used was aluminum trichloride. With the development of heterogeneous solid a n d supported acid catalysts, the use of AICI3 was soon superceded, since its activity was mainly due to the ability to bring a b o u t acid-catalyzed cleavage reactions. The development of highly acidic superacid catalysts in the 1960s again focused attention on acid-catalyzed cracking reactions. H S O a F i S b F s , trade-named Magic Acid, derived its n a m e due to its remarkable abhity t o cleave higher-molecularweight hydrocarbons, such as paraffin wax, to lower-molecular-weight components, preferentially C4 a n d other branched isomers. As a model for cracking of alkanes, the reaction of 2-methylpentane ( M P ) over SbF5-intercalated graphite has been studied in a flow system, the hydrocarbon being dhuted in a hydrogen stream^^. A careful study of the product distribution vs time on stream showed that p r o p a n e was the initial cracking product whereas isobutane a n d isopentane (as major cracking products) appear only later. This result can only be explained by the ^-scission of the trivalent 3-methyl-4-pentyl ion as the initial step in the cracking process. Based on this a n d on the product distribution vs time profile, a general scheme for the isomerization a n d cracking process of the methylpentanes has been proposed (Scheme 5)^^.


622

MP

+ H MP

MP*

/-C4H

MP

/ - C 4 + CgColefin)

C4(olefin) +

/-C5

+ MP

/-C«H

MP*

MP*

. + -10

C11

Cracking

IVIP= 2 - m e t h y l p e n t a n e

SCHEME 5 T h e propene which is formed in the j5-scission step never appears as a reaction product because it is alkylated immediately under the superacidic condition by a Cg ^ carbenium ion, forming a Cg^ carbocation which is easily cracked t o form a o r C j ^ ion and the corresponding C4 or C5 alkene. The alkenes are further alkylated by a C^^ carbenium ion in a cyclic process of alkylation and cracking reactions (Scheme 6). The 0 4 ^ or C^^

C12-/+

C^(olefin)

SCHEME 6

8

+

H

V

+

H

SCHEME 7 As is apparent in the last step, isobutane is not alkylated but transfers a hydride t o the Cg ^ carbocation before being used u p in the middle step as the electrophhic reagent (t-butyl cation). T h e direct alkylation of isobutane by an incipient r-butyl cation would yield 2,2,3,3-tetramethylbutane which, indeed, was observed in small a m o u n t s in the reaction of t-butyl cation with isobutane under stable ion conditions at low temperatures {vide infra). The alkylating ability of methyl a n d ethyl fluoride-antimony pentafluoride complexes have been investigated by Olah a n d his group^^'^^ showing the extraordinary reactivity of these systems. Self-condensation was observed as well as alkane alkylation. W h e n CH3F: SbFg was reacted with excess of CH3F at 0 °C, at first only an exchanging complex was observed in the ^ H - N M R spectrum. After 0.5 h, the starting material was converted into the Nbutyl cation (equation 33). Simhar reactions were observed with the ethyl

625


fluoride-antimony pentafluoride complex (equation 34). W h e n the complex was treated with isobutane or isopentane direct alkylation products were observed. T o improve the understanding of these alkane alkylation reactions (equation 35), O l a h a n d his g r o u p carried out experiments involving the alkylation of the lower alkanes by stable carbenium ions under controlled superacidic stable ion conditions'^^'

SbF.

FCH2CH3 +

F C H 2 — C H 3 + H"^

SbFfi

FCHp

CH3CH2F — • S b F g -

FCH2CH2CH2CH3

•(CH3)3C

(33)

CH3

C-

•H

+

SbF,

CH3CH2F

(CH3)3CCH2CH3

(34)

CH

R

H

+

R •

R'

"R'

• R ' + H"*

(35)

The (7-donor abihty of the C — C and C — H bonds in alkanes was demonstrated by a variety of examples. The order of reactivity of single bonds was found to be: tertiary C — H > C — C > secondary C — H » primary C — H , although various specific factors such as steric hindrance can influence the relative reactivities. Typical alkylation reactions are those of propane, isobutane a n d n-butane by the t-butyl or sec-butyl ion. These systems are somewhat interconvertible by competing hydride transfer and rearrangement of the carbenium ions. The reactions were carried out using alkyl carbenium ion hexafluoroantimonate salts prepared from the corres ponding halides and antimony pentafluoride in sulfuryl chloride fluoride solution and treating them in the same solvent with alkanes. The reagents were mixed at — 78 °C, warmed u p to — 20 °C a n d quenched with ice water before analysis. T h e intermolecular hydride transfer between tertiary and secondary carbenium ions and alkanes is generally much faster than the alkylation reaction. Consequently, the alkylation products are also those derived from the new alkanes and carbenium ions formed in the hydride transfer reaction. Propylation of p r o p a n e by the isopropyl cation (equation 36), for example, gives a significant a m o u n t (26% of the Cg fraction) of the primary alkylation product. H

(36)

626

G. A. O l a h and G. K. Surya P r a k a s h

The Cg isomer distribution, 2-methylpentane (28%), 3-methylpentane (14%) a n d nhexane (32%) is very far from thermodynamic equilibrium, a n d the presence of these isomers indicates that not only isopropyl cation but also n-propyl cation are involved as intermediates (as shown by ^ ^ C 2 - ^ ^ C i scrambling in the stable ion, see equation 37)^^.

(37)

The strong competition between alkylation and hydride transfer appears in the alkylation reaction of p r o p a n e by butyl cations, or of butanes by the propyl cation. T h e a m o u n t of C 7 alkylation products is rather low. This point is particularly emphasized in the reaction of p r o p a n e with the t-butyl cation which yields only 1 0 % of heptanes. In the interaction of propyl cation with isobutane the main reaction is hydride transfer from the isobutane to the propyl ion fohowed by alkylation of the p r o p a n e by the propyl ions (equation 38).

+

H-

(38) Hexanes

(70Vo)

Even the alkylation of isobutane by the r-butyl cation despite the highly unfavorable steric interaction has been demonstrated'^^ by the formation of small a m o u n t s of 2,2,3,3-tetramethylbutane (equation 39). This result also indicates that the related five-coordinate carbocationic transition state (or high lying intermediate) of the degenerate isobutane-t-butyl cation hydride transfer reaction is not entirely linear, despite the highly crowded nature of the system. -1 +

(39)

+

2,2,3,3-Tetramethylbutane was not formed when n-butane and s-butyl cation were reacted. The isomer distribution of the octane isomers for typical butyl c a t i o n - b u t a n e alkylations is shown in Table 1.


627

TABLE 1. Isomeric octane compositions obtained in typical alkylations of butanes with butyl cations

Octane 2,2,4-Trimethylpentane 2,2-Dimethylhexane 2,2,3,3-Tetramethylbutane 2,5-Dimethylhexane 2,4-Dimethylhexane 2,2,3-Trimethylpentane 3,3-Dimethylhexane 2,3,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3-Dimethylhexane 2-Methylheptane 3-Methylheptane n-Octane

(CH3)3CH

CH3CH2CH2CH3

(CH3)3+C

(CH3)3^C

18.0

4.0

1-2 43.0 7.6 3.0

0.6 Trace 73.6

1.5 3.6 4.2 19.3 0.2

'

7.2 6.9 Trace 7.6

(CH3)3CH CH3+CHCH2CH3 3.8 0.4 Trace 1.6 40.6 12.3 15.5 3.8 10.3 6.8 4.8

(CH3)3CH CH3+CHCH2CH3 8.5 1-2 29.0 6.6 3.2 7.1 6.2 8.8 12.8 6.7 9.5 Trace

The superacid [CF3SO3H or C F 3 S 0 3 H : B ( 0 3 S C F 3 ) 3 ] catalyzed alkylation of a d a m a n t a n e with lower olefins (ethene, propene and butenes) was also investigated.^^ Alkyladamantanes obtained show that the reaction occurs by two pathways: (a) adamantylation of olefins by adamantyl cation formed t h r o u g h hydride abstraction from a d a m a n t a n e by alkyl cations (generated by the p r o t o n a t i o n of the olefins) and (b) direct (T-alkylation of a d a m a n t a n e by the alkyl cations via insertion into the bridgehead C — H bond of a d a m a n t a n e t h r o u g h a pentacoordinate carbonium ion (Scheme 8). In order to gain understanding of the mechanism of the formation of alkyladamantanes, the reaction of a d a m a n t a n e with butenes is significant. Reaction with 2-butenes gave mostly 1-n-butyladamantane, l - s e c - b u t y l a d a m a n t a n e and 1-isobutyladamantane. Occasionally, trace a m o u n t s of 1-tert-butyladamantane were also formed. Isobutylene (2-methylpropene), however, consistently gave relatively good yield of 1-tert-butyladamantane along with other isomeric 1-butyladamantanes. 1-Butene gave only the isomeric butyladamantanes with only trace a m o u n t s of tertbutyladamantanes. The formation of isomeric butyladamantanes, with the exception of tert-hutyla d a m a n t a n e , is t h r o u g h adamantylation of olefins and carbocationic isomerization. The formation of tert-butyladamantane in the studied butylation reactions can, however, not be explained by this path. Since in control experiments attempted acidcatalyzed isomerization of isomeric 1-butyladamantanes did not give even trace a m o u n t s of 1-tert-butyladamantane, the tertiary isomer must be formed in the direct (T-tert-butylation of a d a m a n t a n e by tert-huiy\ cation t h r o u g h a pentacoordinate carbonium ion. The same intermediate is involved in the concomitant formation of 1-adamantyl cation via intermolecular hydrogen transfer (the major reaction). The formation of even low yields of tert-butyladamantane in the reaction is a clear indication that the pentacoordinate carbocation does not attain a linear geometry — H — C < - (which could result only in hydrogen transfer), despite unfavorable steric interactions (equation 40). This reaction is similar to the earlier discussed reaction between tert-butyl cation and isobutane to form 2,2,3,3-tetramethylbutane. An alternate pathway (equation 41) for the formation of tert-butyladamantane through


628

7C-ADAMANTYLATION OF OLEFINS olefin

+

H

+ RH

+

C = C

/-

»• ( 1 - A d ) — C — C+

\

I

. - A d ) - | - C (

^-^Z^5F

1-(R)Ad

^

/-C3H7, n-C^Hg,

\

+

5ec-C^Hg,/-C4H9,/e/-/-C4H9

(T-ALKYLATION OF ADAMANTANE olefin

+

+

H'^

R"

1-(R)Ad

-I- H"^

.'R

SCHEME 8 hydride abstraction of an intermediate 1-adamantylaikyl cation would necessitate involvement of a n energetic 'primary' cation o r highly distorted 'protonated cyclo p r o p a n e ' which is n o t likely under the reaction conditions.

(40)

+

(CH3)3CH

13. Electrophilic reactions o n alkanes

( 1 - A d ) —V—CHp"^

(1-Ad)

629

1-(/-C4H9)Ad

(41)

The observation of 1-t^rt-butyladamantane in t h e superacid-catalyzed reactions of a d a m a n t a n e with butenes provides unequivocal evidence for t h e a-alkylation of a d a m a n t a n e by the tert-butyl cation. As this involves a n unfavorable sterically crowded tertiary-tertiary interaction, it is reasonable to suggest that simhar a-alkylation can also be involved in less strained interactions with secondary a n d primary alkyl systems. Although superacid-catalyzed alkylation of a d a m a n t a n e with olefins occurs pre dominantly via adamantylation of olefins, competing direct o--alkylation of a d a m a n t a n e can also occur. As the a d a m a n t a n e cage ahows attack of the alkyl g r o u p only from the front side, t h e reported studies provide significant new insight into t h e mechanism of electrophhic reactions at saturated hydrocarbons and the nature of their carbocationic intermediates. The protolytic oxidative condensation of methane in Magic Acid solution at 60 °C is evidenced by the formation of higher alkyl cations such as t-butyl and t-hexyl cations (equation 42). It is n o t necessary t o assume a complete cleavage of [CHg]"^ t o a free, energeticahy unfavorable methyl cation. The c a r b o n - c a r b o n b o n d formation can indeed be visualized through reaction of the C — H b o n d of methane with the developing methyl cation.

H

I •C

- C - — ^

H

CH3'+ H .

I H

(42)

CH3* -H CH4

Combining t w o methane molecules t o ethane a n d hydrogen is (equation 43) endothermic by some 16 kcal mol Any condensation of methane t o ethane a n d subsequently to higher hydrocarbons must thus overcome unfavorable thermodynamics. This can be achieved in condesation processes of an oxidative nature, where hydrogen is removed by the oxidant. I n our original studies, the SbFg o r FSO3H component of the superacid system also acted as oxidants. The oxidative condensation of methane was subsequently studied further in more detah^'^. It was found that with added suitable oxidants such as halogens, oxygen, sulfur or selenium t h e superacid-catalyzed condensation of methane is feasible (equation 44). Significant practical problems, however, remain in carrying out the condensation effectively. Conversion so far achieved has been only in low yields. D u e t o the easy cleavage of longer-chain alkanes by t h e same superacids, C3-C6 products predominate. 2CH4—>C2H6 + H2

(43)

halogens, 0 2 , S ^ , S e

CH, superacid catalyst

' hydrocarbons

(44)

630


A further approach found useful was the use of natural gas instead of pure methane in the condensation reaction^^. W h e n natural gas in dehydrogenated, the C 2 - C 4 alkanes it contains are converted into olefins. The resulting methane-olefin mixture can then be passed without separation through a superacid catalyst resulting in exothermic alkylative condensation (equation 45). CH4 + R C H = C H 3 — > C H 2 C H R C H 3

(45)

Alkylation of methane by olefins under superacid catalysis was demonstrated b o t h in solution chemistry under stable ion conditions'^ and in heterogeneous gas-phase alkylations over solid catalysts using a flow system'^. N o t only propylene and butylenes but also ethylene could be used as alkylating agents. T h u s alkylation of methane, ethane, p r o p a n e and n-butane by the ethyl cation generated via protonation of ethylene in superacid media has been studied by Siskin^^, Sommer and c o w o r k e r s ^ \ and Olah and coworkers, respectively^^. The difficulty lies in generating in a controlled way a very energetic primary carbenium ion in the presence of excess methane and at the same time avoiding oligocondensation of ethylene itself. Siskin carried out the reaction of methane-ethylene (86:14) gas mixture t h r o u g h a 10:1 H F : T a F 5 solution under pressure with strong mixing (equation 46). Along with the recovered starting materials 60% of C3 was found (propane and propylene). Propylene is formed when propane, which is substantially a better hydride donor, reacts with the ethyl cation (equation 47). H CH,

•CH.

CHjCH^

^CH^

V - H *

(46)

CH3CH2CH3 CH3CH2CH3 + CH3 - C H 2 ^

> CH3 - CH3 + CH3 - C H - CH3

(47)

CH3—CH=CH2 P r o p a n e as a degradation product of polyethylene was, however, ruled out because ethylene alone under the same conditions does not give any propane. U n d e r similar conditions but under hydrogen pressure, polyethylene reacts quantitatively to form C3 to Cg alkanes, 8 5 % of which are isobutane and isopentane. These results further substantiate the direct alkane-alkylation reaction and the intermediacy of the pentacoordinate carbonium ion. Siskin also found that when ethylene was allowed to react with ethane in a flow system, n-butane was obtained as the sole product (equation 48)^° indicating that the ethyl cation is alkylating the primary C — H b o n d through a five-coordinate carbonium ion. ^+ H -CH,

CHo=CH5

CH3CH2

CH3CH^'

A.

CH2CH3

-H

C H 3C H gC H gC H 3

(48)


631

If the ethyl cation had reacted with excess ethylene, primary 1-butyl cation would have been formed which irreversibly would rearrange to the more stable s-butyl and subsequently t-butyl cation giving isobutane as the end product. The yield of the alkene-alkane alkylation in a homogeneous H F : S b F 5 system depending on the alkene:alkane ratio has been investigated by Sommer and coworkers in a batch system with short reaction times^^ The results support direct alkylation of methane, ethane and p r o p a n e by the ethyl cation and the product distribution depends on the alkene:alkane ratio. Despite the unfavorable experimental conditions in a batch system for kinetic controlled reactions, a selectivity of 80% in n-butane was achieved through ethylation of ethane. The results show, however, that to succeed in the direct alkylation the following conditions have to be met: (1) The olefin should be totally converted to the reactive cation (incomplete protonation favors the polymerization and cracking processes); this means the use of a large excess of acid and good mixing. (2) The alkylation product must be removed from the reaction mixture before it transfers a hydride to the reactive cation, in which case the reduction of the alkene is achieved. (3) The substrate to cation hydride transfer should not be easy; for this reason the reaction shows the best yield and selectivity when methane and ethane are used. Direct evidence for the direct ethylation of methane with ethylene was provided by Olah and his g r o u p ^ ' using ^^C-labeled methane (99.9% ^^C) over sohd superacid catalysts such as T a F 5 : A l F 3 , T a F g and ShF^: graphite. P r o d u c t analyses by gas c h r o m a t o g r a p h y - m a s s spectrometry ( G C - M S ) are given in Table 2. These results show a high selectivity in mono-labeled p r o p a n e ^^CC2H8 which can only arise from direct electrophilic attack of the ethyl cation on methane via pentacoordinate carbonium ion (equation 49).

CH3—CH2

-

CH3

CHg'

'"''^CH3

CH3CH2''^CH3

(49)

An increase of the alkene:alkane ratio results in a significant decrease in single-labeled propane, ethylene polymerization—cracking and hydride transfer become the main reactions. This labeling experiment carried out under conditions where side reactions were negligible is indeed unequivocal proof for the direct alkylation of an alkane by a very reactive carbenium ion. Polycondensation of alkanes over H S 0 3 F : S b F 5 has also been achieved by Roberts and Caliban^^. Several low-molecular-weight alkanes such as methane, ethane, propane, butane and isobutane were polymerized to highly branched ohy oligomers with a

TABLE 2. Ethylation of ^^CH^ with C2H4 Label content of C3 fraction (%)

Products normalized {yX' ^^CH4!C2ll4

Catalyst

98.7:1.3 99.1:0.9 99.1:0.9

TaF5:AlF3 TaFs SbF 5: graphite

"All values reported are in mole percent. Êxcluding methane.

C2H6

C3H8

1-C4H10

51.9

9.9 15.5 31.5

38.2 3.0

64.1

C2H5F

^^CC^Hg

C3H8

81.5 4.4

31 91 96

69 9 4

G. A. Olah a n d G. K. Surya P r a k a s h

632

molecular-weight range from the molecular weight of monomers to a r o u n d 700. These reactions again fohow the same initial protolysis of the C — H or C — C b o n d which results in a very reactive carbenium ion. Similarly, the same workers^"^ were also able to polycondense methane with a small a m o u n t of olefins such as ethylene, propylene, butadiene a n d styrene t o yield ohy polymethylene oligomer with a molecular weight ranging from 100 to 700. VII. CARBOXYLATION

Alkanecarboxylic acids are readhy prepared from alkenes a n d carbon monoxide or formic acid in strongly superacidic solutions^^. T h e reaction between carbenium ions generated from alkenes a n d carbon monoxide affording oxocarbenium ions (acyl cations) is the key step in the well-known K o c h - H a a f reaction used for the general preparation of carboxylic acids^^'^^. T h e conventional protic acid such as H2SO4 was found t o be less effective for the generation of oxocarbenium ions. Subsequent investigations^'^ found that the superacidic H F i B F g or C F j S O g H ^ ^ are very efficient t o effect this process. T h e volatility of the former catalyst system, however, necessitates high-pressure conditions. The use of superacidic activation of alkanes to their related carbocations allowed the preparation of alkanecarboxylic acids from alkanes themselves with C O 2 fohowed by aqueous work-up. The formation of Cg or C7 carboxylic acids along with some ketones was reported in the reaction of isopentane, methylcyclopentane a n d cyclohexane with C O in H F i S b F s at ambient temperatures a n d atmospheric pressures^^.

TABLE 3. Superacid-catalyzed reaction of alkanes with CO'' Product distribution (%)

Substrate 2-Methyl butane n-Pentane 2-Methyl pentane n-Hexane 2,2-Dimethyl butane n-Heptane 2,2,4-Tri methylpentane n-Octane n-Nonane

Total yield^

C3

C4

acid

acid

55

Some

53 61 69

3 — 2

57 80 102 90 61

Some

— Some Some

C5 acids sectert-

Some 4 67 14 26 27 Some 3 67 10 18 13 Some 10 80 47 48 90 — 100 100 6 87 90 34 31 87

33 73 33 87 20 10

Ce acids ten 95 38 57 39 3 40 5 39 15 40 5 38

sec-

C7 acids sectert-

Cg acids

Trace

—

Trace

—

94 71 29 65 67 33 75 65 35 Some

—

62 61 60 61 60

Some

Some

62

— 0 10 13

7 38 33 38

Some

Some

2

Some

62 62

"Reaction time, 1 h. Reaction temperature 30 °C. Alkane 20 mmol, SbPg/alkane = 2 mol ratio, H F / S b F g = 5 m o l ratio. ''Based on alkane used.


633

Yoneda a n d coworkers have also found that other alkanes can also be carboxylated with C O in HFiSbEg superacid s y s t e m T e r t i a r y carbenium ions formed by protolysis of C — H bonds of branched alkanes in H F i S b F s undergo skeletal isomerization a n d disproportionation prior to reacting with C O in the same acid system t o form oxocarboxylic acids after hydrolysis. Alkyl methyl ketones with short alkyl chain (less than C4) d o not react under these conditions due to the proximity of the positive charge on the protonated ketone a n d the developing carbenium i o n ^ ^ T h e results are shown in Table 3. When using tertiary C5 or Cg alkanes a considerable a m o u n t of secondary carboxyhc a c i d s a r e produced by the reaction of C O with secondary alkyl carbenium ions. Such cations are formed as transient intermediates by skeletal isomerization of the initially formed tertiary cations. Carboxylic acids with lower number of carbon atoms than the starting alkanes are formed from the fragment alkyl cations generated by the protolysis of C — C bonds of the straight-chain alkanes. Intermolecular hydride shift between the fragment cations a n d the starting alkanes gives rise to a large a m o u n t of carboxyhc acids with alkyl groups of the same number of carbon atoms as the starting alkanes. F o r alkanes with more than C7 atoms, ^-scission occurs exclusively t o produce C4-, C5- and Cg- carboxylic acids. Sommer a n d coworkers"^^^ have achieved selective carbonylation of p r o p a n e in superacidic media p r o m o t e d by halogen. When p r o p a n e - c a r b o n monoxide mixture ( C O : p r o p a n e ratio = 3) was passed through H F - S b E g in a Kel-F reactor at — 1 0 ° C with the addition of a smah a m o u n t of sodium bromide (Br~/Sb:0.5mol%), the N M R spectrum indicated the formation of isopropyloxocarbenium ion in 9 5 % yield with a total conversion of 9% of the propane. This remarkable reaction can be rationalized as in equation 50.

Br~

+

Br"^

Br —

2H

+

H2

(50) CO CO

Br"

CHsCHgCHj-

CH3CHCH3+ HBr

CH3CHCH3

VIII. FORMYLATION

Whereas electrophilic formylation of aromatics with C O was studied under both the G a t t e r m a n - K o c h condition a n d with superacid c a t a l y s i s ' ^ i n some detail, electrophilic formylation of saturated aliphatics remains virtually unrecognized. Reactions of acyclic hydrocarbons of various skeletal structures with C O in superacid media were recently studied by Yoneda a n d coworkers^^"^^ as discussed in the previous section. Products obtained were only isomeric carboxylic acids with lower number of carbon atoms than the starting alkanes. F o r m a t i o n of the carboxylic acids were accounted by the reactions of parent, isomerized a n d fragmented alkyl cations with C O t o form the oxocarbenium ion intermediates ( K o c h - H a a f reaction) followed by their quenching with water. N o formylated products in these reactions have been identified. We have recently reported the superacid catalyzed reaction of the polycyclic cage hydrocarbon a d a m a n t a n e with C O (equation 51)^^. 1-Adamantanecarboxaldehyde was obtained in various percent yields (Table 4) in different superacids along with


634

TABLE 4. Percentage yield of 1-adamantanecarboxaldehyde superacids in Freon-113"

different

Yield 1-Ad-CHO (%)

Adamantane acid

Acid systems

in

CF3SO3H

0.2 9.1^ 3.4 14.5' 8.2 21.0''

C F 3 S 0 3 H - h B ( O S 0 2 C F 3 ) 3 (1:1) C F 3 S 0 3 H + SbF5 (1:1)

"All reactions were carried out from — 78 °C to room temperature. ''Isolated yields.

1-adamantane-carboxylic acid and 1-adamantanol (the products of the reaction of 1-adamantyl cation). The mechanism of formation of 1-adamantanecarboxaldehyde has been investigated. F o r m a t i o n of aldehyde product from 1-adamantanoyl cation via hydride abstraction (Scheme 9) from a d a m a n t a n e is only a minor pathway. The major pathway by which 1-adamantanecarboxaldehyde is formed is by direct ^-insertion of the protosolvated formyl cation into the C — H b o n d of a d a m a n t a n e at the bridgehead position (equation 52). COOH 1.C0 (1200

+

Superacid

r. 2.

psi)

(51)

t. H,0

C=

COt

0+

c=o

CO

Zl-/

Zl^ COOH H,0

OH

CHO

SCHEME 9

Zt:/

C = 0

—HA


V + [HCO]

635 CHO (52)

Whereas the formyl cation could n o t be directly observed by N M R spectroscopy^^'"^^j its intermediacy has been well estabhshed in aromatic formylation r e a c t i o n s ' ^ I n order to account for the fahure to observe the formyl cation, it has been suggested that C O is protonated in acid media to generate protosolvated formyl cation^^'^\ a very reactive electrophhe. Protosolvation of the carbonyl oxygen allows facile deprotonation of the methine proton, thus resulting in rapid exchange via involvement of the isoformyl cation. Insertion of protosolvated formyl cation into the C — H a-bond has further been substantiated by carrying o u t the reaction of 1,3,5,7-tetradeuteroadamantane with C O in superacid media. 3,5,7-Trideutero-l-adamantanecarboxaldehyde-H a n d 3,5,7trideutero-l-adamantanecarboxaldehyde-D were obtained in the ratio 94:6. This work provides the first direct evidence for the electrophilic formylation of a saturated hydrocarbon by C O under superacid catalysis. IX. OXYFUNCTIONALIZATION

Functionalization of aliphatic hydrocarbons into their oxygenated c o m p o u n d s is of substantial interest. In connection with the preparation a n d studies of a great variety of carbocations in different superacid systems^', electrophilic oxygenation of alkanes with ozone a n d hydrogen peroxide was investigated by O l a h a n d coworkers in superacid media under typical electrophilic conditions^'. T h e electrophhes are the protonated ozone (ÔgH) or the hydrogen peroxonium ion H 3 0 2 ^ . T h e reactions are depicted as taking place via initial electrophihc attack by the electrophhes on the a-bonds of alkanes through the pentacoordinated carbonium ion transition state followed by p r o t o n elimination to give the desired product. W h e n hydrogen peroxide is protonated in superacid media, hydrogen peroxonium ion ( H 3 0 2 ^ ) is formed. Certain peroxonium salts have been weh characterized a n d even isolated as stable salts^^'^"^. Hydrogen peroxonium ion is considered as the incipient ^ O H ion, a strong electrophhe for electrophilic hydroxylation at single (cr) bonds of alkanes. T h e reactions are thus simhar to those described previously for electrophhic protonation (protolysis), alkylation a n d formylation. Superacid-catalyzed electrophilic hydroxylation of branched alkanes were carried o u t using H S 0 3 F : S b F 5 : S 0 2 C l F with various ratios of alkane a n d hydrogen peroxide at different temperatures^^. Some of the results are summarized in Table 5. P r o t o n a t e d hydrogen peroxide inserts into the C — H b o n d of alkanes. T h e mechanism is illustrated in Scheme 10 with isobutane. The intermediate pentacoordinate hydroxycarbonium ion, in addition to giving the insertion product, gives tert-butyl cation (by elimination of water) which is responsible for the formation of dimethylmethylcarboxonium ion through the intermediate tert-butyl hydroperoxide. Hydrolysis of the carboxonium ion gives acetone a n d methanol. W h e n the reaction was carried out by passing isobutane at r o o m temperature through a solution of Magic Acid in excess hydrogen peroxide, in addition to the insertion product, a number of other products were also formed which were rationalized as arising from hydrolysis of the carboxonium ion a n d from Baeyer-Villiger oxidation of acetone. T h e mechanism was further substantiated by independent treatment of alkane a n d

636

G. A. O l a h a n d G. K. Surya P r a k a s h TABLE 5. Products of the reaction of branched-chain alkanes with H2O2 in HSO3F: S b F 5 : S 0 2 C l F solution

Alkane"

H2O2 (mmol)

Temperature

2

-78 -20 -78 -20 -78 -20 + 20

4

C

1 6

c—c- c

1 6

H

Major Products

in

(CH3)2C=O^CH3 (CH3)2C=0+CH3 (CH3)2C=0+CH3 ( C H 3 ) 2 C = 0 + CH3 (trace), DAP^ (25%), CH3OH (50%), CH3CO—0—CH3 (25%), (CH3)2C-O^C2H5 C2H5(CH3)2C + (CH3)2C = O^C2H5

c

1 C — C - C—c

3

H C

6

1 1

4

-78 -20 -78 -20 -78

6

-40

1 C

"

( C H 3 ) , C = 0 + C H 3 (50%), ( C H 3 ) 2 C = 0 + H (50%) ( C H 3 ) 2 C = 0 + C H 3 (50%), D A P (50%)

c—c- -C-C

1 1 H

c

"Alkane, 2 mmole; ''DAP, dimeric acetone peroxide.

H HOOH +

H

HOOH

,

CH,

CH3

CH,

I CH,

^ ^ 3 — C - H

- C - -
--Br

Ag^bFg

SbFg"-!-

AgBr

R3C'

R3C-

•Br

+

H"^SbFg"

S C H E M E 16 Even electrophhic fluorination of alkanes has been reported. F 2 a n d fluoroxytrifluoromethane have been used to fluorinate tertiary centers in steroids a n d a d a m a n t a n e s by Barton a n d coworkers T h e electrophhic nature of a reaction involving polarized b u t not cationic fluorine s p e c i e s h a s been invoked. G a l a n d Rozen^^^ have carried out direct electrophilic fluorination of hydrocarbons in the presence of chloroform. F 2 appears to be strongly polarized in chloroform (hydrogen bonding with the acidic proton of CHCI3). However, so far n o positively charged fluorine species (fluoronium ion) is known in solution chemistry. In extending the electrophilic halogenation (chlorination and bromination) of methane to catalytic heterogeneous gas-phase reactions, we have recently found^^^ that methane can be chlorinated or brominated over various solid acid o r supported platinum group metal catalysts (the latter being the heterogeneous analog of Shilov's solution chemistry) to methyl halides with high selectivity under relatively mild conditions. Table 8 summarizes some of the results. Mechanistically, both reactions are electrophilic insertion reactions into the methane C — H bonds. In the platinum insertion reaction subsequent chlorolysis of the surface

644


T A B L E 8. C h l o r i n a t i o n a n d b r o m i n a t i o n o f m e t h a n e o v e r s u p o r t e d a c i d c a t a l y s t s

Catalyst

GHSV"

Conversion

CH4/CI2

Reaction temperature (°C)

(mlg-^h-i)

(%)

CH3CI

CH2CI2

1:2 1:2 1:2 2:1 1:3 1:4 1:4 1:2 1:2 1:2

250 235 235 235 250 270 185 250 200 180

100 50 1400 1200 50 100 100 100 100 100

16 14 15 13 10 34 18 26 11 7

88 82 93 96 90 96 88 90 97 98

\2' 6 7 4 10 4 12 10 3 2

GHSV"

Conversion

CH4/Br2

Reaction temperature (°C)

(mlg-^H-i)

(%)

10% F e O , C y A l 2 0 3 20% T a O F 3 / A l 2 0 3

20% N b O F 3 / A l 2 0 3 10% Z r O F 2 / A l 2 0 3 Nafion-H 20% G a O , C l y / A l 2 0 3 20% T a F s - N a f i o n - H 25% S b F s - g r a p h i t e

Catalyst

Product %

P r o d u c t (%) CH3Br CH2Br2

20% S b O F 3 / A l 2 0 3 5:1 200 100 20 20% T a O F 3 / A l 2 0 3 15:1 250 50 14 Supported platinum metal-catalyzed h a l o g e n a t i o n of m e t h a n e

CH4/X2 Catalyst

(X-Cl,Br)

5% P d / B a S 0 4

1:3 1:3 1:3 2:1 3:1 2:1

05%

2:1

05%

Pt/Al203

Pt/Al203

Reaction temperature

GHSV" (mlg-^H-i)

Chlorination 100 600 150 600 200 600 250 300 250 300 200 600 Bromination 200 300

Conversion

99 99

Product (%)

CH3CI

CH2CI2

11' 16' 32' 23^ 26^^ 30^^

-100 92 92 98 99 99

8 8 ^ Eat.

cat. CH

^

-cat. CH cat.

CHjCHgK CH3OH

+

V

C H 2 = C H 2 '

cat.

CH

S C H E M E 20 considering that surface complexation could somewhat affect t h e otherwise very endothermic thermodynamics (see Scheme 21). [ C H 2 + H 3 O + ] zeolite>-(TT

r^TT

H-zeolite

CH3OH

+

> C H 3 O H 2 ' zeolite [CH3+ + H 2 O ] zeolite-

CH3OH—^CH2 -200.7 2CH3OH 2(-200.7)

+390.4

+H2O -241.8

AH = + 3 4 9 . 3 kcal m o l " ^

> CH3OCH3 + H2O + 184.1 - 2 4 1 . 8 AH = - 2 4 . 5 kcal m o P ^ S C H E M E 21

It is therefore reasonable t o suggest that in t h e zeohte-catalyzed process t o o condensation proceeds via bimolecular dehydration of methyl alcohol t o dimethyl ether,

648

G. A. Olah a n d G. K. Surya P r a k a s h

which subsequently is transformed via the oxonium ylide pathway a n d intermolecular methylation to ethyl oxonium species (the crucial —C2 b o n d formation step)^^^ A radical or radical ion type condensation mechanism inevitably should give also competing coupling products which are, however, n o t observed. Once ethylene is formed in t h e system it c a n undergo acid-catalyzed oligomerization-cleavage reactions, undergo methylene insertion or react further with methyl alcohol giving higher hydrocarbons. With increase in the acidity of the catalyst, methyl alcohol or dimethyl ether undergo condensation to saturated hydrocarbons or aromatics, with no olefin by-products. With tantalum or niobium pentafluoride based catalyst the studies at 300 °C resulted in conversion t o gasoline range branched hydrocarbons a n d some aromatics (30% of the product)^ This composition is simhar to that reported with H - Z S M - 5 zeohte catalyst. T h e condensation of methyl chloride or bromide t o ethylene proceeds by a related mechanistic path involving initial acid-catalyzed dimethylhalonium ion (or related catalyst complex) formation with subsequent p r o t o n elimination t o a reactive methylhalonium methylide, which then is readily methylated by excess methyl halide. T h e ethylhalonium ion intermediate gives ethylene by j5-elimination (see Scheme 22). . C H , = C H , + 2HX

2CH,X CH3X +

> [CH2X—cat]

"cat.

CH3CH2X—cat.

CH2=CH2

2CH3X ^ £ i £ ^ CH3XCH3CI—cat. -H+

jbase

CH3XCH2

^CH3XCH2CH3X—cat. CH3X + C H 2 = C H 2 S C H E M E 22

Similar reaction paths c a n be visualized for condensation of methyl mercaptan o r methylamines. It is interesting to note that Corey a n d Chaykovsky's well-known synthetic studies^ with the use of dimethylsulfonium methylide mentioned the need t o generate the ylide at low temperatures, which otherwise led t o decomposition giving ethylene. Indeed, this reaction is simhar t o that involved in the higher-temperature a c i d - b a s e catalyzed condensation reaction (Scheme 23). 2CH3SH

CHp=CH 2

CH3SH

CH3SCH3

.H+

catalyst

^ ^ 3 \ ^ / c a t

(CH3)2S

cat

catalyst

I

CH2CH3

I

S C H E M E 23

XIII. CONCLUSIONS

O n e of us, in the conclusion of a review in Carbocations and Electrophilic Reactions"^^, wrote some 16 years a g o o n the realization of the electron d o n o r ability of shared


649

o--electron pair: ' M o r e importantly, the concept of pentacoordinated carbonium ion formation via electron sharing of single bonds with electrophhic reagents in three-center b o n d formation promises to open up a whole new i m p o r t a n t area of chemistry. Whereas the concept of tetravalency of carbon obviously is not affected, carbon penta- (or tetra-)coordination as a general p h e n o m e n o n must be recognized. Trivalent carbenium ions play a major role in electrophilic reactions of Ti-and n-donors, whereas pentacoordinated carbonium ions play an equally i m p o r t a n t simhar role in electrophihc reactions of o--donor saturated systems'^ ^ T h e realization of the electron d o n o r ability of shared (bonded) electron pairs (single bonds) could one day rank equal in importance with G . N . Lewis' r e a l i z a t i o n ^ o f the importance of the electron d o n o r unshared (non-bonded) electron pairs. We can now not only explain the reactivity of saturated hydrocarbons and single bonds in general in electrophilic reactions, but indeed use this understanding to explore m a n y new areas and reactions of carbocation chemistry'. It seems that the intervening years have justified that prediction to a significant degree. The electrophhic chemistry of alkanes has rapidly expanded and has started to occupy a significant role even in the conversion of methane.

XIV.

REFERENCES

1. F. Asinger, Paraffins, Chemistry and Technology, Pergamon Press, N e w York, 1965. 2. (a) For a comprehensive early review, see G. A. Olah, Angew. Chem., Int. Ed. Engl., 12, 173 (1973) and references cited therein. (b) For reviews on superacids, see G. A. Olah, G. K. S. Prakash and J. Sommer, Superacids, Wiley-Interscience, N e w York, 1985. 3. H. S. Bloch, H. Pines and L. Schmerhng, J. Am. Chem. Soc, 68, 153 (1946). 4. (a) G. A. Olah and J. Lukas, J. Am. Chem. Soc, 89, 2227 (1967). (b) G. A. Olah and J. Lukas, J. Am. Chem. Soc, 89, 4739 (1967). 5. (a) A. F. Bickel, G. J. Gaasbeek, H. Hogeveen, J. M. Oelderick and J. C. Platteuw, Chem. Commun., 634 (1967). (b) H. Hogeveen and A. F. Bickel, Chem. Commun., 635 (1967). 6. G. K. S. Prakash, A. Husain and G. A. Olah, Angew. Chem., 95, 51 (1983). 7. G. A. Olah and J. Lukas, J. Am. Chem. Soc, 90, 933 (1968). 8. G. A. Olah and R. H. Schlosberg, J. Am. Chem. Soc, 90, 2726 (1968). 9. H. Hogeveen and C. J. Gaasbeek, Reel. Trav. Chim. Pays-Bas, 87, 319 (1968). 10. G. A. Olah, G. Klopman and R. H. Schlosberg, J. Am. Chem. Soc, 91, 3261 (1969). 11. (a) G. A. Olah, J. Shen and R. H. Schlosberg, J. Am. Chem. Soc, 92, 3831 (1970). (b) T. Oka, Phys. Rev. Lett., 43, 531 (1980). 12. H. Hogeveen and A. F. Bickel, Reel. Trav. Chim. Pays-Bas, 86, 1313 (1967). 13. H. Pines and N. E. Hoffman, in Friedel-Crafts and Related Reactions, Vol. II (Ed. G. A. Olah), Wiley-Interscience, New York, 1964, p. 1216. 14. (a) G. A. Olah, Y. Halpern, J. Shen and Y. K. Mo, J. Am. Chem. Soc, 93, 1251 (1971). (b) G. A. Olah, N. Trivedi and G. K. S. Prakash, unpubhshed results. 15. J. W. Otvos, D. P. Stevenson, C. D. Wagner and O. Beeck, J. Am. Chem. Soc, 73,5741 (1951) 16. H. Hoffman, C. J. Gaasbeek and A. F. Bickel, Reel. Trav. Chim. Pays-Bas, 88, 703 (1969). 17. R. Bonnifay, B. Torek and J. M. Hellin, Bull. Soc Chim. Fr., 808 (1977). 18. (a) J. Lucas, P. A. Kramer and A. P. Kouwenhoven, Reel. Trav. Chim. Pays-Bas, 92,44 (1973). (b) J-C. Culman and J. Sommer, J. Am. Chem. Soc, 112, 4057 (1990). 19. W. O., Haag and R. H. Dessau, International Catalysis Congress (W. Germany), 1984, II, 105. 20. For a review, see D. M. Brouwer and H. Hogeveen, Prog. Phys. Org. Chem., 9, 179 (1972). 21. E. W. Colvin, Silicon in Organic Synthesis, Butterworths, London, 1981. 22. W. P. Weber, Silicon Reagents in Organic Synthesis, Springer-Verlag, Berhn, Heidelberg, New York, 1983. 23. J. Bertram, J. P. Coleman, M. Fleischmann and D. Plechter, J. Chem. Soc. Perkin Trans 2, 374 (1973). 24. For a review, see P. L. Fabre, J. Devynck and B. Tremihon, Chem. Rev., 82, 591 (1982).

650 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

43. 44. 45.

46. 47. 48. 49. 50.

51. 52. 53. 54. 55. 56. 57. 58.

59.

G. A. O l a h a n d G. K. S u r y a P r a k a s h J. Devynck, P. L. Fabre, A. Ben Hadid and B. Tremihon, J. Chem. Res., 200 (1979). A. Germain, P. Ortega and A. Commeyras, Nouv. J. Chim., 3, 415 (1979). H. Choucroun, A. Germain, D. Brunei and A. Commeyras, Nouv. J. Chim., 1, 83 (1983). C. D . Nenitzescu and A. Dragan, Ber. Dtsch. Chem. Ges., 66, 1892 (1933). H. Pines and N. E. Joffman, in Friedel-Crafts and Related Reactions, Vol. 2 (Ed. G. A. Olah), Wiley-Interscience, New York, 1964, p. 1211. C. D . Nenitzescu, in Carbonium Ions, Vol. II (Eds. G. A. Olah and P. v. R. Schleyer), Wiley-Interscience, New York, 1970, p. 490. F. Asinger, in Paraffins, Pergamon Press, N e w York, 1968, p. 695. (a) R. Bonnifay, B. Torek and J. M. Helhn, Bull. Soc. Chim. Fr., 1057 (1977). (b) R. Bonnifay, B. Torek and J. M. Helhn, Bull. Soc. Chim. Fr., 36 (1978). D. Brunei, J. Itier, A. Commeyras, R. Phan Tan Luu and D. Mathieu, Bull. Soc. Chim. Fr. II, 249, 257 (1979). G. A. Olah, U.S. Patent 4,472,268 (1984); 4,508,618 (1985). G. A. Olah, U.S. Patent 4,613,723 (1986). (a) F. Le Normand, F. Fajula, F. Gault and J. Sommer, Nouv. J. Chim. 6, 411 (1982). (b) F. Le Normand, F. Fajula and J. Sommer, Nouv. J. Chim., 6, 291 (1982). K. Laali, M. Muller and J. Sommer, Chem. Commun., 1088 (1980). G. A. Olah, J. Kaspi and J. Bukala, J. Org. Chem., 42, 4187 (1977). G. A. Olah, U.S. Patent 4,116,880 (1978). G. A. Olah and J. Kaspi, J. Org. Chem., 42, 3046 (1977). G. A. Olah, J. R. DeMember and J. Shen, J. Am. Chem. Soc, 95, 4952 (1973). (a) P. V. R. Schleyer, J. Am. Chem. Soc, 79, 3292 (1957). (b) R. C. Fort, Jr., in Adamantane, the Chemistry of Diamond Molecules (Ed. P. Gassman), Marcel Dekker, N e w York, 1976. (c) G. A. Olah and J. A. Olah, Synthesis, 488 (1973). G. A. Olah and O. Farooq, J. Org. Chem., 51, 5410 (1986). (a) O. Farooq, S. M. F. Farnia, M. Stephenson and G. A. Olah, J. Org. Chem., 53,2840 (1988). (b) G. A. Olah, A-H. Wu, O. Farooq and G. K. S. Prakash, J. Org. Chem., 54, 791 (1989). (a) M. Vol'pin, I. Akhrem and A. Orhnkov, New J. Chem., 13, 771 (1989). (b) L. Paquette and A. Balogh, J. Am. Chem. Soc, 104, 774 (1982). (c) W.-D. Fessner, B-A. R. C. Murty, J. Worth, D. Hunkler, H. Fritz, H. Prinzback, W. R. Roth, P. V. R. Schleyer, A. B. McEwen and W. F. Maier, Angew. Chem., Int. Ed. Engl, 26, 452 (1987). G. C. Schuit, H. H o o g and J. Verhuis, Reel. Trav. Chim. Pays-Bas, 59, 793 (1940); British Patent 535054 (1941). H. Pines and R. C. Wackher U.S. Patent 2,406,633 (H. Pines to Universal Oil); Chem. Abstr., 41, 474 (1947). For a review, see G. A. Olah, Carbocations and Electrophilic Reactions, Verlag Chemie, Wiley, N e w York, 1974. For a review, see D. M. Brouwer and H. Hogeveen, Prog. Phys. Org. Chem., 9, 179 (1972). (a) G. A. Olah, M. Bruce, E. H. Edelson and A. Husain, Fuel, 63, 1130 (1984). (b) G. A. Olah and A. Husian, Fuel, 63, 1427 (1984). (c) G. A. Olah, M. Bruce, E. H. Edelson and A. Husain, Fuel, 63, 1432 (1984). G. A. Olah, J. R. DeMember and R. H. Schlosberg, J. Am. Chem. Soc, 91, 2112 (1969). G. A. Olah, J. R. DeMember, R. H. Schlosberg and Y. Halpern, J. Am. Chem. Soc, 94, 156 (1972). G. A. Olah, Y. K. M o and J. A. Olah, J. Am. Chem. Soc, 95, 4939 (1973). G. A. Olah, J. R. Demember and J. Shen, J. Am. Chem. Soc, 95, 4952 (1973). G. A. Olah and A. M. White, J. Am. Chem. Soc, 91, 5801 (1969). G. A. Olah, O. Farooq, V. V. Krishnamurthy, G. K. S. Prakash and K. Laah J. Am. Chem. Soc, 107, 7541 (1985). G. A. Olah, U.S. Patent 4,443,192; 4,465,893; 4,467,130 (1984); 4,513,164 (1985). G. A. Olah and J. A. Olah, J. Am. Chem. Soc, 93, 1256 (1971); M. Siskin, R. H. Schlosberg and W. P. Kocsis, in New Strong Acid Catalyzed Alkylation and Reduction Reactions (Eds. L. F. Albright and R. A. Gikdsktm), American Chemical Society Monographs, N o . 55, Washington, D.C. (1977). G. A. Olah, J. D. Felberg and K. Lammertsma, J. Am. Chem. Soc, 105, 6529 (1983).

13. Electrophilic reactions on alkanes 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.

100.

101. 102. 103.

651

M. Siskin, J. Am. Chem. Soc., 98, 5413 (1976). J. Sommer, M. Muller and K. Laali, Nouv. J. Chim., 6, 3 (1982). G. A. Olah, J. D . Felberg and K. Lammertsma, J. Am. Chem. Soc, 105, 6529 (1983). D. T. Roberts, Jr. and L. E. Caliban, J. Macromol. Sci (Chem.)., A7(8), 1629 (1973). D . T. Roberts, Jr. and L. E. Caliban, J. Macromol. Sci (Chem.)., A7(8), 1641 (1973). G. A. Olah and J. A. Olah, Friedel-Crafts and Related Reactions, Vol. 3, Part 2, Wiley-Interscience, N e w York, 1964, p. 1272. H. Hogeveen, Adv. Phys. Org. Chem., 10, 29 (1973). W. F. Gresham and G. E. Tabet, U.S. Patent 2,485,237 (1946). B. L. Booth and T. A. El-Fekky, J. Chem. Soc Perkin Trans. 1, 2441 (1979). R. Paatz and G. Weisberger, Chem. Ber., 100, 984 (1967). N. Yoneda, T. Fukuhara, Y. Takahashi and A. Suzuki, Chem. Lett., 17 (1983). N. Yoneda, H. Sato, T. Fukuhara, Y. Takahashi and A. Suzuki, Chem. Lett., 19 (1983). (a) N. Yoneda, Y. Takahashi, T. Fukuhara and A. Suzuki, Bull. Chem. Soc Jpn., 59,2819 (1986). (b) S. Delavarnne, M. Simon, M. Fauconet and J. Sommer, J. Am. Chem. Soc, 111, 383 (1989). G. A. Olah, F. Pelizza, S. Kobayashi and J. A. Olah, J. Am. Chem. Soc, 98, 296 (1976). S. Fujiyama, M. Takagawa and S. Kajiyama, German Patent 2,425591 (1974). J. M. Delderick and A. Kwantes, British Patent 1,123,966 (1968). W. F. Gresham and G. E. Tabet, U.S. Patent 21,485,237 (1949). O. Farooq, Ph.D. thesis. University of Southern California, Los Angeles, CA (Dec. 1984). G. A. Olah, K. Laah and O. Farooq, J. Org. Chem., 50, 1483 (1985). O. Farooq, M. Marcelh, G. K. S. Prakash and G. A. Olah, J. Am. Chem. Soc, 110,864 (1988). G. A. Olah and S. Kuhn, J. Am. Chem. Soc, 82, 2380 (1960). H. R. Christen, Grundlagen des Organische Chemie, Verlag Sauerlander-Diesterweg, Aarau-Frankfurt am Main, 1970, p. 242. G. A. Olah, D. G. Parker and N. Yoneda, Angew. Chem., Int. Ed. Engl., 17, 909 (1978). K. O. Christe, W. W. Wilson and E. C. Curtis, Inorg. Chem., 18, 2578 (1976). G. A. Olah, A. L. Berrier and G. K. S. Prakash, J. Am. Chem. Soc, 104, 2373 (1982). G. A. Olah, N. Yoneda and D . G. Parker, J. Am. Chem. Soc, 99, 483 (1977). G. A. Olah, D. G. Parker, N. Yoneda and F. Pelizza, J. Am. Chem. Soc, 98, 2245 (1976). (a) G. A. Olah, N . Yoneda and D . G. Parker, J. Am. Chem. Soc, 98, 5261 (1976). (b) G. A. Olah, T. D . Ernst, C. B. Rao and G. K. S. Prakash, New J. Chem., 13, 791 (1989). R. Tambarulo, S. N. Ghosh, C. A. Barrus and W. Gordy, J. Chem. Phys., 24, 851 (1953). P. D. Bartlett and M. Stiles, J. Am. Chem. Soc, 77, 2806 (1955). J. P. Wibault, E. L. J. Sixma, L. W. E. Kampschidt and H. Boer, Reel. Trav. Chim. Pays-Bas, 69, 1355 (1950). J. P. Wibault and E. L. J. Sixma, Reel. Trav. Chim. Pays-Bas, 71, 76 (1951). P. S. Bailey, Chem. Rev., 58, 925 (1958). L. Homer, H. Schaefer and W. Ludwig, Chem. Ber., 91, 75 (1958). P. S. Bailey, J. W. Ward, R. E. Hornish and F. E. Potts, Adv. Chem. Ser., 112, 1 (1972). Further oxidation products, i.e. acetylium ion and CO2, were reported to be observed in a number of the reactions studied. Such secondary oxidations are not induced by ozone. T. M. Hehman and G. A. Hamilton, J. Am. Chem. Soc, 96, 1530 (1974). M. C. Whiting, A. J. N. Boh and J. H. Parrish, Adv. Chem. Ser., 11, 4 (1968). D. O. Whhamson and R. J. Cvetanovic, J. Am. Chem. Soc, 92, 2949 (1970). (a) J. C. Jacquesy, R. Jacquesy, L. Lamande, C. Narbonne, J. F. Patoiseau and Y. Vidal, Nouv. J. Chim. 6, 589 (1982). (b) J. C. Jacquesy and J. F. Patoiseau, Tetrahedron Lett., 1499 (1977). (c) G. A. Olah, Q. Wang and G. K. S. Prakash, J. Am. Chem. Soc, 112, 3698 (1990). (a) G. A. Olah and H. C. Lin, J. Am. Chem. Soc, 93, 1259 (1971). (b) G. A. Olah and coworkers unpubhshed results. (c) G. A. Olah and N. Friedman, J. Am. Chem. Soc, 88, 5330 (1966). (d) G. A. Olah, Acc Chem. Res., 13, 330 (1980). M. L. Poutsma, Methods in Free-Radical Chemistry, Vol. II (Ed. E. S. Husyer), Marcel Dekker, N e w York, 1969. (a) G. A. Olah and Y. K. M o , J. Am. Chem. Soc, 94, 6864 (1972). (b) G. A. Olah, R. Renner, P. Schilling and Y. K. M o , J. Am. Chem. Soc, 95, 7686 (1973). G. A. Olah and P. Schhling, J. Am. Chem. Soc, 95, 7680 (1973).

652


104. D . Alker, D . H. R. Barton, R. H. Hesse, J. L. James, R. E. Markweh, M. M. Pechet, S. Rozen, T. Takeshita and H. T. Toh, Nouv. J. Chim. 4, 239 (1980). 105. K. O. Christe, J. Fluorine Chem., 519 (1983); K. O. Christe, J. Fluorine Chem., 269 (1984). 106. C. Gal and S. Rozen, Tetrahedron Lett., 449 (1984). 107. (a) G. A. Olah, B. Gupta, M. Farnia, J. D. Felberg, W. M. Ip, A. Husain, R. Karpeles, K. Lammertsma, A. K. Melhotra and N. J. Trivedi, J. Am. Chem. Soc., 107, 7097 (1985). (b) G. A. Olah, U.S. Patent 7,523,040 (1985) and corresponding foreign patents. (c) Y. Li, X. Wang, F. Jensen, K. Houk and G. A. Olah, J. Am. Chem. Soc, 112,3922 (1990). 108. M. Berthelot, Ann. Chim., 52, 97 (1858). 109. (a) K. Weissermel and H. J. Arpe, Industrial Organic Chemistry, Verlag-Chemie, Weinheim, 1978, pp. 4 7 - 4 8 . (b) G. A. Olah and coworkers, unpubhshed results. 110. G. A. Olah, H. Doggweiler, J. D. Felberg, S. Frohlich, M. J. Grdina, R. Karpeles, T. Keumi, S. Inaba, W. M. Ip, K. Lammertsma, G. Salem and D. C. Tabor, J. Am. Chem. Soc, 106, 2143 (1984); G. A. Olah, U.S. Patent 4,373,109 (1983) and corresponding foreign patents. I l l (a) G. A. Olah, G. K. S. Prakash, R. W. Elhs and J. A. Olah, J. Chem. Soc, Chem. Commun., 9 (1986). (b) Also see G. A. Olah, Acc Chem. Res., 20, 422 (1987). 112. G. Salem, Ph.D. thesis, Univershy of Southern California, 1980. 113. E. J. Lewis, J. Am. Chem. Soc, 38, 762 (1916); Valence and Structure of Atoms and Molecules, Chemical Catalog Corp., N e w York, 1923.

CHAPTER

14

Organometallic chemistry of alkane activation R O B E R T H. C R A B T R E E Department

of Chemistry,

Yale University, 225 Prospect

Street, New Haven,

I. I N T R O D U C T I O N A. Mechanistic Types B. Agostic Species and Alkane Complexes C. Theoretical Aspects D. Thermodynamic Aspects II. S H I L O V C H E M I S T R Y III. O X I D A T I V E A D D I T I O N A. Stoichiometric Chemistry B. Catalytic Chemistry C. C a r b o n - C a r b o n Bond Cleavage D. Surface-bound Organometahic Species IV. n - B O N D M E T A T H E S I S V. O T H E R M E C H A N I S M S VI. M E T A L A T O M S , I O N S A N D E X C I T E D M E T A L A T O M S A. Neutral Metal Atoms in the G r o u n d State B. Metal Ions C. Photoexcited Metal Atoms VII. A C K N O W L E D G M E N T S VHI. R E F E R E N C E S

CT06511,

USA

653 654 654 655 656 657 659 660 664 670 672 672 672 673 673 673 674 677 677

I. INTRODUCTION

In this chapter, we consider the interaction of transition metal complexes with alkanes to give alkane-derived products, where organometallic species are either the final products or are suspected intermediates. In this area^ only a few fundamentally different mechanistic reaction types appear to operate.


653

654

R. H. Crabtree

A. Mechanistic Types

The first alkane reactions involving organometallic intermediates were investigated by Shilov. The best current understanding of the pathway involved is shown in equation la. The metal M appears to bind the C — H bond to form a side-on a complex of a type discussed in more detail below. In the Shilov systems, this species loses a p r o t o n (equation la) t o give a metal alkyl which is usually unstable a n d goes o n t o give a variety of catalytic reactions. Occasionahy, however, the metal alkyl has been observed directly.

X

I —

C - H

M

—

^

M—I

(1)

In the second type of process the metal acts as a carbenoid and inserts into the C — H bond, a process generally termed 'oxidative addition' in organometallic chemistry (equation lb). This reaction is believed to go via the same sort of alkane complex as in the Shhov system, but, instead of losing a proton, it goes instead to an alkylmetal hydride. This may be stable, in which case it is observed as the final product, or it may react further. In the third type, predominantly seen for early metals, the C — H bond is broken by what Bercaw a n d coworkers^ have called a-bond metathesis (equation Ic). In this situation an alkyl X already present o n the metal undergoes exchange with the alkane. Here too, an alkane complex is a very likely intermediate. Instead of the proton being lost as H ^ , as in the Shilov case, it protonates the alkyl, a process which is p r o m o t e d by its anionic character, which is in turn a result of the low electronegativity of the early metal. Another type involves homolytic splitting of the C — H bond by a pair of metallo-radicals (equation 2). This has so far been seen in only one case, perhaps because coordinatively unsaturated paramagnetic metal complexes have only rarely been studied.

I M-

I

I C

I H

-M

I

*•

M

C

I H

I

M

(2)

I

We also discuss reactions of metal atoms, ions and excited metal atoms because these are ligand-free analogues of the systems mentioned above; in one case a syntheticahy useful method is based on this chemistry. B. Agostic Species and Allcane Complexes

Several of the mechanisms discussed above are believed to involve C — H • • • M bridged species. A large number of c o m p o u n d s are now known in which a C — H b o n d of the

14. Organometallic chemistry of alkane activation

655

Ph-

\/

CI .CHp

7 2 ° > 3 ° selectivity for attack at different

C—H

bonds. M e c h a n i s m s i n v o l v i n g heterogeneous

catalysis by metal surfaces, which might be f o r m e d by decomposition of the catalyst, have been excluded by several tests including the use of metallic mercury, which poisons p l a t i n u m g r o u p metal surfaces^^^ A detailed study^^ of the chemistry of [ I r H 2 ( 0 2 C C F 3 ) L 2 ] { 1 , L = [ ( p - F C 6 H 4 ) 3 ] P } , which is a thermal alkane dehydrogenation catalyst using tbe as h y d r o g e n acceptor, has given considerable insight into the mechanism of the C — H

activation reactions.

The

addition of C O or even of such relatively w e a k l y - b i n d i n g ligands as alkenes or M e C N leads

to

opening of

the

trifluoroacetate

to

give

the

mono-adduct

(equation

25).

Interestingly, the CH3CO2 complex does not act as a catalyst a n d o n l y gives the reaction in equation 25 with C O but not with M e C N or alkenes. T h e reaction of the trifluoroacetate with alkenes is reversible a n d the K^^ values were measured. These show the

low

coordinating power of tbe relative to other alkenes. This is a very useful p r o p e r t y for a h y d r o g e n acceptor, which must not block active sites at the metal at which the alkane is to b i n d .

L

K > ' | < 0 ^ " = ^ »

L

'

„ > ' | < . - ^

''''

Treatment of the thermal catalyst [ I r H 2 ( ^ ^ - O C O C F 3 ) L 2 ] w h h tbe gives [IrH2(tbe) ( ^ ^ - O C O C F 3 ) L 2 ] , which slowly converts to a species that is p r o b a b l y the agostic alkyl hydride shown in F i g u r e 2. If so, the agostic character of the alkyl hydride increases the t h e r m o d y n a m i c d r i v i n g force to f o r m the alkyl h y d r i d e a n d so facilitates the alkane oxidative addition. After loss of r - B u C H 2 C H 3 , the final p r o d u c t is a n isolable o r t h o metalated species, which is an equally effective catalyst precursor a n d so is presumably in e q u i h b r i u m with the active catalyst. I n benzene, the reaction of I r H 2 ( 0 2 C C F 3 ) L 2 with tbe gives an isolable phenyl hydride. This is the first case in which a catalyticahy active C — H activation system has also given a stable C — H oxidative a d d i t i o n product.

670

R. H. Crabtree

The Ir—Ph bond is unusuahy strong thanks to d^-p^ interactions and the phenyl group cannot easily j5-eliminate. The value of /CHAD for the thermal oxidative addition of benzene is 4.5. This seems to be a reasonable value for an oxidative addition, although lower isotope effects (/CHAD = ~ 1-4) were observed for cyclohexane and benzene addition to the much more reactive intermediates Cp*M(PMe3)-^^'^^ (M = Rh, Ir). The reaction scheme shown in Figure 2 is therefore proposed for thermal alkane dehydrogenation with this catalyst. The phenyl hydride undergoesfirst-orderdecomposition at 65 °C to give an equihbrium mixture with the cyclometalation product with K^^ = 3.6 in favor of the phenyl hydride. It has been shown^^ that the catalytic activhy of IrH2(02CCF3)(PAr3)2 for alkane dehydrogenation falls as the amount of ArH rises. The formation of 0.5 mole of ArH per Ir is sufficient to deactivate the catalyst. These and other deactivation pathways require further study and general methods for slowing or preventing these processes are badly needed. Such methods might also be applicable to other homogeneous catalysts and lead to practical applications. Grigoryan and coworkers^"" have observed H/D exchange between CD4 and methyl groups bound to aluminum in Ziegler-Natta systems such as TiCl4/Me2AlCl at 20-50 °C. Multiple exchange is observed even at short times and Ti—CH2 species were invoked. At 70 °C, CP2V catalyzes H/D exchange between D2 and CH4 and between D2 and solvent benzene. With Ti(OBu-04/AlEt3 as catalyst, methane adds to ethylene to give as much as 15% yield of propane. With CD4 and C2H4, d4-propane predominates. Catalytic H/D exchange between C^D^ and methane has been observed using metal phosphine catalysts. Jones has shown that CpReH2(PPh3)2 loses phosphine on photolysis to give a species active for the isotopic exchange reaction; 68 turnovers were observed after 3h^^. Felkin^^ has studied thermal catalysis using IrH5{P(Pr-03}2 activated by r-BuCH=CH2. About forty turnovers were observed after 46 days at 80 °C. The thermal Ir catalysts also gave evidence for the formation of other products. Ethane, toluene and biphenyl were all observed in small and variable amounts from the C6H6/CH4 reaction. These may have been formed by reductive elimination in an IrH3L2RR' species. Lin, Ma and Lu^^ have applied the IrH5L2/tbe system to dehdrogenation of pinane, which gives largely -pinene. C. Carbon-Carbon Bond Cleavage

Alkane C—C bond cleavage is a possible alternative strategy for alkane activation. So far, direct C—C bond activation by metal phosphine complexes has not yet been observed. This is probably because C—C bond cleavage is kinetically much slower than C—H bond cleavage, and is illustrated (for the reverse reaction) by the contrast between the much readier reductive elimination of alkyl hydride complexes compared to their dialkyl analogues. In addition, a direct oxidative addition of a C—C bond would put two bulky groups on the metal; this would lead to a reduced M—C bond strength. Bergman and coworkers'^^ estimate that the C—C oxidative addition reaction of Cp*Ir(PMe3) with CgH^—CgH^ is exothermic by 22kcal mol" ^ using the Ir—CgH^ ^ bond strength derived from Cp*Ir(PMe3)C6Hi ^(H). We have shown^^ how ^^m-dialkylcyclopentanes can be dehydrogenated to the corresponding diene complexes by [IrH2(Me2CO)2L2]SbF6; these can then undergo the Green-Ehbracht^^ reaction to give alkyliridium complexes (equation 26). Extending the study to the diethyl analogues led to the unexpected formation of 1,2- and 1,3-diethylcyclopentadienyl iridium hydrides. A mechanism involving C—C oxidative addition, followed by migration of the alkyl back to the ring, was proposed. Formation of the aromatic cyclopentadienyl in the C—C bond cleavage step must help drive the reaction; even so, high temperatures (~ 150 °C) are needed.


671

1 5 0 Hg*

(39)

Hg* + R H - ^ [ R — H - - H g ] * H + R H - ->R - h H ^ 2R

^ R + H + Hg

(40) (41)

>R2 + R ( - H ) + R H

R(-H)-hH-

(42)

>R'

(43)

Very recently, this reaction has been used for synthetic alkane chemistry on a multigram scale at ambient temperatures a n d pressures. F o r example, cyclooctane can be converted to the dimer in high yield even at high conversion. This would not have been the case in a solution phase radical reaction, because the product R2 is intrinsically more reactive than the initial substrate, RH. T h e reason for the selectivity proved to be that the dimer has so low a vapor pressure that essentially only the original substrate, cyclooctane, is present in the vapor phase and reaction only happens in the vapor. This vapor selectivity effect allows the initial functionalization product to be isolated^^. The observed selectivity is 3 ° > 2 ° > 1 ° as expected for a homolytic pathway a n d species with 4 ° - 4 ° C — C bonds are very efficiently assembled, especially in the presence of H2 which increases the selectivity because H - atoms which are formed are somewhat more selective for the weakest C — H bonds in the molecule. H atoms are also very tolerant of functional groups, so a variety of functionalized molecules (esters, epoxides, ketones etc.) can also be dehydrodimerized. Methylcyclohexane only gives 12% of the 4 ° - 4 ° dehydrodimer in the absence of H2, but in its presence enough of this dimer is formed to allow it to crystallize from the product mixture (equation 44). Alkanes can also be functionalized by cross-dimerization with other species. Equation 45 shows the results from cyclohexane and methanol. The three products are formed in approximately statistical amounts. T h e polarities of the three species are so different that the glycol can be removed with water a n d the bicyclohexyl separated by elution with pentane.

Hg,H2,/>v

(44)

35%

65Vo

crystallizes

OH .OH Hg*,MeOH

(45) *0H

Cross-dimerizing cyclohexane with the formaldehyde trimer gives a material which yields cyclohexanecarboxaldehyde on hydrolysis (equation 46). T h e radicals formed by Hg* reactions of alkanes can also be efficiently trapped by SO2 to give R S O 3 H after oxidation, a n d by C O to give R C H O a n d R 2 C O ^ ^

676

R. H. Crabtree .CHO hydrol.

(46) Methane and other alkanes with strong C—H bonds are not efficiently attacked by the Hg//iv or W^jkvjW^ systems, but need a stronger H-atom abstractor, such as the oxygen atom. O atoms can be formed efficiently in the system Hg/Ziv/N.O (equation 47). Methanol was used to trap the methyl radicals and give a functionalized product (equation 48). The labeling scheme as well as control experiments confirm the origin of the methyl group of the product ethanoP^. Methane does react with Hg*/02 to give MeOOH in good yield, so the Hg* probably attacks O2 to give O or O2* rather than methane. N20'^N2 +0 C D 3 O H A •CD2OH + -OH

(47)

. C D 2 O H + -CHj + H2O ^ C H 3 C D 2 O H (48)

Green and coworkers"^^ have used metal vapor synthesis (MVS) to make isolable quanthies of a number of organometallic species directly from alkanes (equations 49-51). In each case the complex has the stoichiometry of the parent alkane. Equation 50 is reminiscent of some of the chemistry we saw in the homogeneous metal phosphine chemistry discussed earlier in this chapter.

Os

atoms

c-CjHio-

Os a t o m s

(49)

• CpW(PMe3)H5

(50)

(51)

In equations 49 and 51, the metals bind the hydrogefis in /i-H sites in the cluster. In the rhenium case (analogous to equation 49) the carbon fragment from the alkane is bound as a -carbene in the resulting cluster. This may be a reasonable analogy for the way alkane-derived fragments are bound on metal surfaces. The co-ligands, benzene and trimethylphosphine, are required to stabilize the complex. It is perhaps surprising that these ligands are not activated in the products observed. Of course, other species may have escaped detection, and the observed products are no doubt thermodynamic traps, so we cannot deduce anything about the relative reactivity of arene, phosphine and alkane C—H bonds. Photochemical processes may also occur under the MVS conditions, because the presence of a strongly glowing bead of metal near its melting point must generate a broad spectrum of radiation.

14. O r g a n o m e t a l l i c c h e m i s t r y of a l k a n e a c t i v a t i o n VII.

677

ACKNOWLEDGMENTS

W e t h a n k the N a t i o n a l S c i e n c e F o u n d a t i o n , the P e t r o l e u m R e s e a r c h F u n d , D e p a r t m e n t of E n e r g y a n d E x x o n C o r p . for funding o u r w o r k in this area.

the

VIII. REFERENCES

CHEM. REV.,

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AM. CHEM. SOC, J. ORGANOMET. CHEM., ADV. ORGANOMET. CHEM., ANGEW. CHEM., INT. ED. ENGL., J. CHEM. SOC, DALTON TRANS., SELECTIVE HYDROCARBON ACTIVATION

ACC CHEM. RES., ACC CHEM. RES., J. ORGANOMET. CHEM., J. AM. CHEM. SOC, J. AM. CHEM. SOC, INORG. CHEM., AM. CHEM. SOC, J. AM. CHEM. SOC, J. AM. CHEM. SOC, SELECTIVE HYDROCARBON ACTIVATION

POLYHEDRON,

J. PHYS. CHEM., 11,

J. AM. CHEM. SOC,

ORGANOMETALLICS, ZH. FIZ. KHIM.,

THE ACTIVATION OF SATURATED HYDROCARBONS BY TRANSI

SSSR, SER. KHIM.,

J. AM. CHEM. SOC, CHEM. COMMUN., J. AM. CHEM. SOC, KINET. CATAL., KINET. CATAL., IZV. AKAD. NAUK

REACT. KINET. CATAL. LETT.,

KINET. CATAL. LETT., CHEM. COMMUN., AM. CHEM. SOC, J. AM. CHEM. SOC, NEW J. CHEM., NEW J. CHEM., J. CHEM. SOC, CHEM. COMMUN., J. AM. CHEM. SOC, J. CHEM. SOC, J. CHEM. SOC (A), J. AM. CHEM. SOC, CHEM. COMMUN., PURE APPL. CHEM

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65. 66. 67. 68. 69. 70. 71. 72. 73. 74.

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91. 92. 93.

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(1975); E. A. Grigoryan, F. S. Dyachkovskii, S. Ya. Zhuk a n d L. I. Vyshinskaja, Kinet. Katal., 19, 1063 (1978). (b) N . S. Enikopopjan, Kh. R. Gyulumjan and E. A. Grigoryan, Dokl. Akcui Nauk SSSR 249, 1380(1979); E. A. Grigoryan, Kh. R. Gyulumjan, E. \. G u r t o v a y a , N . S. Enikopopjan and M. A. Ter-Kazarova, Dokl. Akad. Nauk SSSR 257, 364 (1981). Y. Lin, D. M a a n d X. Lu, J. Organomet. Chem., 323, 407 (1987). R. H. Crabtree, R. P. Dion, D. J. Gibboni, D. V. M c G r a t h and E. M. Holt, J. Am. Chem. Soc, 108, 7222 (1986). F. W. S. Benfield and M. L. H. Green, J. Chem. Soc, Dalton Trans., 1325 (1974); P. Eilbracht, Chem. Ber., 113, 542, 1033, 1420, 2211 (1980). C H. F. Tipper, J. Chem. Soc, 2043 (1955); D . M . Adams, J. Chatt, R. G u y a n d N . Shepard, J. Chem. Soc, 738 (1961). K. C. Bishop, Chem. Rev., 76, 461 (1976); H. Hogeveen and H . C . Volger, J. Am. Chem. Soc, 89, 2486 (1967). L. Cassar and J. Halpern, J. Chem. Soc f/);, 1082 (1971). H. Hogeveen a n d B. J. Nusse, Tetrahedron Lett., 159 (1974). Y. I. Yermakov, B. N . Kuznetsov and V. Z a k h a r o v , Catalysis hy Supported Complexes, Elsevier, Amsterdam, 1981. J. Schwartz, Acc Chem. Res., 18, 302 (1985). (a) P. L. Watson, J. Am. Chem. Soc, 105, 6491 (1983). (b) G. Parkin, E. Bunel, B. J. Burger, M. S. Trimmer, A. A. Van and J. E. Bercaw, J. Mol. Catal., 41, 21 (1987). J. W. Bruno, G. M. Smith, T. J. M a r k s , C. K. Fair, A. J. Schultz and J. M. Williams, J. Am. Chem. Soc, 109, 203 (1987). C. C. Cummins, B. M. Baxter and P. T. Wolczanski, J. Am. Chem. Soc, 110, 8731 (1988). H. Mergard a n d F. Korte, Monatsh. Chem., 98, 763 (1967). (a) R. F. Renneke and C. L. Hill, J. Am. Chem. Soc, 108, 3528 (1986); 110, 5461 (1988); C. L. Hill, D. A. Bouchard, M. K h a d k h o d a y a n , M. M. Williamson, J. A. Schmidt a n d E. F. Hilinski, J. Am. Chem. Soc, 110, 5471 (1988). (b) A. F. Noel, J. L. Costa and A. J. Hubert, J. Mol. Catal., 58, 21 (1990) a n d references cited therein. K. J. K l a b u n d e a n d Y. T a n a k a , J. Am. Chem. Soc, 105, 3544 (1983). C. B. Lebrilla and W. F. Maier, Chem. Phys. Lett., 105, 183 (1984). D. J. Trevor, R. L. Whetton, D. M. Cox and A. Kaldor, J. Am. Chem. Soc, 107, 518 (1985). S. C. Davis and K. J. Klabunde, J. Am. Chem. Soc, 100, 5973 (1978); R. J. Remick, T. A. Asunta and P. S. Skell, J. Am. Chem. Soc, 101, 1320 (1979). J. Allison, R. B. Freas a n d D. P. Ridge, J. Am. Chem. Soc, 101, 1332 (1979). P. B. Armentrout, in Selective Hydrocarbon Activation (Eds. J. A. Davies, P. L. Watson, J. F. Liebman and A. Greenberg), C h a p 14, V C H , Weinheim, 1990. L. F. Halle, R. Houriet, M. M. Kappes, R. H. Staley and J. L. Beauchamp, J . Am. Chem. Soc, 104, 6293 (1982). J. Allison, R. B. Freas and D. P. Ridge, J. Am. Chem. Soc, 101, 1332 (1979); R. B. Freas and D. p. Ridge, J. Am. Chem. Soc, 102, 7129 (1980); 106, 825 (1984). Z. H. Kafafi in Selective Hydrocarbon Activation (Eds. J. A. Davies, P. L. Watson, J. F. Liebman and A. Greenberg), C h a p 12, V C H , Weinheim, 1990. G. A. Ozin, J. G. McCaffrey a n d J. M. Parnis, Angew. Chem., Int. Ed., 25, 1072 (1986). R. J. Cvetanovic, Prog. React. Kinet., 2, 77 (1964). (a) S. H. Brown a n d R. H. Crabtree, Chem. Commun., 927 (1987). (b) S. H. Brown and R. H. Crabtree, J. Am. Chem. Soc, 111, 2935 (1989). (c) S. H. Brown and R. H. Crabtree, J. Am. Chem. Soc, 111, 2946 (1989). (d) C. G. Boojamra, R. H. Crabtree, R. R. Ferguson and C. A. M u e d a s , Tetrahedron Lett., 30, 5583 (1989). (e) C. A. Muedas, R. R. Freguson and R. H. Crabtree, Tetrahedron Lett., 30, 3389 (1989). R. R. Ferguson a n d R. H. Crabtree, J. Org. Chem., in press. R. R. Ferguson and R. H. Crabtree, New J. Chem., 13, 647 (1989). J. A. Bandy, F. G. N . Cloke, M. L. H. Green, D. O ' H a r e a n d K. Prout, Chem. Commun., 240 (1984); 355, 356 (1985); M. L. H. Green and G. Parker, Chem. Commun., 1467 (1984).

CHAPTER

15

Rearrangements and photo chemical reactions involving alkanes and cycloalkanes T. OPPENLANDER* F. Hoffmann-La

Roche

AG, CH-4002

Basle,

Switzerland

G. ZANG and W. ADAM Department Germany

of

Organic

Chemistry,

University

of

Wurzburg,

D-8700

L INTRODUCTION II. R E A C T I O N S A. Simple Alkanes 1. Skeletal rearrangements on transition metal surfaces 2. Photochemistry 3. The a d a m a n t a n e rearrangement B. Strained Cycloalkanes 1. Cyclopropanes a. Transition metal catalysed rearrangements b. Photochemistry c. Quadricyclane/norbornadiene interconversion 2. Cyclobutanes 3. Bicyclo[2.1.0]pentanes 4. Bicyclo[1.1.0]butanes 5. Propehanes III. A C K N O W L E D G E M E N T S IV. R E F E R E N C E S

* N o w at Fachhochschule Furtwangen, Abteilung Villingen-Schwenningen, Verfahrenstechnik, D-7730 VS-Schwenningen, G e r m a n y .

Wurzburg,

681 683 683 683 687 691 692 692 692 700 705 710 711 724 733 735 735

Fachbereich


681

682

T. Oppenlander, G. Z a n g a n d W. A d a m I. INTRODUCTION

The present chapter deals with a heterogeneous field of organic chemistry with respect to the b r o a d range of organic substrates involved a n d with respect to the apphcation of a variety of different preparative thermal and photochemical methods. T h e fascinating aspect of ah activities related to the chemistry of alkanes, however, is the understanding of the chemical a n d photochemical reactivity of hydrocarbons (C„H J , especially the activation of C — C a n d C — H bonds ^ Furthermore, there are continuing research interests in the chemistry of strained organic molecules^ focussing o n the use of cyclopropanes in organic synthesis^, their thermodynamic properties^, the 'aesthetic' chemistry of 'platonic' structures like tetrahedrane^, cubane^ a n d the related strained ( C H ) 8 hydrocarbons^ and the construction of spherical molecules hke dodecahedrane^. Significant industrial applications of C — H activation techniques are the development of hydrotreating catalysts for the petroleum industry^ a n d the ultraviolet laser ablation technique (ablative photodecomposition) which employs pulsed A r F excimer lasers (A = 1 9 3 nm) as powerful U V light sources in material processing (microlithography) and in medicine (microsurgery, dentistry, ophthalmology)^^. The use of tunable vacuum U V excimer lasers in the range of 100-200 nm is very promising for the exploitation of new photochemical processes in this wavelength range ^ \ but the broad industrial application of excimer lasers seems to be limited due to economical considerations. This limitation may be overcome by the use of novel incoherent U V excimer light sources of high intensity and of high spectral purity. They are avahable over a suitable wavelength range ( 1 2 0 n m - 3 6 0 n m , Figure 1) a n d a variable range of geometries, i.e. planar or cyhndrical discharge tubes. F o r example, the Xe source emits n a r r o w - b a n d vacuum U V radiation peaking at 172nm (7.2 eV) characterized by a half-width of 12-14 n m a n d n o other emissions in the wavelength region of 100nm to 800nm^^^. Promising commercial applications of these lamps are photodeposition of metal films for semiconductor p r o c e s s i n g ^ p h o t o a b l a t i o n techniques'^ a n d their use in p h o t o chemistry'^, particularly waste water treatment. Further highlights in this field of research are the investigation of the photochemistry on solid surfaces'^, e.g. semiconductors a n d p h o t o c a t a l y s i s ' ^ photochemical conversion of solar energy'^''^, reactions initiated by photoinduced electron transfer (PET)'"^ a n d

Wavelength

Energy

(nm) 1-120

VUV

-150

(eV) -10 -

9

-

8

-

7

.Ar2 •Kr* •Xe*

• ArCI

^/HgAr* •ArF*

200 UV-C U\/jB_-300 UV-A

-

6

-

5

-

4

•KrCI*

^HgXe* •KrF''

. •XeF*

ArgF

Hg2

Xe2CI*,Kr2F*,XeO*,Hg3

F I G U R E 1. Wavelength range of potential excimer sources. Reproduced by permission of the International Union of Pure and Applied Chemistry from Reference 12b

15. Rearrangements and photochemical reactions

683

the 185-nm photoreactivity of cycloalkanes^^. New trends in the 185-nm photochemistry of bicyclic and tricyclic alkanes^^ are presented in Sections II.B.3 a n d II.B.4. Photochemistry, by defmition^^, deals with excitation energies of /I ^ 4 0 n m ( < 30 eV), whereas radiation chemistry (radiolysis) studies the photochemical effects of ionizing radiation (e.g. from radioactive sources or synchrotron radiation) such as the phenomenon of photoconductivity^^ a n d the formation of alkane radical cations (RH"^)^^. In this chapter we whl concentrate on photochemical reactions of alkanes and cycloalkanes and their rearrangements. We mainly considered the literature since 1980. II. REACTIONS A. Simple Alkanes

1. Skeletal rearrangements

on transition metal

surfaces

Investigations which concern the mechanisms of skeletal rearrangements of saturated hydrocarbons induced by heterogeneous transition metal catalysis are of great interest for industrial applications, e.g. for petroleum reforming p r o c e s s e s ^ ' T h e developments in this field were reviewed recently by Hejtmanek^""^, a n d by Maire a n d Garin^"^^, w h o focussed o n the probable reaction mechanisms which include bond-shift a n d cyclic mechanisms for the skeletal isomerization of acyclic alkanes. Scheme 1 summarizes the + 2

in>e)

adsorbe(j species

( f +

R

o

1)H2

Aromat ization

f

i 2

R dehydrogenated

C(HV C(HV

^C(H);, C(H),

species on metal surface

x = 2

>r=0,1

A'=0,1

^n^2n+2

^n^2n+2

bond-stilf t

cyclic mechanism

mectianism Hydrogenolysis,

Isomerization

Hy drocracking

S C H E M E 1. Rearrangements of hydrocarbons on metal surfaces

684

T. Oppenlander, G. Z a n g and W. A d a m

four m a i n r e a c t i o n p a t h w a y s o b s e r v e d for h e t e r o g e n e o u s c a t a l y s e d r e a c t i o n s o f s a t u r a t e d h y d r o c a r b o n s o n m e t a l surfaces^"^^'^^. T h e r e a c t i o n s i n c l u d e h y d r o g e n o l y s i s o r h y d r o c r a c k i n g (rupture of C — C b o n d s ) , i s o m e r i z a t i o n , d e h y d r o c y c h z a t i o n a n d a r o m a t i z a t i o n of t h e C„H2„ + 2 molecules^"^'^^. T h e y are o b s e r v e d w i t h v a r y i n g selectivities, w h i c h d e p e n d o n t h e e x p e r i m e n t a l c o n d i t i o n s , e.g. t e m p e r a t u r e , p r e s s u r e a n d t h e t y p e of catalyst. A m u l t i t u d e of s u p p o r t e d ( A l 2 0 3 , S i 0 2 ) or u n s u p p o r t e d c a t a l y s t s (e.g. m o n o m e t a l l i c t r a n s i t i o n metals^^, interm e t a h i c c o m p o u n d s ^ ^ , b i m e t a l l i c alloys^^, etc.) are a p p l i e d t o i n d u c e skeletal r e a r r a n g e m e n t s o f h y d r o c a r b o n s . T h e latter, h o w e v e r , are t h e m o s t i m p o r t a n t c a t a l y s t s u s e d in industrial practice, w h i c h a l l o w r e f o r m i n g p r o c e s s e s at l o w pressure a n d at l o w temperatures. I n t h e c a s e o f a k y l s u b s t i t u t e d h y d r o c a r b o n s w i t h at least five c a r b o n a t o m s in t h e c h a i n (e.g. m e t h y l p e n t a n e s ) , t h e c y c l i c m e c h a n i s m c o m p e t e s w i t h t h e b o n d shift m e c h a n i s m o n catalysts of m e d i u m and l o w d i s p e r s i o n ^ w h e r e a s n-hexane never

•^^C

label

,(b,c)

S C H E M E 2. Isomerizahon pathways of 2-methylpentane labelled by ^^C at the 2- and 4-positions

15. Rearrangements a n d photochemical reactions

685

participates in the cyclic pathway using Ir catalysts^^. T h e evaluation of t h e relative contribution of b o n d shift versus cyclic mechanism t o the overah reaction is best accomphshed by using the ' ^ C tracer technique^^'^"^^'^^^'^^. F o r instance, 2-methylpentane specifically ' ^ C labelled at the 2- or 4-position was used t o distinguish between those two mechanisms by leading t o different product mixtures (Scheme 2). The nature of t h e reactive intermediates involved in hydrocracking or in skeletal rearrangements of hydrocarbons is sthl under active discussion. M a n y arguments are in favour of metalla-carbyne o r metaha-carbene like complexes^'^'^^^. However, several experimental results m a y only be explained by proposing metaha-cyclobutanes or o--alkyl-metal species^° as adsorbed reactive intermediates^'^*', a n d they depend strongly on the nature of the active s i t e s ( e . g . large or small size particles, single crystal metal surfaces ^^). The ring-opening reaction of methylcyclopentane (Scheme 3) is the reverse reaction of the dehydrocyclization of methylpentanes (Scheme 2). Reactions of alkylcyclopentanes on supported a n d unsupported transition metal catalysts are also very i m p o r t a n t in n a p h t h a reforming processes^^'^^.

Selective hydrogenolysis (large Pt particles)

dehydrogenation

non-selective ring enlargement

hydrogenolysis

aromatization

(small Pt particles)

demethylation

S C H E M E 3. Skeletal rearrangements of methylcyclopentane on metallic catalysts

The skeletal rearrangement of methylcyclopentane o n monometallic or intermetallic catalysts (Pt^'^^CePd3^^) in a hydrogen atmosphere may lead t o C — C b o n d rupture with formation of hexane a n d methylpentanes in a selective or non-selective m a n n e r depending o n the particle size of the catalyst^"^^. Ring enlargement gives cyclohexane and benzene, accompanied by demethylation reactions t o Cg-isomers (Scheme 3), dehydrogenation t o methylcyclopentenes a n d methylcyclopentadienes, a n d successive

686

T. Oppenlander, G. Z a n g a n d W. A d a m

formation of lower alkanes C 5 — C ^ . The intermetallic catalyst CePdg exhibits a very low activity^^ a n d the product distribution is different from the P d catalysed reaction. However, the activation of C e P d j with air at r o o m temperature or at 120°C increases the catalytic activity dramatically. This was attributed to the rearrangement of the surface generating catalytic active P d shes. Thus, the air-activated C e P d j catalyst shows the characteristic reactivity of P d atoms in the skeletal rearrangements of methylcyclo pentane, 2-methylpentane a n d 3-methylhexane^^. The main goal of research in catalysis is to control the surface reactions by introducing a second metal into a supported monometallic catalyst^ ^. F o r example, doping of P t / A l 2 0 3 with Sn gives the supported bimetahic catalyst S n — P t / A l 2 0 3 ^ ^ . Using this catalyst, the aromatization of methylcyclopentane to benzene can be strongly suppressed compared to the undoped catalyst. T h e product distribution in the presence of hydrogen gas at 250 °C (methylcyclopentenes, methylcyclopentadienes, benzene) is also dependent on the type of catalyst used a n d the formation of ring-opened products (2-methylpentane, 3-methylpentane, hexane) under these conditions is negligible (less t h a n 5%)^^. O n the other hand, the application of P t black or P t / S i 0 2 as catalyst for the h y d r o genolysis of the alkylcyclopentanes 1-5 leads mainly to ring-opened products a n d alkylcyclopentene formation, whereas aromatization is not significant. T h e product distribution is strongly dependent on the hydrogen gas pressure^^.

(1)

(2)

(3)

(4)

(5)

A N i metal catalyst was recently used t o produce benzene from methane under ultrahigh vacuum conditions^"^^ (equation 1) by activation of CH4 physisorbed on the N i catalyst at 47 K by molecular beam techniques at pressures less t h a n 1 0 " ^ t o r r . The selectivity of benzene formation under these conditions is 100% a n d the reaction proceeds via collision-induced dissociative chemisorption^^''. T h e collision of K r a t o m s with physisorbed CH4 leads to dissociation into adsorbed H - a t o m s and methyl radicals; the latter dissociate to C H fragments which successively recombine to adsorbed C2H2. Trimerization of C2H2 on the metal surface yields quantitatively C^H^.

-

3 HO

(Ni)

[C2H2]

•

O

(1)

T h e a r o m a t i z a t i o n o f p r o p a n e o n s u p p o r t e d ( S i 0 2 / A l 2 0 3 ) G a , Z n o r P t c a t a l y s t s is l i m i t e d d u e t o h y d r o c r a c k i n g , d e a l k y l a t i o n a n d h y d r o g e n transfer r e a c t i o n s w h i c h l e a d t o t h e f o r m a t i o n o f m e t h a n e a n d e t h a n e a s t h e m a j o r p r o d u c t s , a n d e t h e n e a n d propene^^. H o w e v e r , t h e u s e of a P d m e m b r a n e reactor^ ^ increases t h e yield o f a r o m a t i c s (e.g. b e n z e n e , t o l u e n e , C 8 - C 1 2 a r o m a t i c s ) d r a m a t i c a l l y b y effective s e p a r a t i o n o f t h e p r o d u c e d h y d r o g e n g a s from t h e r e a c t i o n m i x t u r e b y u t h i z i n g t h e H2 p e r m e a b h i t y o f P d t h i n films. A n i m p o r t a n t field o f industrial c h e m i s t r y is t h e i n v e s t i g a t i o n of c a t a l y t i c d e g r a d a t i o n m e t h o d s of saturated polymers in view of recycling techniques. F o r example, the d e g r a d a t i o n o f p o l y p r o p y l e n e o n a s i l i c a - a l u m i n a catalyst^^ g i v e s different p r o d u c t m i x t u r e s ( g a s e o u s , liquid a n d o l i g o m e r i c fractions) w h i c h d e p e n d o n t h e r e a c t i o n t e m p e r a t u r e a n d t h e c o n c e n t r a t i o n o f t h e catalyst.

15. Rearrangements and photochemical reactions 2.

687

Photochemistry

In contrast to the heterogeneously catalysed transformations of alkanes, the direct photochemical and radiolytic reactions with high-energy radiation in the vacuum U V are usually less selective. The reason for this non-selective photochemical behaviour is probably the excitation to different coupled excited states of the singlet manifold of the alkanes. Despite the high chemical stabhity of alkanes and cycloalkanes, the vacuum-UV photolysis or radiolysis of alkanes in the liquid or vapour phase leads to H2 elimination, H radical detachment, elimination of low molecular mass alkanes and to decomposition into two-radical fragments in the primary photochemical step^"^. The final product distribution can be explained by the k n o w n reactivity of these primary radical fragments. Nevertheless, the frequency of C — H and C — C b o n d ruptures in alkanes by applying ionizing radiation is far from a statistical distribution and is directly correlated to the chemical structure of the substrates^^. This structure effect in the radiolysis and photolysis of liquid alkanes is attributed to the reactivity of low-energy singlet excited states populated near the absorption onset. Therefore, branched alkanes like 2,2-dimethyl propane and 2,2,4-trimethylpentane decompose mainly by C — C b o n d scission. This is in contrast to the decomposition of n-alkanes and C5—Cô cycloalkanes, which yield mostly hydrogen gas and dehydrogenation products^^. Extensive fluorescence studies^^ on alkanes reveal two decay channels for the -state: the temperature independent S^-T^ intersystem crossing (ISC) which can be accelerated in the presence of xenon (Xe heavy atom effect"^^), and the temperature-dependent singlet decomposition channel with an energy barrier of = 10-20 kJ mol ~^ (equation 2). By investigation of the temperature dependence and the Xe effect on the q u a n t u m yields of the photodecomposition, the different contributions of versus reactivity can be assigned. O n this basis, the primary decomposition pathways of liquid ethylcyclohexane photolysis at 7.6 eV (163 nm) can be interpreted as follows: H2 elimination occurs from the Si reaction channel and is the main process, whereas H - a t o m detachment and ring-opening processes are a consequence of intersystem crossing to the triplet state of ethylcyclohexane. Consequently, low-temperature photolysis of hydrocarbons in solid xenon"^^ reveals the formation of caged H atoms or thermally unstable Xe„H molecules. Table 1 summarizes the q u a n t u m yields of hydrogen gas production (OH2) during the photolysis of several alkanes and cycloalkanes in the liquid a n d / o r vapour phase, which demonstrate the structural influence"^ alkane

[alkane]^'

singlet decomposition (2)

[ a l k a n e ] ^ " — t r i p l e t decomposition A selective coupling of liquid cycloalkanes to the corresponding bicycloalkyls by 193 nm laser irradiation"^^^ was recently described to proceed via homolytic C — H bond cleavage (equation 3). N o olefinic products could be detected and the reaction is very inefficient at 185-nm irradiation.

/;v)(193

nm)

(3) ( 77 = 1 , 2 , 3 , 4

This wavelength dependence is rationalized in terms of a one-photon absorption process at the absorption edge of the cycloalkanes (excitation to the lowest excited singlet

T. O p p e n l a n d e r , G. Z a n g a n d W . A d a m TABLE 1. Photolysis at 7.6, 8.4 and 10.0 eV of several alkanes and cycloalkanes and the quantum yields of hydrogen gas production (H2)

Molecule

Wavelength of irradiation ( n m e V " ^)

163

O

(7.6)

Phase

liquid

0.73

37

163 (7.6) 147 (8.4) 147 (8.4) 123.6(10.0) 123.6(10.0)

hquid vapour hquid vapour liquid

0.86 0.74 1.0 0.57 1.0

38a 42 44 42 44

163

(7.6)

liquid

0.77

43

163

(7.6)

hquid

0.46

163

(7.6)

liquid

0.39

163

(7.6)

hquid

0.59

163

(7.6)

liquid

0.66

163

(7.6)

liquid

0.61

163

(7.6)

hquid

0.56

163 (7.6) 147 (8.4) 123.6(10.0)

hquid

0.93 0.73 0.65

45

147

(8.4)

vapour

0.22

38b

147

(8.4)

vapour

0.44

147

(8.4)

vapour

1.1

38c


689

state), a n d successive generation of the radical intermediates in high concentration by laser irradiation which favour the intermolecular dimerization. T h e carbene route to dicyclohexyl was unequivocahy excluded by conducting a competition experiment with a 1:1 mixture of N o formation of the intermolecular C — H insertion products Ci2E)i2Hio a n d C j was detected by G C / m a s s spectrometry. This photochemical behaviour clearly contrasts the results obtained with higher-energy U V radiation'^'^''^^, which probably proceeds through carbene formation (equation 4) t o yield significant amounts of cyclohexene"^^. The combined yield of photodimers of n-pentane'^^^ on 193-nm laser excitation (equation 5) is similar to that of cyclohexane (equation 3). The relative reactivity of the cycloalkanes compared to n-pentane (primary C - H coupling = 1.0) shows a significant dependence on ring size (Table 2)^^^

C6H12/C6D12.

2^)10^12

/70(147nm)

(4)

ArF

excimer (193

laser

nm)

(5) Dehydrodimerization of cyclohexane to bicyclohexyl was also achieved by mercury photosensitization''^. However, Hg-, Cd- a n d Zn-photosensitized reactions of acyclic

T A B L E 2. Relative photoreactivity of cyclo alkanes C„H2„ and n-pentane at 193 nm'^^'^ Cycloalkane

C„H2„ n = n =

5 6

n-8 n-pentane: (CH)^^^.

(CH)p,j^

Relative rate of dimerization 3.0 3.8 2.0 1.6 5.4 1.0

690

T. Oppenlander, G. Z a n g a n d W. Adam

alkanes (e.g. propane) are usually unselective a n d lead t o complex mixtures of decomposition products""^ Carbene formation during vacuum-UV photolysis (7.6 eV) a n d radiolysis of cyclooctane by unimolecular H2 elimination from a single carbon a t o m (1,1-elimination) was shown t o be the main reaction channel of excited cyclooctane (equation 6)"^^. T h e carbene 6 is formed with an efficiency close t o 100% in the long-wavelength photolysis of the sodium salt of the p-tosylhydrazone 7 as well as in the v a c u u m - U V photolysis and radiolysis of cyclooctane. This was deduced from the similar product distribution of both reactions t o give cyclooctene (8), bicyclo[3.3.0]octane (9) a n d bicyclo[5.1.0]octane (10)^^ Tos N

NH

hM

/ ? 0 ( A > 3 0 0 nm)

(163 nm)

and r a d i o l y s i s

(6)

(7)

(6)

5 4 - 5 9 V 0

38-43Vo

2-3V0

(9)

(10)

(8)

The interesting p h e n o m e n o n of wavelength-dependent selectivity (cf. equations 3,4,6) in the vacuum-UV photolysis of organic substrates was also noticed by Inoue a n d coworkers^^ in the U V photolysis of 2,3-dimethylbutene. T h e product distribution is strongly dependent o n the excitation wavelength over the n a r r o w range of 185 n m t o 228 nm. Novel industrial applications may evolve from continuous wave (CW) C O 2 laser-driven homogeneous pyrolysis of hydrocarbons^^ (e.g. C 4 H l o ^ ^ ^ n-heptane^^''), which seems to be advantageous over conventional pyrolysis m e t h o d s ^ ^ F o r example, the C W CO2 laser SF^-sensitized decomposition of cyclohexane in the gas phase yields mainly ethene and 1,3-butadiene (equation 7). T h e product distribution is almost invariable with t h e extent of conversion and different from conventional pyrolysis^ N o acetylene is formed CWCO2 laser ^2^4

+

ir~\

^

^

^

^

^

^ 2 ^ 6 +

CH4 (7)

direct

CO2

loser

r\

+

C2H2


691

due t o the absence of reactor surface effects. O n the other hand, direct vibrational multip h o t o n (nhv) excitation of cyclohexane by using a focussed high-energy pulsed C O 2 laser (100mJ t o 1.5 J) leads t o H2, ethene a n d acetylene as the major products^^; t h e latter results from fragmentation of primarily formed butadiene (equation 7). U n d e r these conditions a bright luminescence is observed, indicating that high concentrations of C2 radicals a n d electronically excited hydrogen atoms are present^^.

3. The adamantane

rearrangement

The Lewis-acid-catalysed rearrangement of polycyclic h y d r o c a r b o n s C„H2„-4;c (x = 1,2,3,...) into their thermodynamically more stable diamond-like isomers is usually referred t o as t h e adamantane rearrangement^^'^^. T h e archetype of this unique isomerization is t h e AlCl3-catalyzed transformation of enô-tricyclo[5.2.1.0^'^]decane (11) (tetrahydrodicyclopentadiene) into a d a m a n t a n e (Ad-H) (Scheme 4), which was first discovered by Schleyer^'^ m o r e t h a n 30 years ago. This process is thermodynamically controhed and it involves carbenium ion intermediates which rearrange via successive 1,2-C b o n d a n d 1,3 hydride shifts. N u m e r o u s theoretical a n d experimental investigations^^'^^ have established the most direct thermodynamically feasible p a t h w a y (exo-11-> 12 ^ 1 3 ^ 1 4 ^ 1 5 - > Ad-H) for the isomerization of endo-W t o a d a m a n t a n e . This pathway is defined by t h e complex rearrangement graph for t h e interconversion of the 19 tricyclic CôHig isomers^^. F u r t h e r m o r e , the prediction of the most stable C„H^ isomer, the so-called stabhomer^^, based o n force field calculations, is consistent with experimental results for A I X 3 isomerizations. The identification of intermediates in the rearrangement of tetrahydrodicyclopentadiene (11) t o a d a m a n t a n e is extremely difficult because of the extraordinary thermodynamic stabhity of a d a m a n t a n e , which constitutes a n energy bottleneck [endo-\\ ^ 12^XA-Hf^^. Nevertheless, a recent renaissance^^ of research in this field led t o substantial information which concerns t h e isomeric intermediates a n d the mechanisms of the CioHjg isomerizations.

(12)

(13)

S C H E M E 4. The most direct pathways in the adamantane rearrangement of tricyclo[5.2.1.02'^]decane (11)

692


Thus, the nitric acid catalyzed rearrangement of endo-11 undoubtedly leads t o t h e formation of the tricyclo[4.2.2.0^'^]decane skeleton. This was shown by t h e isolation of its corresponding dinitrate 16^^ (equation 8). Reaction 8 proves that the first stage of the a d a m a n t a n e rearrangement of endo-U proceeds through the intermediate 12 (Scheme 4). O n the other hand, tricyclo[4.2.2.0^'^]decane (12) itself reacts in the presence of AlBrg in C S 2 at 0 ° C (30min) t o a d a m a n t a n e , ^xo-11 a n d tricyclo[5.3.0.0'^'^]decane (17)^^ (equation 9). This reaction represents a n entirely new pathway (exo-ll ^ 12 ^ 17 ^ Ad-H, Scheme 4) for the formation of a d a m a n t a n e from 11, which was not predicted by theoretical considerations^^. Novel insights into the complex Lewis-acid-catalysed isomerization of the 1,2-trimethylenenorbornanes exo-l3 a n d endo-13 (tricyclo[5.2.L0^'^]decanes) were achieved recently by deuterium- a n d ^^C-labelling experiments^^'^-P''. T r e a t m e n t of deuterium-labelled exo-13 a n d endo-13 with AlBrj in CS2 at — 6 0 ° C for 5 - 1 5 min leads t o specificahy D-labelled 2-endo, 6-c?i(io-trimethylenenorbornane 18 (tricyclo[5.2.1.0^'^]decane), which indicates t h e involvement of t h e degenerate rearrangement AB (Scheme 5). ONO2 HNO3/AC2O

^ ONOg^ J

_ H N O , ONO2)

(16)

(11)

(8)

(9)

26Vo (Ad-H) F u r t h e r information on the multiple pathways of isomerizations in the ' A d a m a n t a n e p a n o r a m a ' may be gathered from Table 3, which summarizes the k n o w n rearrangements of the C10H16 isomers of adamantane^'^"^^'^^"^^ B. Strained Cycloalkanes 1.

Cyclopropanes

a. Transition metal catalysed rearrangements. T h e A g ^ ion-catalysed rearrangement of strained polycyclic molecules was first recognized in the late 1960s^^ a n d turned o u t


693

(18) SCHEME 5. Degenerate rearrangement in the AlBrg-catalysed isomerization of the 1,2-trimethylenenorbornanes exo- and endo-13 (1,2-C, 1,3-H

shifts)^^°'P''*

to be a powerful synthetic tool for obtaining a wide range of interesting carbocyclic structures'^. F o r example, the synthesis of 7,7-dimethyl- and 7,7-diphenylcycloheptatriene (19) was m a d e readily accessible by reaction of the tetracyclo[4.1.0.0^''^.0^'^]heptanes 20 with AgC104 (equation 10)'"^. This methodology uthizes benzvalene as a benzene equivalent and is superior to conventional syntheses of a variety of 7-mono- and 7-disubstituted 1,3,5-cycloheptatrienes. Interestingly, the d e h y d r o p r o t o a d a m a n t a n e s 21 and 22 rearrange on treatment with AgC104 in boiling benzene to the tricyclic olefins 23-25, but with different product selectivities (equation 11)'^. Despite the fact that bicycio[2.1.0]pentane itself is inert to

TABLE 3. The 'Adamantane panorama', which covers rearrangements of tricychc C^QH^^ isomers of adamantane (Ad-H)

Structure

Reaction condhions

AlBr3/AlCl3 12h

Products

D

Yield

Reference

12-13%

54 55j,r,s

12-13%

54,55j

(Ad-H) AlBr3/AlCl3 12h

Ad-H

O2NO HNO3/AC2O 10°C, 4 h

65%

58

41%

59a,b,c

OgNO

AlBr3/CS2 0 ° C , 60 min

11% Ad-H

26% 10%

AlBr3/CS2 -60°C, 30 min

55 g, o , p 56 b

not stated

(Ad-H)

not stated

AlBrs/CS^ -60°C, 1 min

80%

AlBr3/CS2 -10°C

not stated

55f,g,p,q

56 b

not stated

AlBr3/CS2 0°C

>90%

551

AlBr3/CS2

>90%

551

15. Rearrangements and photochemical reactions TABLE 3.

Structure

695

(continued) Reaction conditions

Products

Yield

AlBr3/CS2

Ad-H

53%

55 h

AICI3/CH2CI2

Ad-H

90%

59 b

AlClg/n-hexane reflux, 45 h

Ad-H

91%

55 i

AIX3

Ad-H

not stated

61

AlBr3/CS2

Ad-H

not stated

55 n

- 7 0 ° C , 5 min

Reference

not stated

10%

55 m

AlBr3/CS2 -75°C

AlBr3/AlCl3

Ad-H

60%

Ad-H

85%

Ad-H

not stated

56 a, 60

70 °C, n-hexane, 2h

AlBr3/CS2

55 e

25 °C

AICI3/CH2CI2

traces

15°C/10h

Ad-H

not stated

59 b

696


the Ag^-induced rearrangement^^, the strained pentacyclic c o m p o u n d 26, which contains a bicyclo[2.1.0]pentane structural element, leads t o tetracyclo[5.3.1.0^'^.0^'^]undec-4-ene (27) in 8 5 % yield (equation 12)^^^. This result was attributed to the favourable geometry of the strained central b o n d in 26, which promotes carbocationic skeletal rearrangement, and to the stabhizing interaction between silver a n d the rearranged carbocation 28^^^.

AgCI04

(20a)

(10)

(19)

R = Me

( 2 0 b ) R = Ph

(28)

(26)

(27)

(12)

A mechanism was proposed which engages metal-stabilized carbenium ion inter mediates like 29 a n d 30 in the rearrangement of alkyl-substituted cyclopropanes induced by the olefin metathesis catalysts WCl6/SnPh4 a n d PhWCl3/EtAlCl2

\

6+ 6-

-w 6-

H3C

(29)

(30)

15. Rearrangements a n d photochemical reactions TABLE 4. Ring-opening reactions WCl6/SnPh4 and PhWCl3/EtAlCl2. Cyclopropane

of alkyl

substituted

cyclopropanes

Catalyst

Products

697 with

the catalysts

Yield

WClJSnPh^

Z 47%

WCl4/SnPh4

Z

n-C6Hi3

A

CH3

'I'CgH.i.l

A A CH3

b 54%

n-CgH.!.,

60%

WCl6/SnPh4

WCl6/SnPh4

a

8%

PhWCl3/EtAlCl2

Z

d 19%

n-CgH^j

not stated WCl6/SnPh4

not stated

Conversion of the cyclopropane: "68%; ''98%; 45%; ''91%.


698

The products of several alkyl-substituted cyclopropanes with these electrophhic catalysts are compiled in Table 4^^. Interestingly, Z - a n d £-non-3-ene a n d Z - a n d £-non-2-ene could not be identified as reaction products of Z - a n d E-l-methyl-2-n-pentylcyclopropane. These products would correspond to the fission of the most substituted central cr-bond of the cyclopropane. F u r t h e r m o r e , methylene-carbene elimination leading t o the lower homologous alkenes seems to be an unfavourable process with those catalysts. This is in contrast t o the behaviour of bicyclo[2.1.0]pentane, which reacts in the presence of PhWCl3/EtAlCl2 t o cyclobutene in 70% yield^^^'^ T h e reactions of Pd^"^ with cyclopropanes^^ lead to skeletal rearrangements a n d appear to be initiated by the heterolytic cleavage of the most substituted C — C o--bonds of the cyclopropane moiety (equation 13). T w o cleavage modes were observed which lead in the primary step to the formation of tertiary carbocations followed by successive deprotonation to the f/^-ahyl complex 31 as the major pathway.

Pd(MeCN)4

Pd(MeCN)2

87.8%

(31)

7.6Vo

4.6Vo

(13) O n the other hand, Pd^ catalysts are k n o w n t o react with the C — C bonds of cyclopropanes via oxidative addition^^^'^^. F o r example, when hexacyclo[7.3.1.0-'^.03'^0^'^^0^'«]tridecane (32) is treated w h h P d black a n d H2 simultaneous hydrogenolysis of the two cyclopropane rings took place t o yield the saturated

Pd^

(32)

(14)

(35)

(34)


699

hydrocarbon 33 accompanied by the formation of 34 (equation 14). The reaction is initiated by complexation of Pd^ to the two strained (IR)

-C,H4

(42) /;0(IR),SF6

(19)

(41)

a c o m m o n precursor of methylenecyclopropane a n d cyclobutene was also proposed in the 185-nm photochemistry of cyclobutene^^ to produce ethene, acetylene, methylenecyclopropane a n d 1,3-butadiene. Direct photolysis of the unique tetramethylene-bridged prismane 43^^ (pentacyclo[4.3.1.0^''.0'^'^.0^'^^]decane) leads cleanly to the expected tetralin 44 (equation 20).

fi\)

- 5 0

( 2 5 4 n m , - 5 0 **C)

• RT

(20)

2

(43)

(45)

This photochemical behaviour is in accord with the well-known photoreactivity of prismane itself, which o n direct excitation gives benzene^ ^ as the sole product. However, the direct photolysis of 43 at low temperature is accompanied by its thermal rearrange ment to the fulvene 45. T h e mechanism of this novel isomerization was established by deuterium labelling experiments^^ (Scheme 7) a n d was proposed t o proceed through the intermediary benzvalene derivatives 46 a n d 47. The products d-44 a n d d-45 exhibit less than 4% D scrambling.

704

15. Rearrangements a n d photochemical reactions c. Quadricyclane

I norbornadiene

interconversion.

705

T h e isomerization of n o r b o r n a d i e n e

(NBD: bicyclo[2.2.1]hept-2,5-diene) to quadricyclane (Q: tetracyclo[3.2.0.^''^.0^'^]heptane, equation 21) stih receives much attention^^'^^ as a potential solar-energy storage process.

/y\)(sens.) ^

(21)

catl

Unfortunately, NBD does n o t absorb in the visible a n d U V - A (400-320 nm) range of the solar spectrum. This problem m a y be overcome by the use of a wide variety of photosensitizers, which includes transition metal c o m p l e x e s ^ a n d organic sensitizers like acridones^^^ a n d aromatic ketones^^'^^'''^'^ In this section, however, new trends in the exothermic back-isomerization Q NBD are of considerable interest because in this two cyclopropane ring moieties are involved. This ring-opening reaction m a y be achieved by transition metal complexes^"^ or by Lewis acid catalysis; the latter, however, leads t o side reactions which include cationic oligomerization^'*^^. M o r e interestingly, Q can be converted to NBD by way of intermediary radical cations formed by photoinduced electron transfer (PET)^^ to suitable electron acceptors^^ (Scheme 8).

NBD

S C H E M E 8. Photoinitiated catalytic cycle of the valence isomerization of Q to N B D (A = electron acceptor)

Transition metal complexes like PdCl2(^'^-NBD)^^' a n d [ R u ( b p y ) 3 ] 3 + 8 5 a or 9,10-dicyanoanthracene a n d 1,2,4,5-tetracyanobenzene^^^ have been successfuhy used as electron-accepting sensitizers. Reductive quenching of the excited singlet state of the electron acceptor (A*) by Q leads t o the formation of its radical cation Q ' ^ which

706

T. Oppenlander, G. Z a n g a n d W. Adam

undergoes a rapid irreversible rearrangement t o the thermodynamically more stable N B D " ^ radical cation (Scheme 8). N B D " ^ m a y be reduced to N E D either by A ~ or by quadricyclane itself to lead t o regeneration of Q ^ . Consequently, Q re-enters the cycle, which accounts for q u a n t u m yields of N E D formation above 100. This catalytic cycle exhibits a significant solvent dependence in the presence of singlet or triplet sensitizers like 1-cyanonaphthalene (l-CN)^^^-^', a n d decreases the efficiency of the ring-opening process with increasing polarity of the solvent. This p h e n o m e n o n was attributed to the reversible formation of solvent-separated ion pair intermediates ( 1 - C N ~ / Q ' ^ ) in polar solvents, whereas in non-polar solvents the isomerization proceeds through initial formation of a singlet exciplex^^^'^'. The valence isomerization of Q, mediated by photocatalysis on n-type semiconductors^"^, seems to be a rather inefficient process. T h e yield of N E D varies with the type of semiconductor used in the order C d S > T i 0 2 ^ Z n O , a n d the nature of the solvent^ The q u a n t u m yields of these photoreactions are in the range of O = lO'^^-lO"^ A schematic representation of the valence isomerization Q N E D at the surface of an hluminated semiconductor particle is shown in Scheme photochemical excitation of a semiconductor promotes an electron from the fihed valence b o n d (VB) t o the vacant conduction b a n d (CB) with formation of a short-lived electron-hole pair (e~,h^)^^. T h e

'NBD-

BULK

SOLUTION

S C H E M E 9. Valence isomerization of Q at an hluminated semiconductor particle. VB = valence band, CB = conduction band, D P A = diphenylamine, M V = methylviologen. Re printed with permission from Ikezawa and Kutal, J. Org. Chem., 52, 3299. Copyright (1987) American Chemical Society

15. Rearrangements and photochemical reactions TABLE 6. Oxidation potenUals vs. SCE^^^'"'^

707

(Y)

pox

Compound

^1/2

Cds

1.6 2.3 2.4 0.91 1.54

Ti02

ZnO

Q NBD

positive holes thus formed may be reduced by an appropriate electron d o n o r like Q. The decisive requirement for this redox coupling is that the oxidation potentials of the photogenerated holes are sufficiently positive to oxidize Q; the oxidation potentials for several n-type semiconductors are given in Table 6. Therefore, a positive hole at the semiconductor surface oxidizes Q to Q"^, which readhy isomerizes to NBD"^ fohowed by the reduction to NBD. A charge transfer mechanism induced by photogenerated alkali hahde colour centers of the 'missing electron' type was recently proposed by Michl and coworkers^^ for the rapid conversion of Q to NBD in a Csl matrix after hlumination (equation 22). The electron deficient h-centers which are formed upon irradiation of Csl are able to oxidize Q by electron transfer to Q ' ^ to initiate a catalytic cycle simhar to that described in Scheme 9 for the photocatalytic action of semiconductors.

Csl

h\)

(254

nm)

.

,

^

• r2"(h)+ e-(F)

+ 21"

+ l2"(h)

L-

(NBD)

(22)

In contrast to the photoinduced electron transfer reactions of quadricyclane, its direct 185-nm photolysis^^ in the liquid phase leads to NBD and to the formation of two side-products, namely 1,3,5-cycloheptatriene and 6-methylfulvene (Scheme 10). O n the other hand, selective excitation of the C H bonds of gaseous Q by absorption of 598.8 n m laser p h o t o n s produces a vibrationally 'hot' [NBD]''^''*, which fragments into cyclopentadiene, acetylene and 1,3,5-cycloheptatriene^^ (Scheme 10). These C H overtone transitions involve excitation energies greater than the activation energy for the Q NBD isomerization to account for the 'hot' molecule effect. The photoproducts 6-methylfulvene and 1,3,5-cycloheptatriene are also formed in trace amounts in the direct 254-nm ( < 5%) and triplet-sensitized ( < 0 . 5 % ) photolysis of Q, which limits the usefulness of the NBD ^

728

Q0 0 0§ I § I § c> 6 0 O

.

I

o

8

PQ

^ oo

c

§1 X5

00 ON

W PQ

p 0 bo"

0

O

729

3

B

k o

fe • u

730

T. Oppenlander, G. Z a n g and W. A d a m

The pyrolysis of bicyclo[1.1.0]butane, however (Table 9; entry lb), occurs by way of a stepwise, stereoselective, twofold, lateral C — C b o n d c l e a v a g e ^ T h e 185-nm photolysis of bicycio[1.1.0]butane was described recently by groups of Adam"^^^ and of Srinivasan'^^'' (Table 9; entries lc,d). Although both groups found a different ratio of 1,3-butadiene and cyclobutene, they agreed that the dominating primary step is central C — C b o n d cleavage (equation 34)'^^''-

AO,,

:MX'

major

pathway

D

minor

:>o 1.04 MeV) p h o t o n s give rise t o formation of pairs of electrons a n d positrons. W e see that the energy of the highenergy p h o t o n s is converted into kinetic energy of charged particles. The charged particles then parcel out their energy in many small losses forming a track of electronic excitations and ionizations, as we shall see below. N e u t r o n s have n o C o u l o m b interactions a n d energy loss takes place by elastic cohisions with the nuclei, which m a y result in ejection of ionized atoms with kinetic energy. Here again the chemical effects result from the energy losses of charged particles. High-energy charged particles lose their energy predominantly by C o u l o m b interaction with the electrons of the medium, in mostly small energy losses, which results in a large number of electronic excitations a n d ionizations along their paths. Secondary electrons are formed that cause further electronic excitations a n d ionizations, if their energy is sufficient, until they finahy become thermalized. In this way high-energy charged particles form tracks of electronically excited molecules, positive ions (which m a y o r m a y n o t be electronically excited) a n d thermalized electrons. These species subsequently undergo various reactions which eventually lead t o stable products. While the spectrum of reactive species formed initially is n o t largely different for different primary charged particles a n d different energies of these particles, the spatial distribution of these species is. While for M e V electrons in the condensed phase subsequent ionizations along the path are spaced o n the order of 200 n m apart, for 1 M e V a-particles this is o n the order of 0.4 nm. This difference in the density of the initially reactive species in the track has important consequences for the ensuing chemical reactions. In the fohowing we shah discuss the energy deposition in the tracks of high-energy charged particles. F o r a more extensive treatment the reader is referred t o the chapters by Magee a n d Chatterjee in References 2 a n d 3 a n d the chapter by M o z u m d e r in Reference 5. B. Energy Losses of a Fast-moving Charged Particle

W h e n a fast-moving charged particle traverses a medium, energy is transferred t o the electrons of the medium. I n a simple picture the interaction is described as a fast-moving charged particle that passes along a free electron at rest. D u e t o t h e C o u l o m b fdrce the free electron is set in motion at the expense of the speed of the primary particle. This classical model is very good for the so-called hard collisions in which relatively large amounts of energy are transferred. It may be shown that the probability for a primary charged particle with charge ze a n d velocity v t o transfer a n energy between Q a n d dQ to a n electron of the medium with mass m^, when passing a unit distance through the medium, is given by ,P = -

^

N

Z

^

(1)

A. H u m m e l

746

where N is the number of molecules per unit volume and Z the n u m b e r of electrons per molecule, so that NZ is the electron density. We see that dP has the dimension of length It represents the probability of events in the interval Q to Q-{-dQ per unit p a t h length or the number of such events per unit p a t h length of the primary particle. The quantity dP/NZ has a dimension (length)^ and represents the (differential) cross section for the events per electron. W e see that small losses are favoured. ( F r o m the inverse proportionahty with the mass of the electron we also see that relatively little energy is transferred to the nuclei of the medium). F o r low values of g , where Q is comparable to the binding energy of the electron, the picture of a collision with a free electron at rest is not any more correct. In these distant or soft cohisions the effect of the varying electric fields due to the passing of the primary particle on the whole molecule has to be considered. This electric field varying in time is experienced by the molecule as electromagnetic waves with a range of frequencies v, or energies hv. These waves may now cause electronic excitation by resonant transition the same way as occurs with the absorption of light. F o r these soft collisions dP is given by dP =

dfN^ {Amofmy

dQ Q

In

(2m,v

dQ

(2)

The quantity df /dQ, called the differential oschlator strength, is simply proportional to the optical absorption coefficient, s. Since the logarithmic term varies only slowly with Q, we see that the probabihty for resonant transitions is roughly proportional to {df/dQ)/Q or to e{hv)/hv. The transitions described by equation 2 are called optical or resonant transitions. The differential oschlator strength distributions have been determined in detah a n d over a wide range of energy for a number of molecules in the gas phase. An important feature of these df /dQ distributions is that a m a x i m u m is always found a r o u n d twice the ionization potential, i.e. a r o u n d 2 0 eV for hydrocarbons. In Figure 1 we show the

•al^

0.2

40

50

60 Energy

70 loss

(eV)

F I G U R E 1. Oscillator strength distribution for methane. The dashed line indicates the oscihator strength for ionization. Reprinted with permission from Ref 6. Copyright (1975) Pergamon Press PLC

16. Radiation chemistry of alkanes and cycloalkanes

747

case of gaseous methane as an example. M u c h less is k n o w n a b o u t the oscihator strength distributions in the condensed phase. F r o m the few cases that have been studied, however, it appears that the distributions in the gas and the condensed phase are not grossly different. The oschlator strength distribution for CH4 shown in Figure 1 is a sum of contributions for different transitions. The small peak a r o u n d 7 - 8 eV, for example, represents the transition that leads to the molecular elimination CH2 + H2. At higher energies other neutral dissociation processes are found. The ionization cross section has an onset at 12.5 eV for the process C H ^ ' + e " , however at larger energies dissociative ionizations are found (e.g. C H ^ -f H ' + e~ starting at 14.4 eV). We shall discuss the various processes more extensively in Section III. Using the two expressions in equations 1 and 2, together with the df /dQ distribution, we can now calculate the n u m b e r of each energy loss that takes place along the p a t h of the high-energy charged particle through the medium. If the contributions of the different processes to the overall df/dQ are known, the distribution of the different initial events in space can be calculated. The total energy lost by the primary charged particle per unit p a t h length can be obtained by integrating over all losses {^QdP), using equations 1 and 2 for the hard and soft collisions, respectively, and summing the two. It may be shown that the contribution of both losses in the total energy loss of the primary particle is about equal. The energy loss per unit path, or the linear energy transfer (LET), for non-relativistic heavy particles is given by - ' - l ^ ^ ^ N Z m ' - ^ dx (47iSofm^v^ I

(3)

where / is called the mean excitation potential, which turns out to be approximately 50 eV for saturated hydrocarbons. We see that the L E T is approximately inversely proportional to the square of the velocity v^, and proportional to the square of the charge z^, but that the mass of the fast-moving particle does not appear. The linear energy transfer is also called the stopping power. F o r non-relativistic electrons the term under the logarithm is somewhat different l(meV^/2I){e/2y^^ and for relativistic particles the expression for —dE/dx is again modified. It has been shown that the linear energy transfer is determined to a good approxi mation by the atomic composition of the medium only and is virtuahy independent of the chemical binding of the atoms. The L E T divided by the electron density NZ is approximately independent of the state of aggregation. We have seen that the energy loss distribution is heavily weighted towards small energy losses. F r o m equation 2 and the oscihator strength distribution we find that the average loss of a fast primary particle due to resonant collisions is a r o u n d 20 eV; the most probable energy loss is a r o u n d 15 eV. About half of the total energy lost is in losses below 100 eV. The overall average energy loss is a r o u n d 40 eV. In Table 1 we show the number of energy losses Q in intervals of Q that appear when a 1-MeV electron slows down in a molecular medium such as a saturated hydrocarbon. F o r the calculation a 'typical' oscillator strength distribution has been used. The values given for the lowest losses may therefore be somewhat different in actual cases. We see the predominance of the small losses a r o u n d the peak of df/dQ in the interval 10-30 eV. We have also indicated the fraction of energy lost in each interval of Q, which shows that although the large losses are few in number, they represent a non-negligible fraction of the energy.

748

A. H u m m e l TABLE 1. The number of primary energy losses in the track of a 1-MeV electron slowing down in a saturated hydrocarbon'' Energy interval (eV) Qi 0 10 30 80 100 300 500 1 X 10^ 5 x 10^ 1 X lO'* 1 X 10'

Number of losses between

and Q2

Fraction of total energy lost in interval Qi to Q2

Q2 10 30 80 100 300 500 1000 5 X 10^ 1 X 10^ 1 X 10' 5x10'

5600 14300 4300 330 24530 320 80 58 46 5.8 5.2 05 515 Total: 25045

0.04 025 019 0.03 0.51 O056 O033 0.040 O093 0.040 0134 O093 0.49 Total: 1.0

C. Spatial Distribution of Energy Losses in the Track

First we consider the spacing of the energy losses along the p a t h of the primary charged particle. Using the value for the L E T for a given particle with a given energy for a certain medium, we can estimate the average spacing between primary events. F o r a 1-MeV electron in a medium with density I k g d m " ^ the L E T is a b o u t 0 . 2 e V n m ~ ^ . With a n average primary energy loss of 40 eV we find that t h e average spacing is 40/0.2 = 200 nm. With decreasing energy of the primary (v lower) the L E T increases a n d therefore the average spacing decreases. F o r electrons of 10 keV and 1 keV the spacings are ca 40 n m and 5 nm, respectively. A 1-MeV a-particle, due to the large mass and z = 2, has an L E T approximately 500 x larger than that of a 1-MeV electron. Since the energy loss distributions are n o t very different, the average spacing of a primary loss will be ca 500 x smaller, i.e. 0.4 nm. W e see that in this case subsequent events are very close together. The vast majority of the primary losses involves ionization a n d formation of a secondary electron, which in turn may cause further ionizations as long as the energy is sufficiently high. As we have seen above, most primary losses involve only a few tens of eV, which a t most results in only a few more ionizations by t h e secondaries. Calculations of the energy losses of these low-energy secondary electrons (i.e. a few tens of eV) can be carried out only for a few simple molecules in the gas phase, where sufficient knowledge is avahable about the nature of the transitions involved and the cross sections for the various processes. In the condensed phase in most cases great uncertainty remains about the processes involved on excitation, except for the lowest levels; also the interaction of the low-energy secondary electrons with the medium is not very well understood. It is often assumed, however, that for consideration of the electronic transitions t h e assumption that t h e hquid behaves as a high-density gas is not grossly in error. Using the gas-phase cross sections for the low-energy secondary, tertiary, etc., electrons,


749

the spatial distribution of the events in the complete track can be calculated. Let us return to the case of a 1-MeV electron in a medium of I k g d m " ^ . As we see from Table 1, a b o u t 9 8 % of the losses of the 1-MeV electron is below 100 eV. T h e secondary electron emerging wih carry a kinetic energy of at most a r o u n d 90 eV, and gives rise to a few (about 4) further ionizations within a distance on the order of 1 or 2 nm. The secondary and tertiary electrons of which the energy has d r o p p e d below the lowest electronic level continue to lose energy in interactions with vibrational and rotational modes of the molecules and with p h o n o n s , unth they finahy become thermalized. As we shall see below, in saturated hydrocarbon liquids the thermalization distance is usually on the order of several (and in a few cases, a few tens of) nanometers. W e have found that the average spacing between primary events for a 1-MeV electron and density 1 kg d m ~ ^ is ca 200 nm. W e see now that, because of the large dominance of the low-energy losses, the track of a fast electron mainly consists of single ionizations and small groups of a few ionizations close together that are separated from each other by a considerable distance. Occasionahy, a much larger loss appears that gives rise to a track of a secondary electron that consists of a m u c h larger n u m b e r of ions and that is more extended in space. Very large energy losses (above ca 50 keV) lead to electron tracks very similar to that of the primary, and which may be sub-divided into independent groups again. (These losses represent a b o u t 13% of the energy loss of a 1-MeV electron.) At this point it is of interest to realize the importance of the C o u l o m b interaction in non-polar liquids. The C o u l o m b energy between single charges is given by U = e^/4mQ8,r and the distance at which the energy U is equal to k^T with s, = 2is equal to ca 3 0 n m at 300 K. We see that with the thermalization ranges for the liquids mentioned above, the thermalized electrons stay well within the range of attraction, with the result that recombination/neutralization is a predominant process in the liquid. W e shall return to this in a later section. In the gas phase the situation will be different. With a density typically 100 times smaher t h a n in the hquid, the sub-excitation electrons whl mostly escape from the C o u l o m b field of the positive ions. The distribution of the n u m b e r of ionizations in the groups in the tracks of high-energy electrons in the gas phase has been determined from cloud-chamber experiments as well as by calculation. Results are shown in Table 2. We see that a b o u t 2 3 % of the energy is

TABLE 2. The fraction / „ of groups containing n ion pairs in the track of a high-energy electron, and the fraction of the ions found is groups of n pairs, F„ = nfJY.nfr, n 1 2 3 4 >4 5 6 >6 5-10 11-100 >100

062 0.20 O09 0.04

0.66 019 O06 0.031 O066

0.23 0.13 0.06 0.044

0.02 OOl 0.02

"Obtained from cloud-chamber experiments^'*''', ''Calculated^^

O106 0.160 0.256

750

A. H u m m e l

deposited in single ion pairs a n d 4 7 % in groups of 4 pairs a n d less (which corresponds to energy losses below a b o u t 100 eV). As we have seen above, a-particles have a much higher L E T t h a n electrons with t h e same energy, due t o the proportionality of the L E T t o z^/m^v^. In the case of the 1-MeV a-particle, t h e spacing of the primary events was found t o be 0.4 n m in t h e condensed phase (^ = 1 kg d m " % so that all the groups of ions resulting from the small losses merge and form a cylinder with a high ionization density. Occasionally, short side tracks emerge due t o larger losses. The heavy particle tracks whl be more straight t h a n electron tracks of simhar energy, d u e t o the fact that the m a x i m u m energy loss for the heavy particle in a cohision with an electron is smaller (roughly m/M) t h a n in electron-electron collisions (0.5). F o r heavy particles with even higher L E T , the track may be considered as a cylindrical core of high ionization density due t o the low-energy losses ( < 100 eV) a n d a cylindrical region a r o u n d it (called the penumbra) with a lower ionization density due to the energetic secondary electrons. About half of the energy of the primary is spent in each of the t w o regions. D. The Radiation Chemical Yield

T h e radiation chemical yield is defined as t h e n u m b e r of species or events produced per unit energy absorbed by the medium. T h e yield is traditionally expressed in units of events per 100 eV energy absorbed and denoted as G. W e shah use the symbol g when it is expressed in other units or when t h e units are n o t specified. W h e n g is expressed in mks units (mol J~^), t h e relation between g a n d G is g (in mol J - ^) = 1.04 X 1 0 " ^ X G (in events per 100 eV)

(4)

The yield is determined experimentally mostly by determination of a concentration Cj of a species ; formed in a given a m o u n t of material, while also the average total a m o u n t of energy absorbed per unit mass, the dose D, in that material is known, with Cj = gjDd

(5)

where d is the density of the material. The mks unit for the dose D is J k g ~ \ called the G r a y (Gy). With gj in mol J " ^ Cj in mol d m ~ ^ and D in J k g " ^ the density is t o be expressed in kg d m " ^ in order t o have a consistent set of units. (An old unit for the dose is the rad, which is equal to 0.01 Gray.) W e have seen above that we can distinguish two kinds of energy losses of the fast-moving charged particle, the optical o r resonant losses a n d the losses in the h a r d collisions. T h e relative distribution of the various optical excitations is independent of the charge a n d the mass of the primary, a n d only weakly dependent o n t h e velocity (see equation 2). Therefore the fast-moving secondary electrons that are created as a result of the large losses in h a r d cohisions whl give approximately the same spectrum of optical excitations as the primary particle. (For the very slow secondary electrons this does n o t hold.) As a first-order approximation it is often assumed that all the secondary electrons (and tertiary, etc.) give the same spectrum of optical excitations. I n this way all the kinetic energy of the primary particle is converted eventually into optical excitations with the same spectrum, a n d this spectrum is rather independent of the initial energy of t h e primary. Since the energy of g a m m a radiation is first converted into kinetic energy of electrons, the spectrum of t h e resulting primary events caused by these electrons whl therefore also be approximately the same again. As a result the total n u m b e r of the various primary events divided by the total energy deposited (which is the radiation chemical yield) is rather independent of the (high-energy) radiation.

16. Radiation chemistry of alkanes a n d cycloalkanes

751

W h h e the yield of the initial events is n o t very different for different radiations, the yield of the end products m a y be very different. An important reason for this difference is the difference in the spatial distribution of the initial events. I n tracks of a high L E T particle (low velocity) the intermediates are formed close together a n d much more reaction with each other wih take place than in a low LET-pardcle track. W e shah return t o this below. II. THE GAS PHASE A. Introduction

A significant characteristic of the radiation chemistry in the gas phase is the importance of the fragmentation of the excited molecules a n d ions. I o n fragmentation competes with collisional deactivation, b u t also with ion-molecule reactions a n d charge neutralization, the relative importance of which is dependent o n the pressure a n d o n t h e radiation intensity (dose rate). Dissociation of neutral excited states is of course also affected by the pressure. As a result the final product distribution wih in general be dependent o n the pressure as weh as o n the dose rate. The radiation chemistry in the gas phase is complex a n d mostly cannot be explained completely. I n several cases, however, a fair knowledge exists, especiahy about ionic processes, since these (in a low-pressure gas) c a n be studied by mass-spectrometric techniques. In the fohowing we shall discuss the radiation chemistry of methane in the gas phase, which may serve as a n hlustration of the various aspects of the radiation chemical effects in the gas phase. W e shall also consider the effect of pressure a n d dose rate o n the com petition of the various processes. Finahy we shah discuss briefly the effect of pressure on the fragmentation in cyclohexane. F o r a more detahed study the reader is referred t o the review article of Gyorgy^ a n d the references cited therein. B. Primary Processes; Methane

In Figure 1 we have shown the optical oscillator strength distribution for methane in the gas phase. I n this picture the contributions of neutral excitation a n d ionization are indicated. The ionization onset is at 12.5 eV. W e see that a substantial a m o u n t of oscihator strength for neutral excitation is found above the ionization potential, which is due t o so-called superexcited states. T h e phenomenon of the superexcited state was in fact discovered in CH4. Using the oschlator strength distribution for total optical absorption and assuming the yields of ionization a n d neutral excitation t o be determined by j(df/dQ)'{l/Q)dQ above a n d below the ionization potential, led t o a calculated ratio of yields of neutral excited states a n d ionization much smaller t h a n the experimental value It was therefore concluded that part of the oscihator strength for neutral excitation h a d to be present above the ionization potential. T h e p h e n o m e n o n of superexcited state formation has been found t o be quite general for molecular compounds, a n d is due t o excitation of electrons in deeper-lying orbitals a n d double excitation. T h e overall probabhity of ionization after excitation above the ionization potential shows an isotope effect due t o competition of dissociation a n d ionization. It is interesting t o see that superexcited states are formed also at energies of several tens of eV. There are several dissociation processes of neutral excited states^'^^: CH4

. C H 3 + H— > C H 2 + H2

(6a) (6b)

752

A. H u m m e l >CH2 + 2H*

(6c)

. C H + H2 + H-

(6d)

>C + 2 H 2

(6e)

All these processes take place from singlet levels above ca 8.5 eV, the level of the first excited singlet. Process 6a is believed to be the prominent decay process of the lowest triplet (at ca 6.5 eV). At 12.5 eV we have the onset of the ionization^^: CH^

.CH^ + ' + e-

(7)

Several dissociative ionization processes have been observed, as is presented below, with the various onsets in parentheses^^: CH4

>CH3++H* + e-

(

14.4eV)

(8a)

CH2-''-fH2 + e-

(

15.3 eV)

(8b)

C H - ' + H 2 + H- + e -

(

22.4 eV)

(8c)

C H + + 3 H - + e-

(

23.0 eV)

(8d)

C +- + . . - + e -

(^25.2eV)

(8e)

T h e relative abundance of the various ions has been studied by low-pressure massspectrometric measurement. It has been found that the relative abundance is approxi mately constant for electron energies above ca 100 eV. F o r methane the following abundances are found^^: CH4 + - 46%, CH3+ 40%, CH2^* 7.5%. Together with a total yield of ionization^ ^ of 3.6 (100 eV)~ ^ this leads to the yields of fragment ions as presented in Table 3. At higher pressures the relative abundances of the ions change due to deactivation of excited ions before fragmentation can take place. Yields of fragments of neutral excited states have also been obtained from final product analysis. At pressures between 100 and 700 torr 'primary' yields of CH3, CH2 and C H radicals of 1.4, 0.7 and ca 0.2 (lOOeV)"^ have been obtained^^. A total yield of neutral TABLE 3. Yields of primary species in CH4 in the gas phase G value (100 eV)-^

CH4-^CH3+ CH2+-

1.7^^ 1.4" 0.3"

Other

0.2

Ah ions

3.6

CH3 CH2 CH*

1.4" 0.7" 0.2"

Neutral excitation

2.3

"From low-pressure mass-spectrometric measurements. ^From product analysis, 1 0 0 - 7 0 0 torr.


753

excitation of CA 2.3 (lOOev)"^ follows from these values and a ratio of yields of neutral excited states to ions of a r o u n d 0.6. Theoretical calculations have been made of the yields of ionization, singlet and triplet excitation for 100-keV electrons slowing down, using the so-called binary-encounter cohision theory^ Yields for the various processes have been calculated for electrons originating from three orbitals (1^2, and la^) with ionization potentials 13.0 eV, 23.1 eV and 290.7 eV, respectively. It is of interest that from the total yield of processes leading to ionization of 3.6 (lOOeV)"^ a yield of 0.11 (lOOeV)"^ is calculated to arise from double ionization and a yield of 0.018 (lOOeV)"^ is found to originate from K-sheh ionization. The latter wih give rise to Auger ejection of electrons, which is assumed to lead to CYL^^ ^ ions. A total yield of neutral excited states (not leading to ionization) of 4.23 (100 eV)"^ is found, of which 0.78 (lOOeV)"^ is triplet. We see that a ratio of neutral excitation to ionization of 4.23/3.60 ^ 1.2 is found, which is higher than found above from experiment. The branching ratios for ionization and the various fragmentation processes cannot be calculated accurately. O n the basis of some semi-empirical estimates yields for CH4-'*, CH3+ and CH2^* have been found of 1.63, 1.42 and 0.32 ( 1 0 0 e V ) - \ respectively, in agreement with experiment. C. Kinetics

As we have seen earlier, the ionization by high-energy charged particles takes place nonhomogeneously, in tracks. In the gas phase the thermalization range is very large, so that the secondary electrons escape from the C o u l o m b field of the positive ions. The positive ions that are formed close together will repel each other. The spatial correlation of the ions and the electrons wih get lost and the charged species wih become homogeneously distributed throughout the irradiated volume. Neutralization of ions and electrons whl therefore take place by homogeneous second-order reaction kinetics, characterized by - ^ = aec^ dt

(9)

where C is the concentration of positive ions and electrons and the second-order specific rate of recombination. With a continuous rate of production q ion pairs per cm^ and per second, the stationary concentration wih be given by c = (qKy" (10) The average lifetime with respect to recombination is now Tr

The recombination coefficient atmospheres can be written as

= ( l / a e C ) = (l/a,^)^/^

(11)

in hydrocarbon gases at pressures below a few

(X^ = (X2 + (X^C

(12)

where (X2 and are coefficients representing the two- and three-body recombination processes, respectively. We see that increases with pressure. (For neopentane, for example, a2 = 7.0 x l O ^ ^ c m ^ s " ^ and = 2.5 x 10~^^cm^s~^). At high pressure ( > several atmospheres) the recombination is diffusion controhed and now a^ is given by ae==-^(w++tie)

where w+ and

(13)

are the mobilities of positive ion and electron, e the electron charge

754

A. H u m m e l

and £o, Sr the permhtivity of vacuum a n d of the gas, respectively. Since t h e mobhities are inversely proportional t o pressure, at large pressures cc^ccp'^. W e can now m a k e an estimate of for a given dose rate a n d pressure. F o r a typical dose rate for a gamma-irradiation experiment, dD/dt is o n the order of 1 M r a d h " ^ ^ 3 G y s - ^ Using g = 4 ( l O O e V ) - I = 4 x I Q - " (mol J"^) = 2.4 x lO^"^ ( m o l J " ^ ) for t h e yield of ion pairs, we find for a gas of molecules with a molecular mass M = 100 at a pressure of 1 at a n d a temperature 273 K, a rate of production of ion pairs o( q = {dD/dt)dg = 32x 10^^ c m " ^ s " ^ Taking a typical value of AE = 1 x 1 0 " ^ cm^ s " ^ we find Tr = {l/oL^qy^ = 2 X lO'^^s. F o r p = 1 torr we find a value of a r o u n d 6 x 1 0 " ^ s. In a pulse radiolysis experiment, however, the dose rates m a y be very m u c h larger. With a dose rate of 3 x 10^^ G y s~^ we find values of T,ca3 x 10^ lower t h a n t h e ones given above. F o r p = 1 atmosphere we have n o w T^ = 6 X 10~^°S a n d for p = 1 torr, Tr = 2 x 1 0 - « s . The primary fragmentation after ionization by the high-energy charged particle takes place largely at a time scale of 10~^^s a n d t h e fragmentation pattern does n o t change any m o r e drasticahy between 10"^° a n d 10"^ s. Thermalization of the electrons takes place in a few times 1 0 " ^°s in CH4 a n d C2H6 at one atmosphere a n d t h e t h e r m a h zation time is inversely proportional t o pressure; T^h?^ lO~^^/p{a.t) seconds. The time between cohisions of ions with the molecules is o n t h e order of T , « 1 0 " ^7p(at) seconds; at p = 1 at, T, = 1 0 " s. W e see n o w that ion-molecule reactions a n d deactivation m a y start t o interfere seriously with the fragmentation above ca 1 atmosphere. Also, except at very high dose rates a n d low pressures, ion-molecule collisions compete with neutralization, a n d there fore ion-molecule reactions have t o be taken into consideration. D. Reaction of the Transients in IVIethane

In Table 3 we have shown the yields of the 'primary species'. W e have seen that CH4-'* a n d CH3 are the predominantly occurring ions, a n d CH3' is the most i m p o r t a n t p r o d u c t of neutral excitation. T h e most i m p o r t a n t ion-molecule reactions in t h e radiolysis of CH4 are^'^^'^^ CH4+- + C H 4

.CHs^ +CH3-

(14a)

CH3 + + CH4

> C2H5 + + H2

(14b)

.C2H3++2H2

(14c)

The cross section for the first reaction decreases with increasing kinetic energy of t h e ion. The latter two reactions probably take place via the intermediate excited ion C2H7"'; C 2 H 3 ^ originates via fragmentation of excited C 2 H 5 ^ . T h e ratio of C 2 H 3 ^ / C 2 H 5 ^ is approximately 0.04 for thermal C H g ^ b u t increases dramatically with increasing kinetic energy of C H 3 ^ . The ions C H s ^ a n d C 2 H 5 ^ are relatively unreactive towards CH4 a n d are t h e major ionic species in the radiation chemistry of CH4. T h e reaction of the fragments of neutral excited states have been studied also by means of photolysis, using resonance lamps providing p h o t o n s of various energies^. Reactions of CH2 a n d CH* with CH4 have been observed. Both species insert into CH4. CH- + C H 4

>C2H5*-

(15)

is found; the resulting excited ethyl radical m a y again fragment: C2H5*-

^C2H4 + H .

(16)

16.

Radiation chemistry of alkanes and cycloalkanes

755

With CH2 the process is

CH2 + CH4

^QHG*

(17)

If the excited ethane molecule is not deactivated, the reaction

C2H6*^2CH3-

(18)

take place. H o t hydrogen atoms react with CH4

to give H2 and C H 3 ' radicals:

H- + CH4 . H 2 + CH3(19) As we mentioned above, the electrons get thermalized far away from the parent positive ion, outside the C o u l o m b field. Eventually, recombination of the electrons with the positive ions wih take place under formation of excited species, either in the singlet or in the triplet state. The C H s ^ ion, on recombination, may yield either H* or H2^'^:

CH5+ + e - — ^ C H ^ + H-

(20a)

— > C H 3 - + H2 (20b) The C2H5'^ ion, on recombination, will give an excited C2H5* radical, which may be deactivated or fragment into C 2H4 + H* as mentioned earlier (equation 16). We see now that the major 'stable' radicals remaining to react with each other are CH3-, C2H5- and H*. In Table 4 we present yields of final products as obtained from gamma-irradiated CH4. The yields have been found to be constant for the range of pressures of 0.12-1.2 bar. The major product, ethane, results from reaction of two CH3* radicals and from CH2 + CH4. P r o p a n e and butane are formed from CH3*-hC2H5* and 2C2H5*, respectively. There seems to be uncertainty about the yield of C2H4, since it may be that part of the C 2H4 formed reacts with H atoms. The mode of formation of the polymer (whh a composition approximately C 20H40) is not entirely certain. It has been proposed that the ionic mechanism

CH4

+

C„H+„^,

> C„ + IH+„^3 +

H2

is operative^. It may be concluded that whhe the gross features of the primary processes are fairly TABLE 4. Yields of final products in CH4 in the gas phase at pressures 0.12-1.2 bar, Co-60 gamma irradiation^

G(100eV)-I

Product

H2 C2H6 C2H4 C3H8 n-CJiio i-Butane Pentanes Pentenes Hexanes 'Polymer' ( — C H J

5.7

2.2 1.4 036 Oil 0.04 ^ > J

0.03 2.1

(21)

756

A. H u m m e l

well k n o w n for methane, the detailed mechanism of the product formation has not been elucidated. E. Cyclohexane

W e briefly consider cyclohexane as another example in order t o hlustrate t h e effect of density o n the fragmentation. I n Table 5 we show product yields obtained for pulseirradiated (high dose rate) cyclohexane at 55 torr (a) a n d for gamma-irradiated cyclohexane at densities varying from 0.004 kg dm ~^ t o t h e hquid density (b-d). T h e general trend in the product distribution is a pronounced increase of the yield of C — C break with decreasing density. In the pulsed experiments (a) with a gas pressure of 55 torr t h e ions have a lifetime o n t h e order of a few nanoseconds, whhe t h e collision interval is a b o u t 0.4 x 10"^ s. Some collisional deactivation may be expected (as we shall indeed see t o be the case below). The charge recombination wih only interfere with slow ion-molecule reactions. In the gamma-radiolysis experiments with 1000 torr (b), with a dose rate o n the order TABLE 5. Yields of products, in G-value units of ( 1 0 0 e V ) ~ \ in the radiolysis of cyclohexane in the gas and liquid phase a room temp. 55 torr 2.5 X l O - ^ k g d m - 3 pulsed electrons

H2 CH4 C2H2 C2H4 C2H6 CH2=C=CH2 CH3C—CH CH3CH=CH2 cyclo-CaHe

C3H8 1,2-C4H6 1,3-C4H6

I-C4H3 cis-2-C4H8 trans-l-C^HQ

cyclo-CgHio "-QHio CHs-cyclo-CsH^ C2H5-cyclo-C6Hii C3H7-cyclo-C6Hii bicyclohexyl Other C12

0.75 0.66 4.62 0.14 017 013 1.32 0.009 023 0.07 092 0.53 Oil 013 019 1.1

b 373 K 1000 torr 0.004 kg d m - 3 y-radiahon

c 573 K 78 at 014kg dm-^ y-radiation

d room temp. lat 0.78 (hquid) y-radiation

4.8 0.36 0.35 1.7 1.4

5.4 0.13

001

—

0.025

037 0.18

010

0.55

0.15

0.44

0.09

0.025 0.006 0.011

—

0.004

06

5.6

0.015

O025

1.2

1.9

0.3 0.2 1.0

1.1

0.008 3.26 046 0.2

1.81 0.1

"Reference 16; 80 ns pulses from a field emission source, with a total dose of 2 9 k G y per pulse (dose rate 0.36 X l O ^ k G y s - i ) . ''Reference 17; gamma irradiation. ^Reference 18; gamma irradiation. ''G values from various authors, taken from Reference 19; gamma irradiation.


757

of 10 G y s " ^ we have lifetimes of the ions o n the order of lO'^^s, a n d collision intervals shorter than 10" s. Here the charge recombination does not compete with ion-molecule reactions. The lifetime of the charged species is in fact so long that reaction with impurities may present a problem. T h e short cohision interval, however, causes deactivation a n d decreases the fragmentation, as is observed in the product distribution. The initial yields of the ions have been determined from g a m m a radiolysis in cyclo hexane at a pressure of 55 torr by isotopic labelling techniques. I n Table 6 we show the initial yields of the various ions together with those obtained from mass-spectrometric determinations at very low pressure. The yields are given as ion-pair yields, i.e. the yield of species per ion pair produced. The ion-pair yield M/AT^ can be converted into species produced per unit energy absorbed, by multiplication by the yield of ionization G = 4.4 (lOOeV)"^ W e see that the decomposition of the parent ion is appreciably suppressed in the gas at 55 torr, due to collisional deactivation. The decrease in decomposition of C^llj^2^ of 0.3 in the ion-pair yield is matched by an increase in the fragmentation yield of 0.35. The fragmentation reactions are ( Q H i 2 ^ - ) — ^ C 4 H 8 ^ - + C2H4

(22a)

C5H9^-hCH3"

C,U,^'

(22b)

+ C,He

(22c)

CsHZ+CsHs*

(22d)

(C4H8 +r - ^ C 3 H 5 ^

+CH3-

(23a)

TABLE 6. Fragmentation pattern of the ions in cyclohexane obtained mass spectrometrically (70 eV electrons) and from gamma radiolysis of cyclohexane at 55 torr

Mass

Gamma radiolysis p = 55 torr

spectrometer

QHi,^ QHio

C5H/ C4H8^'

C4H/ C4H6^-

C4H5" C3H/ CaHe"CaHs^ C3H4^ C3H3^

C2H5" C2H4"-

C2H3"

M/N^"

M/N"-"

0.16 0.0098

0.46 (014)-^ (0.08)^^

0.049 0.22 0077 0.015 0.011 0.031 0.068 0.15 0.014 0.063 0.028 0.032 0.067

— Oil 0.044 0.015

— O027 0.036 0.054 0.003

— 0.014 0.002 0.043

G(lOOeV)2.0 0.62 0.35

— 0.48 0.19 0.07 — 012 0.16 0.24 0.01

— 0.06 0.01 0.19

"M/N ^ expressed as the fraction of the total number of ions formed. ''The yield in (lOOeV)"^ calculated from M/N^ using, for the total yield of ionization, G = 4.4 (100 eV)~ ^ ^The yields of C g H n ^ and C g H i o ^ are products from secondary reactions.

758

A. H u m m e l

(CgH^^T

QH/-hH-

(23b)

^C3H3^+H-

(24)

The ions Q H n ^ a n d CgHio"^' are formed from C 6 H i 2 ^ ' reacting with unsaturated molecules by H~* a n d H 2 ~ transfer. W e see n o w that in the gas at 55 torr the ions C6Hi2'^*, C g H n ^ , CgHio"^* a n d C4H8^* with abundances 0.46, 0.14, 0.08 a n d 0.11, respectively, represent close t o 80% of the ions. Extensive experiments have been carried out, with g a m m a irradiation as well as with pulsed irradiation, with radical scavengers present in order t o depress products from radical reactions, a n d with electron scavengers t o prevent formation of products from neutralization. I n this way estimates of the contribution of some of the various possible reaction pathways have been made. F o r a detailed discussion the reader is referred t o Reference 16. IV. LIQUIDS A. Introduction

W h e n comparing the early processes in the liquid a n d gas phases, some i m p o r t a n t differences can be observed. I n t h e first place, in t h e liquid, b o n d dissociation of the primary excited molecules a n d ions takes place less frequently than in the gas, d u e t o cohisional deactivation a n d the cage effect. Another difference concerns what is called the charge separation. I n a low-pressure gas t h e electrons get thermalized a t a large distance away from the positive ions a n d they escape from the C o u l o m b attraction. I n hquid saturated hydrocarbons t h e electrons get thermalized well within t h e C o u l o m b field of the positive ions and, in most liquids, the vast majority of the charges recombine at a very short time scale. T h e charge recombination leads t o excited species that in turn m a y undergo dissociation into neutral fragments. Whether or n o t the primary excitation a n d ionization processes in the hquid a n d gas phases are the same, we d o n o t know. As we shall see below, the yield of ionization in the liquid appears to be somewhat larger t h a n in the gas phase, possibly at the expense of direct excited states. Excited states formed in the primary excitation m a y subsequently ionize, but, o n the other hand, ion-electron recombination may take place at a n extremely short time scale a n d excited states m a y be formed. T h e earliest processes are n o t very well understood at present. In the following we first discuss the charge separation. Next, we consider some examples of the chemistry of the ions a n d of the excited states formed after recombination. Then we shall discuss the overall product formation for cyclohexane and n-pentane and indicate some general features of the decomposition of the various saturated hydrocarbons. All this work concerns the radiolysis with low L E T radiation (gamma radiation, fast electrons). I n the last section we give some results for radiation with different L E T s for the case of cyclohexane. W e also indicate h o w the non-homogeneity in the initial spatial distribution of the reactive species is accounted for in the (non-homogeneous) kinetics. B. Charge Recombination and Escape from the Track

As we have seen in Section II, the slowing down of a fast electron in the liquid leads to a track of single ionizations a n d groups of ionizations, a t a considerable distance from each other. T h e electrons ejected from the molecules get thermalized some distance away from the positive ion b u t within the C o u l o m b field. These thermal 'excess' electrons do n o t react with saturated hydrocarbon molecules, b u t are stable species that are more

16. Radiation chemistry of alkanes a n d cycloalkanes TABLE 7. Values of G

n-Hexane Iso-octane Neopentane Cyclohexane cis-Decahn frans-Decahn

759

, r^, b,u{ — ) and a/k for various hquids at room temperature^^'^^

(lOOeV)-i

(10-^^m)

(10-i^m)

0.13 033 1.1 0.13 014 013

299 286 318 297

67 95 230 61

"(-) (lO-^m^V-^s-i) 0.08 5.3 70 0.23 0.10 0.013

a/k

(lO-i^s) 15 0.7 2.2 13 43

"The b value is the width of the gaussian distribution, used for / ( r o ) in equarion 27 (see text).

or less trapped by potential fluctuations in the liquid. In most liquids only a minor fraction of the excess electrons and positive ions escapes recombination in the track. The yield of escape, also called free ion yield, has been measured for m a n y liquids. Some examples are given in Table 7. We see that there are considerable differences between the liquids. W e d o not k n o w the total yield of ionization in the liquid accurately, but h we take a value of 5 ( 1 0 0 e V ) ~ \ we see that the overah probability of escape for cyclohexane is approximately W^^^^ 0.026 and for neopentane 1^^^^:^0.24. The difference in escape probability reflects the difference in thermalization lengths of the electrons in the different hquids. In order to obtain an estimate of the thermalization length it has been assumed that in the track only single pairs of oppositely charged species are present. F o r single ion pairs the probability of escape is given by the simple expression Hêsc(ô) = e x p ( - r > o )

(25)

Here VQ is the initial separation and the distance at which the C o u l o m b energy between two singly charged species is equal to k^T; = e^/4nsQ£,k^T is called the Onsager length. F o r 8^ = 2, and T = 3 0 0 K , r , ~ 3 0 n m is found. W e see that for ro = r^ = 3 0 n m , W,,, = 1/e = 0.37. If in the track a distribution / ( r o ) of initial separations is assumed, we can write for the track consisting of single pairs W esc =

/(ro)exp(-r,/ro)dro

(26)

0

or with an initial yield GQ of single pairs /(ro)exp(-r,/ro)dô (27) Jo Different trial distributions have been taken for / ( r o ) ; for Go mostly the gas-phase value has been assumed. C o m p a r i s o n with the experimentahy determined value of G^^^ gives an estimate of the width of the distribution / ( r o ) . In Table 7 we have given the width parameters for a gaussian distribution f(ro)

=

{4nrl/n"V)cxpi-rl/b')

taking for Go the gas-phase yield. We see that the thermalization distances differ considerably for the different liquids and that the spherical molecule neopentane has the largest value. The differences are thought to be due to differences in the efficiencies of energy loss of the electrons with energies close to thermal. An interesting correlation exists between the thermalization ranges and the mobhities of the electrons in the various

760

A. H u m m e l

hydrocarbon hquids, as is shown also in Table 7. W e see that the largest mobhities a r e found for the liquids with the largest yields of escape a n d therefore t h e largest thermalization ranges. It m a y be noted that the mobilities given in this table are a h orders of magnitude larger t h a n the mobilities of molecular ions in these hquids, t h e latter of which have values in the range o f l O ~ ^ t o 1 0 ~ ' ^ m ^ V " ^ s ~ ^ A consequence of these large mobilities is that the recapture of the electrons by the positive ions may take place very rapidly, as we shall see below. T h e single-pair treatment given above is extremely approximate since the majority of the charged species is present in multi-ion-pair groups, as we have seen above. T h e single-pair treatment was suggested at a time when calculation of escape probabhities for multi-ion-pair groups was n o t possible. Such calculations have recently been carried out using computer simulation techniques'^. It h a s been shown that the ion pairs in groups of various sizes in the track of a fast electron have considerably different escape probabhities. It appears, however, that due t o a compensation of errors t h e single-ionpair treatment gives reasonable estimates of t h e width of the thermalization range distributions.

C. The Time Scale of Charge Recombination; Charge Scavenging

In saturated hydrocabon hquids most recombinations of the charged species in t h e track take place within a nanosecond. Direct experimental observation of a substantial yield of these charged species h a s n o t proved possible d u e t o limitation in t h e time resolution of the detection techniques. W e c a n obtain information a b o u t t h e lifetime (distribution) of the charged species by adding a solute t o the liquid that can react with the excess electrons (or the positive species) with a known specific rate a n d determining the a m o u n t of reaction taking place. Solutes in the liquid, that c a n react with the charged species, are called charge scavengers. An example of a n electron scavenger is methyl bromide: CHgBr + e"

^CH3* + Br-

(28)

The methyl radical subsequently abstracts a hydrogen a t o m from a h y d r o c a r b o n molecule and CH4 is formed. The yield of CH4 therefore represents the electron scavenging yield. At low concentrations of C H g B r only the yield of escaped electrons is scavenged; however, with increasing concentration a n increasing fraction of the electrons whl be captured before recombination has occurred. If G{t) represents the yield of the charged species as a function of time (in the absence of a scavenger), the yield of scavenging in the presence of a scavenger with concentration c is (approximately) given by Gs(c) =

G(t)Qxp(-kct)kcdt

(29)

W e see that if the yield of scavenging as a function of concentration Gj^c) is known, a n d the specific rate of scavenging k is known, then G(t), the yield of survival against time, can be determined. It has been found that for a n u m b e r of saturated hydrocarbons Gîc) can be approxi mately represented by the simple expression

'^''' = ' - ^ ' T ^ ^

''''

where for n a value of a r o u n d 0.5 is found, a n d for A a value of 4 - 5 (100 e V ) " ^ T h e parameter a is a measure of the efficiency of the scavenging reaction.

761

16. Radiation chemistry of alkanes a n d cycloalkanes time ô-^2

^Q-^^

I I \\\\\\\—I

I I I iiii{—I

^0-13

(S)

^Q-S

ô-ô

I I I iiii|—I

I I I iiii{—r

\ \ \

3

-

y

\

> o °

2

5

ml

I I i i mil

10-*

I I I I Mill

10"^

I I I I Mill

10-2

I II

10""1

concentration (nnol dnn^) F I G U R E 2. The yield of excess electrons scavenged by methyl bromide as a function of methyl bromide concentration in the gamma radiolysis of cyclohexane (lower scale). The yield of survival as a funchon of time for the charged species after instantaneous irradiation in cyclohexane (upper scale); the upper curve has been obtained with equation 31, the lower one with a more extensive treatment(see text)

In Figure 2 we have plotted Gîc) for electron scavenging by C H s B r in cyclohexane as an example. W e see that n o plateau is reached even at the highest concentrations applied, a n d we d o n o t obtain a value for the total yield of electrons formed. Higher scavenger concentrations have the disadvantage that the scavenger itself absorbs energy and wih decompose a n d correction for this effect is uncertain. F o r several liquids the electron scavenging can be reasonably weh represented by equation 30 using n = 0.5. In this case equation 29 leads to the expression G(r) = G

+Aexp(/cr/a)erfc[(/ct/a)i/2]

(31)

which can be approximated by G(0 = G

1

+ ^ n"^

(/ct/a)^/^-h(fcr/a+ 4/71)^/2

(32)

The second term on the right-hand side in equation 32 decays steeply at short times;

762

A. H u m m e l

for kt/oi = 1 this term is equal t o 0.45 A and at long times it approaches Alnî\kt/oLy^, which decays slowly with time. In Figure 2 we have plotted the survival of the charged species as a function of time, G{t\ as obtained by equation 32 for cyclohexane (dotted curve). I n order t o obtain G{t) the value of a//c has t o be known. Values of a have been determined for different charge scavengers from plots of GJ^c) as presented in Figure 2 for C H j B r reacting with excess electrons. Values of the specific rate k of reaction with the charged species have been obtained from pulse-radiolysis experiments, in which the decay of the concentration of charged species after a pulse of radiation due t o reaction with the scavenger is followed by measuring the conductivity. F o r cyclohexane a value of a//c equal t o 2.3 x 10~^^s is found [with a value of 5 (lOOeV)"^ for the parameter A in equation 30]. The value of a//c represents the time at which the initially recombining part of the charged species (the second term o n the right-hand side of equation 32) has decayed t o 4 5 % of its initial value; for cyclohexane at t = a//c, G(0 = 0 . 1 3 + 5 X 0.45 = 2.38 ( 1 0 0 e V ) - ^ As we mentioned, equation 29 relating G^{c) a n d G(r) is only approximately correct. An improved calculation (using a modified version of equation 29, taking a timedependent specific rate k as well as 'static' scavenging into consideration^^) for cyclohexane gives t h e curve d r a w n in Figure 1. W e see that this treatment leads t o a faster decay than the approximative calculation. The value of a//c, however, provides a fair measure of the decay of the charged species for longer times. Values of a//c have been given in Table 7 for a few liquids. The smallest value for a//c reported is 0.7 ps for iso-octane, the largest for trans-decalin of 43 ps. The lifetime distribution is determined by the initial spatial distribution a n d the mobilities of both the negative- a n d positive-charged species. Larger initial separations increase the recombination time a n d larger mobilities decrease it (roughly inversely proportional t o the sum of the mobhities). As we mentioned above, the mobilities of the excess electrons given in Table 7 are all several orders of magnitude larger than those of molecular ions in these liquids. I n some liquids also the positive charge has been found t o have a mobhity far in excess of that for a molecular ion, and which is ascribed t o a fast transfer of the positive charge from the parent positive ion t o the neutral molecule. This p h e n o m e n o n of the electron hole has been studied by charge scavenging and by pulse radiolysis^ F o r a more detahed treatment of the charge separation problems, see References 2 0 - 2 5 . D. Ions and Excited States

Neutral excited states are produced in saturated hydrocarbon liquids by direct excitation as weh as by recombination of the positive ions a n d electrons. As we have pointed o u t earlier, the yield of ionization in molecular liquids is uncertain. While in the gas phase the yield of ionization can be determined by collecting the charged species in an electric field (ionization chamber), in hydrocarbon liquids this does n o t prove possible. Sufficiently large external fields cannot be applied in order to obtain a saturation current. I n liquid noble gases (where the thermalization lengths are very large), total yields of ionization have been measured by determination of the saturation currents in a dc field, a n d yields have been found substantiahy in excess of the gas-phase values [4.2 vs 3.8 ( 1 0 0 e V ) - ^ for argon, 4.9 vs 4.2 ( 1 0 0 e V ) - ^ for K r and 6.1 vs. 4.6 (100eV)"^ for x e n o n ] I n (hquid) water, where the yield of solvated electrons has been measured spectrophotometricahy at a picosecond time scale after pulsed irradiation, a yield of 4.7 (lOOeV)"^ h a s been found^"^ while in the gas phase the yield of ionization^^ is 3.3 ( l O O e V ) " ^ It seems likely that in saturated hydrocarbon liquids also, the yield of


763

ionization is larger t h a n in the gas phase. In the gas phase these yields are a r o u n d 4 ( 1 0 0 e V ) " ^ ' ^ the yields in the liquid may be estimated at a r o u n d 5 (100 e V ) " ^ Saturated hydrocarbon liquids have optical absorption edges in the far U V (CA 1 eV and above) and, on optical excitation, show fluorescence with a wavelength m a x i m u m around 200-230 n m (6.2-5.4 eV), which is believed to arise from the lowest excited singlet (Si). The lifetimes of these excited states are a r o u n d a nanosecond and the q u a n t u m efficiencies for fluorescence are small ( < 0.02), the competing process being decomposition of the molecule. These fluorescent excited states have also been observed with high-energy radiation. Yields have been determined for compounds containing six-membered rings (which have high yields of fluorescence). The highest yields have been found for CIS- and TRANS-DQCDXIN and bicyclohexyl [3.4, 2.8 and 3.5 ( 1 0 0 e V ) ~ \ respectively'^]. A substantial fraction of the fluorescent singlets in CIS- and trans-decalin as well as in cyclohexane has been shown to originate from charge recombination''^. The neutral excited states, single pairs and groups of pairs of positive ions and electrons formed initiahy in the track are formed in an overall singlet state, since no exchange of spin of the high-energy particle takes place. (The low-energy secondary, etc., electrons may exchange spin, but we disregard this for the moment.) It turns out that, in saturated hydrocarbon hquids, the spin state of an electron and its parent ion remains conserved for a considerable period of time (on the order of 10~^s). Single pairs that recombine within that time will therefore remain singlet (geminate recombination). In multiple pair groups the situation is different, however. An electron may now recombine with another positive ion rather than its parent ion (cross recombination). In this case there is no spin correlation and the ratio of probabhities for the formation of singlets and triplets is 1/3. It can be shown that the overall probability for singlet formation for the group depends on the number of pairs initially as well as on the initial spatial distribution of the charged species. F o r a track of a high-energy electron in a low-yield hquid (like cyclohexane and the decalins) the overall probabhity for singlet formation may be estimated to be a r o u n d 0.6^^. With an estimated yield of CA 5 (lOOeV)"^ for the total yield of ionization, we therefore expect a yield of CA 3 (lOOeV)"^ of singlets. This is roughly what is found for the yield of Si for the decalins and bicyclohexyl, as mentioned above. The yields for cyclohexane and methylcyclohexane are lower, however. This may indicate that the charge recombination initiahy leads to a higher excited state that only partly converts to the fluorescing Si state or that the parent ion partly fragments. The role of neutral excited states in radiolysis has been investigated by comparing the formation of products and intermediates in radiolysis with that in photolysis with various excitation wavelengths. We consider liquid cyclohexane. In Figure 3 we show the q u a n t u m yields for the two predominant processes as a function of p h o t o n energy^ ^: c - Q H i / — C - Q H 1 0 + H2 C - Q H I / ^ C - Q H ; ^

+ H-

(33) (34)

We see that the yield of H 2 elimination decreases with p h o t o n energy, while that of simple C — H break increases. At the lowest energy employed the q u a n t u m yield for H 2 elimination is approximately 0.8. It has been shown from deuterium-labelling studies that the molecular hydrogen formation takes place from one carbon atom under formation of a biradical^^. The chemistry resulting from the two primary reactions 33 and 34 is very simple. The H atom abstracts a hydrogen atom: H - + C-C6H12 ^ H 2

+ c-QH-

(35)

764

A. H u m m e l

9

8 Q

10

(eV)

F I G U R E 3. Quantum yields for the processes (a) c-C5Hi2->' and (b) c - Q H i ^ ^ c - Q H i i ' + H* ( • ) in the photolysis of hquid cyclohexane at different photon energies. Reproduced by permission of the American Inshtute of Physics from Ref 31

C-QH10 + H2 (O)

and the cyclohexyl radicals react with one another leading to either disproportionation 2 c-C^Hi /

> c - C g H i o + c-C^Hi 2

(36)

or to dimer formation (37) The ratio of specific rates for disproportionation and combination, kjk^ is 1.1 at r o o m temperature^^. We can deduce eashy that the q u a n t u m yield for H2 elimination (equation 33) is given by (/>H2 = ^(CgHio) — 1-1 x 0(Ci2H22), where (p (CgHjo) and (p (C12H22) are the overah q u a n t u m yields. In the radiolysis of hquid cyclohexane the major products are H2, cyclohexane a n d the bicyclohexyl, with yields of 5.6, 3.3 and 1.8 (100 eV)~ \ respectively^^, which suggests an important contribution of cyclohexyl radicals. This has been substantiated by radical titration experiments, where a solute is added that reacts with the radicals R* (e.g. I2) and the products (RI) can be measured^ ^. Also, with radical scavengers present, the yields of cyclohexene and bicyclohexyl decrease with the ratio kjk^ for the cyclohexyl radical. W h e n it is assumed that the dimer is formed only by the radical recombination reaction 37 [with a yield of 1.8 ( 1 0 0 e V ) " ^ ] , h follows that c-CgHio is formed concomitantly with a yield of 1.1 x 1.8 = 2.0 (100 eV)" K Since the total yield of c-CgHio is 3.3 (100eV)"^ h follows that a yield of c-CgHio equal to 1.3 (100 eV)"^ is found that is formed in another process than disproportionation of cyclohexyl radicals. It appears that this process is molecular H2 elimination of the S^ state (that also fluoresces), with (/)H2 = 0.8 as obtained from photolysis at the lowest p h o t o n energies (equation 33). The


765

yield required for this process would be 1.3/0.8 = 1.6 ( 1 0 0 e V ) ~ ^ which is in agreement with the yield of fluorescent singlets found. The total yield of c - C g H n ' radicals involved in the formation of c-C^Hio a n d C12H22 is 2 X (2.0 + 1.8) = 7.6 (lOOeV)"^ If these radicals would be formed by C — H scission of excited cyclohexane (equation 34) followed by H abstraction, this would correspond t o a yield of 3.8 (lOOeV)"^ of C — H scission. T h e ratio of H2 elimination a n d C — H scission is now found to be 1.3/3.8 = 0.33. In the photolysis at 7.6 eV, a value of ca 4 is found, a n d at 11.6eV approximately 0.6, as can be observed from Figure 3. T h e low value of 0.33 for the radiolysis m a y be an indication that highly excited states are involved. Another explanation is that a fraction of the cyclohexyl radicals originates from triplets. It has been suggested also that part of the parent positive ion decomposes, whhe excited^"^: (CeH^^;)*-^QHi/+H-

(38)

The cyclohexyl radicals would be formed after charge recombination a n d by H abstrac tion. Holroyd compared the photochemistry at 8.4 eV a n d the radiolysis of liquid n-pentane and iso-octane^^. It was shown that the relative distribution of the yields of the different radicals originating from C — C scission is strikingly similar for t h e radiolysis a n d t h e photolysis, for both liquids. The total q u a n t u m yield for formation of these radicals is a r o u n d 0.1. W h h e the relative frequencies of C — C scission are rather simhar, the a m o u n t of single C — H scission (and formation of the parent radical) relative t o C — C scission is much larger in radiolysis. Although the simharity between t h e distribution of yields of radicals originating from C — C scission in photolysis a n d radiolysis is important evidence that excited states are the precursors, the contribution of ion fragmentation cannot be excluded. In most cases it is very difficult to distinguish experimentahy between fragmentation of the excited neutral molecule and that of the parent ion. In some cases an observed difference in yields of the two parts of the molecule is evidence for ion fragmentation of t h e ionic fragment after neutralization [e.g. G ( C H 3 ' ) » G(C4H9*) in neopentane^ ^ ] . Also, the change of product yields with and without electron a n d positive ion scavengers has provided evidence for parent-ion fragmentation t o be operative in some cases. In neopentane the fragmentation neo-CsHj^;

>Cni + r - Q H /

(39)

has been shown t o take place with a yield of 1.0 (100 eV)"^^^. I n iso-octane a yield of t-C4Rg ^ of 0.4 (100 eV)" ^ was determined^^. Evaluation of the contribution of parent-ion fragmentation in general remains problematic. It appears that in branched saturated hydrocarbons this process contributes significantly t o the overall C — C scission. E. Final Products

In Table 8 we show the final product distribution observed in the radiolysis with low L E T radiation for cyclohexane. Such product distributions have been determined for a great number of liquids^'^^'^^. With increasing dose the products accumulate in the hquid, and reactions of the intermediates (radicals etc.) with these products become more probable, thus causing the product distribution t o change. At sufficiently low doses the so-called zero-dose yields, or initial yields, can be obtained. T h e radiation chemical yields in principle are also dependent o n the dose rate. High dose rates cause higher stationary concentrations of the reactive intermediates (radicals, ions, etc.) and shorter lifetimes due to the increased rate of the reaction of the intermediates with one another. Reaction of radicals with each other may then be favoured, e.g. compared t o H - a t o m abstraction. This effect has been observed in a few cases^^. In practice, however, the dose rate effects

766

A. H u m m e l TABLE 8. Product yields in liquid cyclohexane, irradiated with ^^Co gamma radiation at room temperature''

G(lOOeV)-^ Hydrogen Cyclohexene Methane Ethane Ethylene Acetylene Propane Cyclopropane Propene n-Butane But-1 -ene + but-2-ene Buta-l,3-diene n-Hexane Hex-l-ene Hex-2 and -3-enes Methylcyclopentane n-Hexylcyclohexane 6-Cyclohexylhex-1-ene Bicyclohexyl

5.6 3.26 0.01 OOl 5 OlO 0.025 0.011 0.006 0.025 0.008 0.025 0.004 0.08 0.36 O02 0.20 0.08 0.03 1.81

"The yields of hydrogen, cyclohexene and bicyclohexyl have been taken from Reference 39, those of the other products from References 18 and 40.

appear at dose rates many orders of magnitude higher than applied with conventional g a m m a sources. However, on irradiation with particle beams this m a y play a role. The ratio of the total yield of carbon and hydrogen atoms in the products must, of course, be equal to that in the original molecule; this is called the material balance a n d provides an indication about the completeness of the product spectrum. F r o m Table 8 we find a ratio of H to C equal to 2.03 as compared with an expected value of 2 for C6H12. F o r the total yield of decomposition 7.9 (lOOeV)"^ is found. T h e principal products from cyclohexane are H2, cyclohexene a n d bicyclohexyl with yields of 5.6, 3.2 and 1.8 (100eV)~S respectively. The yield of H2 formation represents the yield of decomposition of cyclohexane molecules due to C — H scission (either by H2 elimination or otherwise). The yield of C — C scission is very small. F r a g m e n t hydrocarbons account for a yield of ca 0.2 ( 1 0 0 e V ) " \ corresponding to a yield of decomposed cyclohexane molecules of a r o u n d 0.03 (lOOeV)"^ Straight-chain Cg hydrocarbons are found with a yield of 0.46 (100 e V ) ~ \ methylcyclopentane has a yield of 0.2 (100 eV)"^ and alkylcyclohexanes have a yield of ca 0.1 (lOOeV)"^ Altogether this corresponds to a yield of cyclohexane molecules decomposed by C — C scission of ca 0.8 (100 e V ) - ^ The total yield of 'primary' decomposition is now 5.6 + 0.8 = 6.4 (100 e V ) " ^ This is lower t h a n the yield of 7.9 (lOOeV)"^ found for the total yield of decomposition. T h e latter is higher due to 'secondary' reactions of intermediates with cyclohexane molecules, like hydrogen abstraction by hydrogen atoms. It should be remarked, however, that back-formation of cyclohexane also takes place, e.g. in the reaction 2 C^H^^' C^Hio + C^Hi2 As an example of a straight-chain alkane we show the product distribution of

16. R a d i a t i o n chemistry of alkanes a n d cycloalkanes

767

TABLE 9. Product yields" in liquid n-pentane, irradiated with ^^Co gamma radiation at room temperature^ G(100eV)-i Hydrogen Methane Ethane Ethylene

5.3 0.26 0.61 0.37

Propane Propene n-Butane But-l-ene trans- and c/5-But-2-ene

0.58 0.35 0.10 0.08 0.02

Pent-l-ene trans-Pent-2-ene cis-Pent-2-ene

1.00 1.23 0.53

2-Methylbutane n-Hexane 2-Methylpentane 3-Methylpentane

0.061 0.025 0.016 0.0072

n-Heptane 3-Methylhexane 3-Ethylpentane 3-Ethylpent-l-ene 4-Methylhex-l-ene

0.050 0.119 0.0573 0.0047 0.0042

n-Octane 4-Methylheptane 3-Ethylhexane 2,3-Dimethylhexane 3-Ethyl-2-methylpentane Octanes

0.041 0.0917 0.040 0.011 0.014 0.003

n-Nonane 4-Methyloctane -I- ethylheptane 3-Methyloctane 3,4-Dimethylheptane -1- 4-Ethyl-3-methylhexane

0.0047 0.029 0.010 0.03

n-Decane 3,4-Diethylhexane -h 3-Ethyl-4-methylheptane 4,5-Dimethyloctane 3-Ethyloctane -I- 4-Methylnonane Decenes

0.0344 0.183 0.751 0.0734 0.06

"The yield of hydrogen has been obtained with a dose of 0.37 x 10^^ e V g ~ \ the yields of methane through pent-2-ene with 5 x 10^ e V g ^ and the remaining ones with 14.2 x l O ^ ^ e V g - ^

n-pentane in T a b l e 9. In this case we find a value of 2.43 for the ratio of H a n d C a t o m s in the p r o d u c t s , which c o m p a r e s very well with the expected ratio of 2.4 for C5Hi2- T h e total yield of d e c o m p o s e d molecules is found to be 6.9 (100 e V ) " ^ T h e p r o d u c t spectrum of n - p e n t a n e is m o r e complicated t h a n t h a t of cyclohexane. T h e m a i n p r o d u c t s are H2, ethane, p r o p a n e , pentenes a n d the various decanes. T h e decanes a n d a major p a r t of the pentenes are formed by r e c o m b i n a t i o n a n d dispropor tionation of the p a r e n t radicals (C5H11*), like in cyclohexane.

768

A. H u m m e l

The yields may be divided into yields originating from C — H scission and from C — C scission. The yield of H2 represents the sum of the yields due to H2 elimination a n d breaking of a single C — H bond. The total yield of decomposition involving C — C scission can be obtained from the yields of the various products with a carbon skeleton differing from the original molecule. F o r n-pentane this is found to be G(C—C) = 1 . 5 (100eV)"^ (higher t h a n in cyclohexane). Together with the yield of 5.3 (100eV)"^ for decomposition with H2 or H formation, we find a yield of 6.8 (100 eV)"^ for molecules undergoing 'primary' decomposition (much the same as in cyclohexane). As we have seen above, from the total yield of C and H in the products we found 6.9 (100 eV)~ ^ for the total yield of decomposition; the agreement is accidental. F o r n-alkanes with different length up to C 1 2 the yield of H2 formation is a b o u t the same, as is shown in Figure 4a. F o r longer chains the hydrogen yield appears to d r o p . The yield of fragment products for alkanes is also shown in Figure 4a, which shows that also the fragment yields for n-alkanes do not change much with chain length between C5 and C 1 2 . In Figure 4b we show the H2 yields for cycloalkanes together with the yields of fragments and open-chain products. F o r Cg and larger rings the yields d o not vary much, however C3 and C4 a n d to a lesser extent C5 show large yields of fragmentation and ring opening at the expense of H2 formation: this is obviously caused by the ring strain in these molecules. We now turn to the branched alkanes. As an example we consider the hexane isomers. In Table 10 we show the yields of H2 formation, together with the yields of C — C

> O O

10 NUMBER

15 OF

C—ATOMS

F I G U R E 4. Yields of products in the gamma radiolysis of (a) n-alkanes and (b) cycloalkanes: O , hydrogen. A , fragments; • , open-chain products from cycloalkanes. The yields for the alkanes with up to 12 C atoms have been determined at room temperature^^ and the value for C20 at 55 °C'^^


769

TABLE 10. G values of H2 formahon and C — C scission in units of (100 eV)~ ^ in the radiolysis of different hexane isomers^

G(H2)

G(H2) +

G(C—C)

G(C—C)

n-Hexane 3-Methylpentane 2,3-Dimethylbutane 2,2-Dimethylbutane

5.0 3.4 2.9 2.0

1.5 2.4 3.9 5.1

6.5 5.8 6.8 71

G(C—C)

G(H2)

03 07 1.4 2.5

scission. We see that the ratio of decomposition by C — H and C — C scission varies considerably for the different isomers, whhe the sum of these yields does not change much. The yields of C — C scission have been studied extensively for a large number of compounds, and an empirical expression has been found that describes the yields of radical formation resulting from C — C scission^: G(R) = ;

1

^

(1.0 C i + 2.8 C2 + 8.6 C3 -h 29

(40)

In this expression n represents the total number of C atoms in the original molecule; C„ represents the number of the C — C bonds in the molecule that, on scission, lead to formation of the radical R, and which have n C—C bonds adjacent to the breaking bond. F o r example, ethyl radicals can be formed from 3-methylhexane in two ways, either by breaking b o n d 2 - 3 or 4 - 5 :

I c—c—c—c—c—c 1

2

3

4

5

6

b o n d 2 - 3 classifies as C3 (bonds 1-2, 3 - 4 and 3 - 7 are adjacent), and there is one of these bonds, therefore C3 = 1; C2 = 1 (bonds 3 - 4 and 5-6 are adjacent); = 0 (applies only when R = CH3) and C4 = 0. We therefore find G(C2H5-) = ^

(2-8 -h 8-6) = 0.32 (100 e V ) " ^

We see now that in n-alkanes we have, for methyl radicals, G(R) = 2.0/(n — If- and, for larger radicals, G(R) = 5.6/(w — 1)^. This shows that the ratio of the scission probabhity for the ultimate and the penultimate C — C b o n d is 2.0/5.6 = 0.36. An interesting correlation is found between the yield of C — C scission for a particular bond and the dissociation energy of the bond, for the various bonds in a molecule as well as in isomeric molecules"^^. This is shown in Figure 5. Each curve refers to a group of molecules with a given number (n) of C atoms. The curves decrease about exponentially with the dissociation energy in excess of that of the weakest bond. Furthermore, for each dissociation energy the yield of decomposition is lower for molecules with larger numbers of C atoms.

770

A. H u m m e l

300

320

340

360

380

D i s s o c i a t i o n E n e r g y ( k J m o l ^) F I G U R E 5. Yields of scission of C — C bonds in the gamma radiolysis of alkane isomers as a function of the dissociahon energy of the bond, for molecules with a different number of C atoms: O, Cg; C^; A , C5; • , C4. Reprinted with permission from Ref 42. Copyright (1976) Pergamon Press PLC F. Non-homogeneous Kinetics and LET Effects

In Section II we have discussed h o w the energy of the fast-moving charged particles is deposited in tracks. W e have seen that subsequent energy losses along the track of a fast electron in a condensed medium are far apart ( ^ 200 nm). M o s t of the losses give rise t o only one ionization, which results in a positive ion a n d a n electron, thermalized within the C o u l o m b field. Also, groups of more ionizations close together are formed, with a frequency decreasing with the n u m b e r of ions (Table 2). In Section IV.B a n d IV.C, we have discussed the spatial separation of the thermalized electrons a n d t h e positive ions, t h e time scale for the recombination process a n d t h e probabhity of escape. W e have seen that the fraction of the charges that escape a n d become homogeneously distributed in the liquid is small for most liquids a n d that most of the initial non-homogeneous recombination of the pairs a n d groups of pairs of oppositely charged species takes place o n a time scale of 1 0 " ^ ^ - 1 0 ~ ^ ^ seconds. T h e non-homogeneous kinetics of single pairs of oppositely charged ions in each other's field can be treated exactly by solving the differential equation that describes the motion of one ion with respect t o the other, d u e t o diffusion a n d drift in the C o u l o m b field. Also, t h e scavenging probabhity c a n be calculated^^. F o r multi-ion-pair groups


771

the problem can be solved by computer s i m u l a t i o n ' ' . It should be remarked at this point that when excess electrons with a very large mobility, a n d therefore a very large mean free path, are involved, the existing theories are inadequate. O n recombination of the positive ions a n d electrons, excited molecules are formed that, in general, dissociate. In this way pairs of fragments a n d groups of pairs of fragments wih be formed. In the case of cyclohexane this wih be CÛn' a n d H*, C^H^Q a n d H2 (and some fragments resulting from C—C scission). Some of the fragments are formed with kinetic energy, notably the H' atoms. The initial spatial distribution of these species in the regions of high concentration (called spurs) will depend on where the neutralization takes place, i.e. on the position of the positive ions at the m o m e n t of recombination. Subsequently, these species wih start to carry out a diffusive motion. P a r t of them whl encounter other species of the group, and react (non-homogeneously), the remaining part whl escape from the group and become homogeneously distributed in the liquid, where they react with species from other groups. We consider the following reactions for cyclohexane:

QHi^*

QHi

QHio, H2

2 Q H i / —.(QHi 1)2, QHio + QH12 H- + Q H i 2 - ^ H 2 + Q H i /

(41) (42)

(43)

H- + C 6 H i / - ^ C 6 H i 2

(44)

H- + Q H i o — ^ Q H i /

(45)

QHi/ + Q H i o ^ C i 2 H 2 r

(46)

A large fraction of the H* atoms is hot initiahy. T h e h o t H atoms abstract an H atom very efficiently (equation 43); thermalized H atoms [formed with a yield on the order of 1 (lOOeV)"^ with low L E T radiation] abstract much slower. Experiments with radical scavengers (e.g. I2) have shown that with low L E T radiation ca 60% of the cyclohexyl radicals escape from the track; with increasing L E T this fraction decreases. Also the yield of CgHio and C12H22 decreases, as is shown in Figure 6. The yield of H2 first decreases somewhat with increasing L E T , but then increases steeply at higher LET^^'^^ The escaped yield of CgHn* decreases at higher L E T , which is, of course, expected for a track where the spurs are formed more closely together. T h e decrease in the yield of CgHjLo a n d C12H22 m a y be explained by the increased occurrence of H' + €^¥1^^^' and CgHii' reacting with C^Hio (equation 44) in the spurs. Reaction of C 121^21* leads to higher molecular weight products. Indeed 'polymer' yields have been observed with G = 0.65 (100eV)"^ (on the basis of units) for a L E T value of 1 3 0 e V n m ~ ^ a n d G = 0.80 (100eV)-^ for 4 0 0 e V n m - ^ ^^'^^ F o r values of L E T below l O O e Y n m " ^ the decrease in the H2 yield agrees roughly with the decrease in C^H^Q a n d C12H22 a n d the increase in polymer yield, according to material balance. The diffusion a n d reaction of the various species in the groups for initial spatial distributions representative for the different L E T values have been treated theoretically by solving numerically the diff'erential equations describing the development in time of the average local density distribution of the species in the groups: ^-^ dt

= Dyn,-Y^k,jn,nj j

(47)

where Ui is the density distribution in the group of species i, the diffusion coefficient, kij the specific rate of reaction between species i a n d j , a n d averaging over the various groups in the track.

772

A. H u m m e l

6

—

5 """Ox

> CD O O

4

-

L

~~

0)

A

3 u

1

• 1 10-1

1 1

1 1 11 m l

1 1 1 11 m l

10

102

----- B

1 1i

Mill!

10^

LET (eV nm"')

F I G U R E 6. The yield of products in the radiolysis of cyclohexane as a funcdon of LET"^^; O, H^; A , Q H i o ; • , C 1 2 H 2 2

It appears that for L E T values u p t o 100eV n m " ^ the non-homogeneous kinetics can be rather satisfactorily described in this way"^^. At larger L E T values other processes must be involved. T h e increase in the hydrogen yield exceeds by far t h e hydrogen deficiency in the polymer yield. An increase in the low molecular weight fragments, resulting from multiple C — C scission of the cyclohexane ring, h a s been observed. It appears that effects of h o t radicals have increasing importance at the high L E T values. Also, local heating in the track at the larger L E T values may start t o play a role. While we have a fair degree of understanding of the radiation chemistry with low L E T radiation in liquid saturated hydrocarbons, the situation is rather unclear for the chemical processes occurring in high L E T charged particle tracks. V. THE SOLID PHASE A. Trapping of the Intermediates

An important aspect of the radiolysis in the solid is that, due t o the rigidity of the matrix, the movement of reactive intermediates is often restricted t o some degree. As a result certain reaction pathways involving these intermediates m a y be retarded or inhibited in the solid as compared t o the liquid (and other processes m a y become more predominant in the solid). Electrons m a y be trapped in hydrocarbon glasses'*"^'Yields on the order of a few tenths to one (100 eV)~ ^ have been observed at 77 K. T h e trapped electrons (e^") show a wide absorption spectrum in the infrared with a k^^^ of a r o u n d 1600 n m at 77 K, simhar t o what is observed in the liquid. T h e trapped electrons can also be observed by ESR. At lower temperatures the yields are somewhat larger. At temperatures of 2 0 - 4 0 K the trapped electrons are found to decay by (temperature-


773

independent) tunnelling t o positive ions a n d radicals o n a time scale of hours"^^. (If electron scavengers are present, tunnelling t o these molecules also takes place.) It is interesting that t h e red part of the spectrum of e^" decays first, which shows that we deal with electrons of different t r a p depths. At this point it is of interest of mention that, in the presence of solutes in the glasses, large yields of negative (and positive) ions can be obtained. I n 3-methylpentane containing SFg and 2-methylpentene-l, a yield of 5.4 (lOOeV)"^ of S F ^ " has been observed"^^. It is generally considered that electron trapping in crystalline solids does n o t take place efficiently. In fact electron mobhities have been measured in various sohd crystalline compounds. I n CH4, cyclohexane, iso-octane a n d neopentane m o b h e excess electrons have been observed"^^. Stable radical cations have been observed opticahy a n d by ESR after irradiation in matrices containing a n electron scavenger'^'^''^^. However, ESR spectra have n o t been observed in the neat solids. Possible line broadening a n d overlap with radical spectra prevent definite conclusions about the absence of the ions from t h e ESR spectra. T h e optical absorption spectrum of the radical cation has been observed in neat 3-methyloctane at 6 K a n d 77 K (A^^^ = 600 nm)^° a n d in squalane (C30H62) at 77 K (^max = 1400nm) at 100ns after a 40-ns pulse^^ Trapped radicals are produced in both glasses a n d crystahine solids a n d have been studied mainly by ESR^^. In glasses the yield of radicals is typicahy 3 - 4 (lOOeV)"^ a n d in polycrystalline material 4 - 6 (lOOeV)"^ (In perdeuterated c o m p o u n d s this is about a factor of 1.3 lower"^"^.) The radicals are formed non-homogeneously. F r o m the time dependence of the decay of the radicals in 3-methylpentane at 77 K it was concluded that ca 60% of the radicals decays by reaction in regions of high local concentration^^. At 77 K a small percentage of the radicals is trapped in pairs with a distance of 5-25 A, as is evidenced by ESR experiments. At 4 K t h e percentage of pairs h a s been found t o be as high as 100%'^'^. The pairs may originate from H abstraction by hot H atoms o r by tunnelhng (see below), whhe the H a t o m may be formed by dissociation of a neutral excited molecule: RH

> R* + H '

(48)

Also, formation of the protonated molecule has been hypothesized: RH* ^ + R H

>

RH2 ^ + R*

(49)

fohowed by formation of a second radical R* by H2 expulsion from R H 2 ^ a n d neutralization of R ^ , or by neutralization of R H 2 ^ fohowed by H2 expulsion^"^. A high probability for finding two radicals close together would also be expected in regions of high ionization density. Evidence for this effect being operative has been found from studies of the L E T effect o n radical pair formation in eicosane^^. N o trapped hydrogen atoms have been observed except in CH4 at 5 K , where G(H-) = G(CH3-) = 3.3 (100 e V ) " ^ and G(e^") = 0. The hydrogen atoms react either while hot o r by tunnelhng abstractions from C — H bonds by thermalized atoms. Carbanions are formed by reaction of electrons with radicals: R * - l - e ~ - ^ R ~ . In branched alkane glasses they have a n optical absorption spectrum with a X^^^ a r o u n d 2 4 0 n m {& ^ 6300 dm^ m o l " ^ cm"^) and a long t a h extending into t h e red'^'^. B. Product Formation

Product yields are generally determined by analysing the products in the liquid obtained after melting the irradiated sample. In one technique the solid is dissolved at low temperature in a hquid containing a radical scavenger, so that the contribution of radical reactions t o the products is eliminated^^.

774

A. H u m m e l TABLE 11. Yields of products in the gamma radiolysis of sohd n-pentane at 77 K^'^^ G(100eV)-i Hydrogen Ethane Ethylene Propane Propene Pent-l-ene trans-Pent-2-ene cis-Pent-2-ene n-Decane 4,5-Dimethyloctane + 3-ethyloctane 3-Ethyl-4-methylheptane + 3,4-diethylhexane 4-Methylnonane Ci5

5.0 0.34 0.36 0.28 0.21 1.7 1.3 0.3 0.16 0.40 3 . 4 V for n-octane, n-heptane and n-hexane'^'^. The half-wave potentials of some alkanes have also been obtained by the use of ultramicroelectrodes in acetonitrhe without any supporting electrolyte: the values range from 3.87 V for m e t h a n e to 3.5 V for n-heptane vs Ag/Ag"^. These values correlate well with the ionization potentials of the alkanes"^^. C o n t r o h e d potential electrolyses were carried out on saturated solutions of four alkanes in acetonitrhe 0.1 M T B A B F 4 to yield acetamidoalkanes (Table 5)^^. Voltammetry and coulometry indicate a 2e oxidation to a carbenium ion that subsequently reacts with the nitrogen of the acetonitrile in a Ritter reaction (equation 12). RH +

RH

•

R"^

-

-

•

RN =

CCH,

RNHCOCH, (12)

The oxidation of substituted a d a m a n t a n e s has been studied in detail in acetonitrhe by the groups of Miller'^^''^'^ and Mellor'^^~^°. Preparative scale electrolyses of several substituted a d a m a n t a n e s were performed by cpe in a divided cell in acetonitrile-lithium perchlorate at 2 . 5 V (vs Ag/Ag"^). The products obtained are shown in equation 1 3 and in Table 6"^"^. The £ p / 2 values of the a d a m a n t a n e s range from 2 . 5 6 V ( X = C 0 2 M e ) to TABLE 5. Yields and isomer distribution of acetamidoalkanes at cpe of alkanes at a Pt-anode in CH3CN/OI M TBABF4 Isomer distribution (%) Alkane n-Octane n-Heptane n-Hexane n-Pentane

Yield (%) 45 48 45 50

2-isomer 33 45 55 N o t resolved

3-isomer

4-isomer

35 45 45

32 10

TABLE 6. Oxidation products of substituted adamantanes 22 in acetonitrile Product (% yield) Substituent X in 22 H Br CI F

CH3 CH2OH COCH3 CO2CH3 CN OH

OCH3

path (a)

(equation 13)

path(b)

27(90) 27(89) 25,X = C1(91) 25,X = F(65) 25,X = CH3(91) 27(37) 27(44) 25,X = C 0 2 C H 3 ( 6 4 ) 25,X = CN(41) 27(41) 27(58)

793

17. Electrochemical conversion of alkanes X

CH,CN

(25)

NHCOCH3 (23)

(22)

+ CCH3

II

(26)

N

(28)

1.90 V (X = N H C O C H 3 ) vs Ag/Ag^. The peak heights in cyclovoltammetry correspond to n = 2. Two general reaction types are observed: substitution of acetamide for hydrogen (equation 13, path a) and substitution of acetamide for the functional group (equation 13, path b). The isolation of high yields of 27 is only possible because the nonoxidizable precursor 28 is actually the stable product and the amides 27 or 25 result from aqueous work-up. 28 could be verified by quenching it with either D2O or methanol. A larger-scale electrolysis of 22 (X = H) could also be performed in an undivided cell providing readhy gram a m o u n t s of 27. This reaction has therefore synthetic interest as a route to pharmacologicahy useful substituted 1-adamantylamines. Adamantyl chloride and fluoride lead to substitution of nitrogen for hydrogen at C^) (path a), whhst with the bromide 22 (X = Br) 27 was formed in high yield, indicating that bromide competes favorably with hydrogen as leaving group. In each of the three adamantyl halides initial electron transfer involves an orbital from the adamantyl moiety and the substitution of bromine accounts for the weak c a r b o n - b r o m i n e bond, whhst substitution of chlorine and fluorine is prevented by their stronger bonds. In carbon-substituted a d a m a n t a n e s the C O 2 " , C H 2 O H and C O C H 3 groups are cleaved, whhst the CH3, C H 2 O C O C H 3 , CO2CH3 and C N are not. All this chemistry can be rationalized from the stabhity of the fragments formed by the fragmentation of the carbon-substituted bond. The cleavages of 1-acetyl-, 1-bromo- and 1-hydroxymethyladamantane are of great interest. Each of them mimics a mass spectral result and they indicate the feasibhity of preparative-scale mass spectrometry. In a series of alkyl-substituted adamantanes the influence of the carbon substituents upon the competing pathways of substitution and fragmentation have been investigated (Table G o o d coulombic and product yields are being obtained. At first, loss an electron from the adamantyl portion is to be expected in each case. Fragmentation is observed as the dominating pathway of the radical cation when loss of a tertiary fragment can occur (equation 13, p a t h b); no fragmentation is observed when a primary fragment might leave (equation 13, path a). In addition a large number of substituted adamantanes has been investigated by

l)^^^^^.

794

H. J. Schafer TABLE 7. DistribuUon of products from anodic oxidation of alkyl-subshtuted adamantanes in acetonitrile Product (% yield) Compound 22 X H Et i-Fr t-Bu

Substitution (25)

Fragmentation (27)

74 77 75 7

0 0 9 62

cyclovohammetry. Their Ep/2 values range a r o u n d 2.37 to 2.40 V vs Ag/Ag^ in a c e t o n i t r h e / T B A B F 4 . F o r comparison the corresponding values of other cycloalkanes have been determined, e.g. for diamantane: 2.14 V, bicyclo[3.3.1]nonane: 2.58 V, methyl cyclohexane: 2.85 V and cis/trans-dQcalin: 2.57 V. N o evidence of a cathodic wave was observed even at — 78 °C. The peak heights indicate a 2e wave and a diffusion-controlled oxidation. The results suggest that the a d a m a n t a n e s are being oxidized by an E C E process to an adamantyl cation via an intermediate delocalized radical cation. T h e radical ion can undergo deprotonation or fragmentation; the balance between the two processes is determined by the nature of the fragmenting group. In acetonitrhe 1-t-butyla d a m a n t a n e gives mainly fragmentation, while in contrast 1-ethyladamantane gives n o fragmentation and 1-isopropyladamantane fragments only to a small extent. A difference of temperature of ca 50 °C hardly affects the product distribution. The comparison of the oxidation of a series of substituted a d a m a n t a n e s (t-butyl, methyl, adamantyl) by lead(IV), cobalt(III) and manganese(III) trifluoroacetates with the corresponding anodic oxidations in acetonitrhe or trifluoroacetic acid shows that the electrochemical oxidation proceeds via a radical cation intermediate, whhst the metal salts form products by C H abstraction"^^. The preparative result is that, in anodic oxidation, preferentially products of fragmentation of the intermediate radical cation are found, whilst with the metal salts hydrogen substitution is being obtained preferentially. 7. Sulfur

dioxide

In liquid SO2 and CsAsF^ as supporting electrolyte the oxidation of saturated hydrocarbons could be studied u p to potentials of 6.0 V vs see by using platinum ultramicroelectrodes. Irreversible voltammetric waves were found for the c o m p o u n d s m e t h a n e to n-octane that were studied^ ^ T h e anodic peak currents suggest n-values a r o u n d 2; a bulk electrolysis consumed 2 faradays per mole of alkane. The primary products in dhute solutions ( 1 - 1 0 m M ) were shorter chain hydrocarbons. Electrolysis of m o r e concentrated solutions led, via reaction of the oxidation products with starting material, to longer-chain hydrocarbons. The correlation of anodic peak potentials (at — 70 °C: methane 5.1 V to n-octane 3.97 V vs see) with gas-phase ionization potentials and calculated H O M O energies shows that useful d a t a can be obtained even at potentials exceeding 5.0 V vs see. Because of the low solubility of C s A s F g appreciable solution resistance is observed. This presents difficulties when large electrodes are employed, but ultramicroelectrodes create n o problems. Cyclopentane afforded in 0.05 M TBACIO4 and S O 2 / C F 3 C O 2 H (6:1) at - 2 5 ° C at a platinum a n o d e 62% cyclopentyl t r i f l u o r o a c e t a t e ^ F o r chlorocyclohexane the chlorination and dechlorination are reduced in comparison to the electrolyte

17. Electrochemical conversion of alkanes

795

CH2CI2/CF3CO2H. T h e selectivity for the formation of 2-, 3- a n d 4-13 (equation 8) with 1:3.3:9.1 is much more pronounced than in CH2CI2/CF3CO2H. This could be partially due t o the lower reaction temperature. With 1,2-dichlorocyclohexane the same products are obtained as in CH2CI2/CF3CO2H albeit in lower yields. T h e same is true for methylcyclohexane. Unpleasant in these electrolyses, that are conducted in an undivided cell, is the formation of sulfur by cathodic reduction of sulfur dioxide, which partially covers the anode a n d cathode as a sticky coat. 8.

2,2,2-Trifluoroethanol

As the strongly acidic electrolyte CH2CI2/CF3CO2H is prohibitive for the oxidation of acid-sensitive substrates, trifluoroethanol is a possible alternative. It is less acidic (pH = 4.5), has a fairly high anodic decomposition potential (1.9 V vs A g / A g N 0 3 ) and a low bohing point (73 °C, 760 torr). At 0 °C in 0.05 M T B A B F 4 and 2,2,2-trifluoroethanol as electrolyte, cyclopentane afforded 7 1 % (gc yield), 56% (isolated yield) cyclopentyl trifluoroethyl e t h e r W i t h chlorocyclohexane the chlorination a n d dechlorination are less pronounced compared t o the electrolyte CH2CI2/CF3CO2H. T h e yield of chloro2,2,2-trifluoroethoxycyclohexane is, with 46%, twice as high as that of the corresponding product 13 in CH2CI2/CF3CO2H. 9. Other

solvents

Other solvents that have high anodic decomposition potentials (above 2.5 V vs see) are nitromethane^', nitroethane^', propylene c a r b o n a t e ^ ' , sulfolane^', dichloromethane/ methanesulfonic acid^"^ or trifluoromethanesulfonic acid^"^'^^. Except for the latter two^"^'^^ there are n o reports on their use as solvents for alkane oxidation. B. Oxidation off Remote 0 — H Bonds in Ketones, Carboxylic Acids and Steroids

Ketones that lack a-branching are oxidized at 2.2 t o 2.3 V vs Ag/Ag^ in acetonitrile/0.1 N lithium perchlorate at a platinum anode t o form acetamidoketones^"^'^^. In general the mass balance is 60-80%. The products obtained are shown in Table 8. In 2-hexanone, 2-heptanone a n d 4-heptanone the acetamido group is introduced into the penultimate (co — 1) position of the carbon chain. 2-Octanone led to (co — 1)-, TABLE 8. Remote oxidation of ketones in acetonitrile/hthium perchlorate Ketone 2-Hexanone 2-Heptanone 2-Octanone

4-Heptanone 2-Methyl-4-pentanone 2,6-Dimethyl-4-heptanone 2,5-Dimethyl-3-hexanone 4,4-Dimethyl-2-pentanone

Product (% yield) 5-Acetamido-2-hexanone (40) 6-Acetamido-2-heptanone (30) 7-Acetamido-2-octanone (21) 6-Acetamido-2-octanone (30) 5-Acetamido-2-octanone (7) 2-Acetamido-4-heptanone (31) 2-Acetamido-2-methyl-4-pentanone (20) 4-Acetamido-2-hexanone (20) 2-Acetamido-2,6-dimethyl-4-heptanone (20) 6-Acetamido-2-methyl-4-octanone (20) 5-Acetamido-2-methyl-3-heptanone (25) 5-Acetamido-2,5-dimethyl-3-hexanone (35) 4-Acetamido-4-methyl-2-hexanone (50)

796

H. J. Schafer

(co — 2)- a n d to a smah a m o u n t of [CD — 3)-acetamidoketones. With branched ketones two major products are obtained (equation 14). An intramolecular mechanism which explains the products is shown in equation 15. At first the ketocarbonyl group is oxidized to its radical cation. T h e £p/2 values fit a crude correlation with the corresponding ionization potentials. Then a y-hydrogen abstraction occurs, which is analogous t o that found in mass spectrometry a n d photochemistry. With the electrolysis of a ketone in the presence of 2,3-dimethyl p r o p a n e it was shown that the intramolecular abstraction of hydrogen is more rapid than a n inter molecular reaction with a good hydrogen donor. T h e rearranged product is formed by intramolecular H-abstraction at the methyl group, which has been proven by appropriate deuterium substitution (equation 15). RC0CH2CH(CH3)2

»

RC0CH2C(CH3)2

+

RCOCH2CHCH2CH3

NHCOCH3

NHCOCH.

(14)

CH2

I

RC0CH2CH(CH3)2

+ CH2 ^2

HO

(15)

0 HgO

-CHo

CH2-

-c^

CH3CN

CH -CHo

-NHCOCH,

- 2 H ^

^ C H ,

-CH,

In dichloromethane/trifluoroacetic acid, fatty acids are preferentially trifluoroacetoxylated at the (co — 2)- to (co — 4)-CH bonds; n o attack at C-2 to C-6 is observed, or, if at all, only to a small extent (Table 9, equation 16)"'^. The remarkable regioselectivity could be due t o the inductive effect of the carboxylic group, which can be protonated in the more acidic region at the anode surface. In O2CCF3 CHjCI^/CFaCO-H

CH3(CH2)/7C02H

_^

I

^—•

CH3(CH2)^

CH

(CH2)^C02H

(16)

(30)

(29) TABLE 9. Anodic oxidahon of fatty dichloromethane/trifluoroacetic acid

acids

29

to

trifluoroacetoxycarboxyhc

30 in

acids

rec. 29 Yield

Relahve isomer distribution in 30

n in 29

30^^ Yield (%)

y5

6

7

8

9

10

12 10 8

40 15 3

3 12 39

7 23 46

19 26 15

28 29

20 10

16 —

—

—

—

11

(%)

7

27 42 71

— —

"For the determination of the isomeric structures 30 has been oxidized to the corresponding o x o acid.


797

hydrogen abstractions from protonated substrates by radical cations, t h e methylene group farthest removed from the protonated position is preferentially attacked^'^^. I n the anodic oxidation of t h e C H b o n d t h e transition state is undoubtedly more positively charged t h a n that in the radical abstraction a n d consequently is m u c h more sensitive tovârds inductive effects. Skeletal rearrangements as in t h e oxidation in fluorosulfonic acid^^ (see below) d o n o t appear t o occur. The cyclovoltammograms of a series of carboxyhc acids in fluorosulfuric a c i d potassium fluorosulfate (1.0 M) show irreversible oxidation peaks that a r e diffusion c o n t r o l l e d ^ N o peaks for the reduction of stable intermediates can be detected even at rapid potential scan rates. T h e oxidation potentials range from 1.95 t o 1.64 V vs P d / H 2 . They shift cathodically with increasing length of the alkyl chain. T h e acids are oxidized less readhy t h a n the corresponding alkanes due t o the influence of the poshive charge on the protonated carboxyl groups. Preparative scale electrolysis gave different products depending o n whether t h e electrolyte was quenched immediately after the electrolysis o r not. I n the first case t h e major products of heptanoic acid, 4-methylpentanoic acid, 5-methylhexanoic acid or octanoic acid were always y - t o ^-lactones with overall yields of 4 0 - 7 0 % (equation 17a). After being some time in t h e acidic electrolyte t h e lactones a r e converted t o a,j8-unsaturated ketones by a chemical follow-up reaction (equation 17b).

1. F S O , H / K S O , F , - e —

CH3(CH2)eC02H

^ , •

^1

(17a)

63%

1. F S O g H / K S O j F j - e CH3(CH2)6C02H 2 . 2 2 h in the electrolyte

'

3.H,o 34%

'

(Hb)

26%

N M R evidence indicates that t h e electroactive species is t h e p r o t o n a t e d carboxylic acid. With branched chain acids the carbocation, formed similarly t o that obtained in the alkane oxidation, will be a tertiary o n e a n d a single p r o d u c t is obtained. With straight-chain carboxylic acids t h e carbocation is formed at several positions of t h e carbon skeleton, a n d it whl rearrange possibly by cyclopropane formation t o form a stable tertiary carbocation (equation 18). T h e a,j?-unsaturated ketone whl be formed by slow loss of the HSO3F group with t h e formation of a double b o n d a n d subsequent cyclization of the p r o t o n a t e d acid. Whilst medium-chain-length carboxylic acids (six or more carbon atoms) c a n be directly oxidized in anhydrous fluorosulfuric acid containing potassium fluorosulfate, those of lower molecular weight are n o t oxidized before the oxidation of the fluorosulfate anion. F o r their conversion, solutions of peroxydisulfuryl difluoride, which is k n o w n t o react also with short-chain a l k a n e s ' ^ " ' ^ , are prepared by constant-current electrolysis of potassium fluorosulfate and added t o the carboxylic acids in fluorosulfonic acid. 7- a n d ^-Lactones are obtained in yields between 7 a n d 50% (equation 19)^^. In all cases the products isolated were consistent with a mechanism where the initial step is the cleavage of a secondary C H b o n d remote from t h e carboxyl group. Ring

798

H. J. Schafer .CO2H2

_ Z i

^C02H2

OSO2F

0

(18)

(FSO, CH3(CH2)3C02H

-0^

(19)

36Vo

closure occurs probably during work-up. T h e products isolated are simhar to those obtained by direct oxidation of the carboxylic acids. The yields of lactones by the indirect method are, however, as good or better t h a n those obtained by the direct oxidation. O n standing, the longer-chain acids again afforded cyclic unsaturated ketones. Acyclic esters have been oxidized by cpe in a divided cell in acetonitrhe/LiC104 (or TEABF4) at a platinum anode. Ethyl b u t a n o a t e yielded 70% of 3-acetamidobutanoate, a n d a high selectivity for the {co — 1) position was also found for other esters (Table 10)^^. TABLE 10. Remote oxidahon of esters in acetonitrile Ester Ethyl butanoate Methyl hexanoate Methyl nonanoate Methyl 3-methylbutanoate Methyl 2-methylpropanoate

Acetamido ester (% yield) Ethyl 3-acetamidobutanoate (70) Methyl 5-acetamidohexanoate (42) Methyl 4-acetamidohexanoate (11) Methyl 8-acetamidononanoate (25) Methyl 3-acetamido-3-methylbutanoate (68) Methyl 2-acetamido-2-methylpropanoate (58) Methyl 3-acetamidobutanoate (4)


799

In a n undivided cell the yields are reduced substantially. Methyl hexanoate gave (co—l) and also some (co — 2) products. The selectivity of the reaction is reminiscent of the ester chlorination with N-chloro amines^'^°. In the anodic oxidation, however, carbocations seem t o be involved, being formed most remote from the ester function. I n suitable cases carbocation rearrangements are observed. Remote oxidation has also been achieved with a covalently attached mediator.Anodic oxidation of 5a-cholestan-3a-yl esters with a carbonyl or m-iodophenyl g r o u p at their 3a-substituent gave in acetonitrile 0.1 M LiC104 at cpe the 6a-acetamidated cholestanyl esters in 7 t o 26% yields together with esters carrying two or m o r e acetamide functions^ ^Cyclovoltammetry indicates that the oxidation of the carbonyl c o m p o u n d s takes place at 2.3 to 2.7 V (vs AgNOg). The results suggest that a radical cation is formed first by oxidation of the carbonyl or iodophenyl groups at the 3a-substituent which abstracts intramolecularly a n equatorial 6a-hydrogen (equation 20)

26 Vo

C. C — C Bond Cleavage In Hydrocarbons, Cyclopropanes and Other Strained Cyclic Hydrocarbons

By analogy with their behavior in mass spectrometry, branched h y d r o c a r b o n s are being cleaved u p o n oxidation in acetonitrile/TEABF4 at — 45 °C. C p e of different branched hydrocarbons affords the acetamides of the fragments. These are formed by cleavage of the initial radical cation at the C — C bond between the secondary a n d tertiary carbon to afford, after a second electron transfer, carbocations which react with the acetonitrile (Table 11 a n d equation 21)^^. n-Octane, however, leads t o the anodic substitution of the 2-, 3- a n d 4-H. In cyclopropanes a C — C b o n d can be cleaved by way of anodic oxidation. The electro chemical oxidation of bicycio[4.1.0]heptane (31) a n d bicycio[3.1.0]hexane gave products in which the cyclopropane ring was opened. Anodic oxidation was conducted at a carbon r o d anode in m e t h a n o l / T E A T o s . T h e products obtained from 31 are given in equation 22^^. T h e products found are completely different from those of the acidic hydrolysis of the cyclopropanes. Whhst in the methanolysis of 31 in methanol/toluenesulfonic acid the selectivity of external/internal b o n d cleavage is 88/12, that of anodic oxidation is 0/100. Also, in the cleavage with P b ( O A c ) 4 or Tl(OAc)3 the external b o n d

800

H. J. Schafer TABLE I L Anodic oxidation of branched hydrocarbons in acetonitrile/TEABF4 Hydrocarbon

Products

2,3-Dimethylbutane 2,2,4-Trimethylpentane 2,2-Dimethylbutane t-Butylcyclohexane n-Octane

2-Propylacetamide t-Butylacetamide, 2-propylacetamide, 2-butylacetamide t-Butylacetamide, t-pentylacetamide, isopentylacetamide t-Butylacetamide, cyclohexylacetamide 2-Octylacetamide, 3-octylacetamide, 4-octylacetamide

(CH3)3C-

(CH3)3C .

1.-
i^CH^ + N a l + BH

3

and 1,5-cyclooctadiene, stirring overnight

82% yield, 400 mCi

3. Synthesis

(7)

N a B H . in M e O C H , C H , O C H , C H - O M e

- - > '^CH,\

4C02

^

and chromatographic

radiochemical purity > 99%

separation

of

C-methane

^^C Radiopharmaceuticals of very high specific radioactivity are needed f o r ' m vivo' studies of specific receptor binding. The maximum specific activity achieved in the course of synthesis of various ^ ^C-labelled c o m p o u n d s had been of the order of 1-2 Ci iimo\~^ after taking ah precautions concerning pohution with atmospheric ^^C02 at all stages of the synthesis^. T h e maximum possible specific radioactivity of ^^CH4 equals^ 8.38 x 10^ Ci g~^ or 76.1 Ci fimol'K In a preliminary study^ ii has been shown that ^^CH4/^^CH4, '^CU^D/'^Cn^, '^CD^n/'^CU^ a n d '^CDJ'^CU^ isotopic derivatives can be sep arated at — 206 + 1 °C using a 100-m-long solft-glass capihary tube. ^^C methane with a specific activity of 40 Ci / i m o P ^ has been obtained by c h r o m a t o g r a p h y using a capihary (300-m-long soft-glass columns) in the presence of 10% N2 in helium, performed at - 207 °C t o - 208 °C. T h e starting ^^CH4 h a d been produced in ^^N(p, ocy^C nuclear reaction by irradiating (N2 + 5% hydrogen) with 20 MeV protons. T h e non-reactive methane has been transformed quantitatively into more reactive methyl iodide, methanol, hydrogen cyanide, C N H and formaldehyde without isotopic dhution for rapid labehing of radiopharmaceuticals. CD3CH3 has been p r e p a r e d f r o m methyl-^H3 benzenesulphonate with dhithium methyl 2-thienylcyanocuprate.

B. Synthesis of Isotopically Labelled Propanes 1. Synthesis

of ^^C-labelled

propanes

Propane-l-^^C a n d 2-methylpropane-1-^^C equations 9 a n d 10: Et^^COOH

Et'^CU.OU

have been obtained^^ according to

Et^3CH2l

'"^^'S Et^3CH3 couple

(9)

814

Mieczys/aw Zielihski a n d M a r i a n n a K a h s k a Me^CO

"""'^'^ ) ^^CHsCMe^

^^CHsCHMe^

I

>

I

OMgl

I

[^^C]H3C=[^3C]H2

[^^C]H3CHMe2

(10)

I CH3 2 . Synthesis

of propane-1-d

and

2-methylpropane-1-d

These c o m p o u n d s have been prepared^ ^ from 1-bromopropane a n d 2-methyl-1b r o m o p r o p a n e via the corresponding G r i g n a r d reagent (equation 11). T h e appearance of the C — D stretching b a n d at 2 1 8 0 c m " M n the IR spectrum of 1 has been observed. Ms

RBr

^

D2O

RMgBr

RD

THF

l a : R = n-Pr l b : R = /-Bu 3. Synthesis

of

^^^^

propane-1

Propane-1,2-^"^C, specific activity of a b o u t 110 mCi m m o P \ has been synthesized from doubly labehed acetylene in reaction series shown in equation 12. This synthesis included preparation of doubly labelled acetylene from barium carbonate-^"^C according to C o x a n d Warne^^, nearly quantitative hydrogenation of acetylene t o ethylene, addition of hydroiodic acid to the latter to form iodoethane, preparation of ethylmagnesium iodide followed by carbonation to yield propionic acid a n d reduction o n-propanol with 7 0 - 7 5 % yield. T h e latter yielded a tosylate which was finally reduced to ^^C doubly labelled p r o p a n e 2 with sodium borohydride, a n d purified by gas c h r o m a t o g r a p h y on alumina or shica. Its specific activity was close to the maximal possible specific activity of ^'^C2acetylene (i.e. 124.9 mCi mmol ~^). B a - C 0 3 - ^ B a - C , ^ - C , H ,

"^^'"^

•

RT, overnight

sp. act. 5 0 - 6 0 m C i m m o l " ^ Hl(sat.wa.er solution)

'^C.H^Mgl

^

150-160°C, I h CO2, E t . O

^

LiAlH.

^^C2H5COOH dry ice temp.

> ^^C2H5CH20H ether, 6 h refl.

7 0 - 7 5 % yield p-MeC6H4S03H/ether

NaBH4(excess)

i^C2H,CH20Ts N a O H , stir 4 h at 5 °C

'''''

under He, 85 °C, 3 h

-CH3-CH,CH3 (2) 60% yield, sp. act. l l O m C i m m o r '

(12)

18. Syntheses and uses of isotopicahy labehed alkanes and cycloalkanes

815

C. Synthesis of ^"^C-Labelled Pentane, Heptane and Other ^^C- and ^^C-Containing Allcanes 1. Synthesis

of

2,2,4-trimethylpentane-^"^02

This c o m p o u n d (isooctane-^''^C2), ^''^C-labehed at both methyl groups of the isopropyl moiety, has been p r e p a r e d a c c o r d i n g to equation 13. 3,3-Dimethylbutyric acid, synthesized from vinylidene dichloride, has been utilized as one of the starting materials. The mixture of isomeric diisobutenes, obtained by direct dehydration of the tertiary carbinol-^^C intermediate, has been hydrogenated according to Reference 15, to yield 3. 94% H 2 S O 4 , B F 3 ETHERATE

H2C=:CCl2 +

McsCOH +

H2O

>

Me3CCH2COOH

0 5 C, 2H ( - H C 1 ) ETOH, H 2 S O 4

2^'^CH3MgI, E T 2 0 , 1 H REFLUX

MejCCHsCOOEt

-

-

-

-

>

10 H REFLUX, WATER SEPARATOR 1 H REFLUX

Me3CCH2C(i''CH3)20H Me3CCH2C(^^CH3)=^^CH2 + M e 3 C C H = C ( i ^ C H 3 ) 2 2H/METHANOLIC HEXACLOROPLATINIC ACID; 1M

Me3CCH2CH(i^CH3)2

ETOH SOLUTION OF SODIUM BOROHYDRIDE/ CONE. HCI, RT, 1 H STIRRING WORK UP

(13)

(3)

b.p. 9 9 - 1 0 0 °C, 55% chem. and radiochem. yield relative to diisobutene mixture 2. Synthesis

of ^"^C-labelied

heptanes

a. Synthesis of [l-^'^C]- and [2-'^'^C]-n-heptane. [l-^'^C]-n-Heptane has been pre pared in five steps (equation 14). The first four steps are weh documented in the periodical hterature and m o n o g r a p h s I n the last step [l-^'^C]-n-C6Hi3^'^CH2Br has been added dropwise to hthium aluminium hydride a n d lithium hydride in tetrahydrofuran, the content refluxed for several hours, cooled, dhuted and acidified [2.5 M sulphuric acid) and the product 4 was worked up by microdisthlation. 4 has been used to study the structure and composition of micelles formed by dinonylnaphthalenesulphonic acid in n-heptane in the presence of water QHi3Br ^

C6H,3MgBr LIALH4

C6Hi3^^C02H

QHi3i^C02MgBr ^^

HBR, H 2 S O 4

> C6Hi3i^CH20H

>

LIALH4, L I H

QHi3i^CH2Br

- - > C,H,,'^CU,

(14)

(4) b.p. 98.4 °C, 90% yield in last step n-Heptane-l-^'^C has also been prepared by Pines and coworkers^^'^^ by dehydrating n-heptanol-l-^'^C and subsequent hydrogenation at 150 °C at 100 atm. Mitcheh^^ prepared 4 in a simhar m a n n e r and applied it to study the mechanism of the

816

Mieczys/aw Zielihski and M a r i a n n a K a h s k a

dehydrocyclization of n-heptane to toluene when 29% of the ^"^C was found in the methyl group of toluene. Pines and Chen^^ investigated aromatization of n-heptane-l-^'^C over chromia-alumina and suggested a mechanism involving five-, six- and seven-membered ring intermediates. Balaban and coworkers^ ^ obtained 4 and (2-^'^C)-n-heptane according to equations 15 and 16, using ^'^CHgl as the source of ^"^C in the former case. In the latter case, ^"^€02 was the source of the isotope. -CH3I ^

- C H 3 M g I i ^ ^ ! ^ (-CH3)3Cd 2hrenux

n-CsHiiCO'VHj (5) 67% yield

~

(15) benzene, 15»C

.n-QH,3'*CH3

^^couoh'ên":

ether, reflux

^"

^

(4) sp. act. 14 pCi mmol ^

- 20 °C, 5 h stirring

c»

- C = " . . " ' : ° O H3 ih reflux !^„.C,H,."COC,:^ (6)

n-CsHii^^COMe

151-153 X , 56% yield

^'"^ > n-C5Hi/^CH2Me

(16)

(7)

25% yield, overall, chem. and radiochem. b. Synthesis of n-heptane ) . This compound, 8, has been synthesized by reacting n-propylmagnesium bromide with ethyl formate carboxyl-^"^C. The 4-heptanol-4-^'^C obtained was acetylated, pyrolyzed to n-heptene and hydrogenated over a platinum catalyst^^"^"^ (equation 17). OEt

H^^COOH

Hi^C02Et - ^ ^ f l ^ H ^ ^ C ~ P r - n

" . ± 1 ^

\ OMgBr

OH H ^ ^ C - P r - n -h^!^ \

n-Pr-i^CH2Pr-n

2.400°C Pr-n

^•"2'Pt02

(17)

^ (8)

c. l,4-Dimethylcyclohexane-7-^'^C. This has been obtained^^'^"^ from 4-methylcyclohexanone with ^"^CHjMgl and hydrogenating the product at 100 °C and 150 atm over Raney Ni. l,2-Dimethylcyclohexane-7-^'^C has been prepared simharly from 2-methylcy clohexanone and ^"^CHjMgl. Cyclic hydrocarbons are produced as intermediates in the course of synthesis of ^"Re labelled benzene via carboxyl-labelled acids^^ (equation 18). 3. Syntliesis

of ^^C-ring-labelied

adamantane

derivatives

a, 2-Methyladamantane-2-^'^C. This has been prepared^^ according to equation 19. Ring expansion of a d a m a n t a n o n e 9 with ^"^C-labehed diazomethane yielded the 4h o m o a d a m a n t a n o n e 10 which was converted to the diazoketone 11, followed by photolytic

18. Syntheses a n d uses of isotopically labelled alkanes a n d cycloalkanes •""^CHgOH

I

*fiH2

CH ^

CH2 ^ C H 2 CHo

817

14

-CHo

CH2

CH2

CHo

-CHp

(CH2

"CH2

CH2

'"CH2

I

CH2-

-CH2

I

-CH2

(18)

CH2CH, 14.

H2C^

14 ^ C H CH^

CHp

H2C

-CHp

:CH2 XH2

^CH2 ^CH2

W o h ring contraction t o 2-adamantanecarboxylic acid-2-^'^C (12) a n d reduction of the latter resulted in 2-methyladamantane (2-^'^C), 13 (m.p. of white waxy crystals 144-146 °C, purity greater than 99%, specific activhy 8.52 nCi per mgC, 5% yield from ^ ' ^ C H 2 N 2 ) . 0

II n-CAHgONO MeOH

/ -C4H9OK

CH2 / ^CHf/ //CH2.^ / CH2 CH2

(10) 49.8V0

(9)

from

yield

'''*CH2N2

.N2

-NOH

NH2CI THF,Et20

THF —H2O NoHCOs

(19)

(11) (•) denotes

C,CH

or

CHgi

(X) denotes

^COOH LiAIH4

^'*CH2, ^"^CH

or

"''^C

.CHgOH

T

TsCI pyridine

(12) 11.5%

yield from

^'*CH2N2

23.1 Vo overall yield from 10

78.5Vo

yield

( 2 - a d a m G n t y l - 2 - "•Ômethonol

Mieczys/aw Zielihski a n d M a r i a n n a K a h s k a

818

1"

LiAIH4 work up

94%

yield

(2-adamantyl-2-

( 1 3 ) 6 3 . 5 V o yield from the tosylate Ocarbinyl

tosylate

h. l-Methyladamantane-2 or These have been prepared^^ by ring expansion of a d a m a n t a n o n e with diazomethane-^"^C, oxidation of the 4-homoadamantanone-4-^'^C to h o m o a d a m a n t a n e diketone 14, benzylic acid rearrangement of 14 to the hydroxy acid, 15, a novel conversion of 15 with SOCI2 t o 2-adamantanone-2-^'^C (16) with overall 66% yield, Wolff-Kishner reduction of 16 t o adamantane-2-^'^C (17) a n d conversion of 17 into 18a and 18b by treatment of 17 first with bromine and then with methylmagnesium bromide^ ^ (equation 20). The conversion of the 2-hydroxy acid 15 t o ketone 16 proceeds K0H,H20 ^^CHgNz MeOH

SeOz '

in

dioxane

dioxane

2 h reflux

••'7'

sp. act. 3 7 . 9 2 nCi/mg C

( 1 4 ) 8 7 % yield

8 5 V o chem. yield

sp. act. 3 8 . 6 nCi/mg C

5 3 % radiochem. yield

homoadamantan - 4 , 5 - d i o n e

purity

9 9 % , m.p. 2 6 9 — 2 7 1

NH2NH2,0(CH2CH20H)2, KOH^

SOCI2 benzene

1. 1 0 0 - 1 2 0 * * C , 2 . 5 h

3 h stirring

2. 2 0 0 - 2 2 0 * * C , 4 h

under reflux

XO2H ( 1 5 ) 9 7 % yield

(20)

( 1 6 ) sp. act. 21.85 n C i / m g C

sp. act. 3 8 . 1 7 nCi/mg C

m.p. 2 8 4 - 2 8 5 Br

MeMgBr,

/

^

/

Bra

--7

"

/ --7

/

+ \ B r

"

ether 1 0 0 * ' C , 2 5 min

/

in

Fisher

bomb

( 1 7 ) 8 9 % yield sp. act. 2 1 . 8 0 nCi/mg C m.p.

2 6 8 - 2 6 9

mixture of ( 2 - ^ ^ C )

and

( 4 - ' ' ' * C ) isomers, 9 2 % yield

18. Syntheses and uses of isotopically labelled alkanes and cycloalkanes

.Me

819

+

(18b)

(18a) sp. 3.52

act. nCi/mg C

82Vo yield probably through the cyclic intermediate 19, which decomposes according to equation 21. The rearrangement of adamantane-2-^'^C to adamantane-l-^'^C taking place^^ in

\

=0 + SO2 +

S

14,

CO

(21)

(19) A l B r 3 / C S 2 at 110°C (after 8h) and the corresponding rearrangement of 2methyladamantane-2-^^C studied in A l B r 3 / C S 2 at 250 °C during 45 h^° have been briefly reviewed by M u c c i n o ^ ^ 4. Synthesis

of n-octadecane

[l-^'^C]

and n-hexadecane

[1-'"^C]

These c o m p o u n d s have been prepared^^ according to equation 22. In a similar m a n n e r M e ( C H 2 ) i 4 ^ ^ C H 2 0 H (m.p. 4 7 - 4 9 °C, y. 92-95%), Me(CH2)i4 ' ^ C H 2 l (m.p. 18-20°C) and LiAlH4/Et20

Me(CH2)i6'^CH20H

Me(CH2)i6'^C02H RT, 100 h stirring

9 3 % yield, m.p. 5 6 - 5 8 °C E t 2 0 , Zn, A c O H sat. with H C l

I, red P

Me(CH2)i6'^CH3l 100 °C, 30 min stirring

180 °C, I h stirring

Me(CH2)i6'^CH3 8 5 - 9 5 % yield m.p. 2 7 - 2 9 °C

(22)

M e ( C H 2 ) i 4 ^ ^ C H 3 (76%, b.p. 14: 156-158 °C) have been obtained starting from palmitic acid (l-^'^C), M e ( C H 2 ) i 4 ^ ' ^ C 0 2 H . Reduction of cetyl iodide with lithium aluminium hydride yields -n-hexadecane in higher (95%) yield^^ (equation 23): 4RX + L i A l H 4 —> 4 R H + L i A l X 4 5. Synthesis

of hydrocarbons

labelled

with ^^C at 1,2 and 3

(23) positions

These ^"^C-labehed hydrocarbons have been s y n t h e s i z e d ^ " ^ ' m o s t l y according to the schemes shown in equations 24-26. The Wittig reaction is also suitable for preparing^ ^ alkenes and alkanes labelled with ^""^C in various positions (equations 27 and 28). ^'''Clabelled alkenes have been reduced to the corresponding alkanes. The yields of

820

Mieczys/aw Zielihski and M a r i a n n a K a h s k a 14(^02

>

R14CH2X

R'^COOH

> R^^CH20H

>

R^^CH2X

>

R^^CHs

(24)

Ri^CH2^^CN Ri^CH2^^CH20H

> Ri^CH2^^CH2X — > Ri^CH2^''CH3

(25)

(CH2)20

> Ri'^CH2MgX

Ri^CH2X

Ri^CH2(CH2)20H

R^^CH2(CH2)20H

> R^^CH2(CH2)2X

Ri ^^CH2X >IR'

^^CH2PPh3]X

R^^^CHPPhg

'^COOU . R ^

> R^^CH2CH2CH3

(26)

Ri — I ^ C H = C H R 2

(27)

> RCHO^

i^CHO_^^!^!!!^Ri

I'^CH^CHR

(28)

hydrocarbons in the Wittig reaction is rather low (10%) but h is nevertheless useful for the preparation of alkenes possessing a ^"^C label and double b o n d in the same position. The starting alkyl halides (specific activity 2000 G B q m o l " ^) have been synthesized according to equation 29. ^"^C-labelled aldehydes have been produced from ^"^C-labehed carboxylic acids through the imidazolides reduced in turn^^ with L i A l H 4 (equation 30). 3 R O H + PX3

> HPO(OH)2 + 3 R X

(29)

4 0 - 8 5 % yield chemical purity > 9 8 % o R14COOH

•

.OH

R ^"^C^

C H = N

^

^^C^H

^ C H = N

6. Synthesis

of methyl-''^C-labelled

C H = N

^ C H = N

•R^'^CHO

(30)

hydrocarbons

[l-^^C]pentane, [l-^^C]nonane, [l-^^C]undecane, 2-[^^C]methylnaphthalene and [^^C]methylbenzene have been obtained by selectively coupling ^^C methyl iodide with the appropriate hthium organocuprates^^"^^ (equation 31). The lithium dialkylcuprates l[^^C]H3l/ether

R CuLi

-->R[^^C]H3

(31)

2. H + , H 2 0

R ^ n - Q H g , n-CgHiv,

n-CioH2i

have been prepared^^'^^ by reacting cuprous iodide with alkyllithium and the [^^C]methyl iodide from [^^C]carbon dioxide'^^, produced in ^^N(p,a)^^C nuclear reaction. The starting key compounds [ ^ ' C ] 0 , [ ^ ' C ] 0 2 , H [ ^ ^ C ] N ^ \ [iiC]OCl2'*^ and H[^^C]HO'^^''^'^ are frequently obtained"^^ ""^^ direcdy at the target in the course of nuclear syntheses of ^C]. In the [1-^ ^C]pentane synthesis metal-halogen exchange took place and the by-product ^ C ] H 4 in 20% yield has been produced. The coupling reaction is very slow at low temperatures (— 40 °C). The specific activhy of the ^C]methyl iodide used was of the order of 10-30 mCi /imol" ^. (The maximal possible specific activity of ^ is 9 X l O ^ C i m o r ^ )


821

[l-^^C]nonane 1. [ ^ ^ C ] H 3 l

Cul/ether + 2C8Hi7Li/hexane — > (C8Hi7)2CuLi

> C8Hi7[i^C]H3 2. HYDROLYSIS

(31a) [l-^^C]undecane. Lithium didecylcuprate, prepared by reacting copper(I) iodide in ether with decyhithium in hexane, has been coupled with [^^CjHsI. The above [^^C]-labelled aliphatic and aromatic hydrocarbons have been used to study their effects on man, since they are c o m m o n components in air pollutants. Aliphatic saturated and unsaturated hydrocarbons act also as pheromones and defensive secretions a m o n g some social insects such as ants and bees. The ^^C-labelled c o m p o u n d s have been applied for in vivo studies^^'^^ 7. Radiocliemical

syntliesis

of ^^C-labelled

tiydrocarbons

Direct interaction of recoh ^^C atoms or ^^CH fragments, obtained in the ^^C('y,n)^^C process with various Cg hydrocarbons, resulted in the formation of ^ ^C-labelled methane, acetylene, ethane + ethylene, p r o p a n e + propylene and l,3-butadiene'R'^^ Methane-^^C and acetylene-^^C have been produced in the radiochemical reaction between ^^C and liquid benzene, with the yield ratio (CH4/C2H2) being in the range of 0.02 to 0.03. Synchrotron irradiation of 2,2-dimethylbutane yielded ^^C-labehed methane, ethane, ethylene, acetylene, propane, propylene and butadiene. The yields of methane and ethylene + ethane relative to acetylene, extrapolated to zero dose, where 0.12 ± 0.03 and 0.49 ± 0.00, respectively. Iodine does not affect the purely hot a t o m reactions producing ^^CH4 and C2 compounds. The yield ratios to acetylene extrapolated to zero dose were found to 0.15 + 0.05 for propylene, 0.1 ± 0.05 for p r o p a n e and 0.1 ± 0.05 for butadiene. Synchrotron irradiation of 2-methylpentane produced ^^C-labelled methane, ethane + ethylene, acetylene, p r o p a n e + propylene and 1,3-butadiene. The yield ratios of methane and ethane + ethylene to acetylene were 0.16 + 0.01 and 0.40 + 0.04, respectively, while the yield ratios for p r o p a n e + propylene and butane were 0.097 ± 0 . 0 1 5 and 0.15 ± 0.02, respectively. Six synchrotron irradiations of n-hexane'^^^ with initial iodine concentration of 0.0061 mole fraction yielded ^^C-labelled methane, ethane + ethylene, acetylene, p r o p a n e -h propylene and 1,3-butadiene. Yields of methane and ethylene + ethane relative to acetylene were 0.19 ± 0.01 and 0.25 ± 0.02, respectively. The yield ratio was 0.059 ± 0.008 for p r o p a n e -h propylene and 0.14 ± 0.03 for butadiene. The (C2H4 + C2H6/)/C2H2 yield ratios observed in the case of propane^^^^ and isobutane'^^^ were equal to 0.48 and 0.47, respectively. The above observations fit a mechanism which involves the insertion of an energetic ^^C or ^^CH fragment into a C — H bond, and formation of an intermediate decomposing into two-carbon or three-carbon stable products. Thermal reactions of the ^^C group occur mainly with surrounding molecules, since the concentration of the radicals is small and iodine as scavenger cannot be used to distinguish between hot and thermal reactions. The relative experimental yields of CH4, C2H4 + C2H6 and C j H g extrapolated to zero dose are therefore independent of the iodine concentration. In benzene and in cyclohexane all the C — H bonds are identical and only one kind of intermediate is formed, designated 'CgHsCH:' and 'CgHi^CH:'. In n-hexane, 2-meth ylpentane and 2,2-dimethylbutane different intermediates are possible depending on the particular C — H b o n d attacked. The yields of ^^C-labelled products increase in going from benzene to cyclohexane to n-hexane, parallelling the hydrogen avahabhity on carbon. The number of hydrogen-rich M e sites increases with increase of branching in the

822

Mieczys/aw Zielinski a n d M a r i a n n a K a h s k a

hexane isomers a n d the observed (C2H4 -f C 2 H 6 ) / C 2 H 2 ratio increases in the sequence: benzene < cyclohexane < n-hexane < 2-methylpentane < 2,2-dimethylbutane. The above insertion is t o a great extent a statistical process with little chemical selectivity. T h e methane yield from several hydrocarbons is relatively constant, which implies that ^ ^CH4 is produced in the hot region by a series of abstraction reactions as the ^ fragments cool down. Irradiation of gaseous NH3 with 10-MeV protons (using a 60-in. cyclotron) resulted in ^^C production by a ^'^N(p,a) ^ nuclear process, a n d in direct synthesis of ^ ^ C H 4 a n d ^^CH3NH2 (major reaction products)^^^

D. Synthesis of Dodecane-1,12-^^C2 and Hexadeuteriododecane

Dodecane-l,12-^^C has been synthesized'^^*' by the procedure shown in equation 32. 1,10-Dibromodecane treated with c y a n i d e - ^ i n aqueous e t h a n o F ^ gave the dinitrile which was hydrolyzed in situ to the acid, 20, and in turn reduced with a b o r a n e - d i m e t h y l sulphide complex^^'^^ i42-dodecanediol-l,12-^3C in 90% yield. The bis-tosylate of 20 has then been reduced to the required dodecane (1,12-^^C) in 30% yield, enriched with ^^C up t o 88.9%. ^^^^

BRCH2(CH2)8CH2Br

> H00^3C(CH2)io''COOH

1. E t 0 H / H 2 0 , 5 h reOux 2. HCl(conc.), 12 h reflux

(20) 86% yield, m.p. 127-128 °C ( M e 2 S - B H 3 ) / T H F , 25°C RT, 8 h

p-MeC6H4S02Cl

HQi ^CH2(CH2)i 0 ' ' C H 2 O H

py, 0 ° C , 2 4 h

90% yield, m.p. 81-83 °C LiAlHWether

TS0^3CH2(CH2)io''CH20TS

>^3CH3(CH2)io''CH3

(32)

2 days reflux

80% yield, m.p. 90-91 °C

(21) 212-216 °C, b.p. at 760 mole fractions: ^^C-2.2%,

^^Ci —19.4%, 13C2—78.4% The reduction of a 1,6-dicarboxylic acid dimethyl ester to the corresponding hydrocar bon h a d been described ^ In a simhar manner hexadeuteriododecane (22) has been prepared^^*' (equation 33). The hnal L A D reduction yielded dodecane-l,l,l,12,12,12-2H6 (22) which contained, according to mass spectra: ^ H Q — 0 % , ^Hj —0%, ^H2—0.9%, ^H^— 0.9%, ^ H 4 - 0 . 9 % , ^ H 3 - 6 . 3 % , 'U,~-90J%.

HOOC(CH2)ioCOOH

H O C D 2 ( C H 2 ) I O C D 2 0 H

)ME02C(CH2)IOC02ME

^'^'^^

>

T S O C D 2 ( C H 2 ) I O C D 2 0 T S LIALD.

CD3(CH2)ioCD3 ether, 8 h reflux

(22)

(33)

18. Syntheses a n d uses of isotopicahy labehed alkanes a n d cycloalkanes

823

E. Syntheses of Deuteriated Alkanes 1. Synthesis

of

n-decane-d^^

T h e synthesis of n-decane-d22, needed for n e u t r o n diffusion studies, h a s been elaborated^^ by optimization of a patented process^^^" based o n H / D isotopic exchange over P d / C catalyst. I n a typical experiment 142 g of decane a n d 20 g of P d o n c a r b o n (5%) were used. After 995 h at 165 °C, deuteriation of 99.4-99.7% has been reached as measured by M S , N M R a n d densimetry.

2. Synthesis

of 1,1-dideuterio-

and

2,2-dideuterio-4-phenylbutane

a. Synthesis of 2,2-dideuterio-4-phenylbutane (23). This h a s been u n d e r t a k e n t o study the fragmentation of deuteriated alkylchromium c o m p o u n d s . 23 has been prepared^^ using L A D in the reduction steps (equation 34). T h e p r o d u c t 23 contained 2,2-dideuterio4-phenylbutane (96.3%), 2-deuterio-4-phenylbutane (3.5%) a n d a trideuterio species (0.2%). LiAlD.

PBr3

PhCH.CH.CO.Et

PhCH.CH.CD.OH

- - >

2 h reflux

-5°Cto20°C

1 Mg

PhCH2CH2CD2Br

LiAlH4

—

2. CO2,

-70°C

>PhCH^CH^CD^COOH m.p. 4 8 - 4 9 °C

PBr

PhCH2CH2CD2CH20H

3 ^

PhCH2CH2CD2CH2Br 1. M g / T H F

PhCH2CH2CD2CH, 2. H2O

2

2

2

3

(34) V

/

(23) 99.2% chem. purity LiAlD.

Ph(CH2)3C02Et

> Ph(CH2)3CD20H

— ^

Ph(CH2)3CD2Br U^^H^ 2. H2O

Ph(CH2)3CD2H

(35)

(24) 99.4% chem. purity b. 1 ,l-Dideuterio-4-phenylbutane (24). This has been obtained simharly in the reaction sequence shown in equation 35. The product 24 contained l,l-dideuterio-4-phenylbutane (97.2%) and monodeuterio-4-phenylbutane (2.8%). N o H / D exchange took place during the formation or hydrolysis of the organomagnesium halide intermediate compounds or during age chromatographic separations of the hydrocarbons obtained, nor in the reaction of deuterated alkylmagnesium bromides with CrCl3(THF)3 (equation 36). In the course of methanolysis of solvated trialkylchromium compounds 25 with oxygen-free methanol at — 4 0 ° C , the 2,2-dideuterio- and l,l-dideuterio-4-phenylbutanes have been obtained (as shown by gas chromatographic analysis fohowed by mass spectrometry and N M R spectroscopy).

3 R M g X + CrCl3(THF)3

— -70

C to - 4 0 ° C

> R3Cr(THF)„ (25)

R = PhCH2CH2CD2CH2 or Ph(CH2)3CD2

(36)

824


3. Synthesis Grignard

of dideuteriomethylene

hydrocarbons

by copper

catalysed

reaction

of

reagents

H y d r o c a r b o n s containing a single specific methylene g r o u p labelled w i t h d e u t e r i u m have been needed for a v i b r a t i o n a l

study o f chain conformations a n d o r g a n i z a t i o n a l

changes occurring d u r i n g phase transitions^^.

D h i t h i u m tetrachlorocuprate

has been

f o u n d to catalyse effectively the c o u p l i n g ^ ^ o f G r i g n a r d reagents w i t h alkyl halides a n d long-chain alkyl p-toluenesulphonates^^ L i t h i u m dimethyl cuprate, M e 2 C u L i , has also been used for p r e p a r a t i o n of deuteriated hydr ocar bons ^ ^ ' ^ ^ . Deuteriated toluenesulphonates of the desired chain length are easily prepared f r o m esters of fatty acids by L i A l D 4 treatment followed b y tosylation i n p y r i d i n e . E q u a t i o n 37 has been applied^"*^ to synthesize n - C 5 H i i C D 2 C H 3 , n - C i o H 2 i C D 2 C H 2 C H 3 , n - C i 9 H 3 9 C D 2 C H 3 , n - C i 7 H 3 5 C D 2 C 3 H 7 , nC i 5 H 3 i C D 2 C 5 H i i - n a n d n - C i o H 2 i C D 2 C i o H 2 i - n . T h e yields of heneicosanes deuteriated in the 2-, 4-, 6- a n d 11-positions were 85% , 74%, 50% a n d 8 3 % , respectively.

RT, 2 h stirring

TsCl, P y

RCD.OH

R C O X H , + LiAlD.

T CH3CH2CHTCH3

> CH3CH2CH2T > CH3CH2T

> CH3T

(50)

Radiolysis of the parent molecules is smaher when a heterogeneous paste consisting of L i 2 C 0 3 (or other lithium derivatives) mixed with the c o m p o u n d to be labelled is neutronirradiated. In this case a-particles and tritium atoms leave the sohd a n d enter the hquid


829

phase with smaher energy, when their destructive action u p o n the molecules t o be labelled is smaller than in the case of neutron irradiation of a homogeneous solution of a lithium salt in a n organic substance. Irradiation of 1 g of N2 during 1 h with a neutron flux of 1 0 ^ ^ n c m " ^ s ~ ^ yields 0.03//Ci of ^"^C only, since the cross section for the reaction ^''^N(n,p) equals a = 1.76 b. Irradiations for ^''^C-labehing are therefore carried o u t using 10^^ n cm~^ s~ ^ fluxes. Recoil tagging has been applied for labelling petroleum hydrocar bons with tritium a n d carbon-14 by direct neutron irradiation of the hydrocarbon mixed either with 5 - 1 0 / / of Li powder (10-50% yield) or with 2-methylpyrazine (0.1-4% yield)^^''. Approximately 10^^ thermal neutrons per gram of mixture of hydrocarbons a n d radioisotope precursors h a d been applied. T h e more detahed treatment of h o t atom chemistry is presented in Section III of this chapter.

III. HOT ATOM RADIOCHEMICAL STUDIES OF SATURATED HYDROCARBONS A. General Chemical and Physical Introduction 1. Physical

aspects

A nucleus formed in the a-decay processes experiences^^^ a recoh energy

which, for instance, in t h e case of the

^

, 208pb = 8.78 M e V

decay a m o u n t s t o ^(recoil 208pb) =

208

X 8.78 M c V ^ 0.169 M e V ^ 170 K e V

This value is large in comparison with chemical binding energies ( < 5 eV). Atom ôspj^ jg therefore called a 'hot' atom. Its 'temperature' corresponds to 2 x 10^ K. T h e thermal energy of atoms at 295.2 K, E = ^kT, equals 0.0382eV only. T h e 'hot' a t o m breaks ah chemical bonds by which it is b o u n d t o other atoms. The recoil energy received by a nucleus of mass M in the single y-emission process equals ^(recoil, y)(eV) = 536.78 Ej(MeV)/M (a.m.u.). P h o t o n s emitted, for instance, in the nuclear reaction ^^Âu(n,7)^^Âu have energy Ey = 6.497 MeV. T h e recoh energy received by the 'daughter' ^^Âu therefore equals a b o u t 114.4eV. In the case of emission of two y-quanta (Eyi, Ey2) the recoh energy of the atom of mass M depends on the angle 0 between the directions of emission of these gammas (equation 51): ^(recoil ,) = (£n +

+ 2£,i£,2COS^)/2Mc^

(51)

(where c is the velocity of light in vacuum.) The maximum and minimum values of the recoh energy are therefore equal in this particular case (equation 52): ^(recoil ,) = 5 3 6 . 7 8 ( £ , i ± Ey^r/M

(eV)

(52)

(Ey are given in MeV, M in a.m.u.). The recoh energy

£ ( r e c i . n u c D ^ expressed in eV, received by the daughter nucleus of mass M (a.m.u.) in the emission of monoenergetic electrons by the nucleus, is given by the equation

^(recoil ^)(eV) = (536.78 E', + 548.59 E J / M

(53)

830

Mieczys/aw Zielinski and M a r i a n n a K a h s k a

where is expressed in MeV. In the jS-decay processes two particles are emitted simultaneously at the angle 6: a negatron of energy E^ and an antineutrino (v) of energy E~, or a positron (P^) and a neutrino (v). The daughter recoh energy in j?-decay is given by E(eY) = (536/M)[£E^ +

imiE, + £^ + 2-E,^{El

+

imiE,) cos 0']

M a x i m u m and minimum values of the recoil energy £(EXTR. RED.) received by the daughter nucleus, corresponding to angles 6 = 0 and 6 = 180°, are equal (equation 55): £(EXTR. RED.) = ( 5 3 6 . 7 8 / M ) [ ^ ( f , ^ + 1.022EJ ± E,y

(55)

W h e n a j9-particle and a neutrino are emitted in the same direction or when all the energy is carried away by one particle (by an electron or an antineutrino), the daughter nucleus experiences m a x i m u m recoil energy. The value of E^^^ in the j?-decay of ^^^Bi 210Bi

L

,210pQ

5.013 days

equals 1.161 MeV. The m a x i m u m recoh energy of ^^^Po is 6.5 eV. In the j5-decay 32p

T

^ 323

7 1 / 2 ^ 14.3 days

= 1.7104 M e V ( 1 0 0 % i 5 ~ ) a n d f o r. 33 22cS h i s E ( ^ , , . ÊCI. 32s) = 78.46 eV. These energies are sufficient to cause atomic rearrangements in the surrounding molecules. However, in the j5-decay of ^"^C and ^H the m a x i m u m energies of the emitted electrons are equal to 0.15647 M e V and 0.01859 MeV only, and the m a x i m u m recoh energies of the daughter ^"^N and ^He atoms, as estimated from equation 55, are 7.2 eV and 3.46 eV, respectively F r o m the laws of conservation of energy and m o m e n t u m it follows that only a p a r t of these recoh energies equal to ^(INTERNAL) = ^(RECOII)'^R/(^ + ^ R ) is used for breaking of the chemical b o n d to the daughter atom, M - M ^ , where M is the mass of the recoh daughter a t o m and M R is the mass of the remaining part of the molecule. W h e n M R » M , ^(INTERNAL) = ^(RECOIL)- W h c U M R = M , ^(INTERNAL) = i^(RECOIL). W h c U M R « M , ^(INTERNAL) = 0

aud

the chemical b o n d is not broken. F o r instance, in the case of neutron capture, (n, y), by iodine in hydrogen iodide, HÎ(n,7)H^^ Î, the H — I b o n d is conserved. In the case of ( ^ H — ^ H e ) ^ ion, formed in the j9-decay of the molecule, £(INTERNA,) = 3 . 4 6 3 ^ = 1.73

eV

In the majority of j5-decays the recoil energy is much less than the m a x i m u m energy and retention of the recoil daughter a t o m in the parent molecule is frequently observed. Detahed information concerning the degree of retention of the recoil a t o m s and the nature of the products obtained from fragments of the parent molecule which decomposed in the ^-decay are presented in the following sections. Detailed experimental studies are necessary, since the breaking of the chemical b o n d may also occur as a result of internal photoelectric processes (Auger electrons) causing the formation of positive charges at the a t o m which, u p o n neutralization, liberates sufficient energy to break chemical bonds. The probabhity that the state n in the daughter a t o m arises from state m of the parent a t o m is given^^'^^^'^^^ according to q u a n t u m mechanics, by the square of the overlap integral of the total wave functions ij/^ of the parent molecule and that of the daughter in state n, namely i//„: PMN = KÂnl'Am)!^- The probabilities of the transitions Is >ls,ls >2s. Is ^38, Is yoo (shake off) in the j5-decay of tritium, T ^^He + i 5 " + v , are equal to 0.70, 0.25, 0.013, 0.025, respectively^^"^^

(54)


831

According to Wexler^"^ jg-decay of tritium in H T produces (^HeH)"^ in 89.5 ± 1.1% yield, ^He^ in 8.2 ± 1.0% yield and H"" in 2.3 + 0.4% yield as primary ions. Decay of one tritium in a T2 molecule produces (^HeT)+ in 94.5 + 0.6% yield and (T + ^He+) in 5.5 ± 0 . 6 % . 2. Chemical

aspects

Hydrocarbons, both aliphatic and aromatic, have been the permanent object of study in hot a t o m c h e m i s t r y ^ S u c h chemical reactions occurring in systems not being in thermal equilibrium have been discussed by Rowland^^. Atoms with high translational energies are generated by various methods. Thus: (a) Nuclear reactions^ ^ yield hot neutral monovalent atoms of tritium, chlorine and fluorine in ^}lQ{n,pfU, i ^ F ( n , 2 n ) ^ « F and ^'C\in,yf^C\ processes. (b) U V photolysis of suitable molecules, such as hydrogen bromide (bond energy ^ H B r = 3.75 eV, see equation 56), gives hot ^ H and Br atoms:

^HBr ^-"^^^^•^•"-^',3H- + Br-

(56)

(c) Accelerators produce monoenergetic beams of atoms or molecules with energies located in the 2 - 5 0 eV interval. H o t reactions in such systems may initiate abstraction processes ((equation 57) i8p + R H . H ^ ^ F + R(57)

r or substitutions

+ RH

. HT +

R-

(equation 58) i « F + RX

(X =

H,

D,

F,

>Ri«F* + X

Cl, Br,

I,

(58)

NH2, O H , etc.)

or additions to a 7r-bond system (olefins, acetylenes, aromatic molecules; see equation 59): ^«C1+ ^C=C(

/

^—C—C^

\

I

(59)

\

3«C1

(the asterisk * denotes an excited state). The highly excited products formed in these reactions undergo secondary isomeriz ations or decompositions and also typical thermal reactions. The 'hot' nature of such reactions is established: (a) by finding reaction products which d o not appear in thermal systems (for instance, i « F + CH4 gives Me^«F); (b) by their insensitivity to the concentration of scavengers such as O2, N O , Br2,12, H2S, C2H4, butadiene, etc.; (c) by suppression of the reaction via addition to the system of a non-reactive m o d e r a t o r (usuahy a noble gas) which is able to accept the energy of the energetic reacting atom; (d) by the temperature insensitivity observed in 'hot' a t o m reactions (for instance, an increase in the temperature from 100 to 200 °C has no effect on the replacement of H by T in cyclobutane). The following phenomena also distinguish between hot a t o m reactions and thermal reactions: (a) Predominant retention of configuration, e.g. in the substitution of T for H at an asymmetric carbon a t o m in gas- and liquid-phase hot reactions.

832


(b) N u m e r o u s unusual secondary reactions of vibrationally excited molecules activated in h o t a t o m reactions a n d their pressure dependence. (c) Presumable electron-density origin (rather than from a steric interference) of substituent effects o n the yields of, e.g., T for H substitutions. (d) Correlation between abstraction of hydrogen from C — H b o n d s by h o t tritium a t o m s a n d b o n d dissociation energies of alkanes a n d cyclanes. (e) Observations of thresholds in various systems, which are characteristic only for true hot a t o m reactions a n d n o t found in the corresponding thermal systems. Examples of h o t a t o m reactions i m p o r t a n t for synthetic isotope chemistry or for theoretical h o t a t o m chemistry of hydrocarbons are presented in Sections I I I . B - E . B. Reactions of ^He^H^ Ions with Gaseous Hydrocarbons 1. Reactions

of^He^f-l'^

ions witti

metliane

^ H e ^ H ^ a n d ^He^H"^ are singly charged molecular ions a n d strong Bronsted acids which are able t o p r o t o n a t e exothermically almost any organic c o m p o u n d . They are produced in the ground state in the j5-decay of tritium hydride, H ^ H , a n d of molecular tritium ^H2^^^''^^. The latter process therefore affords a convenient means of generating a highly reactive protonating reagent in gaseous systems at any pressure. By minimizing the concentration of it is possible t o eliminate practicahy all the radiation-induced reactions, since the rate of formation of ^ H e ^ H ^ is proportional t o the first power of the ^H2 concentration while the rate of radiolytic labelling is proportional t o a higher power of the molecular tritium concentration. Exposure of a gaseous mixture consisting of CH4 (98 mol%) and O2 (2 mol%) to 1.7 mCi of ^H2 at 760 torr at r o o m temperature (in the dark) for 1 t o 4 m o n t h s yielded tritiated methane, CH^Û (40-38%), ethane, C2H53H (about 2%) and ethylene, C2H3^H (13%) as the major products. The combined yield corresponds t o 50% of the total activhy present initially at ^ H e ^ H ^ . The presence of 2 m o l % of oxygen as radical scavenger did not affect the product pattern. In the system containing CH4 (96%) + C3H8 (2%) + O2 (2%) the yield of tritiated ethane increased t o 32% and the total activity of the identified products rose to 70%. The above results were interpreted as indicating that ^ H e ^ H ^ ions p r o t o n a t e exothermically methane^^^ giving excited CH4^H^ ions which decompose into tritiated methyl ions a n d hydrogen or are collision stabhized (equation 60). The stabilized ions react with CH4 yielding tritiated methane. The tritiated methyl ions react with methane forming ethyl ions (equation 61). The same ions are quite unreactive toward methane (rate constant ca 10~^^-10~^^ccmolecule~^ s~^), b u t remarkably reactive toward p r o p a n e (k= 10~^ c c m o l e c u l e " ^ s~^), butanes, higher al kanes, water, etc. (equation 62): ^He^H ^ + CH4

> (CHs);^^ + ^He + Q + 6 7 - 8 9 kcal m o l ' '

(CH5)1.^CH + H2 (CHsb);^^ + M — . C H 5 + M CH5 ^ + CH4 — > CH4 + CH5 +

(60)

Asterisk * denotes a tritium label CH3+ + CH4 —> €2^,^ C2H5 ^ + C3H8

+ H2

C 2 H , + C3H7 ^

(61) (62)

The observed 32% yield of tritiated ethane, which is slightly higher t h a n the calculated one (28%) indicates a kinetic tritium isotope effect in the second reaction of equation

18. Syntheses and uses of isotopically labehed alkanes and cycloalkanes

833

* 60 (tritium concentrates in C H 2 T ^ ion). About one-third of the excited C H g ^ ions from tritiation of CH4 with ^He^H^ are stabilized by collision in methane at 1 atm.; the rest dissociate to produce methyl ions. The reaction of tritiated ethyl ions with traces of water is probably responsible for production of tritiated ethylene (equation 63) in the absence of added propane. C2H5+ + H2O

> C2H4 + H s O ^

(63)

The tritium exchange between ^H2 gas and CH4 gas at r o o m temperature, both alone and in the presence of He, Ne, Ar, or Kr, Xe, I2 or N O added, has been studied by Pratt and Wolfgang^"^^ and the rate R of the formation of radioactive methane was found to be = 8 X lO'â^/^ for unscavenged experiments and R = 92x lOâ -h 7.8 x lOâ^ for scavenged samples, where a is the activity of ^H2 in m C i c m " ^ . The a-term is attributed to the processes Û^ > ^He^H^ -f e and ^He^H^ + C H 4 > CU^Û, the a^/^-term to the CH4"^ + ^H2 ^ CHg^H reaction and the a^-term to the exchange with radiationactivated ^H2 or to reactions involving radicals or excited states. Besides tritium-labelled methane, labelled ethane, ethylene, propane, i-C4Hio, n-C4Hio, M e l and higher hydrocar bons have also been isolated. 2. Reactions

of^He^H^

ions witli

etiiane

Tritiated methane and ethane are produced in 14% and 3 4 - 3 6 % yields, respectively, in the reaction of ^He^H^ ions both with pure ethane as well as with ethane containing 2 mol% of oxygen^^^. The low yield of tritiated ethane can be explained by the formation of excited C2H6^H^ ions which decompose into labelled ethyl ions (without any appreciable tritium isotope effect)^ ^ (equations 64a-c) or by the simultaneous exothermic hydride ion transfer reaction (equation 65) competing with the tritiation of êthane (equation 64a), since in the reaction (equation 66) of the stabilized tritiated ion C2H7 ^ n o activity is lost as hydrogen tritide. ^He^H + + C2H6 — > (C2H7);e. + ' H e

(64a)

^ (C2H7):,e.— C2H5^+H2

(64b)

C2H5 + -h C2H6 C2H6 + ^He^H^ C2H7 + + C2H6

> C2H6 + C2H5 +

(64c)

> C2H5+ + He + ^H^H

(65)

. C2H6 + C2H7 +

(66)

The excited tritiated (C2H7)e^c. ions have enough excitation energy to dissociate through other reaction pathways energetically less favourable than that in equation 64b, leading to the observed tritiated methane formation (equation 67): (C2H7);xc.CH3++CH4

(67)

CH3 + + C2H6 — > CH4 + C2H5 + 3. Reactions

of ^l-ie^l-l^ ions witti

propane

Tritiated methane (13.9%) and p r o p a n e (14.6%) are the major products in the reaction of ^He^H^ ions with propane. Smaller a m o u n t s of ethane (4.7%), ethylene (4.5%) and traces of butane have also been produced. The above yields are insensitive to the addition of 2 mol% of oxygen as a radical scavenger and to a decrease in pressure from 760 to 20 torr (except for an increase in the methane yield from 14 to 18%). These results have been

834


explained^^ by equations 6 8 - 7 1 . •^He + (C3H,):,,.

(68)

100% C 2 H 5 " + CH4(15%)

(a)

c A ^

(5%) + C H 4

(b)

C3H/

(157o) +

H2

(a)

C3H/

+ H2 (65%)

(b)

20%

(69)

(70)

>C3H/+C3H8(15%) (71)

- ^ C 3 H / + c A T h e combined yield of all identified tritiated products accounted for only 3 0 - 4 0 % of the ^ H e ^ H ^ ions produced, owing to the probable formation of large a m o u n t s of hydrogen tritide which has been difficult to determine due to its presence as impurity in the molecular tritium. In addition, n o long-lived C^Hg^ intermediate seems to be formed in the initial p r o t o n a t i o n step. Reaction 71a is probably the single channel which leads to the formation of tritiated propane. The high yield of tritiated methane in reaction 69a and the low yield of tritiated ethyl radicaUn reaction 69b indicate the non-statistical distribution of tritium within the excited (€3119)^"^^ ion 37 (equation 72). (CH3CH2CH4);,, (37)

^(CHsCH^)^ + C H 4

(72)

The product yields given by the authors^^ indicate that hot tritium atoms insert preferentiahy into terminal methyl groups of p r o p a n e and the time between insertion a n d decomposition of 37 is insufficient for full equilibration of tritium within the excited ion 37. This 'tritium effect', that is, the preferential presence of a tritium a t o m in one of the two terminal groups,^should stimulate tritiated methane formation by r u p t u r e of the methylene c a r b o n - C H 4 b o n d due to electronic rearrangements and n o t due only to the mass eff'ect of tritium. Simharly, the preferential (65/80)-100% = 81.25% localization of tritium in H2 in the reaction shown in equation 70a also indicates the non-equhibrium nature of this decomposition process. H.

CH3CH2

C—T I^H

C2H5—c;

3"7

(70a)

H

The 'tritium effect' is not the simple result of the higher mass of tritium relative to }H, which lowers the frequency of c a r b o n - h y d r o g e n vibrations, but rather the effect of the local excitation of the electronic structure a r o u n d the terminal carbon of p r o p a n e caused by collisions and 40% fragment according to equation 79b. The remaining 35% dissociate preferential tritiated methane formation (equation 72a). D u e to its higher mass the tritium a t o m is located more closely to the terminal carbon than the light hydrogens and

18. Syntheses a n d uses of isotopicahy labelled alkanes a n d cycloalkanes

835

participates less frequently than }H atoms in the 'migration exchange' with the C2H5 radical. But this is only a secondary mass effect, a n d the stimulation of the electronic rearrangement a r o u n d the terminal carbon caused by insertion of the tritium ion is the principal reason for the preferential CH3T formation. Also, the stronger a n d more stable C H 3 — T bond ( = 104 kcal m o l " ^) is formed in larger abundance in this process than the weaker C 2 H 5 — T bond ( = 9 5 - 8 5 kcal mol"^). H

H

I/' CH3CH2 - C — H

[CH3CH2-CH3T]e

• C H 3 C H 2 + CH3T

(72a)

The results of earlier studies^ ^ of a system containing p r o p a n e gas a n d T2(2.2Ci) have been summarized in the form of linear equations 7 3 - 7 5 of the type L(X) = a + ^ [ T 2 ] , where a a n d b are constants a n d [ T ] denotes the total j5-activity in the sample; L(X), the number of tritium atoms incorporated per T decay, increases linearly with increasing tritium concentration [ T 2 ] in the 0 - 1 0 0 Ci interval. L(CH4-T) = (0.11 ± 0.01) + (0.020 ± 0.002)[T2]

(73)

L(C2H6-T) = (0.020 ± 0.003) + (0.011 ± 0.001) [ T 2 ]

(74)

L(C3H8-T) = (0.15 ± 0.01) + (0.022 ± 0.001)[T2]

(75)

The rate of formation of tritiated products in the propane-tritium system at a total Pparticle activity of 2.2 Ci depends linearly on time (20-100 h period). The yields decreased to about half when T2 was replaced by HT. Irradiation of the propane-T2 system with an external ^^Co y - source (1 x 10"" Ci) has increased the L(X) values due to an increase in the rate of electron production. The tritium-labelling process is initiated by two reactive species: the ^He^H^ ion (so-called 'decay labelling') and the electron (^-labehing)^^'^^. Nitric oxide reduced the L(X) values. 4. Reactions a. Gas-phase

of^He^l-l^ reactions

ions witti cyclopropane of^He^H^

and with

ions with cyclopropane.

1,2-dimethylcyclopropane These yield tritium-labehed

methane (22%), ethylene (15.2%) and cyclopropane^^ (18.8%) as the major products. Ethane (4%), p r o p a n e (2%) and propylene (7.1%) are the minor ones. T h e relative yields of main products appear to remain constant upon decrease of the cyclopropane pressure in the system from 760 to 20 torr and by addition of O2. The total yield of the products corresponds to 70% of the radioactivity of the generated ^ H e ^ H ^ ions. Excited p r o t o n at ed cyclopropane rings are produced in the hrst reaction step (equation 76). They dissociate partly or are stabilized by cohision (equation 77). T h e stabhized ions transfer protons to cyclopropane molecules (equation 78) forming tritiated C3H6 hydrocarbons. Tritiated cyclopropane is the major product with only relatively minor rearrangement of cyclic C3H7 ^ ions to a linear structure. About 25% of the excited protonated ions are stabilized by collisions and 40% fragment according to equation 79b. T h e remaining 35% dissociate to form a hydrogen molecule a n d a C3H5^ ion (equation 79c). (76) (77) C3H,

+ +

C-C3H6

>

CjHe, + C 3 H , +

(78)

836

Mieczys/aw Zielinski a n d M a r i a n n a K a n s k a (a) + M 25%'

(b) (C3H7).xc.

40%

C 3, H ^7

C2H3

(79)

+ CH4 23%

17Vo

(c) 35%

+

C3H5'

Hp

Hydride transfer (equation 80) from cyclopropane to C 2 H 3 ^ excited ions, formed in reaction 79b, is one of the possible routes of the tritiated ethylene formations (AH^^"^ = - 5 8 kcal mol "M. (80)

C«H 2"4

b. Reactions of helium tritide ions with cis- and irsins-f 2-dimethyIcyclopropane^^^. Storage of 2 m C i of ^H2 mixed with an organic substrate at 300 torr (in the presence of 2 m o l % O2 during 176 to 246 days in sealed ampoules) resulted in the formation, in the case of CIS-1,2-dimethylcyclopropane, of tritiated methane (9.3%), cis-l,2-dimethylcyclop r o p a n e (8.3%), 2-methyl-2-butene (8.3%) a n d tran5-2-pentene (2.4%), the total yield of the organic products being 28.3%. Using trans-1,2-dimethylcyclopropane the combined yield of the labelled organic products was only 20.7%, containing m e t h a n e (6.7%), trans-1,2-dimethylcyclopropane (8.3%) a n d an u n k n o w n (probably tritiated cyclopentene, 5.7%). T h e low total yields of tritiated products in both systems indicate that besides the reaction ^He^H^ + R H ^He^H^ + R H

• R H ^ H + + 3He

(81)

> R+ + H ^ H + ^He

(82)

which lead to tritiated hydrocarbons, hydride-ion abstraction (equation 82) also takes place, yielding hydrogen tritide as the only labelled product. The different total yields show that the competition between reactions 81 a n d 82 depends on structural factors. T h e retention of configuration after the ^ H e ^ H ^ attack rules out any intermediacy of linear pentyl ions a n d provides additional evidence for the occurrence of gaseous p r o t o n a t e d cyclopropanes 38 (equation 83). Me CH Me—CH-

+

-CH2

.CH

RH Me

CH-

(RH),,

(83)

-CH2

(38)

F o r m a t i o n of tritiated methane in both systems and the absence of C4H7^H hydrocarbons in the products indicate that production of methane involves the attack of ^ H e ^ H ^ on a methyl group of the substrate followed by fast dissociation of the methyltritiated intermediate (equation 84). The butenyl ions, C 4 H 7 ^ , are transformed by hydride-ion abstraction from the substrate to butenes. M et h an e formation according to a


837

CHS^H"!

-I---

.CH

' H e ^3Hu +

CH-

Me

He

.CH

+

:H2

Me

CH,^H

+

CH-

-CH2

C.H + 4"^ 7

(84)

(39)

protolytic cleavage mechanism has also been observed in the case of alkanes dissolved in H F S O g - S b F s solutions^^^ The products of cis- and trans-dimethylcyclopropane tritionation, apart from tritiated methane and tritiated parent, are significantly different. The cis isomer yields two linear amylenes via cleavage of the cyclopropane ring (equation 85) and subsequent p r o t o n transfer from these ions to molecules of the substrate. N o labelled amylenes have been found in the products of the reaction of TRAM5-l,2-dimethylcyclopropane with helium tritide ions. (MeCH^HCH2CHMe)'^

Me

I CH2^H Me

CH—^—CH2 •a

5. Reactions

(85)

(MeCHCHMe)""

I

of ÎHe^f-i'^ ions witli n-butane,

i-butane

and

cyclobutane

a. Reactions of helium tritide ions with n-butane^^. Tritiated m e t h a n e (15%), tritiated butane (15%) tritiated ethane (6%), ethylene (3.4% and 2.5% yields in the absence and presence of 2% O2, respectively) and p r o p a n e (2.3% both in the absence and presence of oxygen) are obtained in this reaction. The attack on n-butane by the ^ H e ^ H ^ ions (equation 86) forms the exched protonated cations that fragment and react subsequently according to equations 87 and 88.

(C.H.i);,,. + ^He

n-C4Hio + ' H e 3 H ^ (a)

C 4 H / ( 1 4 % ) + H,(64%)

78%

(b)

(C4H1JI

(86)

CoHc + C2H6

(87)

6%

.C3H/+CH4(14%)

(c)

U

6%

16%

*

n-C4Hio + C2H5 n-C4Hio + C 3 H ,

+

+

• C4H9

*

-h

Cjiie

i l Q H , + + C3H3 (2%)

(88)

n-QH,o + Q H , + - ^ Q H , + + n-C^Hio ^ (14%) The distribution of tritium a m o n g the different radioactive species isolated indicates that the hfe time of the excited (C4H1 ,)"^ species is t o o short for the attaintment of the equihbrium distribution of the label within the tritiated cation.

838


b. Reaction of^He^H^ ions with isobutane. Tritiated isobutane^^ (ca 18%), methane (25.3% with pure i-CJiô and 23.4% in the presence of 2% O2), ethane (2.2 and 1.7% respectively), ethylene (3.9 and 3.5%) and p r o p a n e (3.4 and 3.2) are the products. Equations 89 and 90 hlustrate the distribution of tritium label in the products. Most of the tritium activhy (90%) is contained in the methyl group ^ of the labelled /-C4H10 ^ The attack at the branched carbon is probably followed by elimination of ^H^H (equation 89b).

> 'He

^He^H^ + / - Q H i o

{CJ{,I)L

+

100% (a) 28%

C 3 H / ( 3 % ) + CH4(25%) (89)

(b) 72%

Q H / ( 1 8 % ) + H2(54%)

/-C4H,o + C 3 H /

>C4H/^C3H8(3%)

/-C4H10 + C 4 H /

. C 4 H / +i-C4Hio(18%)

(90)

The schemes in equations 86-90 d o not involve stabilized protonated ions such as were postulated in the cyclopropane reaction in which evidence for cyclopropanium ion formation has been found. c. Reactions of^He^H^ ions with cyclobutane. These were unaffected by the presence of added oxygen. The following tritiated hydrocarbons have been^^"^ isolated in the reaction (at 400 torr): rraMs-2-butene (12.1%), ethylene (11.1%), propylene (8.4%), cyclobutane (6.9%), ethane (6.1%) and methane (1.3%). The total yield of organic tritiated products represents 45.9% of the reacting ^ H e ^ H ^ ions. As before, tritiation of cyclobutane (equation 91) is the first step in the formation of labelled products, fohowed by cohisional stabhizations and reactions of the stabilized cation (equations 92) which retains partly a cychc structure, or undergoes fragmentations (equations 93). The yield of tritiated ethylene is about twice as high as the yield of tritiated ethane ^He^H^ + C-C4H8

> (C4H9)etc. + ' H e

i^^^9)L. + M ^ ^ (C4H9)^ + C4H8

+ M_. > CÛg^

c-C4H9^

^ (-cyclobutane + C4H J + ^trans-2-butene

• secondary-C4H9"^

(C4H9);,,.

CH4 + € 3 6 5 ^ —

(91)

C2H4 + C2H5 ^

(92)

rrans-2-butene C3H6 + C4H7 ^ C2H6 + C4H7 ^

(93)

d. Reaction of fast T2 and with n-butane. The translational energy dependences of the probabhity of reaction between n-butane and accelerated T ^ ions or T2 molecules have been determined by efficient collection of the tritiated n-butane molecules and measuring their radioactivity by a radio gas-chromatographic m e t h o d ^ T 2 ^ ions have been accelerated to discrete energies ranging from 5 to 100 eV in a specially designed 'chemical a c c e l e r a t o r ' T h e energy-selected tritium ions either collided with a crossed beam of the organic molecules or were transformed to T2 of the same translational energy using D2 and then reacted with the n-butane. The threshold of 6.0 ± 0.6 eV has been found for hydrogen displacement between neutral energetic T2 and n-butane. The probabhity of this reaction increases with increase in the translational energy of T2 and reaches a rather flat

18. Syntheses and uses of isotopically labelled alkanes and cycloalkanes

839

plateau extending between 30 eV and 100 eV. The threshold energy of 6.0 eV is close to the endothermicity (5.0 eV) of reaction 94. > n-C4H9T + T + H

T2 + n-C4Hio

(94)

A simhar Walden inversion mechanism has been proposed for displacement of H atoms in methane and ethane by fast T atoms^ ^ reaction cross section for the formation of n-C4H9T as a function of translational energy of T2 ^ decreases rapidly with increase in the energy of the ion from 5 eV to 20 eV, then remains relatively constant u p to 40 eV and hnahy shows a broad maximum centered at about 60 eV. The shape of the observed experimental yield curve has been rationalized by suggesting that there are at least two mechanisms for the reaction of T2 ^ with butane. Below ca 20 eV T2 ^ energy, the most likely mode is tritiation fohowed by loss of H2 and hydride abstraction (equation 95). At higher energies, collisional dissociation of the butane by fast T2 ^, followed by reaction of the butyl radical with molecular tritium, has been suggested (equation 96). T2 ^ + n-C4Hio

C4HioT^ + T

C4HioT^^C4H3T^+H2 C4H8T+ + H - ( w a l l )

(95)

^n-C4H9T

T 2 ^ + n-C4Hio

C4H9 + H + T ^ + T

C4H9 + T2

^C4H9T + T

These experimental observations have been compared with theoretical considerations of P o r t e r ^ M e n z i n g e r and W o l f g a n g ^ a n d Porter and Kunt^^^ concerning the reacting systems consisting of T2 (or T ^ ) and solid cyclohexane. A similar shape of reaction probabhity curves for both organic targets has been obtained. 6. Reactions

of ^He^l-(^ ions with cyclopentane

and

cyclohexane

a. Reactions with cyclopentane. The total yield of tritiated^^"^ products formed from cyclopentane ( + 2 mol% O2) with ^He^H ^ ions at 100 torr a m o u n t s to 34.2% of the total tritium activity present in the helium tritide (cyclopentane—11.1%, r r a n 5 - 2 - p e n t e n e — 4.5%, p r o p a n e — 4 . 6 % , ethylene—^4.1%, propylene—3.4%, ethane—2.6%, u n k n o w n product, probably pentadiene—3.9%, m e t h a n e — n o t determined). Cyclopentane and its rearrangement product, trans-2-pentene, arise in reaction 97. ^He^H^ + C-C5H10

CsHn +

^(CsHii);,,.

^M^C.nt,

{cAi)L.

C-C5H10

+ He

+ M,,,.

(97)

^ C5H10 + C5H11 +

Ethane and ethylene are formed in fragmentation processes (equation 98) and p r o p a n e and propylene in hydride ion transfer reactions (equation 99). {Csîi)L.—^cA^+cA (CsHiJexc.

^^3^1

(98) +C2H4

C3H5 ^ + C-C5H10 — > C3H6 + C5H9 + C3H7 ^ + C-C5H10

(99)

^ C3H3 + C5H9 ^

b. Reactions opHe^H^ with cyclohexane + Imoiy^ O2 at 100 torr. Tritiated cyclohexane has been produced in 9.7 + 0.9% yield in this reacdon^^"^. The other products are produced in much smaller yields (rrans-2-hexene 3.1%, rrans-2-pentene 1.3%, propylene 3.0%,

840


p r o p a n e 2.7%, ethylene 1.6%, ethane 1.2%, m e t h a n e — n o t determined). F o r m a t i o n of the tritiated cyclohexane (equation 100) requires one to assume the existence of the cyclic p r o t o n a t e d intermediate cyclohexanium ion, 40, Isomerization of 40 and subsequent p r o t o n transfer lead only t o one of the possible hexenes, trans-l-hQXQUQ. 'Hc'U^

+

c-C,n,2 — > iCeî3)L. + H e [(40)]

{Ceî3)L. + M - ^ Q H , 3

^ +M_.

(100)

C 1 - C 5 hydrocarbons arise from t h e fragmentation of the excited carbonium i o n (equation 101):

(C6Hi3)ETC.-^CH4 + C 5 V (^6^,3)1.

cA

+ C4H7 ^

(101)

iCeî^3)L-^cA + C,U,(C6Hi3)E^XC.

^ C3H6 + C3H7 ^

and in the exothermic hydride ion transfer reactions 102: C5H9 ^ + C - Q H 1 2

C5H10 + Q H i i +

C3H7^ + C - Q H 1 2

C3H8 + Q H i i ^

(102)

c. Concluding remarks concerning reactions of c-alkanes with helium tritide. After reaction of cycloalkanes with ^ H e ^ H ^ part of the tritiated carbonium ions retains a cyclic structure. N o r m a l tritiated alkanes are not formed in the reactions of the corresponding cycloalkanes. This means that the linear alkyl ions formed from the isomerization of p r o t o n a t e d cycloalkanes react according t o equation 103:

n-cAn^, + c-C„H2„ —

n-C„H2„ + W

n ^ ,

(103)

and not according t o equation 104: n-C„H,^„^^ + c-C„H2„ — n - C „ H 2 „ . 2 + C„H,^„_,

(104)

The manner in which ^ H ^ is b o u n d in the cycloalkanium ion is not k n o w n precisely. Combined yields of the isolated organic products diminish from 67% with cyclopropane to 46% with cyclobutane, t o 34% with cyclopentane and t o 2 3 % with cyclohexane. This indicates that the abstraction process ^He^H^ + R H

. R^ + H ^ H + ^He

(105)

prevahs over the tritiation process (equation 106) with increasing n u m b e r of carbon a t o m s in the ring. No-polymeric c o m p o u n d s have been detected in these studies. ^He^H + + R H 7. Reactions

of ÎHeT^ ions with gaseous

> RH^H ^ + ^ e

(106)

bicyclo[n.1.0]alkanes

The gas-phase reactions of ^ H e T ^ with bicyclo[2.1.0]pentane, bicyclo[3.1.0]hexane and bicyclo[4.1.0]heptane (41) have been investigated^ and the formation of tritiated hydrocarbons retaining the bicyclic structure of the starting substrate has been observed. This finding indicates that the gaseous bicycloalkylium ions are formed via exothermic trition transfer from the ^ H e T ^ t o the bicychc substrate (equation 107). D u e t o t h e

18. Syntheses a n d uses of isotopically labelled alkanes a n d cycloalkanes

841

exothermicity of this electrophilic attack, a large fraction of the bicyclic organic ions formed d o n o t undergo stabhization by cohisions in the 100-300 torr pressure range investigated a n d decompose or isomerize by cleavage of one or more C — C bonds. > ^He + (bicyclo[n.l.0]C^H2^_2^H);^^

+ bicyclo[n,l,0]C^H2^_2 + M

1

I

(bicyclo[M.1.0]C^H2^-2'H)+ + M , , , + fragments is bicyclo[^.1.0]C^H2,„-3'H + SH^

(107)

In the case of 41 (experimental conditions: 41—100 torr, o x y g e n — 1 0 t o r r , ^ H 2 — 2 mCi, volume of the pyrex vessel 500 ml, storage period 250-263 days, temperature 90 °C), besides tritiated 41 (6.2%), tritiated methane (15.2%), ethene (1.9%), propene (14.2%), cisbut-2-ene (2.3%) a n d 2-methylbut-2-ene + trans-pent-2-ene (8.1%) have been isolated. I n the case of reaction of ^ H e ^ H ^ with bicyclo[2.1.0]pentane (42), the yields of the trhiated products were: 42—3.8%, m e t h a n e — 1 6 . 1 % , ethene—0.5%, propene—12.2%, 2-methylbut-2-ene—1.4%, cyclopentene—5.7%, other (C4),(C5) p r o d u c t s — 5 % . ^ H e ^ H ^ with bicyclo[3.1.0]hexane (43) gave 43 (1.7%), methane (12.4%), propene (4.0%), trans-pent-2ene (2.9%),l-methylcyclopentene (0.4%), unknown (C4, 5.2%). The above results indicate that the fragmentation of the bicycloalkylium ions is very sensitive t o specific structural factors. The formation of tritiated cyclopentene (the major C5 product from gas-phase tritonation of 42) proceeds according t o equation 108, which involves the initial cleavage of the cyclopropane ring.

/

CH-^r-CH

»

\ 1/

CH +

•CHg

>. c - C g H y ^ H

CH2

(108)

CH2--CH2 3H

N o tritiated cyclohexene has been found in the reaction of ^ H e ^ H ^ with bicyclo[3.1.0]hexane and, contrary t o liquid-phase reactions only a low yield of 1methylcyclopentene has been obtained. Gas-phase electrophilic reactions of ^ H e ^ H ^ with gaseous alkanes a n d cycloalkanes have been reviewed by Cacace^ 8. Reactions hydrocarbons

of tritium

atoms generated

in the ^He(n,pfi-i

nuclear

reaction

with

Recoh tritium atoms, produced in the ^He(n,p) reaction, were studied with different hydrocarbons including^^^" alkanes (C2H6, n - C s H g , n - C 4 H i o , C M e 4 , C H 3 C H M e 2 , n - C 5 H i 2 , n - C g H i J , alkenes ( C H 2 = C H — C H 2 C H 3 , C H 2 = C H C H M e 2 , C H 2 = C H C H 3 , trans- a n d c i 5 - C H 3 C H = C H C H 3 , C H 2 = C M e 2 ) and a n alkyne, C H = C C H 3 in hexafluorocyclobutene, and the normalized yields of C H 3 ^ H formed by the attack of hot tritium on terminal c a r b o n - c a r b o n single bonds have been determined (equation 109). These •CHs^H

^H*

+

+

R

R—CH3

3 •R « denotes a hot' atom

. -h CH3

(109)

842


yields have been found to correlate inversly with the R — C H 3 b o n d dissociation energies. A suggestion^ has been m a d e that the reaction of recoil tritium atoms at C — C single bonds is faster than the vibrational displacement of the ahyl radical. The time for this type of interaction has been assumed to be less than 2 - 5 x 1 0 " ^"^s. Linear (44) and triangular (45) cohisional complexes have been proposed for the CH3^H formation process. The cleavage of the R — C H 3 bond should be the ratedetermining step for the M e abstraction in the linear complex 44 whhe the triangular

H

3H

(44)

(45)

complex 45 implies that the electron-overlapping process and the C — T bond formation should be rate-determining. The dependence of the CH3 yields on D(R —CH3) and the minor role which the electron density plays in determining the yields of tritiated methane support the structure 44 for the 'transition state complex' of the M e ^ H formation. A ^"^C methyl kinetic isotope effect study should help to formulate correctly the mechanism of these reactions. 9. Physico-chemical

studies

of hot tritium

atom

reactions

a. The replacement of an H a t o m by a hot tritium atom is facihtated by the presence of a high electron density in the C — H b o n d under a t t a c k ^ T h i s view has been supported by the linear correlation between the relative yields of R ' — i n reaction ^H* + R^^H > R'^H + ^H, and the N M R p r o t o n chemical shift (ppm) for a series of substituted halomethanes and alkanes: CH4 (100% yield; ^^MR = 0 ppm) > alkanes > C H s B r > CH3CI > CH3F > CH2CI2 > CHF3 (55% yields, (5NMR = - 6.2). The replace ment of H by T is also more probable in M e groups present in M e 3 S i in which the electron density is higher by a factor 1,18 than in Me4C, in good agreement with the above linear correlation^ b. Complete ( > 99%) retention of conhguration at the asymmetric^ ^ ^ carbon atoms has been found in the 02-scavenged gas-phase replacement of hydrogen by energetic tritium in dl- and m^so-(CHFCl)2. l2-scavenged liquid samples showed measurable isomerization on irradiation of a LiF solution with a neutron flux of approximate 1 x 10^^ n c m " ^ s ~ ^ In gas-phase experiments ^He has been used as the source of recoil tritium. In unscavenged gas-phase experiments and in liquid-phase experiments with I2 as scavenger, the formation of 'inversion' products caused by radical combination reactions has been observed. The possibhity of negligible inversion of conhguration in the case of gas-phase T for H substitution in CH4 leading to CH3 formation has been considered^ c. The effect of all 'chemical' factors, such as^^^ electronegativity, electron density and b o n d energy, upon the yields of the hot tritium for hydrogen substitutions in various halomethane and alkane molecules has also been studied by Rowland and coworkers^ They concluded that the p r o b a b h h y of the T / H reaction, i.e. MeX CH2'HX formation, decreases with increasing electronegativity of the substituent X (measured, as before, by the N M R shift). The view has been expressed that highly electronegative substituents such as F might serve as a sink for electron density developed by the departure of the H atom.


843

leaving less electron density in the vicinity of the incipient C — b o n d and minimizing the probabhity of this new bond formation. The hypothesis that halogen substituents influenced sterically the T for H substitution has been rejected. The relative yields of C H g ^ H formation in the reaction of hot tritium with CH3X increased by a factor of 7.5 from C H 3 F to CH3I. The bond dissociation energy of the C — X bond is the most important one a m o n g the factors controlling the yields in these T / H substitution reactions. This means that when tritium atom has an excess of kinetic energy, geometrical and physical factors such as atomic masses and sizes, bond angles, angle of approach at the moment of cohision, etc., are not of great importance. (The cumulative steric alkyl substituent effects in the T / H substitution reactions are between 0 and 10% per alkyl group.) R o w l a n d ^ w a r n s strongly that in the evaluation of primary yields using the observed product yields, it is necessary to consider the secondary isomerization or decomposition of internally excited molecules during the substitution process. 10. Isotope

effects

in the substitution

of 2.8eV tritium

atoms

with

methane

The i n t e r m o l e c u l a r ^ i s o t o p e effect in reactions 110 and 111 for 2.8eV tritium atoms generated by photolysis of TBr at 1849 A, as measured by the ratio [ ( C H 3 T / C H 4 ) / ( C D 3 T / C D 4 ) ] , has been found to equal 7.2. The ratio for the intra molecular compethion for the T for H versus T for D substitution in partially deuteriated methanes (equations 112 and 113) is approximately unity, as measured semiquanthatively by the ratio of product yields, [ C H D 2 T ] / [ C H 2 D T ] = 1.06 + 0.1. T* + C H 4 T* + C D 4

> C H 3 T + ^H

(110)

.CD3T + D

(111)

T* + CH2D2

> CHD2T + H

(112)

T* + CH2D2

> CH2DT + D

(113)

The above results have been classified as 'primary replacement isotope effect of 1.6 ± 0.2 favouring the substitution of H over D ' and as 'secondary isotope effect of 1.6 + 0.2 per H / D favouring bond formation to methyl group with more H atoms in it'^^^. The per bond abstraction yields have also been determined and found to be 1.4-2.0 times higher for H T than for D T formation. Experimental difficulties encountered in the determinations of H T abstraction yields did not ahow a more detahed study of this effect. The probabhity of tritium substitution into the methane molecule by 2.8 e V T atoms increases with the decrease in the number of D atoms in the methane, as shown by the relative yields for this process: CH4(7.2 ± 0.2), CH3D(5.6 ± 0.3), CH2D2 (3.1 ± 0.3) and CD4(1.0). Little preference has been found for replacement of H or D atoms. In the case of CH2D2 target molecule (products C H D 2 T or CH2DT) the ratio of product yields, T for H or T for D, equals 1.06 ± 0.1. F o r the C H D 3 target molecule (CD3T or C H D 2 T formed) the T for H or T for D ratio has been found to be 0.4 + 0.1 (per bond, 1.2 + 0.3). The primary replacement isotope effect for very high energy tritium atoms (192,000 eV) from the ^He(n,p)^H process and substituting into CHX3 versus C D X 3 molecules (where X = CH^''^, CD^''^ or F^2«) equals 1.30 + 0.05, indicating also the preference for H replacement. N o detailed analysis has been given by Rowland and coworkers, but several ideas aimed at understanding the substitution processes have been discussed. The 'bilhard bah' a t o m - a t o m collisions favouring the easier replacement of D do not explain the observed experimental deuterium isotope effects in substitution reactions with hot tritium. The hnear structures, ' T — ' H — R ' , of the transition states have also been rejected. An attempt has been made to rationalize the experimental findings by

844


invoking the participation in equations 110-113 of 'pseudo-complexes' containing five hydrogen substituents near the central C atom, including the energetic tritium atom, which participate actively in the motion along the reaction coordinate. The electron densities between the C a t o m and the five substituents in these complexes are different from that in the normal C — H bonds in methane. A suggestion has been m a d e that the reaction is concerted, involving simultaneous formation of the C — T bond and cleavage of the C — H or C — D bond, but 3-centred calculations are inadequate for the description of these processes. M o r e elaborate calculations taking into account all five hydrogen substituents should explain the d a t a and establish the correct structure of the transient c o m p l e x ^ T h e a u t h o r s ^ r e j e c t the idea that the displacement is a fast direct, localized event occurring on a time scale comparable to a b o n d vibration (ca 10~ s) and express the view that the five-bonded carbon system exists for several C — H vibrations 3 - 7 X 10~^'^s) and substantial distribution, albeit not fuh internal equhibration, of the energy occurs during its life-time. The lack of a large intramolecular deuterium isotope effect in the reaction of hot tritium with partially deuteriated methanes has been explained by Rowland and coworkers^ by postulating the existence of a very large secondary deuterium isotope effect which counterbalances the normal primary replacement isotope effect. Assuming the intermediacy of Tive-bonded carbon pseudo-complexes' the small but preferred formation of H T over that of D T is understood if we accept that the hydrogen abstraction by tritium atoms proceeds through a bent triangular transition state which gives low values for the kinetic isotope effects (equations 114 and 115). F o r m a t i o n of H T H

D

HT -H CD2H (114) and D T by a free radical mechanism with a linear symmetrical transition state, [ T - - - H ( D ) - R ] ^ , would be accompanied by a larger deuterium kinetic isotope effect. The normal deuterium isotope efi'ect observed in equations 110 and 111 might be caused by large zero-point energy contributions of the C — H / C — D bonds weakened substantiahy or broken in the transition state (with retention of configuration) of reaction paths shown in equations 116 and 117, and by some contribution to the total yield of H2 or D2 H

T +

H •

^CC^

TD

+

CHgD

(115)

T

+

TCH,

CH4 H''

D T

+

CD4

D'

•X

.^CH++H2

CH3+

.CH2'^+H

CH2^ H~ CH4

> (^2^4.^ H~ H2

CH2+ + CH4

> C2H3+ + H + H2

(125)

C2H5 + + e — > C2H4 + H

(126a)

The low yield of CH^Hg in methane indicates that the hydride ion transfer (reaction 126b) C^n^ + + CH4

> CH3H3 + CH3 +

(126b)

occurring in the mass spectrometer is slow in comparison with reaction 126c: C^n^^ + CH4

> C2H5 + + H2

(126c)

The primary fragmentation pattern from the decay of tritium in tritiated methane, CH3^H (equation 127), proceeding in the mass spectrometer at low pressure consists of the following charged fragments^^^: (2.40% abundance), H 2 ^ (0.14%), {(^He''), H 3 ^ } (0.12%), '^C^ (4.9%), + , (^'C+)} (4%), C H 2 ^ (4.90%), CH3+ (82.00+ 1.5%). CH33H — ^ [CHTHe^] — >

[CH3 + 3He]

>

CH3+ + ^He

(127)

Mass spectrometric a n d theoretical^^ evidence shows that about 80% of the original ions have little or n o excitation energy and produce stable methyl ions after the loss of ^He. The remaining 20% are in highly excited states (to about 20 eV) a n d undergo further fragmentation producing the secondary ions listed above. In the presence of excess of propane the fragmentation of C H 3 ^ H e ^ at 760 torr is simhar to the fragmentation observed at low pressure in the mass spectrometer. The methyl ions undergo a hydride ion t r a n s f e r ^ ( e q u a t i o n 128) C^H^ + + C3H8

> CH3H3 + C3H7 +

(128)

or react w h h methane yielding ethyl ions (equations 129a a n d 129b). CÛ^^ + CH4 C2H5 ^ + C3H8

> € 2 ^ 5 ^ + H2 CÛe + C 3 H /

(129a) (129b)

In the system [CH4(14%) + C3H8(84%) + 02(2%)], CH3H3 a n d C2H6 are produced in 74% a n d 7.0%, respectively. In the system containing CH4(95%), C3H8(3%) a n d 02(2%), the C^H4 jS-decay produces H2 with 34% yield and ethane with a 49.0% yield through reactions (129a) a n d (129b). T h e low yield of CH^H3 indicates that reaction (128) is not significant a n d ethane is produced according to equation (129b). b. Gas-phase reactions of tritiated methyl cations. Gas-phase reactions of methyl cations (generated in the j5-decay of tritiated hydrocarbons) with molecules of water, alcohols ( M e O H , E t O H ) , hydrogen halides, ethyl halides, benzene, toluene, xylenes, ethylene a n d (ethylene + H2O) have been investigated by Nefedov a n d c o w o r k e r s ^ ~ Oxocations such as those at the t o p of page 848 are formed in the reactions of free carbocations with water a n d alcohols. F u r t h e r transformations of these cations occur with departure of or H"^. Departure of R^ a n d radioactive methanol formation is the preferable


848

Et

Me

C3H3—CH2CH2

> E t ^ + C3H3X

C2H^

C3H3(CH2)3CH2^,etc.

(130) (131)

Non-volatile tritium-labelled c o m p o u n d s have been produced, but the degree of polymerization has been found to be not very high since the intermediate carbocations participate also in other reactions which lead to shortening of the chain length (equation 132). Reaction 132c seems to be the most probable. N o simple saturated aliphatic hydrocarbon has been formed in the system ' ^ C ^ H 3 ' — ' C H 2 = C H 2 ' . In a mixture consisting of "^C^H3, C H 2 — C H 2 and H2O no n-alcohols containing more t h a n two carbon atoms have been detected. This means that the isomerization of the carbocations formed is a faster process than their reactions with water or with ethylene. The reaction H CH2=CH2 (a)

H

H

1 11

1. 11

H

H

RH (b)

^

X~ (c)

^

R

* R

H

I I C = C — H

+

CH,CH

CH2CH3 -I- R+

RCHgCHgX

R denotes the radical containing C^H3 group

(132)

18. Syntheses a n d uses of isotopically labehed alkanes a n d cycloalkanes

849

scheme in equation 133 cannot explain the observed formation of tritiated ethanol. Equation 134 has been suggested as the probable route for the observed C ^ H 3 C H 2 0 H formation. C2H4

C 3, H "7 ""OH

"OH

C^HjOH

CH2=CH2

+

C „5 H "11

"^C^Hj

C2H4

etc.

(133)

HO"

C3H7OH

C^H3CH2CH2"^

CfH3

H2O

;CH-

C^HjCHgOH

+

"^CHj

(134)

H

CH,

In the reaction of free ^ C ^ H 3 cations with a gaseous ethylene-water (1:1) mixture, the relative yields of the tritiated products were as follows: M e O H — 8 2 . 5 ± 8.0%, E t O H — 4 . 1 ± 0 . 8 % , i - C g H ^ O H — 4 . 1 % , t m - C s H i i O H — 3 . 4 ± 0 . 3 % , I-C5H11OH—3.4%, a n d two u n k n o w n products in 3.4 + 0.8% a n d 2.5% yields. I n the reaction of •^C^H3 with 5:1 gaseous mixture of ethylene a n d water, the corresponding relative yields have been found to be 18.9%, 21.2%, 5.7%, 23.6%, 18.5%, 2.5% a n d 9.6%. 2. Reactions

promoted

by the decay

of tritium

atoms

contained

In

ethane

[l,2-^H2]Ethane, obtained by reacting ethylene with ^H2 gas over a chromium catalyst at —7 °c^^^'^^^, has been ahowed to decay either as above or in the presence of 0.5% O2, at atmospheric pressure. T h e labelled ethyl ions formed in a b o u t 80% of the ^-transitions undergo a hydride ion transfer reaction (equation 135) with inactive ethane molecules. C2H4T^ +C2H6

>C2H5T + C2H5^

(135)

The other identified labelled products (produced with the following radiochemical yields: ^H^H—11.6%, methane—3.0%, ethylene—5.5%, p r o p a n e — 1 . 6 % , n-butane—2.7%) originate from fragmentation processes that take place in a b o u t 20% of the decay events and from the reactions of the fragment ions. ^H^H is produced in reactions 136. M e t h a n e and ethylene are formed in reactions 137 a n d also in equations 138 a n d 139. + 'exc.

>C2H2+ + 3 H e + H2 + H

• Q H - " + ^He + 2 H 2 •

(136)

+^He + 2H2 + H

• C7H4. +

C T H C ^

(137) CH.+C,H (138) •CH.+C,H +

(139)

850


The suggestion has been made^^^ that tritiated butane, C4H9T, is formed in ethane (2.7% yield) and in propane ( 1 % yield) by reactions of tritiated fragment ions that give rise to C3 and C4 species. But it is also possible^ ^ ^ that in the presence of a third body ethyl ions could react with ethane at high pressure t o produce C4 ions competitively with t h e reaction shown in equation 135. Quite satisfactory agreement between the experimental and theoretical yields, expected from ion-molecule reactions, has been obtained assuming a lack of large isotope effects in the fragmentation of the primary decay species. Wexler and Hess^^^ have determined mass-spectrometrically the decay-induced fragmentation pattern of a series of tritiated organic molecules including C2H5T. 3. Chemical

consequences

of P-decay

in [1,2-^H2l

propane

The use of multi-labelled alkanes has been extended for reactions of the carbocations produced in the decay of propane-1,2-^H2 both in gaseous and in liquid phase^^"^. Lowpressure, decay-induced fragmentation of p r o p a n e - a n d propane-2-^H h a s been investigated by Wexler, Anderson and S i n g e r ^ b y mass spectrometry, and the yields of C3H7^ ions in the two reactions have been found to be 56% and 4 1 % . In contrast, much higher yields (72-83%) of initial fragments were found in the decay of CH33H, C2H53H, CgHs^H and four monotritiated toluenes. The CjÛ^^ ions undergo fache decomposition into € 3 1 1 5 ^ ions and H2 with an activation energy of 4-10 kcal mol for primary and 3 0 - 4 0 kcal mol for secondary propyl ions. P r o p a n e - 1 , 2 - 2 h a s been obtained by reacting propylene (0.033 mmol) with tritium gas (4Ci) over a chromium oxide-gel catalyst at - 1 2 ° C for 36 h (equation 140).

CH3CH=CH2

CH3CHT—CH2T

(140)

The crude labelled propane has been purified by preparative gas c h r o m a t o g r a p h y and diluted with inactive propane to the desired specific activity {ca I m C i m m o l " ^ ) . Preliminary investigations have shown that the contribution of self-radiolytic processes caused by ^-particles produced in the decay of C3H5^H2 during storage (R.T., 1 atm., 4 weeks) of samples having a specific activity less than 0.5mCimmor^ is negligible. The decomposition has also been studied in pure liquid propane and also in the presence of 2% O2, at — 130°C during 4 weeks. In gaseous p r o p a n e the total tritium activity found in products other than p r o p a n e was only 34.9%. It was assumed that the decay-induced fragmentation processes d o n o t depend o n the pressure (as with m e t h a n e - ^ H 4 a n d ethane-^H2), and that the fraction of C j H g ^ H ^ ions escaping dissociation is higher at 7 6 0 t o r r than at low pressure (lO^^torr) and the dissociation process (equation 141) is C3H,3H^=C3H3^+H2 C3H43H+ + C3H8

> C3H53H + C3H7+

(141) (142)

largely prevented at 1 atm. by cohisional deactivation processes. The yield of propene formed in the hydride ion-transfer process (equation 142) is only one-third of the value expected from low-pressure fragmentation of an equimolecular mixture of propane-1-^H and propane-2-^H following j5-decay^^^. The formation of tritiated products, such as ^H^H, Me^H, Et^H, C2H33H, C2H3H, C3H52H, C3H33H, besides CÛ.Û, suggest that only 7 0 - 8 0 % of organic ions are produced by the nuclear j5-decay in states of low excitation energy and are stabhized in collisions at 760 torr. The remaining 2 0 - 3 0 % of the j5-transitions produces organic ions in higher excited states (up to 20 eV) which fragment into smaher ions and yield finahy tritiated products other than C3H7^H. I n the liquid phase (at — 130 °C) the tritiated propylene is the major product observed, while the yield of


851

other tritiated products is sharply reduced. This suggests that the shorter time required for cohision in the hquid phase tends to stabilize ah the daughter CjHs^H"^ ions formed in lower excitation states, including part of those with higher energies which are dissociating in the gas phase at 1 atm. These stabilized ions react with CjHg (equation 143) yielding tritiated propane.

The highly energetic

CsH^'H^ + C3H8 CgH^^H^ dissociates

.C3H73H + C 3 H /

(143)

according to equation 144: > C3H5+ + H2

C3H6'H+

(144)

The C3H4^H^ ions reacting with inactive p r o p a n e give tritiated propylene, C3H5^H, through a hydride ion transfer process (equation 145): C3H43H+ + C3H8

>

CaHs^H + C 3 H /

(145)

The yields of tritiated methane, acetylene and ethylene in liquid p r o p a n e are much lower than in the gas phase. 4. Chemical

consequences

of P-decay

in

[1,2-^H2lcyclopentane

[l,2-^H2]Cyclopentane, obtained by reacting cyclopentene with over a C r 2 0 3 catalyst at — 10°C during 24 h, has been ahowed to decay during two m o n t h s in pure cyclopentane at 700 torr or in cyclopentane with 2% O2 at pressures ranging from 10 to 700 t o r r O v e r 90% of the jS-transitions yield monotritiated cyclopentane (46) as the CH2

CH^H

CH2

^CH^H

CH^He

CH2

p-decay

fast 100%

CH2 .

^CH^'H

CH2-

I CH2 CH2

^ C H 2

( 4 7 )

+ -CH

+

1

'He

3 (146)

^CH^H

major labelled product (equations 146 and 147). The CsHg^H^ daughter ions 47, formed in the ground state or with an excitation energy insufficient to cause further dissociation, abstract a hydride ion from inactive cyclopentane yielding 46 (equation 147) which could not be detected by r a d i o - G L C , since the available columns did not allow the separation of the undecayed cyclo-C5H8^H2 from the minor ( < 1%) cyclo-CsHg^H component. CH24 7

+

C-C5H10

I

-CH2

I ,

CH2

+

C - C 5S "H9

(147)

^CH^H CH2 ( 4 6 )

A smah fraction of the ions receive in the jS-transition sufficient excitation energy to cause isomerization and fragmentation of the parent molecule to tritiated C 1 - C 5 hydrocarbons. The yields in the case of cyclopentane at 700 torr have been: M e T — 1 . 6 % , E t ^ H 3 — 0 . 4 % , C 2 ' H 3 H — a b o u t 0.1%, n - P r ^ H — 0 . 5 % , n-Bu^H—0.7%, [ ^ H J p e n t - l - e n e — 3 . 5 % , com bined yields of the tritiated products—6.7%. Equation 148 is the likely route to the major linear by-product 48. F o r m a t i o n of tritiated p r o p a n e and acetylene requires the rupture of two C—C bonds in cyclopentyl ions with considerable excitation energy.

852

Mieczys/aw Zielihski and M a r i a n n a K a h s k a CH2-T

CH

H2C —

CH

+

CH^H

.CH^H

H2C^

CH2

CH

CHc

CH2=CH

CH'H

CH2CH3

+ c-CgHg"*"

(148)

(48)

D. Chemical Effects of ^^-Decay of ^"^C Studied by Double Isotopic Labelling 1. P-Decay

of etfiane

doubly

labelled

with ^"^C

The fate of the nitrogen-14 resuhing from the ^-decay of carbon-14 in labehed ethane molecules has been investigated. Doubly labelled ethane, ^'^CH3^'^CH3, was obtained according to equation 149 and was used to observe the rate of formation of singly labelled ^^CH3NH2'3'.

Ba^^C03

H2SO4

HoO

• Ba,C

Pd

(149)

T o the gaseous ^"^€211^, a known a m o u n t of CH3NH2 carrier was added, and t h e ^'^CH3NH2 diluted with ^^CH3NH2 was purified by reacting it with phenyl isothiocyanate (equation 150), followed by repeated crystallization of the ^'^C-methyl phenyl thiourea, 49, up to constant specific activity. Precise specific activity determinations of 49 revealed that the fraction of the labelled ethane molecules which do not dissociate during the ^"^C > ^"^N decay, but become methyl amine molecules, equals 47% in agreement with theoretical e x p e c t a t i o n s T h e maximum energy of j5-particles emitted by ^"^C is relatively low, namely 0.154 MeV; the maximum recoil energy of the daughter ^"^N is also low, 7.0 eV. 59% of this recoil energy (4.1 eV) will go into internal motions of the ^^CH3^'^NH3+ molecule. A recoh energy of 3.56eV is required t o supply a n energy in vibration and rotation equal t o the C — N bond energy of 2.1 eV^^"^ (this energy can be provided in the emission of j5-particles of 80 keV energy). However, the j8-emitting isotopes have an average energy <j5"> per disintegration of ^"^C which equals 49.5keV only^^. Thus, in about 80% of the decay events the jS-particles have less energy than required to cause c a r b o n - n i t r o g e n bond rupture. Probably, electronic excitation of the M e N H 3 ^ cation directly, or in the course of its transformation to M e N H 2 , results in additional ruptures of C — N bonds since the observed bond dissociation versus non-dissociation ratio reaches about the 1:1 level.

(150) P h — N = C = S + ^^CH3NH2

> PhNHC—NH—i^CH3 m.p. 115°C (49)

E. Reactions of ^^C Hot Atoms

The reactions of ^"^C a n d ^^C recoil atoms with simple aliphatic a n d alicychc hydrocarbons investigated in gaseous and hquid phase have been reviewed by Stock-


853

A c e t y l e n e - ^ h a s been the most a b u n d a n t product^^^ when the ^^C(7,n)^^C nuclear reaction took place in benzene, n-hexane, 2-methylpentane or 2,2-dimethylbutane targets. E t h y l e n e - ^ a n d e t h a n e - ^ b e c a m e increasingly important when branching in the target molecules increased. The hot reaction products are the result of insertion of ^ atoms a n d the moieties ^^CH a n d ^^CH2 into C — H bonds fohowed by bond ruptures in the resulting intermediates. Decrease of the fragmentation products a n d increase of stabhization products has been found in the condensed phase. T h e energetic radicals d o not distinguish between various C — H compounds. The recoh chemistry of carbon-11 in liquid C5-C7 hydrocarbons has been investigated by Clark ^"^^ The recoh atoms have been produced in the ^^(y,n)^ ^C reaction. The study of the product yields of ethane, ethylene and acetylene (as well as of methane) from different target molecules has been the main concern in this work. Iodine affected the yields of all the volatile products except acetylene. Acetylene-^^C, the principal products in all the hydrocarbons investigated, is produced in hot reactions with naked ^^C atoms. Insertion of recoil fragments into C — H a n d C = C bonds leads t o various ^^C-labehed hydrocarbons.

l^j^89,i39

IV. ISOTOPIC HYDROCARBONS IN BIOLOGICAL AND NATURAL SYSTEMS

The study of the mechanism of the oxidation and assimilation of fso-parahins and paraffins by microorganisms is needed for the solution of two practical problems: protein synthesis by microorganisms utilizing the by-products of the petroleum industry as a source of carbon a n d of energy ^'^^"^'^'^ a n d decontamination of the marine environment from oh p o h u t i o n T h e elucidation of the role and fate of hydrocarbons in living organisms has also been a general concern of biologically oriented chemists. These researches are described in the following sections. B. Hydrocarbon Oxidations by Bacterial Enzyme Systems 1. Octane[1-'"^C1 oxidation

by Pseudomonad

bacterium

strain

A cell-free, soluble enzyme preparation of a P s e u d o m o n a d bacterium strain, isolated from soil^"^^^, has been found to oxidize octane t o n-octanol a n d octanoic acid. Pyridine nucleotide, oxygen a n d F e ^ ^ ions are involved in this bioconversion. T h e reaction has been studied at 28 °C with a system consisting of buffer, octane[l-'^C] (specific activity 5 X lO'^cpm/imol"^) dissolved in E t O H or acetone, enzyme a n d suitable cofactors. T h e reaction could be stopped by the addition of dhute H2SO4. Suitable work-up of the system yielded unreacted ^"^C-octane, ^"^C-octanol a n d ^"^C-octanoate, respectively. T h e sum of the radioactivity found in octanol a n d octanoate served as a measure of the hydrocarbonoxidizing activity of the enzyme system since the intermediates (hydroperoxide, octanal) do n o t accumulate. A linear relationship has been found between the a m o u n t of enzyme employed a n d the [l-^'^C]octanol a n d [l-^'^C]octanoate produced. T h e products have also been linearly dependent on time. T h e oxidase system could be separated into t w o distinct enzyme fractions. O n e of them is stabilized by ascorbate, the second requires Fe ^ ^ or Fe ^ ^ ions for activity. T h e oxidation is the result of a direct attack by an (activated oxygen) a n d its mechanism in the investigated cell-free enzyme preparations is in accord with the one found in intact bacteria. D P N H (or D P N ) and Fe + ^ (or Fe ^ ^) ions participate in the initial oxidative attack at the methyl group (rather than at a methylene group) of paraffins having seven or more carbon atoms a n d produce primary alcohols with the same carbon skeleton. A suggestion has been made ^'^'^^"^ that flavoproteins participate in enzymatic reactions involving pyridine nucleotides a n d oxygen.

854

Mieczys/aw Zielinski a n d M a r i a n n a K a n s k a

2. Microsomal

hydroxylation

of

[l-'^'^'C]decane

The mechanism of oxidation of decane has been s t u d i e d ^ u s i n g [l-^'^C]decane. The oxidation of decane t o decanol, decanoic acid and decamethylene glycol by mouse hver microsomes required N A D P H and O2. This indicates that the process is initiated by the hydroxylation of decane to decanol. The Michaelis constant for this reaction was found t o be 0.5 m M and the optimum p H was about 8.1. The reaction has been strongly inhibited by C O a n d t-butyl isocyanide. Evidence has been presented indicating that the enzymic systems for decane hydroxylation a n d for decanoate co-oxidation are n o t identical. Organometallic oxidation catalysts have been reviewed by Speier^'^^''B. Metabolism of Isotopically Labelled Paraffins 1. Metabolism

of deuteriated

n-hexadecane

n-Hexadecane containing a n excess of deuterium, fed to rats for a period of 9 days, has been found to be absorbed from the gastrointestinal tract and partially deposited in t h e lipid t i s s u e T h e absorbed deuteriated hexadecane has been oxidized to fatty acid in the body, largely in the hver. 7.8.9.10-Tetradeuterio hexadecane used in this bioexperiment has been prepared by Kolbe electrolysis of potassium a,j?-dideuterio pelargonate CH3{CH2)5(CHD)2COOK, which in turn has been obtained by addition of deuterium t o the double bond of nonen-2-oic, C H 3 ( C H 2 ) 5 C H = C H C O O H , while the latter has been prepared by a malonic acid s y n t h e s i s ^ N o deuterium exchange of a-hydrogens of the acid a n d the hydrogen of the solvent has been noticed in the conditions of the Kolbe synthesis. 2. Oxidation

of

[l-^^C]n-hexadecane

a. T h e oxidation of [l-^'^Cjn-hexadecane t o palmitic acid, C15H31 ^"^COOH, by subcellular fractions of the intestinal mucosa of guinea pig has been investigated by Mitcheh a n d Hubscher^^^'^^^^. N o n h n e a r kinetics have been observed. M a x i m u m formation of palmitic acid occurred when both nucleotides involved in the oxidation and hydroxylation, i.e. N A D and N A D ? + glucose-6-phosphate, were added to the incubation system. A 42% reduction in the a m o u n t of palmitic acid formed has been found when the air phase was replaced by carbon monoxide. Only labehed n-hexadecanol h a d been isolated a m o n g the possible lobelled products. A search for other labelled fatty acids has been unsuccessful. Paraffins are minor components of the dietary lipids and are absorbed from the smah intestine. The presence of an enzyme system transforming alkanes t o fatty acids prevents the harmful accumulation of paraffins in the body. It has been suggested ^^^^"^ that this oxidation proceeds according to two simultaneously operating mechanisms. In the one, the alkane is first hydroxylated and then dehydrogenated to aldehyde a n d in turn oxidized to the acid. In the second mechanism, n-l-alkene is the primary product which is subsequently hydrated a n d dehydrogenated t o aldehyde (and acid). However, the identification of the second intermediate, n-hexadecene, has been tentative because of analytical difficulties encoun tered in the course of separation of n-hexadecane and n-hexadecene. The problem of the correct mechanisms of oxidation in biosystems can be solved by studying t h e kinetic deuterium isotope effects in the oxidation of [ I - D 3 ] - and [l,2-D5]-n-hexadecanes as weh as ^"^C kinetic isotope effects in the oxidation of [l-^'^C] a n d [2-^^C]-n-hexadecanes t o corresponding palmitic acids. b. l-^'^C hexadecane and l-^'^C octadecane are converted directly to the corresponding fatty acids of the same chain length in the rumen of goat, rat and chicken as well as in liver homogenates from goat and rat^^^. Ichinara, Kusunose and Kusunose^^^ have found that


855

the microsomal fraction of mouse liver contains an enzyme system requiring N A D P H and oxygen which hydroxylates long-chain aliphatic h y d r o c a r b o n s ^ T h e same authors^ investigated also the oxidation of n-hexadecane by a mouse liver misrosomal fraction^ Radioactive scan of a thin-layer chromatogram of the oxidation products of l-^'^C hexadecane showed a main peak corresponding to the [l-^'^C] substrate and two additional peaks corresponding to ^"^C-palmitic acid and to ^"^C-cetyl (n-hexadecyl) alcohol, the products of hydroxylation, obtained in 1 0 - 4 5 % yield. C a r b o n monoxide strongly inhibited this reaction, suggesting the involvement of cytochrome P-450^^^. Bergstrom and c o h a b o r a t o r s ^ h a v e found that administration of 2,2-dimethyl[l^^C]stearic acid, CH3(CH2)i5C(Me)2 ^^COOH, to the rat led to excretion of 90% of the administered label in the urine as 2,2-dimethyl[l-^'^C]adipic acid, HOOi^C(CH2)3C(Me)2^'^COOH. This has been used as evidence for the co-oxidation mechanism. W e e n y a d m i n i s t e r e d to rats a 2% solution of [l-^'^C]n-hexadecane in olive oh and found that, after 15 h, 2 0 - 3 0 % of the radioactivity appeared in the lymph lipids as fatty acid. It has been concluded that the oxidation of the alkane occurred in the epithelial cells of the intestinal mucosa. 3. The metabolism

of

octadecane

n-Alkanes have been identified in bovine and h u m a n cardiac muscle and in animal brain^^^'^^^ The metabolism of [l-^'^C]octadecane in rats has been studied by Popovic^^^. A paraffin emulsion containing 10-20//Ci (specific activity 21 mCi m m o l " ^) of [l-^'^Cln-octadecane has been administered to rats both orahy and intravenously. The presence of the ^"^002 in the air expired showed that the rats are able to absorb and metabolise n-octadecane. The radioactivity has been present in all tissues investigated (hver, spleen, heart, kidney, lung, brain). Most of the ^"^C activity has been found in the liver. After intravenous administration of [1-^^C]-n-octadecane, the spleen was found to contain extremely high radioactivity. Liver lipid analysis showed that noctadecane incorporates into fatty acids. 4. The metabolism

of

[8-'"^C]n-heptadecane

The metabolism of [8-^'^C]n-heptadecane, widespread in the marine food chain and one of the components of n-paraffins used for the growing of yeast, has been studied in rats by Tulliez and Bories^^^. About 65% of the ^"^C-labelled heptadecane has been used by the rats as an energy source and completely metabolized to ^"'€02. There was n o hydrocarbon in the urine. The radioactivity in the faeces has been entirely contained in heptadecane. About 7% of the absorbed ^'''C-heptadecane has been stored while the rest has been cooxidized to ^"^C-heptadecanoic acid, which underwent in turn the normal fatty acid degradation pathway and contributed to the synthesis of lipids and non-lipids. The heptadecanoic and heptadecenoic acids are the most strongly labelled acids. The presence of C(i3) and C(i5) fatty acids indicates that the heptadecanoic acid undergoes also the usual jS-oxidation. The presence of ^"^C-labehed squalene, C30H50, and cholesterol (which needed ^'^C-acetate and ^^C-acetyl Co A for their synthesis) indicate that (8^'^C)heptadecanoic acid had been thoroughly metabolized. The even distribution of radioactivity in the fatty acids of the phospholipids implies that heptadecane did not interfere with the biochemical mechanisms of these functional lipids. 5. Metabolism of 2-[^'^C-methyl]n-hexadecane by yeast 0. guilliermondii

and

[l-^'^CJoctadecane

The utilization of 2-methylhexadecane-methyl-^'^C (50) and octadecane[l-^'^C] (51) in various combinations by the yeast Candida guilliermondii has been investigated by

Mieczys/aw Zielinski a n d M a r i a n n a K a n s k a

856

Davidov a n d coworkers

T h e kinetics a n d the rate of yeast assimilation of

C H a C H C ^ ^ C H a ) — ( C H 2 ) i 3 C H 3 (50) a n d

C H 3 ( C H 2 ) i 6 ' ^ C H 3 (51) dissolved in v a r i o u s

combinations in the inert component pristane, 2,6,10,14-tetramethylpentadecane (52), and containing C. guilliermondii, h a s been studied 52 does n o t undergo degradation but enlarges the volume of the hydrocarbon phase t o 1 2 - 1 3 % of the total volume a n d creates conditions imitating the process of cultivation of yeast o n petroleum. ^"^C from 50 has been transformed into ^"^€02 indicating complete degradation of 50 by C. guilliermondii. T h e rate of oxidation of the branched 50 was 5 - 6 times lower than that of the n-alkane 51. 5.5% of the carbon of the biomass originates from carbons of 50, which incorporates mainly into lipidic fractions(triglycerides, diglycerides, phospholipids and free fatty acids) a n d water-soluble products. Cell lipids incorporate only 15-methylhexadecanoic acid formed as a result of oxidation at the unbranched end of the aliphatic chain. It has been noted that signihcant quantities of the ^"^C-label of 50 accumulate in the amines a n d non-proteinogenic amino acids which are released in appreciable a m o u n t s from the cell into the extracellular culture liquid. 8 5 % of the radioactive label of the cellular organic acids a n d the culture liquid has been found in isovaleric acid. Equation 151 has been proposed for the metabolic pathway of 50 in C. guilliermondii.

MeCH(CH2)i3Me

•

MeCH(CH2)i3CH20H

cell lipids

14J

CH3 (50)

MeCH(CH2)i3C00H

metabolites

14

hydrocarbon phase

CH^

of

(151) MeCH(CH2)i3C00H

minor direction

main direction

CH3CHCH2COOH

^4H3

'HOOCCHCCH2COOH

i——; CO2

components of

HOOCCHCH2CCH2COOH

biomass

1

14

HOOCCHCH2CCH2CH2COOH 14

CH,

water soluble metabolites (amines,amino acids)

18. Syntheses a n d uses of isotopicahy labelled alkanes a n d cycloalkanes

857

6. Hydrocarbons, fatty acids and drug liydroxylation catalysed by liver microsomal enzyme systems

Liver microsomes in the presence of N A D P H a n d molecular oxygen catalyse the hydroxylation of various lipid-soluble drugs (equation 152). A hypothesis h a s been R H + N A D P H + H + + O2

> ROH + NADP+ + HÔ

(152)

proposed that these microsomal hydroxylations proceed by way of a c o m m o n enzyme system which involves the N A D P H - c y t o c h r o m e c reductase a n d the cytochrome P-450. This hypothesis h a s been tested ^^"^ by studying the oxidation of [^"^C]testosterone, heptane a n d ca-oxidation of lauric acid, Me(CH2)ioCOOH, in rat liver microsomes. Both laurate a n d heptane stimulated t h e rate of N A D P H oxidation catalysed by liver microsomes isolated from rats. Heptyl alcohol from heptane a n d 12-hydroxylauric acid from lauric acid have been isolated a n d identified besides various hydroxylation products of testosterone (2j8-hydroxy-, 6a-hydroxy-, 7a-hydroxy- a n d 16a-hydroxytestosterone). The inhibition in the presence of C O has been of about 30% (carbon monoxide interacts with cytochrome P-450 forming an enzymatically inactive complex); 10-40% inhibition has been observed when pure nitrogen h a s been used as the gas phase, a n d 4 0 % C O in the gas phase caused a complete inhibition of the stimulation of the rate of N A D P H oxidation by ah four substrates tested (aminopyrine, testosterone, heptane a n d laurate). However, in the absence of any added substrate only one-third of the overah N A D P H disappearance catalysed by the microsomes was cancehed when 40% C O was added t o the gas phase. This indicates that cytochrome P-450 is involved only in part of the reactions in which N A D P H participates. Obviously further experimental work is needed to elucidate this microsomal hydroxylating enzyme system. A mechanism for the hydroxylation of alkanes and fatty acids a n d also for that of the demethylation of various drugs (equation 153) by the liver microsomal cytochrome P-450 system (Scheme 1), has R2NCH3 + N A D P H + H + + O2 — > R 2 N H + CH2O + N A D P + + H2O (153) been proposed as a working hypothesis by C o o n a n d c o w o r k e r s ^ s h o w i n g the possible role of the superoxide radical ion ( 0 2 " ^ 0 4 ^ " ) . It is possible that cytochrome P-450 generates the intermediate 'superoxide' in the presence of molecular oxygen. In the final step, e, the attack of superoxide on the substrate, accompanied by the uptake of a second electron, yields the hydroxylated substrate a n d water (equation 154).

P-450(Fe'+) RH

(O2)

(RH)P-450(Fe''^)

(RH)P—450(Fe''^)

4

V

(02)(RH)P-450(Fe^'^)

(Phosphatidylcholine)

(RH)P-!^50(Fe^"^)

O2

SCHEME 1

858

Mieczys/aw Zielihski a n d M a r i a n n a K a h s k a RH +

202 ~

+ 2H+

> R O H + H2O + O2

(154)

Oxo-bridged binuclear iron centres in oxygen transport, oxygen reduction a n d oxygenation have been studied a n d reviewed by Sanders-Loer a n d coworkers Oxidations a n d reductions in general, including reported reductions a n d oxidations of biological interest, have been reviewed critically by Fleet

C. Isotopic Environmental Bio-geological Studies

T h e recent general availability of precise M c K i n n e y - N i e r - t y p e isotopic ratio mass spectrometers allows one to measure^^^"^^^'^^^^'^'^^^'^^^'' the natural variations in stable isotope concentrations of organic a n d inorganic matter, including hydrocarbons. T h e results are expressed as stable hydrogen (^D) a n d carbon (S^^C) isotope ratios, where S is defined by W=[(«_p,e/R..3„aaJ-l]xlOOO

{R is D / H o r ^^C/^^C, a n d t h e standards are Vienna Standard M e a n Ocean Water^"^^ a n d Peedee Belemnite^'^^ respectively, for SD a n d ^^^C). These data have been reviewed recently^'^^'^'^'^ by T a n for inorganic carbon isotopes dissolved in marine a n d estuarine (Saguenay Fjord a n d St. Lawrence Estuary) environments and by Anati and Gat^^^^ and Pierre^^^^ for restricted marine basins and marginal sea environments. Sackett^^^ wrote a special chapter on stable c a r b o n isotope studies of organic matter in the marine environment and found that stable carbon isotope composition may serve as a good indicator for organic pollutions in marine sediments and as a technique for marine pollution studies in g e n e r a l T h e stable hydrogen a n d carbon isotope composition of sedimentary methane stirred from the Florida Everglades has also been investigated^"^^'^"^^ b u t the mean values ^ ^ ^ C = - 6 1 . 7 % o (standard deviation 3.6%o, n = 51) did n o t differ significantly from the average ^^^C of all natural sources, which is — 58.3%o. T h e mean of Everglades sedimentary methane (^D = — 293%o, standard deviation 14%o, n = 50) has been found t o be slightly enriched in deuterium in comparison with = — 360 ± 30%o corresponding t o m e t h a n e from ah sources. This difference has been explained as the result of partial bacterial oxidation of methane flux evolving from sediments through the marine water t o t h e atmosphere. The ratio of the rate constants (/CHAD) for t h e reactions of CH4 a n d C H 3 D with O H radicals h a s been estimated^^^ t o be 1.5 at 416 K in pulse radiolysis of water vapours. M e a n sedimentary methane values m a y serve as a rough estimate of the average of methane emitted t o t h e atmosphere from the Everglades system. The isotope composition of gases taken from hermetically sealed holes drilled in rocks of the ijolite-urtit complex^ of the Khibiny Massif (Kola Penisula), consisting of C2H6, C3H8, isobutene, butane, isopentane, pentane, C^H^^, H2, O2, N2, Ar, He, C O a n d CO2, is characterized by the ratios ^^C/^^C equal t o 1.1160%-1.11482% in ijolites a n d 1.1160%-1.11482% in urtites (^^C/^'C ^ 0.0112). Bitumens h a d a^^C/^^C percentage ratio equal t o 1.0905%. C a r b o n of hydrocarbon gases from gas a n d oh is, as a rule, lighter than carbon of petroleum. However, the carbon of hydrocarbon gases from rocks of the Khibiny Massif is heavier t h a n carbon from bitumens from the same massif. This implies that hydrocarbon gases have been formed there at higher temperatures t h a n the bitumens (in hne with the hypothesis that bitumens in the Khibiny Massif have inorganic origin). The experimentahy determined ^^^C differences between CH4 a n d C2H6 a n d CH4 and C3H6 of natural gases have been found t o be most important for t h e prospecting for petroleum^^^. The ^^^C values of CH4 vary with the origin and depth of hs location and with the CO2 content. Mass spectrometric determinations of the ^^C/^^C ratios in individual hydrocarbons separated from Italian natural gases by gas c h r o m a t o g r a p h y

18. Syntheses a n d uses of isotopically labelled alkanes a n d cycloalkanes

859

and oxidized t o C O 2 led Tongiorgi a n d his c o w o r k e r s ^ t o the conclusion that whhe the two-fold bacterial a n d chemical mechanism of CH4 origin cannot be discarded, isotopic fractionation taking place in the course of migration of these gases is predominant and responsible for the observed variations in the ^^C/^^C ratios. T h e structure a n d ^^C contents of individual alkanes in b a t guano found in the Carlsbad region, N e w Mexico ^^"^ have been found t o be related t o the photosynthetic pathways of local plants and the feeding habits of insects, which constitute a major percentage of the bat's diet. Two isotopicahy distinct groups of branched alkanes, derived from two chemotaxonomically distinct insect populations having different feeding habits, have been identified (one population of insects feeds o n crops a n d the other o n native vegetation).

V. CHEMICAL STUDIES WITH LABELLED HYDROCARBONS A. Isotopic Tracer Studies with Alkanes and Cycloalkanes 1. ^^C study

of the dehydrogenation

of butane/butene

mixtures

Dehydrogenation of hydrocarbons is a most important industrial process. Rubber production from inorganic matter is one of the related examples t o which the isotopic kinetic method^^^'^^^^ has been applied^^^. ^"^C-labehed butane a n d butene used in this s t u d y h a v e been obtained according to equation 155. Various labelled 1:1 mixtures of Ba-C03

-CO,

14CH3OH

CAHSBR

'^CHJMGL

-CH3I

^

NI, H-,

> -CH3CH2CH=CH2

^

'^CHJCCH^JJCHJ

(155) butane and butene have been used in this investigation. Specific activities of butane, butene and butadiene a n d also of carbon dioxide have been determined in the post-reaction mixture at different 'times of contact' with the chromia catalyst at 635 °C ('contact time' is defined as the reciprocal of the rate of passing the reactant mixture over the catalyst). In the experiments with ^"^C-butene a n d unlabelled butane the specific activities of butene a n d butadiene have been practically the same. However, using ^"^C-butane with unlabelled butene, the specific activity of butadiene has been found to be smaller than that of butene. This fits equation 156, where coj, CO2 a n d co^ are reaction velocities, a, P a n d 7 are specific

C4H10

C4He

(156) C4H6 activities of butane, butene and butadiene, respectively, and where CO2 « C O 3 . This means that butadiene is produced by dehydrogenation of butene, a n d practically n o direct transformation of butane into butadiene takes place. c o 2 - ^ 3 = 1:25 when chromia oxides on alumina are used as catalyst, and (D^:(02 = 20:1. The rates of transfer of the ^^C label from butane to butene a n d from butene t o butane have been found to be simhar (equation 157),

860


CH3CH2CH2CH3 + i ^ C H 3 C H 2 C H = C H 2 = C H 2

>

CH3CH2CH=CH2 + '^CH3CH2CH2CH3 ^'^CH3CH2CH2CH3 + C H 3 C H 2 C H = C H 2

CH3CH2CH2CH3 +

(157)

>

'^CH3CH2CH=CH2+ ~fCH3CH2CH2CH=^^CH2 (157a)

as the rate constants for both the direct and reverse direction have been found to be nearly equal (neghgible ^"^C isotope effect). M o r e t h a n 90% of the butadiene is produced t h r o u g h butene. Simultaneously with the dehydrogenation of butene, dehydrogenation of b u t a n e and hydrogenation of butene also take place. 2. ^"^C- and ^H-tracer

studies

of tine mechanistri

of dehydrocyclization

of

paraffins

This problem has been extensively reviewed In this section we summarize the results obtained by K a z a n s k h and c o w o r k e r s ^ " and by Paal and Tetenyi^^^" The problem of intermediates formed over oxide catalysts has been studied by using ^""Clabelled c o m p o u n d s T h e mechanism of Cg-dehydrocyclization has been inves tigated using n-hexane mixed with various a m o u n t s of ^"^C-labelled cyclohexane. N o decrease in the specific activity of cyclohexane has been observed, meaning that the latter is not an intermediate in the process. n-Hexane is transformed into benzene by-passing the stage of cyclohexane formation^^^. W h e n a mixture of hexane and hexene-l-Cl-^'^C] was used, the radioactivity of hexene decreased in the course of the r e a c t i o n ^ a n d labelled hexadienes were also found, showing that the formation of benzene proceeds via hexene-1. Simharly it has been shown that hexadiene-[^''"C] does not cyclo-isomerize to cyclohexene, since cyclohexene acquires n o radioactivity when a mixture of hexadiene-^'^C a n d cyclohexane is subjected to aromatization. Using a mixture of hexadienes-[^"^C] with hexatriene, the ^"^C label has been found both in the cyclohexadienes and in benzene, leading to the conclusion that benzene formation p r o c e e d s ^ a c c o r d i n g to equation 158: paraffin

> olefins

> dienes

> trienes

> cyclodienes

> benzene

(158)

Thus dehydrocyclization of hexane and of other n-paraffins over oxide catalysts occurs t h r o u g h dehydrogenation steps u p to formation of a triene, which first yields a cyclodiene and then undergoes dehydrogenation to aromatics. C h r o m i a on alumina, m o l y b d e n u m and vanadium oxides on alumina act according to the above catalytic pathway. Paal a n d Tetenyi^^^"^^^ have investigated the dehydrocyclization of hydrocarbons over metallic Ni, P t a n d over mixed N i / A l 2 0 3 and P t / A l 2 0 3 catalysts. The ^"^C-labelled hydrocarbons have been obtained^^^'^^^ according to equation 159: ^"^€©2

CH3(CH2)4MgBr

LiAlH4

> CH3(CH2)4'^COOH

A l 2 O 3 , 3 7 0 ° C , under N 2

- — >

CH3(CH2)4'^CH20H

H2/Ni

> CH3(CH2)3CH=^^CH2

CH3(CH2)4^"CH3 lo5

(159)

C

(53)

specific activity 0.56 m C i g~ ^ The reaction sequence hexane > hexenes > hexadienes > benzene has been verified using the radioactive tracer technique. A mixture of radioactive n-hexane-[l-^'^C] and inactive hexene-1 has been subjected to dehydrocyclization in the presence of P t and N i catalysts used either as free metals or on alumina carriers. In each experiment the increase in the specific activity of the hexene and hexadiene fraction has been observed. These unsaturated hydrocarbons are therefore intermediates in the dehydrocyclization


861

of hexane. The above conclusion has been subsequently corroborated by studying the dehydrocyclization of a mixture of radioactive n-hexene-l-[l-^''^C] and inactive cyclo hexane N o sign of transfer of the radioactivity between hexene and cyclohexane has been found. N o detectable transfer of radioactivity from n-hexane or from n-hexene to cyclohexane has been observed in conversions of various mixtures of open-chain and cyclic hydrocarbons, where one of the compounds has been radioactive. The dehydro genation of cyclohexane and of n-hexane have been found to be parallel reactions^ converging only in some of the final reaction steps (equation 160). n-hexane

> n-hexenes — > n-hexadienes

> (n-hexatriene)-^ benzene

cyclohexane

> cyclohexene — > cyclohexadiene --^"'^^

(160)

Ring closure probably occurs through cyclohexadiene but the elucidation of the exact mechanism of ring closure needs further isotope studies. The initial steps, that is the dissociative adsorption in the dehydrogenation of cyclohexane and in the D / H exchange reactions taking place between cyclohexane and deuterium on metal surfaces, are s i m i l a r ^ C y c l o h e x a n e , cyclohexene and benzene have been found to contain tritium activity when a catalyst covered with tritium has been used in the dehydrocyclization experiments. N o hexane — > cyclohexane reaction occurs. H / D exchange data between gaseous and solid states have been used^^^ to explain the mechanism of the catalytic action of hydrides of transition metals of group IV-VI(Ti, Zr, Hf, V and Cr) in the conversion of hydrocarbons and to formulate equation 161 hlustrating

11

-C—C—H

r1 1 r>

f

+

C

H

H- - M-

-C

-H

nH J

I ;—

H ••••H--M

-

C

nH

'\-/^

H / •

X

'

C

+

H

1 M ••••H

(161)

(/7-2)H

M-H

(/7-1)H

{/7-2)H _

the hydrocarbon interaction with the active site of the catalyst. Hydrogen loss from the hydride crystal lattice takes place during the hydrogenation-dehydrogenation process. The distance between metal atoms in hydrides is longer than in hydrogen-free metals and the latter do not accelerate the reaction. The effective length of the M — H b o n d varies with temperature. The hydrogen a t o m b o u n d to the reactive site ( M — H ) differs from the 'free hydrogen atom'. Whilst discussing the mechanisms of catalytic hydrogenation and hydrogenolysis of methylbenzenes on platinum at 65-110 °C, it was pointed out^^^ that the methyl groups exchange hydrogen to deuterium easier than the ring hydrogens. 3. Catalytic

reactions

of propene[1-''^Cl

on a Y-type decationized

molecular

sieve

The mechanism of heterogeneous reactions of propylene on Y-type decationized molecular sieve catalysts at about or below 200 °C yielding saturated hydrocarbons such as propane, 2-methylpropane (isobutane), 2-methylbutane and 2-methylpentane has been s t u d i e d ^ u s i n g propene-[l-^'^C]. The specific activity of p r o p a n e has been found to be the same as the initial radioactivity of propene. The specific activity of 2-methylpentane

862


has been twice as high as the initial specific activity of propene. The specific activities of isobutane and of isopentane relative to that of propene have been 1.1 a n d 1.6, respectively. These d a t a indicate that p r o p a n e is not a decomposition product of 2-methylpentyl cations but is produced by hydrogenation of the isopropyl cations formed on Bronstedtype acidic sites of the catalyst (equation 1 6 2 ) , probably by intermolecular hydride ion abstraction. The yield of p r o p a n e increased in the presence of c o m p o u n d s rich in weakly b o u n d hydrogen such as tetrahn, etc., and also when the catalyst surface has been covered with 'carbonaceous deposits' from which atomic hydrogen could be split off according to a radical process. 2 - M e t h y l p e n t a n e is formed from isopropyl cations with adsorbed propene molecules (equation 1 6 3 ) followed by intermolecular hydrogen transfer. CH3CH=i^CH2 + { H + Y - }

>i-C,H,^Y-

(162)

{ / - C 3 H / Y - } +(C3Hacis. — > { * Q H , 3 ^ Y - }

(163)

* denotes a ^"^C label The 2-methylpentyl cations undergo isomerization, c a r b o n - c a r b o n b o n d cleavage a n d intramolecular hydrogen transfer leading to isobutane and isopentane (equations 1 6 4 ) . N o methane or ethane has been found in the reaction products, neither have any hydrocarbons containing m o r e t h a n six carbon atoms been isolated. CH3CCH2CH2CH3

C H 3 C H C H 3 + (C2H3 + )

I

I

CH3

CH3

specific activity ^ 2

relative specific activity

CH3CHCHCH2CH3

1.1

(164)

C H 3 C H C 2 H 5 + (CH + )

I

CH3

CH3 specific activity ^ 2 relative

relative specific activity ^ 1.6

The specific radioactivity of the carbonaceous deposits has not been determined. The intramolecular distribution of the ^"^C label in isobutane and in isopentanes has not been studied.

4. ^^C tracer

study

of the degradation

of 3-methylpentane

on a super-acid

catalyst

D o u b l y ^^C-labelled hexane^^^, [ 1 , 5 - ^ ^ 0 2 ] 3 - m e t h y l p e n t a n e , i^CH3CH2CH(Me)CH2^'CH3(54) containing 7 8 % dhabelled in positions 1 and 5 , 2 1 % monolabelled in position 1 a n d 1 % of unlabehed molecules has been used to study the mechanism of degradation of branched hexanes^^^ over a catalyst consisting of antimony pentafluoride inserted into graphite ('Cg^sSbFs'), at 0 ° C . The distribution of the ^^C label in the 3-methylpentane samples and in the paraffins of lower a n d higher molecular weight has been determined mass spectrometricahy. The isotopic distribution in the parent ion has been unaffected but the isomerization to yield M e C H ( M e ) C H 2 C H 2 M e , M e C H 2 C H ( M e ) C H 2 M e and M e 2 C H C H M e 2 is a fast intramolecular process leading to isotopic equilibration of ah six c a r b o n atoms. The isotopic distribution of the initiahy produced p r o p a n e agrees with the hypothesis that it is produced via direct j?-scission of the carbenium ion shown in equation 1 6 5 followed by intermolecular hydride transfer. However, at the end of the run, p r o p a n e is obtained involving a polymerization mechanism. Isobutane and isopentane are also produced by a d e p o l y m e r i z a t i o n polymerization process. N o primary ^^C-isotope effect has been noted in the fragment-


863

ation of ^^C-labelled branched hexanes at 0 ° C . Ah studies of the conversion of ^Re labelled 54 over S b F 5 graphite have been rationalized by the scheme in equation 166.

> CH2=CHCH3 + CH3CH2CH3 (165)

CH3CH(CH3)CH2CHCH3 CH3CH2C(CH3)CH2CH3

(55)

^

(CH3)2C

^

CH(CH3)2

(56)

• (CH3)2CHCH2CH3

(CH3)2CCH2CH2CH3 (57)

(CH3)2CHCH2CHCH3

CH2 = CHCH3 + CH3CHCH3

(166)

• CH3CH2CH3

olefin 55,56, 57

CH2Me2,CHMe3, alkylation,

MegCHCHgMe

propagation

p-scission

oligomer

branched tertiary

rearranged

hexanes and heptanes

oligomer Rearrangement

aging

5. Use of perdeuteriopropene of olefins on iron catalysts

to study ttie isomerization

and

excinange

The use of perdeuteriopropene, C3D6 (containing 5.3% of C3D5H), permitted study^^^ of the isomerization and exchange processes in olefins without interference from H / D exchange reactions. In all cases adsorbed deuterium atoms produced either by adsorption of D2 or by dissociative adsorption of perdeuterioolefins on the catalyst have been found to be the reacting species. The same technique has also been applied to study at — 37 °C the exchange and isomerization of ethylene, propene, butenes, pentenes and 2-methylbutenes on iron films prepared by evaporation under high vacuum of a pure iron wire. Large differences have been observed between H / D exchange rates of a- and jS-olefins. In the weakly adsorbed a-olefins the vinylic hydrogen atoms are eashy exchanged. Thus in ethylene all four hydrogen atoms underwent fache H / D exchange; in 1-pentene and propene a definite break between d3 and d4 in deuterium distribution patterns has been found. (5.7% of D3 molecules but only 0.75% of D4 molecules of 1-pentene, CH3CH2CH2CH=CH2, have been detected after 6 min of H / D exchange of this olefin in the presence of C3D6 on an iron film at — 37 °C; in the case of H / D exchange with C2H4


864

the corresponding numbers for D3 a n d D4 molecules are 34.0% a n d 59.2% after 15 min exchange). The H / D exchange of j8-olefins is extremely slow. Various mechanisms of double-bond migration, taking place on iron films at — 37 °C in the presence of C3D6, in a- and j5-olefins have been studied a n d interpreted.* a-Olefins yield poorly exchanged cis a n d trans isomers, e.g. large a m o u n t s of do cis- and trans-butenes. jS-Olefins yield highly deuteriated a-olefins with maxima in their deuterium paterns. Thus, pronounced maxima at dg a n d were found in 1-butenes a n d 1-pentenes obtained from ci5-butene a n d cis-pentene, respectively. These, as weh as the m a x i m u m at d4 in 3-methyl-1-butene obtained from 2methyl-2-butene, indicate that the dissociative adsorption of the olefin at a vinylic carbon, accompanied by a complete H / D exchange of all adjacent allyhc hydrogen atoms followed by intramolecular rearrangement, is the primary act of the j?-a isomerization (equation 167). The electron attractive character of the metal ' M ' in the c a r b o n - m e t a l b o n d CH,

.c=c:\

CH,

H

CH3

CH3

>4

CH3

CH3

CX3

^ C = C ^ ^

X = isotopic

CH3

M

CH,

^CX2

hydrogen, D or T

M

(58)

2-methyl-2-butene -(H-)

CH,

+(D-)

^CH2

(167) CH3

M

CH,

M

CH,

CX2

CH,

CH3

M

CH3

/

X

CX2

\

X

3-methyl-1-butene

in structure 58 loosens the adjacent allylic C — H bonds a n d ahows multiple H / D exchange, hydrogen migration and 'intramolecular rearrangement'. The formation of d^ molecules from cis-butene and cis-pentene proceeds by addition of a deuterium a t o m t o the double bond, fohowed by free rotation a r o u n d the C ( 2 ) — C ( 3 ) b o n d and dehydrogen ation t o the adsorbed trans olefin. The presence of do isomers implies the possibility of a direct cis-trans process without formation or breaking of any C — H bond. The authors^^^ observed a deuterium kinetic isotope effect of 2.3 for the double-bond migration.

6. Catalytic

tiydropolymerization

of ethylene

in the presence

of ^"^CO

A detailed review (containing 163 references) of catalytic reactions leading t o the synthesis of hydrocarbons and alcohols from ^"^CO and hydrogen has been presented by *a- and j?-olefins are adsorbed with different strength on t w o different adsorption sites o n the surface. Intramolecular hydrogen shifts are responsible for isomerizations and exchanges.

18. S y n t h e s e s a n d u s e s o f i s o t o p i c a l l y l a b e l l e d a l k a n e s a n d c y c l o a l k a n e s

865

Eidus^^^, a n d a l s o b y D e b r e n c e v a n d Isagulyanz^^^. T h e h y d r o p o l y m e r i z a t i o n o f ethylene^^^'^^^ t a k i n g p l a c e at 190 ° C i n t h e p r e s e n c e o f C o o n a l u m i n a c a t a l y s t is i n i t i a t e d b y c a r b o n m o n o x i d e , a n d several m o l e c u l e s o f e t h y l e n e are p o l y m e r i z e d b y o n e m o l e c u l e of c a r b o n m o n o x i d e . C o n d i t i o n s h a v e a l s o b e e n found^^^ i n w h i c h t h e c a r b o n m o n o x i d e initiating t h e p o l y m e r i z a t i o n p r o c e s s is n o t e x h a u s t e d . C a r b o n m o n o x i d e h a s b e e n c o n s u m e d m a i n l y ( u p t o 38%) w h e n freshly r e d u c e d C o c a t a l y s t w a s u s e d a n d a slight e x c e s s o f e t h y l e n e o v e r H2 a p p l i e d . H o w e v e r , 3 - 4 . 5 % o f t h e C O r e a c t e d o n l y w h e n t h e m i x t u r e c o n t a i n e d a large e x c e s s o f C2H4 o v e r H2 a n d a c a t a l y s t w h i c h p a r t i c i p a t e d i n p r e v i o u s r e a c t i o n s w a s used. T h e specific r a d i o a c t i v i t y o f t h e c a r b o n m o n o x i d e d o e s n o t c h a n g e in t h e c o u r s e o f t h e p o l y m e r i z a t i o n , m e a n i n g t h a t it is n o t f o r m e d f r o m e t h y l e n e . T h e h y d r o p o l y m e r i z a t i o n d o e s n o t p r o c e e d in t h e a b s e n c e o f C O , a n d t h u s o b v i o u s l y t h e latter initiates t h e p o l y m e r i z a t i o n p r o c e s s . T h e o b s e r v e d i n c r e a s e i n t h e m o l a r specific r a d i o a c t i v i t y of t h e p r o d u c t h y d r o c a r b o n w i t h i n c r e a s e in its m o l e c u l a r w e i g h t ( e x c l u d i n g fraction C4) p o i n t s t o t h e larger p r o b a b h i t y o f i n c l u s i o n o f t h e ^"^C label f r o m c a r b o n m o n o x i d e i n t o larger h y d r o c a r b o n m o l e c u l e s . It h a s b e e n s u g g e s t e d t h a t C O a n d H2 f o r m a c o m p l e x o n t h e surface o f the c a t a l y s t w h i c h t h e n p l a y s t h e role o f a n a c t i v e centre i n t h e p o l y m e r i z a t i o n . I n t h e c o u r s e o f d e s o r p t i o n o f the c o m p l e x its d e s t r u c t i o n t a k e s p l a c e a n d the ^"^C is i n c o r p o r a t e d i n t o t h e r e a c t i o n p r o d u c t . T h e largest r a d i o a c t i v i t y h a s b e e n f o u n d in a-olefins a n d t h e c o r r e s p o n d i n g s a t u r a t e d h y d r o c a r b o n s . j5-01efins h a d s m a l l e r m o l a r r a d i o a c t i v i t y a n d h a v e b e e n o b t a i n e d preferentially i n t h e cis form. T h e f o l l o w i n g p r o d u c t s c o n t a i n e d t h e ^"^C l a b e l : b u t a n e , b u t e n e - 1 , cis-butene-2, n - p e n t a n e , p e n t e n e - 1 , cr*s-pentene-2, isoprene, n-hexane a n d hexene-1.

7. Steam reformitig

of metliane

and H-D

exchange

T h e m e c h a n i s m o f s t e a m r e f o r m i n g o f m e t h a n e o v e r a n i c k e l c a t a l y s t ( e q u a t i o n 168) o r o v e r different nickel a l u m i n a c a t a l y s t s h a s b e e n i n v e s t i g a t e d at 873 K^^^ T h e rate o f r e a c t i o n o n a c o m m e r c i a l c o - p r e c i p i t a t e d c a t a l y s t 'A' ( p o o r l y crystallized y - A l 2 0 3 c o n t a i n i n g 7 5 % N i ) is g i v e n b y e q u a t i o n 169:

CH4 + H2O — . C O + 3H2 -dPc^Jdt

= kPhl-Pu.'o'

(168) (169)

w h e r e k is i n d e p e n d e n t of proportional to Pco'^'^'Pcoi^^W h e n D2O w a s s u b s t i t u t e d for H2O n o d e u t e r i u m w a s f o u n d i n t h e u n r e a c t e d m e t h a n e a n a l y s e d m a s s s p e c t r o m e t r i c a l l y at 10% c o n v e r s i o n o f m e t h a n e t o c a r b o n m o n o x i d e . N o H - D e x c h a n g e w i t h h y d r o g e n s o f m e t h a n e h a s b e e n o b s e r v e d i n t h e CH4 -h H2O + D2 s y s t e m . I n t h e c a s e o f n i c k e l c a t a l y s t s u p p o r t e d o n y - a l u m i n a ' F ' c o n t a i n i n g 7.0% N i ) t h e k i n e t i c d e p e n d e n c e s ( l o g rate versus l o g Pcn^ a n d l o g PH2O) are different. S o m e i n c o r p o r a t i o n o f d e u t e r i u m i n t o m e t h a n e w a s f o u n d w h e n t h e CH4 + D2O r e a c t i o n w a s carried o u t at 10 torr o f CH4. T h e rate o f t h e r e a c t i o n Wfor l o w m e t h a n e pressures (at c o n s t a n t h y d r o g e n pressure) h a s b e e n f o u n d t o b e W-Pcn/Pl^,l

(170)

A s u g g e s t i o n h a s b e e n m a d e t h a t t h e r a t e - d e t e r m i n i n g s t e p s in t h e s t e a m r e f o r m i n g o f m e t h a n e carried o u t o v e r t w o different c a t a l y s t s are n o t t h e s a m e . T h e a b s e n c e o f H - D e x c h a n g e in m e t h a n e w h e n c a t a l y s t 'A' w a s u s e d i m p l i e s t h a t s t e p 1 is irreversible a n d rated e t e r m i n i n g (see t h e s c h e m e in e q u a t i o n 171). W a t e r is m o r e strongly a d s o r b e d a n d hinders t h e a d s o r p t i o n of m e t h a n e since a d s o r p t i o n of CH4 a n d H2O o c c u r s at t h e s a m e sites. T h e a d s o r p t i o n of m e t h a n e o n a w a t e r - c o v e r e d nickel surface is rate d e t e r m i n i n g . (This c o n c l u s i o n w a s t e s t e d b y s t u d y i n g c a r b o n a n d

866

Mieczys/aw Zielinski a n d M a r i a n n a K a n s k a CH4(gas)

HgCgos)

HgOCgas)

CO(gas)

slow

(171) OH

oxygenated species

////////////////III

I I I I I I I I I I II

hydrogen kinetic isotope effects after a n exchange study between methane a n d trhiated water^^^). The deuterium exchange observed with the lower-nickel-content catalyst ' F ' indicates that in the scheme in equation 172 step 1 is reversible a n d reaction 4 of the methyl groups with hydroxyl groups is rate-determining. T h e rate is proportional to the surface concentrations of ^CH^ a n d ^QHCH4(gas)

(172)

1 CH3

CH3

+ H

oxygenated

CH3

OH

+ OH

Ni

TTTTT

I 111AI2O3 III L

"

' ' '

species

I IIIIIIIIII I I III I

The view has been expressed that the oxygenated species are n o t produced on the nickel crystallites or o n their edges b u t o n nickel sites situated in the close vicinity of alumina sites, produced when nickel aluminate is reduced with hydrogen (equation 173): N i A l 2 0 4 + H2

> N i + AI2O3

(173)

(Methyl groups are adsorbed o n nickel a n d O H groups o n alumina.) 8. Shock-tube

study

of the high-temperature

pyrolysis

of deuteriated

ethylenes

The kinetics of the pyrolytic decompositions of variously deuterium-substituted ethylenes (C2H4, C2H4 + C2D4,trans-l,2-C2H2D2 a n d C2H2 + D2 in argon) have been studied at 1100-1800 K by carrying out single-pulse shock-tube experiments^ Isotopic acetylenes (C2H2/C2HD/C2D2) a n d hydrogens (H2/HD/D2) are the main decomposition products of ethylene. T h e isotopic ethylenes (C2H4/C2H3D/C2H2D2/C2HD3/C2D4) are produced by free-radical rather than molecular mechanisms. According to earlier kinetic investigations^ free-radical chains should predominate at lower temperatures while the elimination of molecular hydrogen should predominate at higher temperatures. Isotope exchange reactions in these systems are considerably faster than either ethylene decomposition or acetylene hydrogenation. T h e rate constant for the reaction step producing C2H3D a n d C2HD3 from C2H4 a n d C2D4 has been found t o be 3.4 x 10"^ exp [ —32000/i^T] s " ^ Temperature dependences of the first-order ethylene pyrolysis rate constants, calculated from the Arrhenius-type equation, \ogk = A -\- B/T, applied t o kinetic data from experiments conducted at 1200-1800 K, are characterized by much higher activation energies (about 46.4-51.7 kcal m o l " ^), while the constants A are in the range 8.95-9.50 (k=l.05 x iQ^Q-^ssoo/RT^-1 o.05mol% C2H4 + 0.05mol% C2D4 mixture at 3 a t m total reaction pressure, including argon as inert gas at 1100-1500 K).


867

Statistical factors corresponding to ethylene isotope exchange reactions (equations 174 and 175) have been discussed also^^^. C 2 H 4

+

C 2 D 4

C 2 H 3 D

9. Radiation

decompositions

+

—

^

C 2 H 3 D

C 2 H D 3

of deuteriated

+

C 2 H D 3

(174)

> 2 C 2 H 2 D 2

(175)

alkanes

a. Gas-phase pulse radiolysis of methane in the presence of perdeuteriated isobutane. Perdeuteriated isobutane, i-CJ^ô, has been used^^^ to study the mechanism of homogeneous neutralization of unreactive hydrocarbon ions produced in pulse radiolysis under high radiation dose rates. Pulse radiolysis has several advantages over conventional low-dose experiments because the charged species has a much shorter lifetime T with respect to neutralization (equation 176), T = (a/)-i/2

(176)

where a is the charge recombination rate coefficient and / is the number of ions formed per unit volume per second, so that the reaction of the ions with impurities or products (both being ion scavengers) is less probable than in low dose rate experiments. Primary ^ 3 " ^ and C H 4 ^ ions produced in the pulse radiolysis of methane react at every collision to form C 2 H 5 ^ and C H 5 ions^^^ (equations 177), which do not react with methane but are intercepted by the reactive i-CJ^^Q via the deuteride transfer reactions 178 to yield stable deuteriated hydrocarbons C 2 H 5 D , C D 3 H and C 3 D 8 . C H 3

+

C H 4 +

C 2 H 5 +

Cn,^

C

3

D

/

+

C D 4

> C 2 H 5 +

+

C H 4

> C H 5 +

+ i-C4Dio

— ^

+

H2

-h

C 2 H 5 D

(177)

-^3

+

C

4

D

/

+ i-CJ)io

> C4DioH-^ + C H 4

C 4 D 1 0 H +

^CsD/

+ i-C4Dio

>

C 3 D 8

(178)

- h C D 3 H

+

CJ),^

Assuming that C 2 H 5 " ^ , CH^^ and C 3 D 7 ^ are neutralized by S F g " with the same rate constant /c = 0.4 x 1 0 ~ ^ c m R m o l ~ ^ s " ^ the experimental yields of C 2 H 5 D and C 3 D 8 in the presence of S F 5 in 300 torr of methane under pulse radiolysis conditions have been successfully reproduced by calculation. b. Isotopic hydrogen evolution from deuteriated saturated hydrocarbons. The mechanism of hydrogen evolution from saturated paraffinic hydrocarbons has been investigated^ ^ by measuring the concentrations of D2, H D and H2 evolved in the radiolysis of mixtures of deuteriated and protiated n-heptane and methylcyclohexane, as a function of the temperature between — 70 and -\- 90 °C. The results have been explained by assuming that, in the course of irradiation of protiated and deuteriated hydrocarbons, three different excited or charged intermediates are formed (equations 179) leading to hydrogen production along three different reaction paths, where R H is the protiated c o m p o u n d with a mole fraction of 1-x and R D is the deuteriated analogue with a mole fraction of (x), R H and R D are excited or charged intermediate species of unspecified nature, RH^ and RD^ produce hydrogen molecules in an intramolecular unimolecular process, whhst RH^ and b participate in a bimolecular reaction (equations 180) which shows no deuterium isotope effect.

868

Mieczys/aw Zielinski a n d M a r i a n n a K a h s k a RH

>RH^ + RHb + R H „

cone. ( 1 - x ) ;

x=0

> G(H2)o

RD

>RD, + RDb + R D „

cone, (x);

x= 1

> G(D2)i

(179) * R D b — > D ' + products, * RHb

^ H ' + product,

D '+ R H

> H D + products

D' + R D

>T>2 + products

(180) H '+ R H

> Uy + products

H +R D

> H D + products

N o information or suggestion concerning the specific nature of R H b or the n a t u r e of the intermediate denoted by H ' has been given^^"^. The third process is also bimolecular, and involves H atoms which abstract hydrogen in reactions 181 accompanied by a kinetic isotope effect (/CH > /CD)RHc

> H + products

RDc

> D + products

H + RH

> H2 + products, /CHH,

H +RD

> H D + products, /CHD,

D +RH

> H D - f products, /CDH

D +RD

> D2 + products,

^HH>^HD

(181)

^DD < ^DH

icoo,

The authors^ pointed o u t that the mutual energy or charge transfer in mixtures of protiated a n d deuteriated species must be investigated before a valid interpretation of isotope effects in radiation chemical processes can be given.

B. Hydrogen Exchange Studies of Saturated Hydrocarbons and Related Problems 1. H-D exchange

studies

with alkanes

in the presence

of transition

metal

complexes

H - D exchange in hydrocarbons such as methane, ethane, etc., with D2O using platinum complexes as the catalysts, has been studied and reviewed by Shhov, Shteinman and their coworkers^ It had been expected that H 3 C o ( P P h 3 ) 3 , which decomposes reversibly with H2 formation, should catalyse the deuterium exchange reaction between D2 a n d R H according t o the scheme in equation 182. However, prolonged contact of CH4 and D2 in benzene solution of H 3 C o ( P P h 3 ) 3 at r o o m temperature resulted in 2% exchange only after 6 days^^^. Deuterium exchange between m e t h a n e or ethane in D 2 O - C H 3 C O O D solution in t h e presence of K2PtCl4 has been found subsequently t o proceed at a m u c h faster rate^^^. Heating in sealed ampoules of various paraffins at 100-150 °C with solutions of chlorides of Pt(II) or Pt(IV) in heavy w a t e r - A c O D (1:1) solutions acidified with H C l (30%) led to extensive deuteriation of these hydrocarbons. F o r instance, after 6 hours at 150 °C, C2H5D in 28.5% yield h a d been obtained. T h e Pt^ which precipitates during decompo sition of the Pt(II) complex does not catalyse the exchange of hydrogens of CH4 and C2H6 with D"^ of the solution. Oxygen does n o t affect the rate of deuterium exchange, b u t its presence hinders the precipitation of metallic platinum. Pt(IV) c o m p o u n d s , N a 2 [ P t C l 6 ] and H 2 [ P t C l 6 ] , also catalyse the deuterium exchange b u t the kinetic curve for ethane is sigmoid a n d a n induction period is observed. Thus, the rate of deuterium exchange corresponds to the rate of Pt(IV) > Pt(II) transformation, whhe Pt(IV) itself does n o t


869

catalyse the exchange process. Complexes of Pt(0) are also inactive and even at 100 °C no deuterium exchange occurs in the presence of P t ( P P h 3 ) 3 or PtCO(HCl)2 after 10 hours^^^. MD3 — ± M D +

D2

D MD + RH.

M—R

DR + M H

(182)

H The rate of deuterium exchange in ethane in the presence of K2[PtCl4] has been found to be proportional to the first power of C2H6, 0.62 order w h h respect to the catalyst concentration and independent of the ionic strength. Polydeuterio ethanes have been found besides E t D in the initial stages of the reactions^^^. This indicates that more than 1 D atom is transferred to ethane in the elementary act of exchange. Equation 183 has been suggested to explain the formation of m o n o - and polydeuterioethanes.

PtClp

+

CpH, 2"6

CIgPtCgHg"

PtCU

(183) 2-

CIpPt-

-CHp

Cl2PtC2H4D"

C2H4D2

II CH2_

The isotope effect /CCH4ACD4 = 3.0 ± 0.5 observed in CD4-H2O and CH4-D2O exchange experiments indicates that the C — H bond rupture is rate-determining. The rates of hydrogen exchange in CH4, C2H6 and A c O H are found to be in the ratio 1:5:0.5. This indicates that electrophilic attack of the platinum c o m p o u n d at electrons of the C — H bond is the most effective one. The activation energy of deuterium exchange in ethane deduced from the data in the 8 0 - 1 0 0 ° C interval equals 1 8 . 6 k c a l m o r ^ The rate of deuterium exchange is 30 times faster in D 2 0 / A c O D ( l : l ) than in D2O only. The above data indicate that the hydrocarbons are activated by entering into the coordination sphere of the central metal atom and that the metal catalyst should have electron-accepting properties (equation 184). [ P t ( I I ) ] - h R H — Pt(IV):

^R ^H

(184)

Pt(IV) and Pt(0) do not catalyse the deuterium exchange owing to saturation of the coordination sphere and to weakening of the electron-accepting properties. The electron accepting properties and the catalytic activity in complexes K2[PtX4] diminish in the series X: Cl > Br > I and in the series PtCl2 > P t C l 3 " > P t C ^ ^ " of chloride complexes which are in equihbrium with K2[PtCl4] in solution. PtCl2 is the most active species in solution. In the presence of excess C l " ions the equhibrium (equation 185) shifts to left. P t C l 4 2 - ^ P t C l 3 " H-Cl" (185)

PtCl3-;=±PtCl2 + C l " Acetic acid plays the role of a weak chelating agent of

PtCl2 (59) and prevents the

Mieczys/aw Zielinski a n d M a r i a n n a

870

Kahska

f o r m a t i o n o f d i m e r s h a v i n g l o w c a t a l y t i c a c t i v h y ( e q u a t i o n 186).

187

have

been

proposed

as

the

route^^^

leading

to

E t D

T h e reactions in e q u a t i o n

formation

ACOD/D2O

in

solutions.

..•\ ClgPt.

^—CH3

(59) CI PtCh

.CI Pt

,Pt CI

(186)

+ 2L

CI

C2H5 :CH3

^ci

^0

C

,PtCl2

^

'

PtCl2

D

0

CH, (187)

CH3 C2H5D

The is

the

+

C

R—H

>tCl2"

ciaPt.

^ =

^c—CH3

b o n d r u p t u r e f o h o w e d b y the f o r m a t i o n

rate-determining

step

in

the

activation

of

o f the m e t a l - a l k y l b o n d

saturated

hydrocarbons

by

Pt—R metal

complexes. T h e e x c h a n g e rate decreases w i t h the increase o f b r a n c h i n g in the h y d r o c a r b o n m o l e c u l e s . T h e s c h e m e i n e q u a t i o n 188 chlorides

and

unsaturated

hlustrates the simultaneous f o r m a t i o n o f o r g a n i c

hydrocarbons

besides

the

deuteriation

of

saturated

h y d r o c a r b o n s (methane, ethane, p r o p a n e , n-butane, /-butane, n-hexane, c-hexane, toluene in

0.1-0.7 M

water

ampoules22i,222

solutions

of

HjPtClg,

containing

5%K2PtCl4

at

120 °C

in

sealed

RCH2CH3 -I- P t ( i i ) — C I

(188) RCH2CH2 — Pt(ii)—ci Pt(IV)

RCH2CH2CI

RCH=CH2

RCH2CH2D


871

Deuteriation of methane a n d simultaneous reaction of K 2 P t X 4 (X = Cl, Br, CN) with R H g B r ( R = M e , E t , B u ) carried o u t in D2O/ACOD (1:1), 0.02 M Pt(II), 0.02 M D C l at 100 °C is ihustrated^^^ in equation 189. T h e same distribution of deuteriated methanes CH4

^CHjD

:H3HgBr

CH2D2

^Pti-:^CH2

^

P f i ^ C H D

Pti:^CD2

(189)

obtained both in direct H / D exchange of CH4 catalysed by K 2 P t C l 4 a n d in the reaction of M e H g B r with K 2 P t C l 4 convincingly indicates the formation of P t — R c o m p o u n d s in the course of homogeneous activation of saturated hydrocarbons. Both exchanges proceed through the same intermediate c o m p o u n d RPt(II)X. All reactions of saturated hydrocarbons including H / D exchanges in solutions of transition metal complexes have been reviewed by Shilov a n d Shteinman's groups^'^: Earlier deuteriation studies including saturated hydrocarbons have been reviewed by Agova^^^. Systematic studies of isotopically labelled aliphatic a n d aromatic hydrocarbon ligand exchanges in different ^"^C-labehed organometallic complexes have been carried o u t by K o r s h u n o v , Batalov and their coworkers^^^"^^^. Deuteriation of hydrocarbons has also been investigated using a deuteriated phosphoric a c i d - b o r o n trifluoride complex^^^. M u c h information on radiation-induced methods of tritium labelling^ o n photochemical methods of labelling including ^"^C-diazomethane (equation 190)^^^ a n d o n catalytic exchange methods of hydrogen isotope labehing^ has been published recently.

CH2N2 CH3(CH2)3CH3 4-

CH2:

^^CH2N2

>

^^CH3(CH2)4CH3 + ^^CH3CH(CH3)(CH2)2Me + CH3CH2CH(^^CH3)CH2CH3

"to. c—C5H10

+

^^CH2N2

hu

CHp

- ^ ^ ^

2. Interaction

of isotopic

methanes

with

CHo

I CHp

(190)

(190a) C H2

dimethylcadmium

In the course of investigations o n the activation of isotopic methanes by organometallic compounds, the n o n - m o n o t o n i c deuterium isotope effect o n the inhibition of the free-radical auto-oxidation by dimethyl cadmium, (CH3)2Cd, in n-decane has been discovered^^^"^^^. T h e inhibitory power of the isotopic methanes increases in the order CD4 < CH4 < CH2D2 < C H 3 D < C D 3 H , where the inhibitory effect of C D 3 H is a b o u t an order of magnitude higher t h a n that of CH4. T h e induction time Zi^d- (in minutes) depends linearly o n the pressure of CH4 (or CD3H) (equations 191 a n d 192). Ti„d.

= 0.136

PcH4

+ 2 8 . 4 3 min

correl. coefficient 0.999

(191)

{Pen, interval 0 - 2 3 0 m m H g ) Ti„d.

= 0.809

PcDaH

+ 32.65 min

(^cD3H

correl. coefficient 0.974

interval 0 - 5 0 m m H g )

(192)

872


(experimental conditions: Co (of Me2Cd) = 3 x 10" ^ mol 1" \ t = 50 °C, over the reaction mixture)

= 260 m m H g

U n d e r simhar experimental conditions, b u t in the absence of oxygen, H / D exchange in the systems (CH3)2Cd-CD3H a n d (C2H5)2Cd-CD3H h a s been noted. These observations indicate that the interaction of methane with dialkylcadmium c o m p o u n d s (Et2Cd, Bu2Cd, etc.) a n d with intermediates takes place in the thermolysis a n d in auto-oxidations a n d that the o r g a n o c a d m i u m c o m p o u n d s activate methane selectively. Simhar conclusions were drawn from an earlier exchange study of methane a n d monodeuteriomethane with atomic d e u t e r i u m ^ ^ w h i c h showed that D / H exchange proceeds by hydrogen abstraction (D + CH4 = CH3 + H D ) followed by fast exchange of the methyl radical w h h D atoms prior t o stabihzation as methane, a n d that C — H b o n d rupture is 20% more probable in C H 3 D than in CH4. 3. Carbon

acid-D2 exchanges

over solid MgO

C H / D 2 exchanges in hydrocarbons over thermally activated M g O at 250-500 °C have been investigated ^39,240 enthalpies of activation AH ^ (given below in parentheses) deduced from experimental Arrhenius activation energies (equation 193) were AH"" = E^-mRT

(193)

(m = 2 for the bimolecular transhion state, R = 1 . 9 8 7 k c a l m o r \ 7 in K is the reaction temperature) determined for ethane (the 300-450 °C temperature interval was studied, AH * = 6.9 ± 0 . 1 kcal mol "^), p r o p a n e (350-450 °C, 17.1+0.3), cyclopropane (250-400 °C, 10.3 + 0.1), i-butane (350-500 °C, 16.2 + 0.3), cyclobutane (300-400 °C, 13.2 + 0.3), neopentane (CMe4, 250-420 °C, 16.3 ± 0 . 1 ) , cyclopentane (300-450 °C, 13.8 + 0.2) a n d cyclohexane (300-400 °C, 14.3 + 0.1). These values were found t o correlate linearly (equation 194) with gas-phase AH^

= 0.38A//° - 144.7

correl. coefhcient 0.9998

(194)

acidities (defined as standard enthalpies A//° for the reaction: R—H^g^-^R"^ + H^^^). A suggestion has been made that gas-phase acidities (Bronsted acidities m the absence of solvent)^'*^ for other carbon acids, AHJ can be estimated by carrying o u t C H / D 2 exchange over a solid base such as magnesium oxide a n d measuring accurately E^ a n d using equations 193 a n d 194. The /CH/^D ratio has been estimated t o be a b o u t 1.6. It h a s been assumed reasonably that D2 a n d H2 dissociate extremely rapidly, that diffusion of R H a n d D2 through the pores is also rapid a n d that the heterolytic dissociation of R H is the rate-determining step. Structure 60 has been proposed for the activated complex. The charge o n the carbanion R~ is locahzed o n the carbon orbital of the C — H bond. The c a r b o n - h y d r o g e n b o n d is elongated b u t the other internuclear distances and angles in the transition state remain unchanged. Besides the thermodynamic cycle the detailed reaction coordinate diagram for heterogeneous H / D exchange has been presented a n d its physical interpretation given. D+....R 2— I

2+ Mg

(60)

H"*" A2— O

denotes weak covalent bonding denotes ionic interaction


873

C. Isotope Effect Studies with Alkanes and Cycloalkanes 1. Hydrogen kinetic isotope related rearrangements

effects in cyclopropane-propene

and

Hydrogen a n d carbon isotope effects are the most sensitive means for studying the elementary acts in hydrocarbon reactions. Unfortunately, precise determinations of isotopic compositions deal mainly with hydrocarbons produced in natural conditions (Section IV.C). N o systematic isotope effect studies for light hydrocarbon production or decomposition were carried o u t in controlled laboratory conditions, except some deuterium isotope effect determinations carried o u t on rearrangements of cycloalkanes, reviewed in this section. a. Tritium isotope effect in the thermal isomerization of cyclopropane-t^. Cyclopropane, hrst synthesized by Freund^"^^ in 1882 (equation 195), has been the object of extensive isotope studies^"^^. It isomerizes thermahy t o propene in a homogeneous a n d unimolecular^"^ (equation 196).

BrCH2CH2CH2Br + 2Na = CH^—CH2 + 2 N a B r ^CH2 \ogk = 15.17 - (65000 ± 2000)/2.3RT

(196)

Chambers a n d Kistiakovsky^"^"^ suggested two possible reaction paths (equation 197) CHg- • • - CHs A.

HgC

CH2 CH2=CH

H2C

CH3

(197)

•CH2

\ AH CH^

leading to propene. In path A a trimethylene biradical is produced in the rate-determining step a n d rearranges t o propene. In path B, primary breaking of a C — H b o n d a n d hydrogen migration take place, leading t o unsaturation. Tritium, deuterium a n d ^^C kinetic isotope effects as well as labehing of the ring by methyl substituents have been used t o solve this reaction a n d other theoretical problems of unimolecular reactions^'^^"^^'^. Tritium isotope effects in the thermal isomerization of cyclopropane-ti, produced in reaction 198, have been examined by Weston^'^^'^'^'^ a n d Lindquist a n d

CH2=CH—CH2Br + H B r

BrCH2CH2CH2Br (198) >C3H6(77% yield, sp. act.

abs.EtOH,reflux

^

&v

/o J

'

r

3mCi m o P ^ ) /

Rollefson^^^ by comparing^^^^ the tritium specific activity of the unreacted labelled cyclopropane from the post-reaction mixture with the specific activity SQ of cyclopropane-ti used as the starting material or with the specific activity of propenes produced at a given fraction of completion ( / ) of the reaction (equation 199): £ = (1 - k^lk) = - log(V5o)/log(l - / )

(199)

where k a n d k* are the rate constants for the isomerization of normal a n d labelled cyclopropane.

874


The tritium isotope effect depends on temperature^"^^ (at a pressure of 2 0 0 m m H g ) in the temperature interval 447-555 °C according to equation 200: e = k/k* = 0.63 ± 0.02 exp((825 ± 60)/RT)

(200)

£ ( a t 4 5 0 ° C ) = 1.1187 or, according to equation 201, at the same pressure and in the temperature interval 4 0 6 - 4 9 2 X^^"^:

£ = /c//c* = 0.86 ± 0.06exp((385 ± 95)/RT)

(201a)

= 0.89 ± 0.06 exp ((332 ± 105)/i^r)

(201b)

£ ( a t 4 5 0 ° C ) = 1.1243 [Equations 200 and 201 have been obtained in different laboratories (see References 246 and 247). Equations 201a and 201b are two experimental dependences from the same laboratory.] The k/k* values are lowered as the pressure decreases and become equal to unity at about 1 m m Hg. The conversions of k/k* values to the kjkj isotope effects defined by equations 202 are of limited value in view of the lack of data concerning secondary tritium isotope effects in this system.

cyclo-CaHg

^CH3

CH—CH2

6/ci

cyclo-CgHsT i i ^ C H 2 T

CH—CH2

2^2

^!^CH2T

CH—CH2

^3

k/k*

^^CH3

CT—CH2

-5i^CH3

CH—CHT

(202)

/C4 2k,

= 6/ci/(2/c2 + /C3 + /C4 + 2/C5)

Assuming that /c^ = /c2 = /C4 = /cg, designating k^/k^, by k^/kj secondary tritium isotope effect, one obtains equation 203: / C / P = 6/[5 + ( / C T / U ]

or

kjkj

= -

and neglecting the

^

(203)

6-5£ By substituting the value e = 1.1243 (at 450 °C) into equation 203 one

obtains

/CHAT = 2.970.

Tritium specific activity determinations are usually carried out with larger uncertainties than mass spectrometric deuterium determinations. Calculations of k^/kj ratios with the use of equation 203 are therefore not very reliable. Nevertheless, the data obtained in the high-temperature region indicate clearly that the 'critical coordinate' for reaction 197 is the C — H rather than the C — C distance and support the Slater assumption^"^^^ based on theoretical considerations concerning unimolecular decomposition of cyclopropane. b. Deuterium isotope effects. The first deuterium isotope effect studies with cyclo p r o p a n e d2 were carried out by Schlag and Rabinovitch^"^^. Unlabehed cyclopropane molecules undergo isomerization 1.22 times faster than cyclopropane-d2 at 718 K.


875

TABLE 1. Pressure variahon of deuterium isotope effect in cyclopropane isomerizahon at 755 K

10^ 1-96

P(cm) (kn/kuU.

-

(VUcaic

2.10

2.08

1 1.70

10 1.88

2.00

1.80

10-1

lQ-2

1.50

1.30

-

1.50

1.19

0.83 0.25

0

Neglecting secondary deuterium isotope effects, this value gives /CHAD = 2.18. The deuterium isotope effect in the thermal copyrolysis of cyclo-CsHg a n d cyclo-CgDg in the temperature interval 407-514 °C has been determined by Blades^^^. At about 60 cm H g the ^HAD ratio depends on the absolute temperature according to equation 204: /CHAD = 0.82 exp (1300/RT) (V^D)482

C = 1-9504, (WkJioo.s °c =

4.7244, ( ^ ^ 0 ) 2 5

(204)

°c =

^-3609,

(WMo °c =

^-9883

The /CH//CD isotope effect is pressure-dependent a n d decreases from 1.98 at 7 6 c m H g to 1.35 at 0.0178 cm H g for temperature 482 °C. This decrease has been confirmed by subsequent studies and by the inversion of the ^ ( C 3 H 6 ) A ( C 3 D 6 ) ^^îo found to occur at about 1 0 " ^ m m H g in agreement with theoretical expectations^^^'^^^ (Table 1, line 3). Below this pressure the wall effects caused the ^ ( C 3 H 6 ) A ( C 3 D 6 ) ^^^^^ constant and equal to about 0.8, down to a pressure of lO"'* ( a t ' 5 1 0 ° C ) . ' The high-pressure results are comparable with the deuterium isotope effect observed in the decomposition of ethyl and ethyl-Ds a c e t a t e s ^ ( / C H A D = 2.23 at 445 °C is comparable with /CHAD = 2.04 with cyclopropanes). The activation energy difference of 1300 cal mol found by Blades^^^ is slightly above the zero-point energy difference of 1150 c a l m o l ~ \ corresponding to C — H / C — D oscihators. This implies that the hydrogen isotope effect observed in this reaction is a primary effect a n d considerable c a r b o n - h y d r o g e n b o n d weakening takes place during activation in the transition state. A suggestion has been m a d e that the hydrogen a t o m is weakly b o n d e d both to the original and the terminal carbon atoms involved in the migration. The deuterium isotope effect of 1.37 at 449 °C (activation energy difference of 1400 cal mol ~^) observed in the decomposition of cyclobutane to ethylene^ ^''^ has been interpreted similarly by assuming C — H b o n d weakening in the transition state. Setser and Rabinovitch have investigated also the unimolecular thermal geometrical and structural isomerization of methyl cyclopropane^ and determined the deuterium isotope effects in the structural isomerization of l,2-dideuterio-3-methylcyclopropane (61). (Geometrical and structural isomerization rates differ by a factor of twenty.) D

Me

D

Me

H

I

I

I

1

I

H

H

H

D

i\V/i

H

^^"^

Me

i W X iH

I

I

I

D

H

D

(61)

(62)

(63)

The nearly identical rate expressions for the geometrical isomerization of 61 to yield 62 and 63 (at a pressure of 1.1cm and temperature range 380-420 °C) are given by equations 205 and 206. ^ 6 2 ) = 1 0 ' ' ' -""-êxp - ((60,400 + 900)/i^T)

(205)

^ 6 3 ) = 10^'-^

(206)

e x p - ( ( 6 0 , 7 0 0 ± 1700)/RT)

876


The thermal structural isomerization rate constants for methylcyclopropane and methylcyclopropane-D2 to yield butenes depend on the temperature according t o equations 207 and 208 in the 4 2 0 - 4 7 5 °C temperature range. Wt.)

= 1 0 ^ ^ - ^ ^ e x p ( - 62,400/RT)

Wuct.)=

(207) (208)

10^---Rexp(-62,300/R7)

where

fc(s.ruc..,AD.,s..uc... Vruct.)/*=D2(struc..)

420

°C =

= l , 5 1 3 6 e x p ( - 100/RT)

1.4075,/c,^,^„^,,//Co^,^,^„^,,, at 450

°C=

(209)

1.4118,

^(struct./^D2(struct.) at 475 °C= 1.4150. T h e precision of these determinations has not been high enough to reveal the very small positive temperature coefficient of the deuterium isotope effect in only partially (D2) deuteriated 3-methylcyclopropanes. In the perdeuteriocyclopropane pyrolysis a m u c h larger positive temperature coefficient for k^Jk^^^ equal to 1300 cal mol ~ ^ has been noted by B l a d e s ^ S e t s e r and Rahnovitch^^^ deduced also the secondary isotope effect for the methylcyclopropane to isobutene isomerization îH^fn l-Ô ± 0.03 a n d estimated the isotope effect per H or D a t o m as defined by equations 210 a n d 211: kîi/k*^= 1.59, /Cch/^*d = 1-41 and /CbH//^*D = 2.36. These values are c o m p a r a b l e to /ch//cd = 2.18 and 1.96 determined for cyclopropane-D2 and cyclopropane-Dg, respectively, near the high-pressure region. — — — y

isobutane

H Me k,^ y trans-butQUQ-l J /

H

^" ) cis-butene-2 butene-1 ) CH2DC(Me)CHD

^

) cis,trans—CH2^CD=CUCH^

K D J\ H

I

J^:^ cis,trans—CHD2CH=CnCH^ ^^CHD=CDCH2CH3 '^bD

.CHD=CHCHDCH3

T h u s the secondary and primary deuterium isotope effects determined in this study also indicate that entropy and zero-point energy factors associated with breaking of the C—D b o n d and migration in the activated complexes are i m p o r t a n t for the structural isomerization to yield butene-1 and butene-2, and reaction p a t h B (equation 197) must be included in the mechanistic considerations concerning the cyclopropane isomerization. But the higher activation energy for isobutane formation (Q = 64.3 kcal m o l " ^) t h a n that for butene-2 or butene-1 (Q = 62.0 ± 0.6 kcal m o l " ^) indicates also that the rupture of


877

the particular C — C b o n d postulated in mechanism A of equation 197 is also important in t h e formation of the transition state. The authors^ suggest a concerted isomerization mechanism with the transition state having the structure 64, b u t are inclined also t o suppose that the structural a n d H.

H2C-

^CH

(64) geometrical isomerizations proceed according to a c o m m o n reaction scheme (equation 212) presented in the review chapter by Carpenter^"^^ which involves the intermediacy of a geometrically equilibrated biradical. ^^C kinetic isotope effect studies^"^^'^^^ have been undertaken t o clarify this problem, since skeletal ring vibrations are insensitive t o deuterium substitutions. CH2 C3H4D2

^

DCH^ ^HCD

•

HDC=CH

CH2D

(212)

c. Rotational kinetic deuterium isotope effects. Double deuteriation^ of the terminal carbon of the vinyl g r o u p caused a 1.125 ± 0.04-fold decrease in the rate constant for cyclopentene formation in the rearrangement (equation 213) of {R, R)-trans-2-mQthy\-l(3,3-dimethyl-l-buten-l,l-D2-2-yl)cyclopropane 65 a n d 1.11 ± 0.04 increase in the diene formation. These values have been interpreted as caused by a rotational isotope effect disfavouring the formation of deuteriated cyclopentene a n d favouring that of the deuteriated diene. CD2 %

CH2

280°C

C—Bu-/

Me^

CH2

^

Me^

CH2—CD2

^CH

^ C H

^

\

CD2H

Bu-/

(65) A rotational kinetic deuterium isotope effect,^^^ = 1.31 + 0.04, h a s been found^"^^ in the thermal structural rearrangement of cis- a n d trans-2,3-dimethyl-ldideuteriomethylenecyclopropane, 65t a n d 65c, t o 66 b u t little effect was found in the geometrical isomerization of 65t t o 65c.

r

r

^ C „ - C „

„C„-CH_

(65t)

(65c)

(66) (2-methylethylidenecyclopropane)

Ratio k^Jkj)^ equal t o 1.08 ± 0 . 0 2 was observed in the interconversion of 2-methyl-6-dideuteriomethylenebicyclo[3.1.0]hexane, 67, into 68 (equation 214). This


878

suggests that the exo methylene rotation occurs in a fast step after rate-determining formation of a planar trimethylenemethane biradical 69^^*^. D

Hcr

^H

H

^CH

I

CH

/

^CH2

Me

D

Me^

\

CH

CH2 ^CH2

"CH2

(214) (67)

(68)

(69)

d. Deuterium isotope effects in pyrazoline decomposition. Secondary deuterium kinetic isotope effects o n the thermolysis of t w o a-deuterated 1-pyrazohnes (70,71) a n d t w o i^-deuteriated 1-pyrazolines (72,73) at 229.40 ± 05 °C (or corrected to 105 °C) have been .CH2 CDs

CH2

^ C D 2 N = N

(70)

(71)

k^/k^=^^^±o.o^{=^.2e±o.o^

at 1 0 5 * C )

CH2

1.40 + 0 . 0 2

CH2

(1.55+0.02)

H2 N = N

(72)

(73)

1.05 + 0.01(1.06+0.01)

1.12 + 0 . 0 1

(1.14 + 0 . 0 1 )

found^^^. These indicated values have been interpreted as supporting a mechanism involving a symmetrical transition state a n d two synchronous C — N b o n d cleavages (equation 215). ^CH2 CH2 N = N

^ C H 2 ^ 'CH2

CH2

CH2

(215)

A thermal deazotization study^^^ of 4-methylpyrazoline-4-d in the temperature interval 170-290 °C has revealed that inctroduction of deuterium at the 4 position decreased the hrst-order decomposition rate constants by a factor of 1.06 + 0.03 at 241.75 °C a n d gave an isotope effect /CHAD = 1.80 in the product-determining step leading t o cyclopropane


879

formation. The results have been interpreted as indicating that the formation of the isobutylene diradical 74 (equation 216) is the rate-determining step of the decomposition whhe hydrogen migration versus ring closure in this intermediate determines the ratio of the products. ^ ^ C kinetic isotope effect studies should provide conclusive evidence supporting this reaction scheme. Me

D.^

CH2

CH2

N = N ^

2. Carbon-13

kinetic

isotope

effect

studies

a. The first ^ ^ C kinetic isotope effect study on the structural isomerization of cyclopropane of natural isotopic composition to propene (equation 217) was carried out by Weston^^^. This was found (at 492 ° C and one atm.) to give ^(12C3H6AI2C213CH6) = 1.0072 + 0.0006. This value should provide indirect information a b o u t ring relaxation in the transition state (T.S.) of the gas-phase isomerization. W h h e the non-skeletal vibrations in cyclopropane are very sensitive to deuterium substitution, they are only very little affected by carbon isotopy. O n the other hand, skeletal vibrations are strongly affected by substitution of carbon-13 for carbon-12. ^ ^ C studies should therefore throw light on the degree of change of these vibrations in the transition state of the ratedetermining step of the cyclopropane isomerization. The results have been interpreted in terms of physical and isotopic concepts^'^^'^^^ presented by the theoretical equation 217 k/k* =

(m* Vmi)^/2[1 +

XG(^-)AU,

-YG{U})AU}-]

(217)

where k corresponds to the lighter molecule and k* to the heavier molecule. Two extreme situations have been considered. In the first, corresponding to the reaction p a t h B in equation 197, it has been assumed that ^ ^ C — H b o n d rupture and subsequent hydrogen migration are the rate-determining steps. In this case {m*^/m^y'^, the temperature-independent term, was calculated^'^^ using a three-centre reaction model ^ ^ C - - - H - - - ^ ^ C in which one C — H b o n d breaks and a new one is formed, and was found to be 0.0010. The temperature-dependent contribution in the square brackets of e q u a d o n 217 should in this case be equal to 0.0062. If ft)î2c_-H) Ô^C—H) assumed to equal 2 9 8 5 c m " ^ and 2976.06cm"^ correspondingly, one finds that G(u)Au = 0.00546 at 492 ° C . The agreement is quite satisfactory. The second extreme reaction p a t h A in equation 197 involves c a r b o n - c a r b o n b o n d s in the rate-determining step (a single b o n d is breaking, a double b o n d is formed). Three-centre formulation gives^"^"^ in this case the value 0.0128 for (m*^/m^)^/^. Weston^"^"^ concluded that 'some tightening of b o n d s ' in the transition state, lowering the ^ ^ C isotope effect, takes place. Increase of the bonding in the transition state should lead to J^G(w.^)Aw.^ - J^G(Ui)Aui = 0.0055. This is more than what corresponds to a change of two single C — C bonds to one double b o n d as given by equation 218, [G(w4_,2c)Awi - 2G(WI3C--I2C)AMJ = 0.00243 calculated taking C0(i2cî2c) = 993 c m " ^ C0(i2c_i2c) = 973.656cm" \ a;(i3c= cm~^ and C i 8 ) when malonyl-coenzyme A a n d N A D P H were added. Often the chain length of the fatty acids produced in vitro did n o t match that of the n-alkanes produced in vivo. As the epidermis generates many classes of lipids, each with its characteristic chain-length distribution, some partial separation m a y have been achieved Enzyme extracts such as produced very long chain acids did not resemble extracts of fatty acid synthetase. N o acyl carrier protein (ACP) was involved^^^; chlorophenyldimethylurea which inhibits the incorporation of acetate into normal-range fatty acids had no effect on n-alkane biosynthesis, and trichloroacetate at low concentration strongly suppressed alkane formation yet did not effect normal fatty acid s y n t h e s i s ^ I n vivo, the absence of light, which inhibits the incorporation of acetate into n o r m a l fatty acids, h a d little effect on the biosynthesis of alkanes provided that the Cjg and Cjg fatty acids were available as s t a r t e r s ^ U n t i l they are solubilized, resolved a n d purified the nature of these microsomal elongation enzymes cannot be elucidated. N o work has been reported on higher plants, but a chain-elongating enzyme has been purified from the mycocerosic acid synthetase complex of Mycobacterium tuberculosis: here 2,4,6,8-tetramethyl-n-C28 acid and related homologues are generated by elongation of a n d C i 8 acids with malonyl-CoA as source of C2 units and with N A D P H ^ ^ ^ . Extracts from tea leaves in the presence of oxygen a n d ascorbate converted fatty acids (n-C 18 to n-C32) into n-alkanes containing 2 carbons less: thus a-oxidation must have preceded final loss of carbon. However, the aldehydes prepared from the C^g and C24 acids were straightforwardly decarbonylated to the acids with one carbon a t o m less. Tea leaves in vivo produced the o d d - n u m b e r series of n-alkanes and it was presumed the latter route here predominated^^^'^^^ T h u s the implication was that the final step in n-alkane formation was a decarbonylation rather t h a n a decarboxylation and studies using particulate preparations from peas have confirmed this. The mechanism is obscure, but tracer studies have shown that the conversion, R C H O R H 4- C O , involves retention of the aldehydic hydrogens, and it has also been demonstrated that a metal ion is implicated (effect of chelating agents)^^^. This type of mechanism is consistent with

CH3(CH2)i4C02H Palmitic acid ( C 1 6 )

^^^''^'^> CH3(CH2)28C02H (C30)

> CH3(CH2)27CH3 n-Nonacosane(C29)

F I G U R E 3. Elongation-decarboxylahon pathway to n-alkanes

912

D. V. Banthorpe

Fatty Acid SyntPietase C2

>

_ Mesophyll; ~ internal palisade cells

> n-Ci6-acid

nxC,

Chain Elongating

Enzymes

nxC^

n-Ci6

^ n-C2s-CoA

• n-C3o-Co.4 etc.

n-C27-CHO

^ Endoplasmic reticulum ~ of epidermal cells

n-C29-CHO

Decarbonylation

n-C27

n-C2

Enzyme(s)

alkane

alkane

etc.

F I G U R E 4. Scheme for chain elongation and (CoA = coenzyme A)

^ Extracellular matrix ~ cell wall-cuticle region decarbonylation in

n-alkane biosynthesis

observations of decarboxylation of fatty acids and aldehydes p r o m o t e d by complexes of Ru and Rh^°^ and by demonstrations that such porphyrin complexes could catalyse decarbonylation at near-ambient temperatures'^^'^^^. Current views on the compartmentation of the enzyme systems that p r o m o t e chain elongation and decarbonylation are represented in Figure 4. This scheme is based on electron microscopy and on studies of enzyme location and i n h i b i t i o n ' T h e chain length of alkanes formed probably depends on the aldehydes avahable rather t h a n on the specificity of the decarbonylation: thus crude extracts of leaves generated n-alkanes from n - C i 6 to n-C32 fatty acids with n o particular preference for substrate. The restricted ranges of n-alkanes observed in vivo presumably result from the specificity of products from the fatty-acid elongation system that produce the substrate for decarbonylation. The widespread occurrence, albeit in lesser amounts, of n-alkane with even rather t h a n odd numbers of carbons implies the existence of a-oxidation (cf Figure 2, a n d

RCH2CH2CO2H

RCH2CHO

(O).

RCH2CO2H

^ RCH2CHO + CO2

> recycle

I. Long-chain fatty acid peroxidase II. Aldehyde dehydrogenase F I G U R E 5. a-Oxidation of fatty acids

> RCO2H

>etc.

19. N a t u r a l occurrence, biochemistry and toxicology

913

References 203 and 204). This route was demonstrated using extracts from germinating peanuts with only NAD"^ as added confactor and H2O2 was implicated as oxygen donor^^'^'^^^. Leaf systems in contrast uthize molecular 02^^^. The process, which can recycle, is shown in Figure 5. As weh as producing odd-carbon fatty acids wherever they are needed for metabolic purposes, a-oxidation can displace the reading frame by one position whenever jS-oxidation of a fatty acid is prevented by a methyl or other blocking group at the j5-position^'°. 3. Branched

and cyclic

alkanes

The reasons for the presence of signihcant a m o u n t s of branched alkanes in some plants but not in others is not clear. Early studies showed that the amino acids valine, threonine, isoleucine and leucine were readily incorporated into the branched alkanes of Nicotiana species^'' and use of valine or isoleucine as starter unit, as in Figure 6, is consistent with later tracer work on incorporations into iso- and anteiso-alkanes'^^. In plants, as well as in Mollusca and Arthropoda, the majority of the iso-alkanes have an odd number of carbons whilst the majority of the anteiso-alkanes have an even carbon number, and this follows from the scheme outlined. The methyl substituent in internally branched alkanes is introduced by transfer from S-adenosyl methionine to an unsaturated fatty acid (cf Figure 6) in blue green algae and a simhar situation may occur for plants'^^. Use of oleic acid ( C j g ; see Figure 6) as the 'normal' fatty acid that is subjected to chain elong ation would result in the ultimate formation of 9- or 10-methylated alkanes, which are types that frequently occur. Feeding of '"^C-labelled isoleucine or isobutyric acid to Brassica species that do not normally produce branched alkanes led to labelled iso- and anteisobranched fatty acids ( < C i g ) : neither very long chain fatty acids nor branched alkanes were f o r m e d ' T h i s suggests that the non-acceptance by the decarbonylation system of short-chain precursors, rather than lack of avahabhity of branched-chain precursors, precludes the formation of the alkanes although compartmentation effects could play a

COA

f> X

CZ

ISO-OLKANE CO2H

-COA

CO2H

^XCZ

(ODDC)

ANTEISOOLKANE (EVEN C )

COGH INTERNALLY BRANCHED (EVEN CARBON) COGH _

^(''"^^-^^ ^^^^^^^^^^^2^

^

QL^.^

^

COENZYME A

F I G U R E 6. Biosynthesis of branched-chain alkanes

914

D . V. B a n t h o r p e

major role. Little is k n o w n a b o u t the biogenesis of the cycloalkanes that sometimes occur as minor components of plant waxes: it is possible they m a y be derived by cychzation of dicarboxylic acid derivatives o r diene derivatives of t h e alkane precursors o r indeed shikimic acid m a y be involved. T h e possible routes t o these a n d other m i n o r alkanes a n d their derivadves h a s been summarized

C. Biogenesis in Other Organisms

Less detailed tracer studies have been m a d e o n a variety of organisms other t h a n higher plants and, except for some observations on bacteria (see later), t h e chain-elongation mechanism t o t h e higher alkanes seems consistent with all results. T h e most extensive work h a s concerned the synthesis of n-C2i t o n-C27 alkanes in microsomal p r e p a r a t i o n from the uropygial gland of grebe^^^. Fatty acids a n d their corresponding aldehydes were efficiently converted into n-alkanes in the absence of oxygen a n d t h e effect of inhibitors a n d chelating agents suggested a decarbonylation mechanism as in plants. However, there were differences. 1-^H-octadecanal was converted into n-heptadecane with exchange of tracer with water a n d the resolution of this discrepancy m u s t await the isolation and purification of the a p p r o p r i a t e enzymes. Extracts of m a m m a l i a n sciatic nerve^^^'^^"^ a n d r a t brain^^^ also synthesized alkanes (n-C^g t o C33) by the chainelongation pathway. The latter pathway also appears t o be present in several insect species^ and b o t h ^^C a n d ^'^C studies revealed that iso- a n d anteiso-alkanes were formed with incorporation of valine a n d isoleucine in Musca (housefly) a n d Blattella (cockroach) species^ However, the situation seems not necessarhy always t o be simhar in higher plants. ^^C-Propionate incorporated during chain elongadon serves as the d o n o r for the methyl of b o t h the anteiso- a n d internahy branched alkanes (e.g. 3-methyl-C25 etc.) that predominate in Periplanata (cockroach) species^^^'^^^ a n d the 3-methyl b r a n c h is added just prior t o chain completion^^^. In contrast, in another cockroach species (Blattella), this g r o u p is introduced early (as in plants)^^^. Blue green algae (Nostoc, Anacystis) species form n-heptadecane from stearate by decarboxylation rather t h a n by decarbonylation^^^'^^"^ a n d branched h y d r o c a r b o n s with methyl at C-7 or C-8 were formed by g r o u p transfer from S-adenosyl methionine^^^'^^^ The sole evidence for construction of alkane chains by coupling of two moiedes rather t h a n by sequential chain elongation comes from work on bacteria. Extracts of Sarcina species synthesized even-chain n-alkanes under conditions where a-oxidation was supposedly inhibited by imidazole a n d head-to-head condensation of t w o fatty acids ( < C i 8 ) was proposed^^^'^^^. Corynomycolic acid ( 1 5 - C O O H , 6-OH-n-C3i) from Corynebacterium species was considered t o be formed by similar c o u p h n g of t w o molecules of palmitic acid^^^, a n d the p a t h w a y was suggested for formation of alkanes of Sarcina species with iso a n d anteiso branching at b o t h ends of the m o l e c u l e ^ T h e status of these claims is difficult t o assess: simhar couphngs were t h o u g h t t o occur in higher plants, b u t the view was discounted on further study (see Section III.B).

IV. IVIETABOLISM A. By Micro-organisms

Oxidation a n d further functionalization of alkanes by microbes h a s assumed great importance in respect of facets of the petroleum industry. T h u s such metabolism c a n exploit petroleum components of low commercial value t o form cheap carbon sources

19. N a t u r a l occurrence, biochemistry a n d toxicology

915

TABLE 9. Main genera of micro-organisms members of which can metabohze alkanes Bacteria Pseudomonas Brevibacterium Achromobacterium Corynebacterium Cellulomonas Micrococcus Rhodococcus Mycobacterium Nocardia Streptomyces

Fungi

Moulds

Candida Mycotorula Trorulopsis

Botrytris Penicillium

for the fermentation industry or to generate biomass for use as edible protein, especially as animal fodder. Also the utilization of alkanes as a sole c a r b o n source by some micro-organisms has led to blockage of fuel leads of cars a n d planes by burgeoning cultures and corrosion of fuel tanks and lines by acidic metabolites. N u m e r o u s reviews summarize the microbial metabolism of alkanes and related hydrocarbons^^^"^^^. Genera (mostly closely related) that encompass the most potent micro-organisms that can oxidize alkanes are hsted in Table 9. A few of the species occur in oh deposits and can utilize gaseous or liquid hydrocarbons as sole carbon s o u r c e ^ b u t most inhabit m o o r l a n d or acidic soils a n d the underlying shales where they utilize soil waxes as well as a variety of other apparently unpromising s u b s t r a t e s ^ n - A l k a n e s seen to be generahy uthized most effectively of the hydrocarbons, although this may reflect the situation that pure samples of branched alkanes have n o t eashy been avahable for laboratory screening. A few select species of micro-organisms only metabolize methane, but there is a fairly clear distincdon between these that grow on n-Cô a n d lower alkanes and those that prefer the n-Cô to n-C2o range. Few grow well on homologues greater than n-C2o^^^- There are an increasing n u m b e r of examples where an organism grown on an n-alkane as sole carbon source is enabled partially to metabolize another alkane which alone is unable to support growth. The usual sequence of metabolism is terminal oxidation to the alcohol a n d thence to the acid, followed by j9-oxidation to clip off acetate units as energy sources or as buhding units for the construction of other metabolites. Fatty acids ( > C i 4 ) produced by the jS-oxidation p a t h w a y can be incorporated directly into the microbial lipids. Some organisms oxidize n-alkanes at C-2 to yield methyl ketones, m a n y of which are i m p o r t a n t c o m p o u n d s in the a r o m a or flavour industry and in some such as Myohacterium species, oxidation at b o t h C-1 a n d C-2 cooccurs^^^. Small a m o u n t s of acids are usuahy secreted into the medium where, in a few documented cases, they inhibit growth. Branched alkanes (e.g. 2-methyl-Cii or pristane) are converted into dicarboxylic acids by a,CL)-oxidadon in a pathway that can be inducible^'^^ Acyclic terpenoid hydrocarbons, e.g. pristane or farnesane, may also be degraded by this route^"^^ but cycloalkanes are rarely attacked^^"^. All attempts to isolate micro-organisms that could oxidize cyclohexane fahed, but marine muds did contain species which could accept this substrate to yield cyclohexanone that could then be further metabolized by a plethora of organisms in situ^"^^. The induction of alkane hydroxylases by unoxidized alkanes (such as n-C7) has been demonstrated in a Pseudomonas species^'^^ a n d cytochrome P 4 5 0 — a principal oxygenase

916

D . V. Banthorpe

of the substate—was induced in a Candida species after two hours^"^"^. I n recent studies the regulatory locus for hydroxylase activity in a Pseudomonas species h a s been explored^'^^ a n d a genomic D N A clone encoding isocitrate lyase (a key enzyme of the glycoxylate cycle), which is a peroxisomal enzyme of the yeast Candida that converts n-alkane into citric a n d iso-citric acids, was isolated with a D N A probe from t h e gene hbrary of the yeast^'*^. Yeasts, especiahy Candida species, mostly grow well o n even-carbon numbered n-alkanes (n-Cio t o Cig) but much less so o n the odd-carbon homologues^'^'^. Both sets of c o m p o u n d s can be metabolized t o yield citric a n d other hydroxy acids in excellent (up t o 50%) yields^^^"^^^. These latter presumably accumulate by flooding of the Krebs cycle with C2 units derived from b r e a k d o w n of the hydrocarbon. Yeasts that metabolize petroleum fractions have also been extensively exploited t o generate biomass t o manufacture 'single cell protein' for animal foodstuffs. O n e t o n of n-alkane yielded roughly the same mass of protein-vitamin conjugate when adapted species were used and the process was economicahy viable^^'"^^^. Such petroleum-metabolizing lines can be immobilized o n clay o r sand^^^ o r can be encapsulated^ M a r i n e bacteria and yeast may ameliorate t h e effects of the apparently inevitable oh spillages at sea^^^. H u n d r e d s of such organisms have been isolated from the Arctic that can metabolize diesel ohs down t o 10 °C a n d bacterial communities that c a n degrade n-chain a n d branched alkanes have been characterized^ B. By Animals and Plants

Appreciable quantities of alkanes are ingested by animals as constituents of plant material a n d also by m a n as artificial additives (e.g. mineral ohs) of foodstuffs o r as components of natural or artificially produced oils and fats. Very little is k n o w n a b o u t the details of the metabolic turnover of such compounds. As in micro-organisms, it is hkely that alkanes are detoxified in animals a n d plants by a mixed-function oxidase which forms the alcohols that m a y be further metabolized or excreted in t h e urine as conjugates, such as glucoronides o r sulphates. M o s t of the c o m p o u n d s reported were characterized ( G C - M S ) after extraction from urine fractions that h a d been incubated with the appropriate enzyme t o cleave the conjugate^^'"^^^. Some biotransformations of alkanes by animal systems (mainly in vivo) are summarized in Figure 7. A few facts are also k n o w n concerning the metabolism of alkanes by plants. Cuticular waxes typicahy contain secondary alcohols, ketones a n d j?-diketones in addition t o alkanes and the former have the skeletons as in Figure 8, where functionalization is near the centre of the molecule and the chain lengths of the alcohols and ketones are closely simhar t o those of the major n-alkanes present in any particular species. Tracer evidence indicates that t h e secondary alcohol a n d ketone are formed in sequence by oxidation of the corresponding n-alkane by a mixed function oxidase which is inhibited by chelating agents. Thus in Brassica species, the 14- or 15-hydroxy- and oxo-derivatives of the n-C29 alkane were thus formed b o t h in vivo a n d in ceh-free extracts^ T h e j?-diketones and their less-common hydroxylated derivatives (a- and 7-ketols) are not c o m m o n b u t have been found t o be t h e major components of the cuticular wax of a few species'^^. Unlike the alcohols a n d ketones these d o n o t have chain lengths corresponding t o the predominant n-alkanes of the species. Genetic studies with barley m u t a n t s indicate that the hydrocarbons and the j8-diketones are generated by two distinct enzyme systems a n d t h e routes c a n be differentially inhibited in tissue slices. There is also tracer evidence that the j9-diketones are n o t derived from the n-alkanes. T h e mechanism of formation of these derivatives h a s n o t been elucidated, b u t it is possible that the keto groups are preserved during the chain elongation as shown in Figure 9. Additional hydroxy groups are presumably introduced later by a mixed-function oxidase simhar t o that responsible for the formation of the monoketones'^^'^^^.

917

19. N a t u r a l occurrence, biochemistry a n d toxicology

References

n-C6Hi4

O

=0

-OH

+

264

267-269

rat

-COgH

270, 271

OH OH

rat

liner

OH at all C

272

trout

273 OH

"

F I G U R E 7. Biotransformahon of some alkanes

Usual C range

Type OH

C.0-C3

0

0

F I G U R E 8. Oxygenated components of plant waxes

OH

918

0


0

0

0

0

CoA

^

^

" A

0^

CoA

'O

0

- r ^ ^ C ' ^ : ^ ^ ^

^ « ^ C H O

n-alkanes

F I G U R E 9. Biogenehc route to j5-diketones in plant waxes (CoA = coenzyme A, M = metal or H)

V. PHARMACOLOGY AND TOXICOLOGY

O n account of their widespread occurrence b o t h as pollutants a n d as c o m p o n e n t s of (mainly vegetable) foodstuffs, the potential toxicology of the alkanes has been subject to severe scrutiny. Their general toxicity^''^'^^^ a n d n e u r o t o x i c i t y ^ h a v e been reviewed. T h e lower alkanes are much less toxic t h a n their chlorinated derivatives. M e t h a n e a n d ethane are simple asphyxiants n o t lethal t o mice except at high ( 6 8 0 m g l ~ ' ) c o n c e n t r a t i o n s ^ T h e C5 to Cg alkanes all cause depression, dizziness a n d uncoordination when inhaled at the 5000 p p m level a n d m a y irritate the respiratory system with narcotic effects at higher concentrations^^^'^^'. T h e lower h y d r o c a r b o n s are also anaesthetics with a cut-off in potency which correlates with the decrease in absorption into the lipid bilayer of nerve cells as the homology increases. This cut-off occurs for n-alkanes at C9 to C 1 2 in different species^^^,^^^. Inhalation of even smah a m o u n t s of the lower alkanes can cause cyanosis, hypopyrexia a n d tachycordia leading to a chemical pneumonotis, a n d oral ingestion can cause hepatic damage. As a consequence, ingestions larger t h a n 1 g k g " ' body weight should be vomited a n d a 10g dose could be potentiahy fataP^^ These consequences m a y be due t o physical damage to membranes by the hydrocarbons, b u t the major effect m a y result from metabolism t o form potentially toxic derivatives. O n either count n o t all alkanes m a y contribute to the symptoms. T h u s n-hexane on ingestion causes polyneuropathy in h u m a n s a n d experimental animals a n d is m u c h m o r e toxic t h a n the n-Cg a n d n-Cv homologues. T h e potency m a y be d u e t o formation of the 2,5-dione which can couple with pyrrole rings in proteins^^"^-^^^-^^^; t-butylcyclohexane is similarly oxidized in rat t o give derivatives hydroxylated in the side chain that can cause renal damage^^^. T h e n - C i 4 alkane has a m u c h greater irritant effect in rat t h a n its near h o m o l o g u e s ^ a n d inhalation by rat of the n-Cg t o n-C^g alkanes at close to air saturation revealed only the first homologue t o be appreciably toxic^^^. T h e lower hydrocarbons comprise a high p r o p o r t i o n (typically 12%) of air pollutants. 2-Methylpentane is a mucus coagulant^^^ but the lower alkanes per se are probably n o t a significant health hazard. However, they are oxidized t o form the highly irritating c o m p o n e n t s of photochemical smogs^^"^.


919

Alkanes found in m a m m a l i a n tissue have usually been considered of exogenous origin (e.g. from diet) a n d have been assigned neither a normal nor a pathological function, but this opinion may have to change. Recendy, the n-alkane c o m p o n e n t of h u m a n epidermal tissues (ca 6% total lipid) has been shown to increase strikingly (up to 25%) in some scaling diseases, a n d ah the evidence is that the enhanced level of alkane is not of exogeneous origin. The implication is that the c o m p o u n d s play a role in the pathology of the d i s e a s e ^ A l k a n e levels are also increased abnormally in the a o r t a of atherosclerotic rabbits^^^. Myelin of both the central a n d peripheral nervous systems contains remarkably high levels of long-chain fatty acids ( > Cjg) a n d their corresponding n-alkanes, which probably affect the physical a n d chemical properties of the sheath^^^'^^"^. Impaired synthesis or incorporation of alkanes during myelin assembly could be the cause of such defective mylenisation in 'quaking' m u t a n t mice^^^. Brain myelin of mouse accumulates especially high quantities of alkanes whhst miochondria, synaphosomes and microsomes possess very little^^^. Aliphatic hydrocarbons including alkanes are widely distributed in the internal organs and non-neural tissue of m a m m a l s at low level, usually 3 to 60 /^g g~ \ such as to suggest exogenous origin^^'^"^^^ Vaseline a n d mineral oils, a n d by implication higher alkanes have been repeatedly cleared as potentially toxic materials. However, oil droplets with ah the characteristics of mineral oils can accumulate a n d cause lesions in spleen and possible that some alkanes at least have insidious effects. Recently a novel, sudden fatal pathological condition has been discovered that is associated with the visceral accumulation of long-chain n-alkanes (n-C29 to n-Cas) in a h u m a n padent. Plant cudcular waxes as source were implicated by this alkane pattern a n d indeed the p a d e n t had indulged in gross consumption of apples (ca 1 kg day over 18 years^°^!).

VI.

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923

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CHAPTER

20

Inverted and planar carbon W I L L I A M 0.

AGOSTA

The Rockefeller

University,

New York, New York 10021,

USA

1. I N T R O D U C T I O N , S C O P E A N D N O M E N C L A T U R E II. T H E O R E T I C A L C O N S I D E R A T I O N S A. General B. Paddlanes C. Fenestranes D . Propellanes E. Bicyclo[1.1.0]butanes . . . . F. Other C a r b o n Skeletons . . . HI. P R E P A R A T I V E C H E M I S T R Y A N D P R O P E R T I E S A. Paddlanes 1. Complex structures . . . . 2. Simple [n.2.2.2]paddlanediones B. Fenestranes 1. [5.5.5.7]Fenestranes . . . 2. [5.5.5.5]Fenestranes . . . 3. [4.4.5.5]Fenestranes . . . 4. [4.4.4.5]Fenestranes . . . C. Propehanes 1. General 2. [4.2.1]Propehanes . . . 3. [4.1.1]Propellanes . . . 4. [3.3.1]Propehanes . . . 5. [3.2.1]Propehanes . . . 6. [3.1.1]Propehanes . . . 7. [2.2.1] Propellanes . . . 8. [2.1.1]Propehanes . . . 9. [ l . l . l ] P r o p e l l a n e s . . . D. Bicyclo[1.1.0]butanes . . . IV. C O N C L U S I O N V. A C K N O W L E D G M E N T . . . VI. R E F E R E N C E S

928 930 930 930 931 933 934 934 935 935 935 936 937 938 939 944 944 947 947 947 948 950 950 951 952 952 953 956 958 958 958


927

928

W. C. Agosta I. INTRODUCTION, SCOPE AND NOMENCLATURE

The effects of angle strain in organic molecules have attracted interest a n d study for more than a century. The hrst notable success in this area was Perkin's syntheses of cyclobutane-^ and cyclopropanecarboxyhc^ acids in 1883 a n d 1884, when it was generally presumed that such small rings could not exist. At the dme, Perkin was a twenty-two-year-old student in Baeyer's laboratory in Munich. Ignoring the collective advice of Baeyer, E m h Fischer a n d Viktor Meyer, he adapted the newly developed malonic ester synthesis to his needs, prepared these novel cycloalkane derivadves a n d opened a new field of investigation. This led directly to Baeyer's strain theory^, which ascribed the unusual reactivity of small carbocyclic rings to the necessary departure from tetrahedral bonding of the carbon atoms involved. T h e concept of strain has since grown far more complex'*'^, but the theory that Baeyer presented in two and a half smah pages in 1885 has provided the qualitative basis for a hundred years of inquiry into the distortion of b o n d angles. During this d m e organic chemists have contrived numerous ways of deforming the ordinary tetrahedral sp^, planar sp^ a n d linear sp bonds of the carbon a t o m in order to assess the effects of such changes on molecular properties. Theory has increasingly provided both understanding of these effects a n d also guidance in devising systems for future investigation, whhe the growing power of synthesis has made ever more structural types avahable for experimental examination. Ah this activity has led to a large body of information which, along with investigations into other types of strain, has been the subject of excellent reviews"'''^. In the present chapter we wish to focus attention specifically on theoretical a n d experimental studies of molecules containing flattened or inverted carbon. 'Flattened carbon' whl denote a carbon a t o m with attached nuclei W, X, Y and Z, having angle deformations that would lead, in the hmit, t o a planar molecular fragment C W X Y Z . Calculations reveal that the energy difference between square-planar a n d tetrahedral methane is considerably greater t h a n typical c a r b o n - h y d r o g e n a n d c a r b o n - c a r b o n bond strengths^, so that the limiting case of a molecule containing planar carbon with these ordinary bonds is not experimentahy likely. In terms of symmetry coordinates such deformations can be analyzed into two types of motion^"^. The first is compression deformation, in which one pair of opposite angles, as ^wx and QYZ in 1, is opened at the expense of the other four angles. If both ^ ^ x a n d open to 180°, a square-planar fragment is formed. T h e second type of motion is a twist deformation, in which one pair of opposite angles remains invariant, a second pair opens up a n d the third closes. This can be visualized as a rotation of, for example, the C W X portion of C W X Y Z relative to C Y Z in 2. In the limit, a rotation of 90° furnishes a planar fragment. Both compression a n d twisting can of course occur in a single system, although ab initio calculations on spiropentane show bending to be energeticahy more economical t h a n twisting^°. By 'inverted carbon' we will mean a fragment C W X Y Z in which all four bonds lie in the same half of a sphere centered on the carbon a t o m C, for example, 3^^ Equivalent definitions are that the plane determined by W, X a n d Y passes between C a n d Z; or that C lies outside the tetrahedron determined by W, X, Y a n d Z. N u m e r o u s c o m p o u n d s containing inverted carbon are known. Before turning to the types of carbon skeletons in which these distortions are imposed on tetrahedral carbon, we should note that an alternative approach to such geometry is through use of other sorts of bonds associated with different hybridization at carbon. Detahs lie outside the scope of this discussion, but calculations indicate that in carbon b o n d e d to two lithium atoms there should be a great increase in stability of a planar arrangement; the u n k n o w n systems 4 - 6 are predicted to the planar^. M o r e recendy, a n Xray structure of the tetramer of (2,6-dimethoxyphenyl)lithium has provided the first experimental evidence for a planar tetracoordinate carbon containing a CLi2 fragment^^. Earlier organometalhc c o m p o u n d s of interest here include a carborane for which an

20. Inverted a n d planar carbon

929 X

V

w (2)

(1)

HB

(3)

.Li

Li

"Li

(5)

(4)

(6)

average stucture with a planar carbon has been proposed a n d a n iron carbonyl derivative, C [ F e ( C O ) 3 ] 5 , for which X-ray d a t a show the o d d carbon a t o m virtuahy in the plane of four of the iron atoms When bonding involves only the more c o m m o n elements of organic chemistry, flattening or inversion of tetracoordinate carbon most often must be imposed structurally, and we shall discuss here the types of c o m p o u n d s that have received attention in this regard. Paddlanes (7), fenestranes (8) a n d propellanes (9) of appropriate ring size should contain one or two distorted quaternary carbons. Paddlanes a n d propehanes were first perceived as potential sources of inverted carbon in 1968^^, while saturated fenestranes were recognized to have flattened carbon in 1972^^. In addition, certain polyunsaturated fenestranes require attention as possible sources of flattened carbon. Systematic nomen clature is cumbersome for these series of c o m p o u n d s and, following earlier recommend ations, we shah employ the commonly used names^^, [m.n.p.^]paddlane^^ for 7, [m.n.p.^Jfenestrane""'^^'^^ for 8 a n d [m.?t.p]propellane^^ for 9, along with systematic numbering a n d the usual suffixes. Tetracyclo[3.3.1.0.^'^0^'^]nonane is then [4.4.4.4]fenestrane. Finally we note that bicyclo[1.1.0]butane (10)^^ a n d its derivatives^^'^^ provide examples of inverted carbon in q u h e simple systems. (CH2),.3

(CH2)p-3

(7) (8) (CHg)^

(CH2)p (9)

(10)

930

W. C. Agosta

Previous general reviews have touched on all of these structural types'^'^, a n d there have been more specialized surveys of the chemistry of propellanes^"^"^^, fenestranes^^'^^ a n d bicyclo[1.1.0]butanes^^ and of theory as applied to highly strained systems^^. Only when their constituent rings are sufficiently small can 7 - 9 lead to the distorted systems that form our central interest here. Discussion below concerns mainly [n.2.2.2]- a n d smaller paddlanes, [3.2.1]-, [4.1.1]- a n d smaller propellanes, a n d [5.5.5.7]- through [3.5.3.5]fenestranes, together with a few pertinent heterocyclic systems. It will be apparent that theoretical treatments, frequently at a high level, are available for m a n y of the significant systems a n d that calculated properties typically are in good agreement with the experimental facts at hand; what are lacking most often are syntheses of the highly strained c o m p o u n d s of greatest interest. II. THEORETICAL CONSIDERATIONS A. General

Theoretical discussions have provided a framework for understanding the properties of distorted tetravalent carbon, a n d they have served as a fruitful source of ideas a b o u t possible targets for synthesis a n d physical study. In 1970 Hoffmann a n d coworkers proposed^^ a structure for planar methane that has furnished the basis for subsequent consideration. T h e molecule has a normal set of sp^ bonds at carbon. T w o of these form normal two-electron bonds with two hydrogen atoms, using two of the valence electrons. The third sp^ hybrid participates in a two-electron, three-center b o n d with the t w o remaining hydrogen atoms, utilizing only hydrogen electrons. The two additional carbon valence electrons are placed in the remaining 2p orbital perpendicular t o the molecular plane, a n d resonance a m o n g equivalent structures renders all four c a r b o n - h y d r o g e n b o n d s equivalent. It was suggested^ ^ not long afterward that a triplet state version of this model should be energeticahy competitive with the closed-shell singlet description, a n d in 1980 Crans a n d Snyder reported^^ calculations indicating that the most stable structure for planar methane, by some 2 5 - 3 0 kcal mol" S was a singlet biradical. This differed from Hoffmann's structure in transfer of one of the unused carbon valence electrons from the 2p orbital into a n antisymmetric hydrogen d-type orbital. Over the years there have been calculations of the total energy of planar methane by a variety of techniques, a n d these have yielded estimates from 95 t o 250 kcal mol ~^ as the energy required t o flatten the tetrahedral molecule'^''^'^^"^'^. Perhaps the most rigorous of these estimations is that of Schleyer, Pople a n d their coworkers. This employed restricted M011er-Plesset secondorder perturbation theory as applied t o calculations at the 6-3IG** level a n d gave a n energy difference between planar a n d tetrahedral singlet methane of 157 kcal mol

B. Paddlanes

Both semiempirical molecular orbital (MNDO)^^'^^ a n d ab initio (6-31G*)^'^ calcul ations yield structures for [2.2.2.2]paddlane (11) reminiscent of the theoretical structures for planar methane. The bridgehead carbons are essentially planar (sp^ hybridization), a n d their out-of-plane p orbitals overlap t o produce a b o n d between them (12). In the ab initio structure the bridgehead-bridgehead distance is 1.525 A, a n d the bridgehead-methylene distance is 1.787 A. This latter value is reasonable for the 0.75 b o n d order indicated for three electrons distributed over four bonds. T h e heat of formation of 12 is 311 kcal m o l ~ \ corresponding t o a strain energy of 349 kcal mol a n d implying a release of 230 kcal m o l " ^ on fragmentation to ethylene a n d [2.2.2]propellane (13)^^. Simhar ab initio calculations for [ l . l . l . l ] p a d d l a n e (14) yielded a n analogous structure w h h b o n d e d


(11)

(12)

(14)

931

(13)

(15)

bridgehead carbon atoms a n d a strain energy of 456 kcal mol ~ ^ Molecular mechanics calculations for [3.3.3.3]paddlane yield a structure with only somewhat flattened bridgehead atoms, b u t extensive n o n b o n d e d interactions between the three-carbon chains, as shown in 15^^. C. Fenestranes

There has been considerable discussion of the possibility of stabilizing a planar carbon atom by placing it at the center of an annulene that would be aromatic if planar. Hoffmann and coworkers originahy suggested that the unsaturated [5.6.5.6]- a n d [5.5.6.6]fenestranes 16 a n d 17 were promising systems in this regard, a n d that the corresponding [4.4.4.4], [4.5.4.5] a n d [5.5.5.5] systems 18, 19 a n d 20 would be unstable^^. M N D O calculations support these conclusions for 18-20, but suggest that 16 also lacks stabhity^^; M I N D O / 3 ^ ^ predicts instabhity for 16,17 a n d 20"^^ It has been proposed, however, that 20 should be stabhized a n d flattened owing t o interaction between the energetically unfavorable highest occupied molecular orbital ( H O M O ) at the central a t o m a n d the lowest unoccupied molecular orbital ( L U M O ) of the peripheral twelve 7r-electron system. Related calculations also indicated that the delocalization energy in homoconjugated 21 is nearly as great as that in 20 a n d suggested that these h y d r o c a r b o n s should be attractive goals for synthesis""^. F o r saturated fenestranes ab initio molecular orbital calculations give acceptable estimates of energies a n d structures'^^. Semiempirical m e t h o d s have also proved quite useful, but molecular mechanics calculations for fenestranes are less accurate. Experience indicates that with the usual force constants molecular mechanics tends t o overestimate the energy required for large deformation of b o n d angles, introducing the possibhity of sizable errors both in absolute strain energy a n d in molecular geometry'^'^''^^. These empirical calculations are very convenient, however, for estimating energy differences between homologous or isomeric systems. Ab initio calculations give strain energies in the range of 148-157 kcal mol ~^ for the u n k n o w n (la,2i?,5a,6j9)[3.5.3.5]fenestrane (22) a n d its la,2jS,5j8,6j5 a n d l a , 2a, 5a, 6a diastereomers^^. This study included simhar calculations o n the two diastereomeric [3.3.5]fenestranes. T h e structure calculated for the known^^'^^ 3 a , 6 ^ isomer 24,

932

W . C. A g o s t a

(16)

(17)

(18) (19)

H

(20)

H

H

H —

H

(21)

f

H

(22)

(23)

H —

H

(24)

H

H

(25)

(26)


933

preparation of which is mentioned below, agrees well with the values obtained experimentally by electron diffraction^^. T h e calculated strain energy of 24 is 80 kcal mol~ \ a n d the u n k n o w n 3a, 6a isomer is predicted to have an energy 46 kcal mol~ ^ greater. Ab initio calculations on (la,5a,7j5)-[4.4.4.4]fenestrane (23) yield a strain energy of 160 kcal mol as weh as several other interesting c o n c l u s i o n s ' ^ ^ T h e c a r b o n - c a r b o n b o n d t o the central a t o m is unusually short, 1.480 A; the external c a r b o n carbon b o n d is rather long, 1.600 A; and the b o n d angle across the central atom is 130.4°. The very short b o n d seems to be the result of p o o r directionality, leading to markedly bent bonds. Fenestranes larger t h a n the [4.4.4.4] system have n o t been the subject of pubhshed ab initio calculations, but there are M N D O studies of several of these hydrocarbons^' F o r [4.4.4.5]fenestrane (25) and its [4.4.5.5] homologue 26, the calculated angles across the quaternary atom agree within 1° or better with experimental results. M N D O calculations for the u n k n o w n [3.5.3.5]fenestrane provide the b o n d angles across the central a t o m as 127° and 67° ^ ^ which may be compared with the ab initio resuhs of 123.8° and 72.4° for [4.4.4.4]fenestrane M N D O gives 132° for the central angle^^, while the ab initio structure has 130.4°"^^'"^^. Using data from crystal structures a n d M N D O calculations for a wide variety of spiro systems, including the embedded spiro systems of several fenestranes, Keese a n d coworkers have classified these systems according t o the a m o u n t s of compression and twisting contributing t o b o n d deformation at the spiro atom^'^'^^ Plots of these data show that a m o n g the systems examined fenestranes are unique in that flattening at the central carbon a t o m occurs almost solely t h r o u g h compression with little or n o twisting.

D. Propellanes

There has been intense theoretical interest in the smallest member of the series, [ l . l . l ] p r o p e l l a n e (27), a n d most of the physical properties of this surprisingly stable c o m p o u n d were correctly predicted from ab initio calculations performed before its s y n t h e s i s T h e central b o n d has been the object of m u c h attention, particularly since earlier studies suggested that it had n o charge density^^. An attractive current description is that this is a rather fat b o n d with charge spread o u t at the midpoint a n d having high local charge density at the bridgehead carbon atoms. The charge density is a b o u t 80% of that in the central b o n d of butane. This comes from a detailed analysis of the charge topology^^ of 27^^, a n d it is supported by other calculations^^'^^. However, there is another detahed theoretical description of the bonding in 27 suggesting that the H O M O is n o n b o n d i n g and not concerned with the C ( i ) — C ( 3 ) bond. In this picture and C^) are held together by a 'o--bridged Ti-bond', consisting of three-center, two-electron orbitals that use 2p7r orbitals on and C^) and sp^ lone pairs on the three methylene bridges^^. Some support for this view comes from the photoelectron spectrum of 27, where little change in structure accompanies the lowest energy ionization, although this also could be the consequence of the rigid cage structure of 27^^ However, later work using this theoretical approach, b u t with correlated wave functions, did indicate bonding between the orbitals on C ( i ) a n d C^)^^. Ab initio calculations on [2.1.1]propehane (28) a n d [2.2.1]propellane (29) suggest that the central b o n d in these hydrocarbons is q u h e weak^^'^^'^^. This is in keeping with the observation that, unlike 27, both 28 a n d 29 are stable only below 50 K in argon matrix^'^'^^ Inclusion of d orbitals in ab initio calculations is necessary in order to achieve consistent relative energies for [4.2.1]- and smaller propellanes^"^. Calculated structures are avahable for six propellanes, and the resulting ab initio energies have been converted into estimated enthalpies of formation ( + 2 kcal m o U ^) using a set of g r o u p equivalents^^. F o r the three

934

W. C. Agosta

(27)

(31)

(28)

(32)

(29)

(30)

(33)

(34)

smallest, [1.1.1]- (27), [2.1.1]- (28) a n d [2.2.1]propellane (29), strain energies were estimated t o be nearly constant at 102, 104 and 102 kcal m o l " \ respectively. F o r 27 the calculated structure and enthalpy of formation are in good agreement with experimental data^l M N D O appears t o provide satisfactory geometry for derivatives of [3.1.1]propehane (30), and H A M / 3 ^ ^ calculations based on M N D O geometry reproduce reasonably well the experimental ionizadon energies of 31, which is a [3.1.1]propehane^^. Molecular mechanics calculations are useful here only for less distorted systems, such as [3.2.2]propehane (32) and larger systems that d o not contain inverted carbon'^^. E.

Bicyclo[1.1.0]butanes

Extended Huckel calculations o n 10 are in substantial agreement with the structure derived from microwave spectroscopic studies^ ^ Extensive restricted H a r t r e e - F o c k calculations have been carried out o n the inversion of substituted bicycio[1.1.0]butanes and on the energetics of variation of the flap angle^^''^^ The results indicate that the ring system is surprisingly flexible, with little energy required for variations of u p to 20° in the flap angle. These calculations also reveal that inversion of the system involves non-leastmotion movement of the substituents at C(i) and C^). F r o m infrared and R a m a n spectra of bicyclobutane and appropriate deuterated isomers a new vibrational assignment was made with the help of the spectrum calculated using the 6-3IG* basis set^^. A normal coordinate analysis furnished atomic polar tensors a n d related properties. The results were compared with simhar data for cyclopropane a n d [l.l.l]propellane. F. Other Carbon Skeletons

Inverted carbon atoms can be incorporated into many other ring systems of lower symmetry than those discussed above. Molecular mechanics calculations have been reported for several such hydrocarbons, along with the opinion that the results indicate

20. Inverted and planar carbon

935

that these c o m p o u n d s should be attractive synthetic targets^^. A characteristic difficulty with such calculations is that they do not allow for energetic changes involved in the rehybridization that necessarily occurs in these distorted systems. F o r two of these hydrocarbons, 33 and 34, M N D O calculations, which have their own limitations, suggest strain energies that may be prohibitively high. The M N D O enthalpy of formation for 33 is 108 kcal m o l " \ and that for 34 is 101 kcal m o l " ^ F o r comparison, M N D O yields 37 kcal m o l " ^ as the enthalpy of formation of [4.4.4.5]fenestrane (25), which is isomeric with 343«.

III. PREPARATIVE CHEMISTRY AND PROPERTIES

O u r purpose here is to review the physical properties indicative of flattening or inversion of carbon in appropriate c o m p o u n d s and also to provide a brief synopsis of the synthetic approaches employed in their preparation. A. Paddlanes 1. Complex

structures

Less progress has been m a d e in preparation of strained paddlanes t h a n in the other areas under discussion. A number of c o m p o u n d s formally represented by 7 or heteroatom derivatives of 7 are known, including some, such as 35^^, 36"^^ and 37'^^, that were prepared without specific interest in inverted carbon. Others result from exploration of routes that might be adapted to highly strained systems but have led so far to c o m p o u n d s with conformational restrictions but not great angle strain. O n e of these is 39, which is available on Diels-Alder addition of dicyanoacetylene to furanophane 38^"^. The p r o t o n N M R

(CH2)io

(CH2)i2

(CH2)9

NMe

(35)

0

(38)

NMe

(37)

(CH2)8

+

NC

C = C — C N

(39)

936

W. C. Agosta

^502" (40)

OTOIO (CH2)8'

(CH2)i4' (42)

(43)X = 0 ( 4 4 ) X=NPh

spectrum of 39 shows evidence for two conformers at — 100 °C. The interesting triptycene derivative 41 results from benzyne addition to the bridged anthracene bis-sulfone 40, fohowed by pyrolytic eliminadon of S 0 2 ^ ^ . Both spectroscopic evidence a n d models indicate that the polymethylene bridge is fixed between two of the aromatic rings and cannot rotate about the triptycene skeleton. Reversal of the order of the synthetic steps was unsuccessful, as benzyne fahed to add to the 9,10-polymethyleneanthracene 42. Maleic anhydride and iV-phenylmaleimide did add, however, to a related bis-sulfide to furnish 43 and 44, in which movement of the chain is also restricted. Wiberg and O'Donnell investigated the addition of dicyanoacetylene to the [n](l,4)naphthalenophanes 45, where n is 8,9,10 and 14"^^. In ah cases the major product was 46, but with /t = 14 a smah a m o u n t of 47 was obtained. There was no evidence of significant distortion in this latter c o m p o u n d . Efforts by W a r n e r and coworkers to close the fourth ring in dibromides 48 and 49, where n = 0 and 1, led instead to dimeric bis-sulfides such as 50^^. 2. Simple

[n.2.2.21paddtanediones

A most interesting series of paddlanes are three c o m p o u n d s prepared by E a t o n and Leipzig^ ^ Reaction of bicyclo[2.2.2]octane-1,4-dicarboxaldehyde with lithium metal a n d 1,12-dibromododecane furnished the paddlanedione 51. Wolff rearrangement of 51 by way of the bis a-diazoketone 52 gave the expected bis ketene 53, which was converted to the new, lower homolog paddlanedione 54 on ozonolysis in the presence of propionaldehyde. Repetition of this sequence furnished the third member of the series, the [10.2.2.2]paddlanedione 55. There is a noteworthy progression of conformational


937

(CH2)i4

(CH2)„

(46)

(45)

(47)

CH2Br CH2Br

(CHsL CH2Br CHgBr

(49)

(48)

(CH2y 2Jn

(CHp)

(CH2)io

(51) X = H2 (52) X = N2

(50)

2^10

(53)

(54)/7 = 10 (55)/7=8

restriction in the series 51,54,55, N M R spectra indicate that motion of the polymethylene chain relative to the [2.2.2]bicyclooctane unit is free in 51, somewhat restricted a n d temperature-dependent in 54 and impossible in 55. This third c o m p o u n d is also the lowest member of the homologous series that can be constructed with space-hlhng models and, of course, it should be possible to attempt additional ring contractions from 55 in a n effort t o reach sthl lower members of this series. Molecular mechanics calculations suggest that, already in 55, there is some distortion of b o n d angles. B. Fenestranes

The material in this section is simply organized by decreasing ring size of the fenestranes of specific interest in the investigation under discussion. Owing t o the use of ring

W. C. Agosta

938

contractions in preparation of m a n y of these c o m p o u n d s , m o r e t h a n one fenestrane ring system m a y be encountered in a particular section. 1.

[5.5.5.7]Fenestranes

These large ring fenestranes are of interest because the only reported naturally occurring fenestrane is the diterpene lauren-l-ene (56). Since the structure was determined by crystallographic methods, b o n d distances a n d angles are available for the derived bromide 57. Angles across the central a t o m are 117.9° [C(i)—C(8)—C(7)] a n d 118.9° [ C ( 4 ) — C ( 8 ) — C ( 9 ) ] , reflecting a smah measure of flattening, a n d bonds to C ( 8 ) are 1.527-1.609 A, indicating n o b o n d shortening in this system. Three quite different syntheses have been reported for 56^^"^"^. In the first of these^^ the previously k n o w n ketol 58 was elaborated into keto aldehyde 59; this cyclized t o yield 60, a n d introduction of the final methyl g r o u p a n d stepwise conversion of the carbonyl g r o u p to a double b o n d gave lauren-l-ene (56). T h e second synthesis^^ proceeds t h r o u g h intramolecular photochemical cycloaddition in the key intermediate 61 with formation of 62. Conversion to 63 a n d then reduction, first with sodium in a m m o n i a a n d then by hydrogenation of the side-chain double bond, furnished 64, a n d this was converted from ester into aldehyde a n d cyclized to 60. Once again, although by a different route, this was converted to the natural product. T h e third synthesis^^, which is due t o Wender a n d coworkers, is the shortest a n d most efficient, a n d is conceptuahy remarkable. It proceeds t h r o u g h intermediate 66, which is prepared by alkylation of lactone 65 with h o m o p r e n y l iodide. This is reduced with hydride to the corresponding lactol, a n d then, in the key step.

^ O H

(58)

(60)


939

intramolecular photocycloaddition of the side chain of the lactol t o the aromatic ring gives 67. Unlike previous cases of this cycloaddition^^ (see Section III.B.2, for example), only a single vinylcyclopropane isomer was detected in this reaction, a result attributed t o the greater strain in the alternative product. Reductive cleavage of the C ^ j — C ( 5 ) b o n d of the cyclopropane with lithium in methylamine a n d concomitant reduction of the lactol yielded diol 68. Deoxygenation of 68 then furnished lauren-l-ene (56). 2.


There has been greater synthetic activity in this series of fenestranes t h a n in any other. The hrst simple member of the series to be prepared was tetraketone 69^^. This synthesis by Cook, Weiss a n d their coworkers is the prototype of several studies by these investigators. In the case at hand, 70 could be cyclized to 69 in good yield in h o t cumenediglyme containing a large quantity of 1-naphthalenesulfonic acid. An X-ray study confirmed the structure of 69 a n d showed that in the crystal the molecule exists in a chiral

COeMe

(61) ^COgEt

(62) R=C02Me

(64)

(63) R = C H = C H C 0 2 E t

HOCH

(65)

R= H

(66) R=CH2CH2CH=CMe2

(67)

CH2OH

940

W. C. Agosta

conformation with each crystal composed of a single enantiomer. As one would expect, in this [5.5.5.5] system there is less flattening at the central a t o m [ C ( i 3 ) ] t h a n in fenestranes with four-membered rings to be discussed below. Angle C ^ ) — C ( i 3 ) — C ^ ^ is 117.5° a n d C(4)—C(i3)—C(io) is 115.1°; b o n d lengths at C ( i 3 ) range from 1.527 A [ C ( 7 ) — C ( i 3 ) ] to 1.568 A [ C ( i o ) — 3 ) ] . T h e stereochemistry of 69 (la,4j5,7a, lOj?) is such t h a t the a p p r o a c h of a nucleophile from either side of the molecule to one of the carbonyl groups is sterically equivalent to the hindered endo a p p r o a c h in a cis-bicyclo[3.3.0]octanone. This unavoid able steric interaction nicely rationalizes the relative stability of 69 to base-catalyzed ring opening of its two jS-dicarbonyl groupings^^. Treatment with methoxide leads to slow, regiospecific cleavage, forming only 71 a n d n o n e of its spiro-fused isomer. Finally, reduction of 69 with diborane in tetrahydrofuran gave a diastereomeric mixture of tetrahydroxy c o m p o u n d s that was dehydrated by h o t hexamethylphosphoramide to provide (Ia,4j5,7a,10j9)-2,5,8,ll-[5.5.5.5]fenestratetraene (72) along with a smaller a m o u n t of the isomeric bridgehead alkene 73^^. P r o t o n a n d carbon nuclear magnetic resonance spectra of 72 are consistent with its expected symmetry. These two h y d r o c a r b o n s are the most highly unsaturated fenestranes presently known. Keese has explored quite different routes to [5.5.5.5]fenestranes. T h e first of these proceeds from lactone 74, which is avahable in several steps from 1,5-cyclooctadiene. This lactone was elaborated into 75, and this diester underwent D i e c k m a n n cyclization to give, after decarboxylation, cyclooctanone 76. Photolysis of the potassium salt of the derived tosylhydrazone then gave a carbene that inserted in the nearer tertiary c a r b o n - h y d r o g e n bond, furnishing the pentacyclic fenestrane lactone 77. In an unusual transformation 77 was converted to (13s,la,4iS,7a,10j5)-[5.5.5.5]fenestrane (78) on heating at 310 °C for 4.5 hours in the presence of palladium-on-carbon a n d hydrogen^^. W i t h o u t added hydrogen, 77 is essentially stable under these conditions; with hydrogen present, the product is a single h y d r o c a r b o n accompanied by ca 10% starting material. This h y d r o c a r b o n h a d spec troscopic properties appropriate for a [5.5.5.5]fenestrane, a n d its stereochemistry was assigned as depicted in 78 on the basis of its ^ ^C-NMR spectrum. This consisted of a threeline pattern compatible only with the symmetry of a Ia,4j8,7a,10j5 fenestrane. In principle, there are two such isomers, 78 (13s) a n d the contorted c o m p o u n d with inverted stereochemistry (13r) at the central carbon atom. Since the calculated strain energy of the latter species is ca 182 kcal m o l " \ Keese concluded that the reaction conditions leading to this product assured that it was the relatively strain-free 78 rather t h a n its highly unstable isomer. A second route t o 78 was first attempted from 7990'9i. Unlike 75 above, 79 did n o t cyclize in the D i e c k m a n n reaction, so it was converted to the corresponding dinitrhe 80 for Z i e g l e r - T h o r p e ring closure. This cyclization was successful, a n d exposure of the resulting enamino nitrhe to acid hydrolysis a n d then Jones oxidation yielded ketolactone 81. In this case the carbene insertion failed. These differences in the fates of closely related carbenes presumably reflect changes in dynamic conformation as a function of specific structure^^. In contrast to the carbene insertion, the thermal reaction in the presence of palladium-onc a r b o n used previously on 77 did succeed with 81, giving directly a modest yield of 78. In an attempt to reach a n isomeric [5.5.5.5]fenestrane, Luyten a n d Keese prepared the epimeric ketolactone 82 from dicyclopentadiene. Here decomposition of the tosylhy drazone salt led only t o olefin 83. Once again the high-temperature palladium a n d hydrogen process was effective, but the product was 78 rather t h a n the desired (la,4a,7a,10j5)-[5.5.5.5]fenestrane^^ According to molecular mechanics calculations this latter u n k n o w n isomer should be a b o u t 13 kcal m o P ^ m o r e strained t h a n 78^^. Keese a n d coworkers have also used the intermolecular a r e n e - a l k e n e photocyclo addition reaction as a key step in another route t o [5.5.5.5]fenestranes^^. Irradiation of 84 gave a mixture of products from which the desired adduct 85 could be isolated. Structure and stereochemistry of this tricyclic ester are supported both by earlier experience with the

20. Inverted and planar carbon Q

941

P

H

RO2C—^—CO2R

1 H

X

0

X

0

(70) R=H

(69)

(71)

R=CH3

—H

H—

(72)

(74) R = H (75)

R= CH2CH2C02CH3

(77)

(73)

(76)

W. C. Agosta

942

0

RCH2CH2 u

CH2CH2R

CH3O (79)

R = C 0 2 C H 3

(80)

R = C N

(81)

(82)

X O C

C H 3 0 2 C C H C H 2 C H 2 C H = : C ( C H 3 ) 2

(83)

(84)

/

/

(85) (86)X

X = C H 3 0 =

N 2 C H

H — -

H - -

OCOCF3 (88)

photochemistry of 5-phenyl-l-pentenes^^ and by N M R spectra. The corresponding diazoketone 86 was prepared by way of the mixed anhydride with isovaleric acid, and on treatment with trifluoroacetic acid this lost nitrogen and closed to a mixture (2.2:1) of fenestradienone 87 and trifluoroacetoxyfenestrenone 88. The structures of these products were estabhshed by p r o t o n and ^^C N M R spectra. Hydrogenation of 87 over palladiumon-carbon in methanol selectively reduced only the less substituted double b o n d and furnished 89. A totally different approach has led to the symmetrical tetrabenzo[5.5.5.5]fenestratetraene 90^^ which is avahable in gram a m o u n t s in nine steps from 1,3-indanedione (91) and dibenzylideneacetone (92)^^. The first key reaction in this synthesis by Kuck and Bogge^'^ is the Friedel-Crafts cyclization of triol 93 to 94, catalyzed


943

by phosphoric acid. Alcohol 94 is converted to 95 by way of Favorskii ring contraction of the derived ketone, followed by decarboxylation. Cycloaddition of 95 with tetrachlorothiophene S,5-dioxide (96)^^ furnishes 97, which is reduced by sodium and alcohol to 90. The X-ray structure of 90 indicates envelope-like bending of each cyclopentene ring, so that the molecular symmetry is S4 rather than D2d- The flattening of the central quaternary carbon is simhar to that of 69 with angle C ( i ) — C ( i 3 ) — C ( 7 ) equal to 116.5°.

(90)

(91)

(94)

(95)

(96)

(97)

944 3.

W. C. Agosta [4.4.5.5]Fenestranes

Several (Ia,3j8,6a,9j5)-[4.4.5.5]fenestranes are known, including the parent hydrocar bon^^, but the only c o m p o u n d for which structural information is available is keto amide 98, which was prepared by D a u b e n and his coworkers from 99^^'^^. Irradiation of 99 yielded the [4.5.5.5]fenestrane 100; ring contraction by way of the a-diazo ketone gave 101, and removal of the shyl protecting g r o u p and oxidation afforded two keto esters. These were separated, and the major isomer was converted to 98 for X-ray analysis. The resulting structure revealed considerable flattening at C^^^; angle — — i s 128.2° and C ( 3 ) — C ( i i ) — C ( 9 ) is 123.0°. These observed values are in good agreement with those from M N D O calculations^'^9'

H—

CH3O2C

R=Si(CH3)2C(CH3)3

4.

(101)


The [4.4.4.5]fenestranes are currently the tetracyclic fenestranes of smallest ring size and most flattened central carbon a t o m that have been synthesized and studied experiment ally. Representatives of this series are accessible from keto ester 102^^. Photochemical [2 -h 2] cyclization of 102 led regiospecifically to 103, and this was converted to diazoketone 104 after formation of the ethylene ketal. The keto carbene formed on exposure of 104 to r h o d i u m acetate cleanly inserted into the only readily accessible c a r b o n - h y d r o g e n b o n d , yielding the [4.4.5.5]fenestrane 105. Removal of the carbonyl g r o u p of 105 and deketalization gave 106. This was converted t o the a-diazoketone, and photochemical Wolff" rearrangement in methanol then yielded the [4.4.4.5]fenestrane methyl ester 107. This c o m p o u n d was thermally reasonably stable, surviving gas c h r o m a t o g r a p h y at 130 °C for a half h o u r with only slight decomposition. The derived p-bromoanhide 108 furnished crystals suitable for X-ray analysis. There are several noteworthy features in the crystallographic studies on 108. The angles C ( i ) — C ( i o ) — C ( 6 ) and C^)—C(io)—Qg), which reflect the enforced flattening at C(io), are 128.3° and 129.2°, respectively. T w o of the b o n d distances involving C(io) are quite short.

945


. . C O C H N 2

C 2 H 5 O 2 C

(102)

(103)

(104)

X O C

(105)

(106)

( 1 0 7 )

X = C H 3 0

( 1 0 8 ) X = p - B r C 6 H 4 N H

with both C(3)—C(io) and —C(io) only 1.49 A. The perimeter bonds for the cyclobutane rings are correspondingly lengthened to an average value of 1.574 A. These values are in quite good agreement with those given by M N D O c a l c u l a t i o n s ^ ' T h e shortened bonds to C(io) are also in line with the ab initio calculations for [4.4.4.4]fenestrane (23) discussed above, although in 108 the two shortest b o n d s to Cô) are associated with the five-membered ring. The chemical effects of these skeletal distortions appear in the thermal and photochem ical behavior of the [4.4.4.5]fenestrane ring s y s t e m ^ T h e observed reactions reveal a significant role in these processes for the short, weak bonds to the central carbon atom. O n heating to 100 °C in benzene keto ester 109, which was prepared from keto ketal 105, undergoes isomerization to two products, 110 (15%) and 111 (45%). The formation of 110 appears to be a symmetry allowed [^2^ + ^2^ -h ^2J thermal cycloreversion^^^ proceeding directly from 109 to the product, as shown in the structure with arrows. The fenestrane skeleton imposes on the six reacting carbon atoms [C(i) and C(6) to C(io)] a rigid boat cyclohexane geometry that is ideal for such concerted fragmentation^^^. Structure 111 for the second thermolysis product was substantiated by an X-ray crystallographic study. There is evidence that the mechanism of this singular transform ation combines homolytic and heterolytic steps. Homolysis of the C(8)—Cîo) b o n d in 109 gives 112, which fragments to 113, and under catalysis by adventitious acid this undergoes a 1,2 alkyl shift to form 111. In keeping with this mechanism, thermolysis of 109 in benzene at 100 °C as before, but in a stirred solution containing solid sodium bicarbonate, yielded 110 but n o 111, and when the thermolysis was carried out in methanol rather t h a n benzene as solvent, the product was 114, the c o m p o u n d expected^^^ from conjugate addition of methanol to 113. The initial major thermal product from 109 then is 113, which does not survive the reaction conditions but can be trapped as 111 or 114. W e see then that the thermal rearrangements of 109 to 110 and 113 involve rupture of either C^)—Cô) or C(8)—C(io)5 the two short central bonds expected to be weakest in the [4.4.4.5]fenestrane ring system'^''''^^^. The photochemistry of 109 probes reactions that can be initiated by electronic excitation of the ketone carbonyl. Irradiation of 109 t h r o u g h Pyrex ( > l > 2 8 0 n m ) in

946

W. C. Agosta

(CH3)3C02C,

(CH3)3C02C|

(CH3)3C02C,

(109)

(110)

(CH3)3C02C,

C02C(CH3)3

(112)

(111)

(CH3)3C02C

--H

CH3O--(CH3)3C02C.^^

y

I (113)

(114)

benzene containing ca 7% methanol led to three isolated products, the Z and E unsaturated esters 114 and 115 (ca 5% each) and aldehyde 116 (36%). Absorption of light leads to an UTT* state of the ketone carbonyl and then ^ cleavage of the C ( 6 ) — C ( 7 ) b o n d to form biradical 117; after conformational relaxation this can cleave to b o t h 113 and 118. Subsequent Michael addition of methanol yields 114 and 115. Such cleavage is not unusual in the photochemistry of cyclopropyl ketones, where its occurrence is attributed to strain. The strain inherent in 109 apparently is sufficient to permit ^ cleavage of a cyclobutane, although simple acylcyclobutanes do not behave in this fashion. F o r m a t i o n of 116 requires a cleavage of 109 toward the adjacent four-membered ring (cf 119), subsequent homolysis of the C ( i ) — C ( i o ) b o n d (cf 120) and then hydrogen transfer. This mechanistic sequence raises an interesting point. Typically, type I cleavage of cyclobutyl ketones takes place preferentially away from the four-membered ring or else gives both possible products, as formation of a cyclobutyl radical is somewhat d i s f a v o r e d C l e a v a g e of 109 toward the cyclobutane suggests that the b o n d suffering initial cleavage here [ C ( 5 ) — C ( 6 ) ] is relatively weak. In these photochemical reactions we see that short, weak bonds to the central carbon a t o m cleave in the second step, following light-promoted a or j5 cleavage of the ketone.

947

20. Inverted a n d planar carbon 0 (CH3)3C02C CHO

CH3O---4

1^ — H

(CH3)3C02C

(116)

(115)

0.

(CH3)3C02C

(CHjjjCOgC

(117)

(118) •CO (CH3)3C02C

(CH3)3C02

(119)

(120)

C. Propellanes 7.

General

We discuss preparation and properties of relevant propellanes according to ring size. F o r the larger ring systems frequently there has been a n X-ray crystallographic study, showing that the system does contain inverted carbon. Typically these c o m p o u n d s undergo rapid free radical reactions with opening of the central propellane bond, and such transformations are n o t specihcally mentioned in all cases. 2. [4.2.1

JPropellanes

Elimination of HCI from 1-cholorquadricyclane (121) leads t o transient olefin 122, which can be captured by anthracene to furnish the highly substituted [4.2.1]propellane 123. T h e X-ray structure of 123 indicates that the bridgehead carbon atoms of the propellane system are very slightly inverted; the plane of the three starred substituents of the nearer bridgehead passes 0.05 A behind the bridgehead. The necessary rehybridization is apparently sufficient t o lead t o typical propellane reactions, a n d 123 adds thiophenol readhy to form 124^°^. Related adducts form with substituted anthracenes. The parent [4.2.1]propehane is also k n o w n and is little more reactive t h a n bicyclo[2.1.0]hexane from which it is formahy derived

948

W. C. Agosta

(121) 3.

(122)

(123)

[4.1.1lPropellanes

The parent [4.1.1]propehane (125) is one of the products of pyrolysis of the sodium salt of tosylhydrazone 126^^"^. This carbene insertion gives a mixture of methylenecycloheptenes a n d the desired propellane. While 125 has been characterized spectroscopically, it is quite unstable. Its solutions are stabhized by addition of a radical inhibitor. Szeimies a n d his coworkers have prepared a number of more stable a n d structurally more complex [4.1.1]propehanes using two related approaches. The bridgehead positions of bicycio [1.1.0] butanes are somewhat acidic, so that 127 can be selectively lithiated a n d

NNHTs

(125)

(126)

(127) X = H (128)

(129)

(130)

X=CI

(131)

CH2(CH2)2CH2CI Br\

(132)

(133)

(134)


949

then converted to, for example, 128. The hrst a p p r o a c h is similar to that described above for preparation of 123. Reaction of 128 with strong base leads to the very reactive olefin 129, which is trapped in the presence of added anthracene as the propellane 130^°^. Similar reactions occur with 128 a n d various other anthracenes substituted at C ( 9 ) o r both C^g^ a n d C(io)» and analogous sequences have also been carried o u t with other bridged bicyclo[1.1.0]butanes, such as 13U^^'^ ^^.X-ray crystallographic studies show that the three starred substituents of 130 define a plane that passes between the two bridgehead atoms 0.31 A behind the near bridgehead^ T h e same extent of inversion is present in the homologous adduct from anthracene and 131^^^. These various [4.1.1]propehanes undergo a general thermal rearrangement that involves cleavage of the central propellane bond. Thermolysis of 130, for example, at 1 8 0 ° C gives 132^^^. In Szeimies's second propellane synthesis 127 was converted to 133 by way of organometallic intermediates. Treatment with butyllithium then gave 134, which is stable to storage in the cold^^^. A second intramolecular carbene addition simhar to that used for 125 has provided another type of complex [4.1.1]propehane. Pyrolysis of the dry sodium salt of 135 furnished the rather stable 136 in 7 5 % yield^^"^. This h y d r o c a r b o n was recovered

NNHTs

(135)

(136)

(137)

X=SMe

(138) X = H

+

,36

"OAc

"OAc

- ^ i ^

(140)

(139)

OAc

CH2OAC AcO

(141)

(142)

(143)

950

W. C. Agosta

unchanged after 24 hours at 80 °C and is inert toward nucleophhes at r o o m temperature. It reacts rapidly, however, with electrophiles and free radicals. Dimethyl disulfide, for example, adds instantaneously to yield 137. Reduction of 136 by lithium in ethylamine-hexane cleaves the central propellane b o n d in an electron transfer process to give 80% of 138. The two inverted carbons of 136 are structurally nonequivalent, and for this reason the behavior of this propellane on p r o t o n a t i o n is of some interest. Glacial acetic acid adds rapidly and essendally quandtatively to 136 to furnish a mixture of 141 (15%), 142 (25%) and 143 (60%). Majerski and Zuniac have suggested that these products arise from the rapidly e q u h i b r a d n g bicyclobutonium ions 139 and 140^^"^. The observation that products from p r o t o n a t i o n of only one of the two inverted carbons were isolated in this reaction was taken as evidence for a difference in electron density at these two sites. 4. [3.3.1

JPropellanes

Although [3.3.1]propehane itself is not expected to have an inverted carbon atom, one of the earliest k n o w n c o m p o u n d s that does is its derivative 1,3-dehydroadamantane (144). This hydrocarbon is prepared by debromination of 1,3-dibromoadamantane (145) with s o d i u m - p o t a s s i u m dispersion it is unchanged after three days at 100 °C in degassed heptane, but the cyclopropane ring is quite reactive with nucleophiles and molecular oxygen, even at r o o m temperature. In aqueous acid 144 rapidly gives 1-adamantanol, and treatment with bromine in heptane yields 145. Bromine in ether at — 70 °C reacts with 144 to form a yehow precipitate formulated as the oxonium tribromide 146. O n warming and isolation this yields 145 and the b r o m o ether 147^^^. 5. [3.2.1

JPropellanes

The parent [3.2.1]propellane 148 is avahable through carbene addition to 1(5)bicyclo[3.2.0]heptene I 5 0 7 ' I 5 , I I 6 , I I 7 jîis was the first c o m p o u n d with inverted carbon

(144)

(145) X=Br O r 3 "( 1 4 6 ) X = 0 E t 2 "+^ B

(150)

(148) X = H ( 1 4 9 ) X = CI

(147) X=OEt

MeOaC

COaMe

COeMe COgMe MeOaC (151)

(152)


951

to be prepared, a n d the X-ray structure of 149, which is the product of addition of dichlorocarbene to 150, indicated that the plane of the starred carbon atoms passes 0.1 A behind the nearer bridgehead^ ^ While 148 is thermally stable to 320 °C, where it fragments to 1,3-dimethylenecyclohexane (151), it reacts rapidly at r o o m temperature with acetic acid, oxygen a n d free radicals. Dimethyl acetylenedicarboxylate adds at 25 °C t o form 152 a n d 153^^^. Simhar reactions take place with the tetracyclic [3.2.1]propellane Several heterocyclic [3.2.1]propellanes are available through addition of furans a n d 1,2,3-trimethyhsoindole (155) to 122. F u r a n , for example, yields 156^°^

N—CH3

(156)

(155)

(154)

OMe

(158)

(160)

(159)

TsNHN.

OMe

(162)

(161)

6. [3.1.1

(163)

(164)

JPropellanes

Treatment of the bridgehead dibromide 157 with sodium in refluxing triglyme (216 °C), with direct distillation of the product into a cold trap, furnishes 7 5 % of the parent [3.1.1]propehane (158)^^^. This c o m p o u n d is stable in toluene solution at room temperature but polymerizes in the absence of solvent. It reacts at — 78 °C with methanol to give largely a mixture of the three isomeric ethers 159, 160 a n d 161. N u m e r o u s [3.1.1]propehanes have been prepared through trapping of transient bicyclo[1.1.03butenes such as 129 with furans, cyclopentadienes a n d isoindole ( 1 5 5 ) 1 0 8 , 1 1 0 , 1 1 2 , 1 2 0 jj^g ^^^^^^ ^jtj^ 129 is 162, the X-ray structure of which reveals that the plane of the starred atoms passes 0.40 A behind the bridgehead a t o m ^ ^ ^ Using the intramolecular carbene insertion route, Mlinaric-Majerski a n d Majerski

952

W. C. Agosta

have prepared two [3.1.1]propehanes. Pyrolysis of the sodium salt of 163 provides 164 in 70% yield^^^. This hydrocarbon decomposes only slowly at r o o m temperature in benzene, but reacts rapidly in radical reactions with methanol a n d with o x y g e n ^ W i t h acetic acid, 164 gives products similar to those formed from the related [4.1.1]propellane 136. Majerski has suggested that these reactions reflect high electron density at the back side of the bridgehead atoms a n d diradicaloid character at these c e n t e r s T h e photoelectron spectrum of 164 has been interpreted as indicating bonding character in the H O M O and, as noted above, M N D O calculations support this conclusion^^. Vincovic a n d Majerski prepared a second [3.1.1]propehane 165 from pyrolysis of 166^^^. This system is more strained than the parent 158, decomposing in 30 minutes at r o o m temperature in benzene. It reacts with HCI at — 8 0 ° C to yield only the nortricyclylmethyl chloride 167. Although this appears to involve external opening, rather than cleavage of the central propellane bond, p r o t o n a t i o n of the central b o n d t o give 168 followed by cyclobutyl t o cyclopropylcarbinyl rearrangement can also provide 167.

CHpCI

TsNHN

(166)

(165)

7. [2.2.1

(167)

(168)

JPropellanes

[2.2.1]Propehane (169) is much less stable than the larger ring systems discussed above. Its preparation involves dehalogenation of 1,4-dhodonorbornane (170) by potassium in the gas phase, with direct trapping of the product at 20 K in an argon matrix^ ^. I n line with calculations mentioned above^'^'^^, the central b o n d appears t o be quite weak; u p o n warming to 50 K a n d softening of the argon matrix, 169 polymerizes. It reacts with bromine to form 171.

(169)

(170) (171)

8. [2.1.1

x= r

(172)

X=Br

JPropellanes

P r e p a r a t i o n and properties of [2.1.1]propehane (172) are analogous to those of 169 just described. In this case 1,4-dhodobicyclo[2.1.1]hexane (173) served as precursor to the hydrocarbon^"^. The dehalogenation a p p r o a c h used successfully for preparation of 134 from 133 was


953

OEt

CH2CH2CI

CHMe

Br'

(176)

(175)

(174)

also applied to 174. Reaction of this intermediate with butyllithium in ether led to 175, presumably by way of the desired [2.1.1]propehane 176, which then added solvent in a radical reaction. 9. [1.1.1

JPropellanes

The original preparation of [ l . l . l ] p r o p e h a n e (177) involved Hunsdiecker degradation of bicyclo[1.1.0]pentane-l,3-dicarboxylic acid (178) to the dibromide 179 and then treatment of 179 with an alkyllithium^^. Unfortunately, 178 was only accessible with difhculty^^^, and [ l . l . l ] p r o p e h a n e remained effectively unavahable unth Szeimies and coworkers reported a remarkable two-step synthesis in 1985^^^. The commercially Br Br

CI

(177)

(178)X=C00H

CI

(180)

CI

CI

(181)

( 1 7 9 ) X = Br

(182)

(184) R = H

(183)

(185)

(187)

(188)

(186)

R=Ph

(189)

954

W. C . Agosta

available dichloride 180 adds dibromocarbene to form the expected cyclopropane 181 in moderate yield, and treatment of 181 with methyhithium gives [ l . l . l j p r o p e l l a n e (177) in good yield. This synthesis has m a d e 177 available in m u l d g r a m quantities and, as we note below, the propellane now provides a convenient starting material for preparation of many b i c y c l o [ l . l . l ] p e n a n e s , including 178. Related syntheses by Szeimies's group yielded tetracyclic derivatives of 177. Reaction of 182 with methyhithium furnished the trimethylene-bridged propellane 183, and a simhar approach led to lower h o m o l o g u e jg4i27,i28 addition, a carbene route to [1.1.1]propehanes was developed. F o r example, treatment of either dhodide 186 or the chloro c o m p o u n d 187 with methyhithium provides an alternative route to 183^^^'^^^, and similar treatment of 188 gives the dimeric propehane 189^3^. The structure of 177 has been determined by a neutron diffraction study^^^ and confirmed by analysis of the vibrational spectrum^'^. The bridgehead to methylene [ C ( i ) — C ( 2 ) ] distance is 1.525 A, while the bridgehead to bridgehead [ C ^ ) — C ^ j ] b o n d length is 1.596 A; the q ^ ) — C — C ( 4 ) b o n d angle is 95.1°. These results may be compared with those from the X-ray structure of the more complex 185^^^. There are two molecules per unit cell, so that two sets of data emerge from the study. The bridgehead to methylene distance is 1.534 (1.526) A, the bridgehead to bridgehead distance is 1.592 (1.586) A and the methylene-bridgehead-methylene bond angles are 89.3° (89.7°) for the symmetric pair and 98.0° (98.1°) for the angle involving the diphenylmethylene group. For ah [ l . l . l ] p r o pellanes for which structural informadon is available, the central bridgehead-bridgehead b o n d is between 1.577 and 1.601 A^^^'^^^. An interesting point to emerge from X-ray studies on 183 and 184 at 81 K is that there appears to be no accumulation of charge between the bridgehead nuclei, but there is charge density outside each bridgehead carbon atom^^^. This provides a nice explanation for the ease of electrophilic attack on the [ l . l . l ] p r o p e l l a n e system. The photoelectron spectrum of 177 has a narrow first band with an intense 0,0 vibrational component, strongly suggesting that there is little change in equhibrium geometry on passing from the hydrocarbon to the radical cation^ ^ As mentioned earlier, this could reflect fahure of the H O M O to provide significant C ( i ) — C ( 3 ) bonding, or it may simply be a consequence of the rigid structure. The ionization potential (— 9.74 eV) lies between that of cyclopropane ( - 10.9 eV) and bicyclobutane ( - 9.25eV). The C ( i ) — C ( 2 ) coupling constant in the ^^C N M R spectrum of 177 is 9.9 Hz, and the C — H c o u p h n g constant is 163.7 Hz. F r o m these data estimates of the hybridization at each b o n d have been made^^^. This approach^ leads to a value of sp^-^ at each bridgehead for the orbital forming the central bond. Thermolysis of [ l . l . l ] p r o p e l l a n e at 1 1 4 ° C in a gas flow system yields methylenecyclobutene (191), presumably by way of carbene 190 and 1,2 shift of hydrogen^^. At 430 ° C in a second study the only product was dimethylenecyclopropane, suggested to result from a symmetry-ahowed [^2s + ^ 2 J rearrangement Simhar thermal reaction of 183 at 370 ° C leads to 192 and 193, which were thought to arise from secondary rearrangement of the unstable primary product analogous to 192, which is 194. F o r m a t i o n of 195 from 184 can be rationalized in parallel fashion by way of 196 and 197^^^. Exposure of 177 to A g B F 4 , Rh(I) or complexes of Pd(II) yields largely the symmetrical dimer 198. A smah a m o u n t of methylenecyclobutene (191) is observed in some cases, and 191 becomes the major product with Pt(0) and Ir(I) c o m p l e x e s ^ R e a c t i o n s of [ l . l . l ] p r o p e h a n e 177 with electron-deficient alkenes and alkynes also occur readily^ Acetylene dicarboxylic ester (199), for example, yields a 1:1 adduct 201 and two 2:1 adducts 203 and 204. These are most easily understood through biradical mechanisms; addition of one of the propehane central bonding electrons to 199 forms 205, which can then collapse to 201 with one bond cleavage. Reaction of a second molecule of 177 with 201 leads to 206, and simple reorganization then furnishes 203 and 204. The same types of


(190)

(191)

(195)

(196)

(192)

955

(193)

(194)

(197)

(198)

Me02C

C02Me

C02Me

C02Me

R

C = C

R

(199)

R=C02Me

(201)

(200)

R=CN

(202)R=CN

Me02C^

R=C02Me

(203)

^C02Me

(204)

CN

-COoMe NC C02Me

(205)

(206)

(207)

(208)

R=

PrC=0

( 2 0 9 ) R = PhS ( 2 1 0 ) R = Li

PhSH

(211)

R=

PhC=0

(212)

R=

PhC=N2

( 2 1 3 ) R = PhC: (214)

( 2 1 5 ) R = Pr ( 2 1 6 ) R = Me

(218)

R=PhCHOEt

956

W. C. Agosta

Li+

EtO

Ph^

(219)

(220)

products are formed with dicyanoacetylene (200) in methylene chloride, but if the solvent is benzene the 1:1 adduct 202 is surprisingly attacked by solvent t o form 207^^^. The free radical additions c o m m o n t o small propellanes take place particularly readily with 177. Aldehydes a d d spontaneously a n d give both 1:1 a n d 1:2 adducts^^^. Butyraldehyde, for example, furnishes a 1:2 mixture of ketone 208 and ketol 215 by way of the bridgehead radical 217. Radical addition t o a n aldehyde carbonyl in successful competition with abstraction of the aldehydic hydrogen is exceptional. Here it occurs preferentially, and both acetaldehyde and benzaldehyde yield only ketol adducts. F r o m acetaldehyde this ketol is 216, and haloform oxidation of this adduct with iodine in base provides a convenient route t o dicarboxylic acid 178. T h e formerly difficult-of-access precursor to propellane 177 is thus now readily available in two steps from the propellane itself. Thiophenol (218) also adds spontaneously t o 177 to give the expected phenyl thioether 209^^^. Cleavage of thioethers with lithium 4,4'-di-tcrt-butylbiphenyl (219) is a useful m e t h o d for preparing organohthium compounds^ and this reaction has been employed here as a route t o l-lithiobicyclo[l.l.l]pentane (210)^^^. This in turn offers syntheticahy useful access t o a variety of 1-substituted b i c y c l o [ l . l . l ] p e n t a n e s through the host of wellk n o w n transformations of alkyllithiums. O n e particularly noteworthy set of reactions m a d e possible by the avahabhity of 210 involves preparation of the phenyl ketone 211 and its conversion to the tosylhydrazone. This permitted examination of the behavior of diazo c o m p o u n d 212, which is formed transiently on decomposition of the tosylhydrazone in ethanolic ethoxide. U n d e r the conditions employed 212 should lose nitrogen a n d form carbene 213. The observed products from this reaction are ethyl ether 214, explainable t h r o u g h insertion of 213 into solvent, and rearranged ether 220. F o r m a t i o n of 220 is nicely explained by way of a bond shift in carbene 213 to yield the anti-Bredt, bridgehead olehn 2 phenyl-l-bicyclo[2.1.1]hexene (221), which should add ethanol rapidly t o give 220^^^ A related transformation that promises t o be equahy useful syntheticahy is the reaction of 219 directly with 177 t o furnish the dihthio derivative 222 of bicyclo[l.l.l]pentane^^^. The bridgehead radicals formed on addition of free radicals t o 177 can also attack a second molecule of the propellane. Depending on the rate constants of the competitive processes involved, this can lead t o dimeric, trimeric and higher oligomeric species with various number of b i c y c l o [ l . l . l ] p e n t a n e unhs^^^'^^^. F o r example, treatment of 177 with dimethyl disulfide leads t o a small a m o u n t of 223, a m o n g other p r o d u c t s ^ M o l e c u l e s containing n bicyclopentane units joined by (n — 1) bridgehead bonds have been cahed [n]staffanes^^^. Both these oligomers of bicyclopentane^^^'^"^^ a n d the conceptually related oligomers in which bicyclopentanes are connected by acetylenic units^^^'^^^ can be prepared from [ l . l . l ] p r o p e h a n e s , and b o t h are of interest as providing a series of rigid molecules of k n o w n dimensions. D. Bicyclo[1.1.0]butanes

The chemistry of bicyclo[1.1.0]butanes is weh developed, with particular attention over the last two decades paid t o reactivity of the central b o n d with metal ions and complexes. Earlier work has been r e v i e w e d ^ a n d here we shah emphasize recent studies in this


957

area. As can be seen from the discussion of propellanes above, in recent years several bicyclobutanes have been prepared as intermediates in the synthesis of complex [n.l.l]propellanes. Two types of reactivity of bicyclobutanes with electron-deficient alkenes a n d alkynes have been k n o w n for m a n y years^"^^. These are an ene-like reaction a n d a cycloadditionlike reaction. The first is typified by the room-temperature addition of dicyanoacetylene (200) to 3-methylbicyclobutane-l-carbonitrhe (224) to furnish 225 as the major p r o duct a n d the second by the reaction between 224 a n d acrylonitrile at elevated temperature to give the bicyclo[2.1.1]hexane 226^^^. M o r e recently a third m o d e of reaction has been d e s c r i b e d f o r which the prototype is addition of tricycio[3.1.1.0^'^]heptane ('Moore's hydrocarbon', 227) to tetracyanoethylene (228) to form cyclopropane 229^"^^. It is noteworthy that 227 is incapable of undergoing either the ene-type reaction, which would produce an olefin violating Bredt's Rule, or the

Li-

MeS-

•Li

-SMe

7>

7>

(222)

(223)

7>

(224)

Me, ,CN

CN

CN

-CN

(225)

NC.

(226)

(227)

COaMe

(232)

CN

NC

CN

(228)

:02Me

MeOgC

CN

(231)

(230)

MeOaC

NC Me

NC

Me02C

C02Me

(233)

(234)

958

W. C. Agosta

cycloaddition-type process, owing to steric hindrance by the trimethylene bridge to the expected^"^"^ m o d e of addition. However, bicyclobutane (230) itself has now been seen to give adducts of this third type in some cases^ While addition of acetylene dicarboxylic ester (199) to 230 yields only ene product 231 in hydrocarbon solvent, this is accompanied by increasing a m o u n t s of a 2:1 adduct 232 in increasingly polar solvent. In acetonitrile or methanol the ratio of 231 to 232 is 3:2. F o r m a t i o n of 232 is most readily understood as the result of an ene-type reaction of a second molecule of bicyclobutane (230) with the initiahy formed third-type adduct 233; kinedc examination of the reaction supports this assumption. Simhar transformations occur with dicyanoacetylene (200). Earlier mechan istic work on these modes of addition t o bicyclobutanes has been summarized It appears that the ene-type reaction is generally concerted a n d that the cycloaddition-type reaction usually has a biradical intermediate. T h e new, third mode of addition appears t o involve ionic intermediates in view of its increasing importance in polar solvents Christl a n d coworkers proposed earlier that reaction between 227 a n d 228 proceeds through zwitterion 234, which then cohapses to product as shown IV. CONCLUSION

Interest in planar and inverted carbon has been driven by curiosity concerning the chemical and physical effects of increasing distortion of the tetrahedral carbon atom. As we have seen, this has led to the preparation of a wonderful variety of new ring systems, a n d there is now structural information for m a n y of these, documenting quantitatively the extent of flattening or degree of inversion at the distorted center. Of equal importance, a n d perhaps of greater interest to more organic chemists, there is now ample evidence that these bonding distortions d o indeed lead t o hitherto unobserved types of chemical behavior, offering new transformations a n d also access to novel or systems otherwise difficult of access. There remain unsolved problems. There are flattened or inverted systems that have not yet yielded to synthesis, a n d there are other systems n o t yet incorporated into structures providing the practical, kinetic stability that permits chemical a n d physical examination of the distorted center at leisure. All this said, it has been a rather successful and stimulating chapter in organic chemistry, so far. V. ACKNOWLEDGMENT

It is a pleasure t o thank Dr. S. T. Waddell for convenient access to his Dissertation^ which provides an excellent review of the chemistry of [ l . l . l ] p r o p e l l a n e s a n d bicyclo[1.1.0]butanes, as weh as a considerable contribution to their chemistry. VI. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

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960 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85.

86. 87. 88.

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W . C. A g o s t a M. D. Newton and J. M. Schulman, J. Am. Chem. Soc., 94, 773 (1972). W.-D. Stohrer and R. Hoffmann, J. Am. Chem. Soc, 94, 779 (1972). K. B. Wiberg, J. Am. Chem. Soc, 105, 1227 (1983). P. Chackrabard, P. Seller, J. D . Dunitz, W.-D. Schluter and G. Szeimies, J. Am. Chem. Soc, 103, 7378 (1981). R. F. W. Bader, Acc Chem Res., 18, 9 (1985). K. B. Wiberg, R. F. W. Bader and C. D. H. Lau, J. Am. Chem. Soc, 109, 985, 1001 (1987). A. B. Pierini, H. F. Reale and J. A. Medrano, J. Mol. Struct. Theochem, 33, 109 (1986). D . Feller and E. R. Davidson, J. Am. Chem. Soc, 109, 4133 (1987). J. E. Jackson and L. C. Allen, J. Am. Chem. Soc, 106, 591 (1984). E. Honegger, H. Huber, E. Heilbronner, W. P. Dailey and K. B. Wiberg, J. Am. Chem. Soc, 107, 7172 (1985). R. F. Messmer and P. A. Schultz, J. Am. Chem. Soc, 108, 7407 (1986). K. B. Wiberg and F. H. Walker, J. Am. Chem. Soc, 104, 5239 (1982). K. B. Wiberg, F. H. Walker, W. E. Pratt and J. Michl, J. Am. Chem. Soc, 105, 3638 (1983). F. H. Walker, K. B. Wiberg and J. Michl, J. Am. Chem. Soc, 104, 2056 (1982). K. B. Wiberg, J. Comput. Chem., 5, 197 (1984). K. B. Wiberg, W. P. Dailey, F. H. Walker, S. T. Waddell, L. S. Crocker and M. Newton, J. Am. Chem. Soc, 107, 7247 (1985). L. Asbrink, C. Fridh and C. Lindholm, Chem. Phys. Lett., 52, 63, 69, 72 (1977). M. Eckert-Maksic, K. Mhnaric-Majerski and Z. Majerski, J. Org. Chem., 52, 2098 (1987). O. Ermer, R. Gerdil and J. D. Dunitz, Helv. Chim. Acta, 54, 2476 (1971); H. Dodziuk, J. Comput. Chem., 5, 571 (1984); N. L. Allinger, Y. H. Yuh and J.-H. Lii, J. Am. Chem. Soc, 111, 8551 (1989). M. N. Paddon-Row, K. N. Houk, P. Dowd, P. Garner and R. Schappert, Tetrahedron Lett., 22, 4799 (1981). K. B. Wiberg, S. T. Waddell and R. E. Rosenberg, J. Am. Chem. Soc, 112, 2184 (1990). H. Dodziuk, Tetrahedron, 44, 2951 (1988). C. F. H. Allen and J. A. Van Allan, J. Org. Chem., 18, 882 (1953). T. Mori, K. Kimoto, M. Kawanisi and H. Nozaki, Tetrahedron Lett., 3653 (1969). C. W. Thornber, J. Chem. Soc, Chem. Commun., 238 (1973). R. Helder and H. Wynberg, Tetrahedron Lett., 4321 (1973). F. Vogtle and P. K. T. Mew, Angew. Chem., 90, 58 (1978); Angew. Chem., Int. Ed. Engl., 17, 60 (1978). K. B. Wiberg and M. J. O'Donnell, J. Am. Chem. Soc, 101, 6660 (1979). P. Warner, B.-L. Chen, C. A. Bronski, B. A. Karcher and R. A. Jacobson, Tetrahedron Lett., 22, 375 (1981). P. E. Eaton and B. D. Leipzig, J. Am. Chem. Soc, 105, 1656 (1983). T. Tsunoda, M. Amaike, U. S. F. Tambunan, Y. Fujise and S. Ito, Tetrahedron Lett., 28, 2537 (1987). M. T. Crimmins and L. D . Gould, J. Am. Chem. Soc, 109, 6199 (1987). P. A. Wender, T. W. von Geldern and B. H. Levine, J. Am. Chem. Soc, 110, 4858 (1988). H. Morrison, Acc Chem. Res., 12, 383 (1979); P. A. Wender and G. B. Dreyer, Tetrahedron, 37, 4445 (1981); J. Am. Chem. Soc, 104, 5805 (1982); P. A. Wender and J. J. Howbert, Tetrahedron Lett., 23, 3983 (1982). R. Mitschka, J. M. Cook and U. Weiss, J. Am. Chem. Soc, 100, 3973 (1978); R. Mitschka, J. Oehldrich, K. Takahashi, J. M. Cook, U. Weiss and J. Y. Silverton, Tetrahedron, 37,4521 (1981). W. C. Han, K. Takahashi, J. M. Cook, U. Weiss and J. V. Silverton, J. Am. Chem. Soc, 104, 318 (1982). M. N. Deshpande, M. Jawdosiuk, G. Kubiak, M. Venkatachalam, U. Weiss and J. M. Cook, J. Am. Chem. Soc, 107, 4786 (1985); M. Venkatachalam, M. N. Deshpande, M. Jawdosiuk, G. Kubiak, S. Wehrli, J. M. Cook and U. Weiss, Tetrahedron, 42,1597 (1986). See also in this regard M. N. Deshpande, S. Wehrii, M. Jawdosiuk, J. T. Guy, Jr., D. W. Bennett, J. M. Cook, M. R. Depp and U. Weiss, J. Org. Chem., 51, 2436 (1986). R. Keese, Nachr. Chem. Tech. Lab., 30, 844 (1982); M. Luyten and R. Keese, Angew. Chem., 96, 358 (1984); Angew. Chem., Int. Ed. Engl, 23, 390 (1984). H. Schori, B. B. Patil and R. Keese, Tetrahedron, 37, 4457 (1981). M. Luyten and R. Keese, Helv. Chim. Acta, 67, 2242 (1984).


961

92. S. D. Burke and P. A. Grieco, Org. React., 26, 361 (1979). 93. J. Mani, J.-H. Cho, R. R. Astik, E. Stamm, P. Bigler, V. Meyer and R. Keese, Helv. Chim. Acta, 67, 1930 (1984); J. Mani and R. Keese, Tetrahedron, 41, 5697 (1985). 94. D. Kuck and H. Bogge, J. Am. Chem. Soc, 108, 8107 (1986). 95. D. Kuck and A. Schuster, Angew. Chem., 100,1222 (1988); Angew. Chem., Int. Ed. Engl., 21,1201 (1988). 96. M. S. Raasch, J. Org. Chem., 45, 856 (1980). 97. V. B. Rao, S. Wolff and W. C. Agosta, Tetrahedron, 42, 1549 (1986). 98. W. G. Dauben, J. Pesti and C. H. Cummins, unpublished results. 99. V. B. Rao, C. F. George, S. Wolff and W. C. Agosta, J. Am. Chem. Soc, 107, 5732 (1985). 100. S. Wolff, B. R. Venepalh, C. F. George and W. C. Agosta, J. Am. Chem. Soc, 110, 6785 (1988). 101. R. B. Woodward and R. Hoffmann, Angew. Chem., 81,797 (1969); Angew. Chem., Int. Ed. Engl, 8, 781 (1969). 102. H. O. House, M. B. DeTar and D. VanDerveer, J. Org. Chem., 44, 3793 (1979). 103. S. Wolff and W. C. Agosta, J. Chem. Soc, Chem. Commun., 118 (1981); S. Wolff and W. C. Agosta, J. Org. Chem., 46, 4821 (1981). 104. A. G. Falhs, Can. J. Chem., 53, 1657 (1975); P. D. Hobbs and P. D. Magnus, J. Am. Chem. Soc, 98, 4594 (1976). 105. O. Baumgartel, J. Harnisch, G. Szeimies, M. Van Meerssche, G. Germain and J.-P. Declercq, Chem. Ber., 116, 2205 (1983). 106. P. Warner and R. LaRose, Tetrahedron Lett., 2141 (1972). 107. D. P. G. Hamon and V. C. Trenerry, J. Am. Chem. Soc, 103, 4962 (1981). 108. U. Szeimies-Seebach, A. Schoffer, R. Romer and G. Szeimies, Chem. Ber., 114, 1767 (1981). 109. U. Szeimies-Seebach, J. Harnisch, G. Szeimies, M. Van Meerssche, G. Germain and J. P. Declercq, Angew. Chem., Int. Ed. Engl, 17, 848 (1978). 110. A.-D. Schluter, H. Harnisch, J. Harnisch, U. Szeimies-Seebach and G. Szeimies, Chem. Ber., 118, 3513 (1985). 111. J.-P. Declercq, G. Germain and M. Van Meerssche, Acta Crystallogr., Sect. B, 34, 3472 (1978). 112. K.-D. Baumgart, H. Harnisch, U. Szeimies-Seebach and G. Szeimies, Chem. Ber., 118, 2883 (1985). 113. J. Morf and G. Szeimies, Tetrahedron Lett., 44, 5363 (1986). 114. Z. Majerski and M. Zuniac, J. Am. Chem. Soc, 109, 3496 (1987). 115. R. E. Pincock and E. J. Torupka, J. Am. Chem. Soc, 91, 4593 (1969); R. E. Pincock, J. Schmidt, W. B. Scott and E. J. Torupka, Can. J. Chem., 50, 3958 (1972). 116. K. B. Wiberg and G. Burgmaier, Tetrahedron Lett., 317 (1969); J. Am. Chem. Soc, 94, 7396 (1972). 117. P. G. Gassman, A. Topp and J. W. Keller, Tetrahedron Lett., 1093 (1969). 118. D. H. Aue and R. N. Reynolds, J. Org. Chem., 39, 2315 (1974). 119. P. G. Gassman and G. S. Proehl, J. Am. Chem. Soc, 102, 6862 (1980). 120. H.-G. Zoch. A.-D. Schluter and G. Szeimies, Tetrahedron Lett., 22, 3835 (1981). 121. U. Szeimies-Seebach, G. Szeimies, M. Van Meerssche, G. Germain and J.-P. Declercq, Nouv. J. Chim., 3, 357 (1979). 122. K. Mlinaric-Majerski and Z. Majerski, J. Am. Chem. Soc, 102, 1418 (1980); 105, 7389 (1983). 123. K. Mlinaric-Majerski, Z. Majerski, B. Rakvin and Z. Veksli, J. Org. Chem., 54, 545 (1989); Z. Majerski and K. Mhnaric-Majerski, J. Org. Chem., 51, 3219 (1986). 124. V. Vinkovic and Z. Majerski, J. Am. Chem. Soc, 104, 4027 (1982). 125. D. E. Applequist, T. L. Renkin and J. W. Wheeler, J. Org. Chem., 47, 4985 (1982). 126. K. Semmler, G. Szeimies and J. Belzner, J. Am. Chem. Soc, 107,6410, (1985); J. Belzner, U. Bunz, K. Semmler, G. Szeimies, K. Opitz and A.-D. Schluter, Chem. Ber., 122, 397 (1989). 127. J. Belzner and G. Szeimies, Tetrahedron Lett., 21, 5839 (1986). 128. J. Belzner, G. Gareiss, K. Polborn, W. Schmid, K. Semmler and G. Szeimies, Chem. Ber., 122, 1509 (1989). 129. J. Belzner and G. Szeimies, Tetrahedron Lett., 28, 3099 (1987). 130. G. Kottirsch, K. Polborn and G. Szeimies, J. Am. Chem. Soc, 110, 5588 (1988). 131. L. Hedberg and K. Hedberg, J. Am. Chem. Soc, 107, 7257 (1985). 132. P. Seller, J. Belzner, U. Bunz and G. Szeimies, Helv. Chim. Acta, 71, 2100 (1988). 133. R. M. Jarret and L. Cusumano, Tetrahedron Lett., 31, 171 (1990).

962

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134. E. W. Delia and P. E. Pigou, J. Am. Chem. Soc., 106,1085 (1984); K. Frei and H. J. Bernstein, J. Chem. Phys., 38, 1216 (1963). 135. (a) S. T. Waddell, Dissertation, Yale University, 1988. (b) K. B. Wiberg and S. T. Waddell, J. Am. Chem. Soc, 112, 2194 (1990). 136. P. K. Freeman and L. L. Hutchinson, Tetrahedron Lett., 1849 (1976); J. Org. Chem., 45, 1924 (1980); C. Rucker, Tetrahedron Lett., 25, 4349 (1984). 137. U. Bunz and G. Szeimies, Tetrahedron Lett., 31, 651 (1990). 138. U. Bunz, K. Polborn, H.-U. Wagner and G. Szeimies, Chem. Ber., 121, 1785 (1988). 139. P. Kaszynski and J. Michl, J. Am. Chem. Soc, 110, 5225 (1988). 140. R. Gleiter, K.-H. Pfeifer, G. Szeimies and U. Bunz, Angew. Chem., 102, 418 (1990); Angew. Chem., Int. Ed. Engl., 29, 413 (1990). 141. U. Bunz and G. Szeimies, Tetrahedron Lett., 30, 2087 (1989). 142. L. A. Paquette, Acc Chem. Res., 4, 280 (1971); P. G. Gassman, Acc Chem. Res., 4, 128 (1971). 143. M. Pomerantz, R. N. Wilke, G. W. Gruber and U. Roy, J. Am. Chem. Soc, 94, 2752 (1972). 144. P. G. Gassman and K. Mansfield, J. Am. Chem. Soc, 90, 1517 (1968). 145. E. P. Blanchard and A. Cairncross, J. Am. Chem. Soc, 88, 487, 496 (1966). 146. M. Christl, R. Lange, C. Herzog, R. Stangl, K. Peters, E. M. Peters and H. G. von Schnering, Angew. Chem., 97, 595 (1985); Angew. Chem., Int. Ed. Engl, 24, 611 (1985). 147. P. G. Gassman, K. Mansfield and T. J. Murphy, J. Am. Chem. Soc, 90,4746 (1968); J. Am. Chem. Soc, 91, 1684 (1969).

CHAPTER

21

Radical reactions of alkanes and cycloalkanes G L E N A. R U S S E L L Department

of Ctiemistry,

Iowa

State

University,

Ames,

Iowa 50011,

USA

L GENERAL INTRODUCTION IL R E A C T I V I T Y O F H Y D R O G E N A T O M S I N B R A N C H E D C H A I N ALKANES A. Bond Dissociation Energies B. Relative Reactivities of 1°-, 2°- a n d 3°-Hydrogen Atoms 1. Methane a n d ethane 2. Higher alkanes 3. Solvent effects a n d complexed chlorine atoms 4. Steric effects in radical attack upon alkanes 5. Reactivity of cycloalkanes 6. Radical reactions of spiroalkanes 7. Radical reactions of bicycio[m.w.O]alkanes 8. Reactivity of bridgehead hydrogen atoms IIL R A D I C A L A T T A C K O N C Y C L O P R O P A N E S IV. R A D I C A L C H A I N R E A C T I O N S I N V O L V I N G H A L O G E N A T O M S . A. Reversibhity of Hydrogen Abstraction Reactions B. Halogenations Involving Mixed Radical Chains V. R E F E R E N C E S

963 966 966 967 967 968 970 973 975 976 978 982 983 986 986 989 994

I. GENERAL INTRODUCTION

Attack of a n a t o m or free radical upon alkanes generahy involves attack o n hydrogen atoms via a more or less linear transition state (1). Attack at carbon in acyclic alkanes is excluded by a number of experimental observations including the absence of rupture of c a r b o n - c a r b o n bonds. Reactions proceeding via transition state 2 are excluded by the observed primary deuterium isotope effects which vary considerably with the nature of the attacking radical or atom. Moreover, when X* = D ' , n o h y d r o g e n - d e u t e r i u m exchange is observed by E P R spectroscopy for the radicals formed by attack of D ' upon


963

964

G. A. Russell

methylene groups ^ R H + X'

[ R — H — X ] i -> R- + HX

(1)

(1)

RH

+

X

X

R

+

HX

(2)

(2)

With cyclopropanes, radical attack can lead either to the cyclopropyl radical via 1 or to the ring-opened 3-substituted propyl radical via 2. The relief in ring strain as well as the high bond strength of cyclopropane c a r b o n - h y d r g e n bonds^ 106 kcal mol are the primary considerations in these competitive processes. With reactive radicals (as judged by the overah AH for reaction 1) such as r-BuO*, CI' or 3,3-dimethyl-Nglutarimidyl radical, hydrogen a t o m abstraction from the cyclopropane predominates^'"^, whereas for less reactive species such as Br' (where AH for reaction 1 is highly endothermic) only the ring-opening process is o b s e r v e d ^ W i t h more highly strained polycyclic compounds, such as [ l . l . l ] p r o p e h a n e , the efficiency of radical attack leading to ring opening increases. Thus reaction of propellane with B r C N forms the telomers 3 with n = 1-3 (X = C N , Y = Br)^ and even higher telomers {n = A or 5) or polymers are formed with benzoyl peroxide initiated reactions leading to 3 with X = Me02C, HO2C,

(Et02C)2CH, (Et02C)3C, (NC)2CH, (Et02C)2C(Ph), Me02CCH(0Me), Me02CCH(CN), (EtO)2P(0) and Y = H ^ Telomers w h h X = Y = Br or MeC(0)S are formed u p o n free radical reactions with Br2 or MeC(0)SSC(0)Me^ and even hydrogen wih add in a free radical manner to give 3, X = Y = H^.

(3)

Hydrogen a t o m abstraction reactions of alkanes (reaction 1) can be observed in chain reactions such as photohalogenation (Scheme 1), autoxidation (Scheme 2) or in nonchain processes such as shown in Scheme 3. In addition to the bimolecular trapping reactions of R* as typified in Schemes 1-3 the intermediate alkyl radicals can undergo competing unimolecular reactions such as ring opening in the cyclopropylcarbinyl radical (reaction 3) or the rupture of an unstrained c a r b o n - c a r b o n bond in alkane pyrolysis. In the absence of a trapping reagent, internal hydrogen atom transfers can occur in alkyl radicals (reaction 4) whhe adduct radicals arising from alkyl radicals often are observed to participate in an internal 1,5-hydrogen a t o m transfer, e.g. reactions 5 and 6^°'^^ Because of the possibhity of intramolecular or intermolecular hydrogen a t o m transfers, the observed radical trapping products are not necessarily a quantitative measured of the point of initial attack upon the alkane. The presence of radical rearrangements involving hydrogen atom migrations can in principle be detected by varying the concentration of the radical trapping reagent or by using appropriately deuterium-labeled alkanes

21. Radical reactions of alkanes a n d cycloalkanes

965

X2^2X'

initiator ^ R *

X- + R H ^ H X + R*

R- + O2

R- + X2 ^ RX + X-

ROO* + R H ^ R O O H + R*

2 X* ^'^^"^^ ) X2

2 ROO* ^ nonradical products

SCHEME 1

SCHEME 2

ROO-

PhN=NCPh3 ^ P h - + N2 + P h s C P h ' + R H ^ P h H + RR' + P h a C ' - ^ P h s C R SCHEME 3

(3) £^,,, = 23 kcal mol

CH3CH2CH2CH2CH, — MegC MeOgC

>CH3CHCH2CH2CH3

CHMeg

CH2

MegC

C=N*

MegC

MeOgC

CMeg

CH2

-N MeOgC

Me2CHCH2CHMe2 + O2

H

R-

CHg

(4)

CMeg

C = N H

MegC

CHg

CMeg

(5)

(-RH) MeOgC

> Me2C(OOH)CH2C(OOH)Me2 (95%)

(6)

The attack of an a t o m or radical upon an alkane whl depend on the energy content of the attacking radical with the rate constant increasing a n d selectivity decreasing with an increase in temperature. It is usually assumed that the attacking radical species is thermally equilibrated. However, for the more reactive attacking species such as Cl*, only a few molecular collisions need occur before a c a r b o n - h y d r o g e n b o n d is broken. If the attacking species has been generated with excess kinetic energy, e.g. in Scheme 1 where the reaction of R' with CI2 is highly exothermic, it is n o t certain that thermal equhibration can compete with hydrogen abstraction, particularly for reactions involving undhuted substrates. Some observations concerning primary deuterium isotope effects in gas-phase chlorination suggest that such h o t atom effects m a y indeed be important. Primary hydrogen-deuterium isotope rate ratios are quite sensitive to the reactivity of the attacking radical as measured by A H for reaction 1. Thus, the vapor-phase reaction of c r with CH4 has an energy of activation for hydrogen abstraction of about 2.5kcalmol~^ and /c(H)//c(D) for the photochlorination of CH2D2 is observed to be 14 at - 2 3 , 12 at 0 a n d 8.2 at 52 °C^^. Absolute rate measurements for the reaction of CH4 a n d CD4 with an excess of photochemically generated chlorine atoms in the absence of molecular chlorine lead to similar values, /c(H)//c(D) = 12-13 at 25 °C decreasing to about 2 at 500 "C with AE^= 1.8 kcal moP ^^-^ O n the other hand, the energy of

966

G. A. Russell

activation for attack of Cl* upon the 3°-hydrogen a t o m of isobutane is n o greater t h a n 0.3 kcal mol ~^ in the gas phase^^ a n d probably very close to 0. The photochlorination of M e g C H and Me^CT> yields /C(H)//C(D) as only 1.4 in the liquid phase at - 15 °C (based on the ratios of t-BuClA'-BuCl a n d t - B u C l / M E 2 C D C H 2 C L formed^^). T h e gas-phase competitive chlorination of C 2 H 6 a n d C 2 D 6 yields values of /C(H)//C(D) = 2.6-2.8 at 2 7 0 ^ 1 7 , 1 8 ^ critical survey of literature d a t a places the energy of activation for Cl* attack upon ethane t o be in the range of 0.1-0.2 kcal m o l " Surprisingly, the absolute rate constants for the reaction of Cl* with C 2 H 5 a n d C 2 D 6 in the absence of a chain chlorination reaction leads to much higher values of k{H)/k{D) of ~ 6 at 22 °C^^. Although the competitive chlorination should lead t o the more accurate measurement, the discrepancy is too large t o be ignored. O n e possibility is that, in chain reactions involving molecular chlorine, the chlorine a t o m carries excess kinetic energy from the exothermic ( ~ 25 kcal mol reaction of C 2 H 5 ' with C I 2 . The chlorine a t o m is essentially h o t a n d in a low energy of activation process yields a /C(H)//C(D) more consistent with a much higher temperature. Vapor-phase competitive photochlorinations in the presence of a n inert dhuent gas generally give a higher selectivity than liquid-phase chlorinations of neat hydrocarbons, possibly reflecting the thermalization of the chlorine a t o m in the presence of inert diluents. An additional complication of chain reactions such as photochlorination in the liquid phase is that, n o t only is the chlorine a t o m generated with excess kinetic energy from the propagation reaction, but the Cl* is generated in close proximity t o the RCl molecule formed by attack of R* upon C I 2 . Although the excess kinetic energy should help the chlorine a t o m escape from the solvent cage, there is a high probabhity of a second hydrogen a t o m abstraction reaction occurring with the RCl molecule in the solvent cage wall unless the cage wah contains molecules which are themselves quite reactive t o chlorine atoms^^'^^ This leads t o the production of di- a n d trichlorination products when photochlorinations are performed at low alkane concentrations in solvents which are inert t o chlorine a t o m interaction.

II. REACTIVITY OF HYDROGEN ATOMS IN BRANCHED CHAIN ALKANES A. Bond Dissociation Energies

The reactivity of c a r b o n - h y d r o g e n bonds towards a given free radical is a function of the b o n d dissociation energy, since this controls the value of AH for reaction 1. Complexities in measuring the enthalpy change in reaction 7, a n d particularly in measuring the energy of activation for the reaction of R* with H I , have led t o widely quoted values of 2°- a n d 3°-alkyl-hydrogen b o n d dissociation energies 3 - 5 kcal mol lower t h a n the best current estimates based o n dissociation-recombination equhibria measured for reactions 8 a n d 9^^. A comphation of 'best values' of b o n d dissociation energies (b.d.e.) based on dissociation-recombination equhibria a n d u p o n a reinvestigation of the energy of activation of the reaction of R* with H I is given in Table l^^'^^ r + R H — H I + R*

(7)

R—R'^R*-hR'*

(8)

R- — alkene -\- H* (or CU^)

(9)

The b o n d dissociation energies of a variety of H — X species are given in Table 2. These values when combined with the d a t a of Table 1 define the enthalpy change of reaction 1.

967

21. Radical reactions of alkanes a n d cycloalkanes TABLE 1. Bond dissociation energies (b.d.e.) for R — H at 25 °C Bond dissociation energy R

AHf^ of R-(25°C), kJ m o l - i

kcal mol ^

kJmol-i

146 ± 1 118.5 + 1.7 100 + 2 89 ± 3 6 7 + 3 48.6 + 1.7

105 101 101 98 99 96

439 420 422 408 411 401

Me Et Pr i-Pr sec-Bu ^Bu

TABLE 2. Bond dissociation energies (b.d.e.) of H — X at 25 °C X F OH CN

NH2 CF3 QHs H CI t-BuO

CCI3 t-BuOO Br

NF2 I

b.d.e. (kcalmol"^) 135 118 111 108 106 105 104 103 102 96 90 87 76 71

B. Relative Reactivities off 1 ° - , 2°- and 3°-Hydrogen Atoms 1. Methane

and

ethane

The high bond dissociation energy for a C — H bond of methane greatly reduces the reactivity towards radical attack a n d methane is quite unreactive compared with other simple alkanes. Cyclopropane hydrogen atoms are similarly unreactive as are the methylene hydrogens in many bicycloalkanes containing a one-carbon bridge. Only the most reactive of radicals whl abstract a hydrogen a t o m from methane at ordinary temperatures. Table 3 gives a compilation of data from gas-phase kinetic studies using critical evaluations of literature data where avahable^^. As shown in Table 3, there is a general correlation between the energy of activation for attack o n methane a n d the selectivity when methane a n d ethane are compared. Evans a n d Polanyi demonstrated that the simple relationship = (x{AH°) + ^ holds in many radical methathetical or transfer reactions such as reaction 1 2 6 , 2 7 value of a, of course, should be less than 1^^. In the E v a n s - P o l a n y i equation the factor a can be associated with the a m o u n t of bond breaking in the transition state. T h e values of a calculated from the energies of activation for attack of halogen atoms o n methane a n d ethane vary from 0.2 for F* t o 0.6 for cr. However, with Br' a n d V values of a > 1 are observed, since the experimental

968

G. A. Russell TABLE 3. Relative reactivities of CH^ and CjU^ at 25 °C /cCC^H^VMCHJ Attacking radical

E,{CH^)

A/Z^CCHJ

molecule

perH

F*

1.2-1.9

cr

2.5 18 34-35 5 1-8 12 10-12 14 22

-35 +2 + 18 + 34 -13 -6 +1 -1 0 +9

3 560 3150 1.2 X 10^ 39 29 42 110 -450 -355"

1:2 1:370 1:2100 1:800,000 1:26 1:19 1:28 1:73 -1:300 -1:250

Br*

r

HO* NC* H* CF3* CD3* CCl3*

"Assuming a constant A value and reported

values.

EJ(2H^)

values of — EJ(C2il6) exceed the difference in b o n d dissociation energies (4 kcal m o l ~ ^) with AE^ = 4.8 for Br* a n d 7.5 for I*. Certainly with these unreactive species participating in highly endothermic reactions there must be a considerable change in the n a t u r e of the transition state when the substrate is changed from m e t h a n e t o ethane. The reaction of alkyl radicals with H I is now postulated to involve an intermediate such as R - - - i - - - H ^ ^ and, by microscopic reversibhity, a simhar intermediate may be involved in the attack of F u p o n a c a r b o n - h y d r o g e n bond. (The overall energies of activation for reaction of t-Bu* with H I and H B r are reported to be a b o u t — 1.5 kcal mol ~ ^)^^. F o r the carbon-centered radicals CF3*, CD3* a n d CCI3* one would expect an increase in selectivity in the order listed. Values of AEJiCH^.—C2H6) are roughly constant at 4 + 0.2 kcal mol ~ ^ a n d are approximately equal to the change in the b.d.e., although at 164°C,CF3* is approximately 100 times m o r e reactive than CD3* or CH3* towards b o t h CH4 a n d C 2 H 6 ^ ^ 2. Higher

alkanes

The reactivity of methyl groups in alkanes towards radical attack is reasonably constant towards Cl* at 25 °C in the gas phase; the reactivities per methyl g r o u p relative to ethane vary from 1.2-1.5 in p r o p a n e , butane, isobutane a n d n e o p e n t a n e ^ ^ Intramolecular competition studies can m o r e precisely determine small differences in reactivity t h a n intermolecular competitions or absolute rate measurements. The gas-phase chlorination of M e 3 C C H 2 C H 2 C H 2 M e at 101 °C is reported to yield (among other isomers) a 2:1 ratio of C l C H 2 C M e 2 C H 2 C H 2 C H 2 M e a n d M e 3 C C H , C H 2 C H 2 C H 2 C P ^ . This would seem to indicate a m u c h lower reactivity of t-butyl mf.thyl groups c o m p a r e d with the methyl g r o u p in a n-alkane. However, in this system the low yield of C l C H 2 C M e 2 C H 2 C H 2 C H 2 M e is accompanied by an unexpectedly high yield of M e 3 C C H 2 C H 2 C H ( C l ) M e (29.6% of the monochlorinated products) when c o m p a r e d with M e 3 C C H 2 C H ( C l ) C H 2 M e (21.9%). This suggests the possibility that the chlorination products are not a true measure of the point of Cl* attack a n d that • C H 2 C M e 2 C H 2 C H 2 C H 2 M e m a y undergo a facile 1,5-hydrogen a t o m migration to form M e 3 C C H 2 C H 2 C H M e in a process which competes with the reaction of CI2 with the r - a l k y l radical. Direct competition of b u t a n e a n d neopentane with F* at r o o m temperature indicates that the four methyl groups of neopentane are 1.8 times as reactive as the two methyl

969


groups of butane in a reaction with zero energy of activadon^^. I n a c o m p e d d o n between ethane a n d p r o p a n e the methyl group reactivities showed a slight preference (35%) for attack on propane^"^. Towards CD3' the rate constants for attack o n ethane .-neopentane .'hexamethylethane are in the ratio 2:3.2:5.2, i.e. very close t o the statistical ratio of 2:4:6^^. In Table 4 some typical r : 2 ° : 3 ° rate ratios are summarized, based on intramolecular competition with the assumptions that ah methyl groups have the same reactivity towards a given radical. Where possible, the values of k(2°)/k{l°) and /c(3°)//c(r) are based o n data for n-alkanes, isobutane a n d 2,3-dimethylbutane. Table 4 presents a fairly consistent correlation of reactivity a n d selectivity. T h e value of a in the E v a n s - P o l a n y i equation increases as the strength of the new b o n d (HX in TABLE 4. Relative reactivities (per atom) Attacking radical F*

cr cr 'Cl" 'Cl" H* H* D* HO* t-BuO* Ph* p-O^NC^H/

CH3CDs'

CF3CCla* Br* NF^*

r PhlCl* CIRCS' CIO* R3CC(C02Me)=N*

Conditions 25 °C, gas 25 °C, gas 25 °C, hquid

25 °C, 4MC6H6 25 °C, 12 M CS2 25 °C, hquid 480 °C, gas 35 °C, liquid 480 °C, gas 40 °C, liquid 60 °C, hquid 60 °C, hquid 77 °C, gas 164 °C, gas 184 X , gas 150°C, gas 150 °C, gas 100 °C, gas 25 °C, gas 40 °C, liquid 0 °C, liquid 95 °C, gas 98 °C, hquid

t-BuOO*

1.1-1.4 3.7-3.8 2.2-3.0 5

1.4 5 3.5-4.5 20

25 6-7 6-6.5 5

225 -90 26 42 8.6 50 44 50 215 100 60 -1300 -1600 -700 -210,000 370 110-120 71 -55

3.3 12 9 11 20 10 10 70 80 8-30 -1850 21 29-33 22 -12

References 33,34,36,37 31 12,38

39 39 40 41 42 41

43 44

45 46 30

47 48 49,50 51 52

53 54 55 10

/c(r)>/c(2°)>/c(3T

56

100 °C, hquid 55 °C, liquid

/c(3°)//c(2°) = 17-22 >10

57 58

25 °C, hquid

/c(3°)//c(2°)= 1 6 - 2 0

59

50 °C, liquid

See Table 9, /c(3°)//c(2°) = 10-20

60

25 °C, hquid

so^cr

k{r)/k{r)

"^(1° at C-4) > k{2°) in 2,2-dimethylbutane and k{r)> /c(3°) in 2-methylbutane. ^Cytochrome P-450 model formed by oxygen atom transfer to chloro(5,10,15,20-tetra-o-tolylporphyrinato)iron(III). With adamantane /c(3°)//c(2°) varies with the aromatic substituent o n the porphyrin ring from 11 to 20 to 4 for the tetramethyl, tetraphenyl and tetra-o-tolyl derivatives^°.

970

G. A. Russell

TABLE 5. Values of k{2°)/k{r)

on a per-hydrogen basis for heptane photochlorination with CI2 Position

Condidons

2

3

4

Average

Reference

Neat, 20 °C Neat, 80 °C Gas, 100 °C Gas, 260 °C Q H g s o l n , 20 °C CS2 soln., 20 X

3.0 2.1

2.9 1.9

2.8 1.8

8.1 27

9.9 35

9.1 31

2.9 2.0 2.4 2.0 8.9 30

62^ 63 64 64 65 66

2.7

2.4

2.0

2.4

64

Cl2C=C(Cl)C(Cl)=CCl2 soln., 80 X "Average of several experimental reports.

reaction 1) being formed decreases. Thus, for CH3' a n d CF3* a is ~ 0.5 while a increases to 0.86 for Br', 0 . 9 0 for N F 2 ' a n d 0.97 for The value for the gas-phase reaction of chlorine atoms with 1° c a r b o n - h y d r o g e n b o n d s is n o more t h a n 0.2 kcal mol~ ^ and is essentially zero for the reaction of 2° a n d 3° c a r b o n - h y d r o g e n bonds^^. Nevertheless, there is a n appreciable r : 2 ° : 3 ° selectivity which is somewhat greater in the gas phase t h a n in neat h y d r o c a r b o n solution. A careful study of the photochlorination of hexane in the gas phase led t o the equation^ ^ /c(2°)//c(r) = (2.2 ± 0.6) exp [ ( 0 . 2 1 4 ± 0 . 1 2 7 ) / R r ] O n the other hand, the selectivities in solution seem to be mainly determined by energy of activation differences. Thus, in the liquid phase hexane yields the equation /c(2°)//c(l°) = (0.8 ± 0.2) exp [ ( 0 . 5 9 7 ± 0 . 0 2 0 ) / R r ] A variety of d a t a for heptane are collected in Table 5. There is n o generally accepted explanation for the differences in selectivities for gas- a n d liquid-phase photochlorinations. As mentioned earlier, in the liquid phase a chlorine a t o m formed by the reaction R ' + CI2 RCl + R* has a good chance of reacting with a molecule in the wall of solvent cage before the chlorine a t o m can diffuse o u t of the cage. The c r m a y also possess excess kinetic energy (from AH of the reaction in which it was formed) a n d this energy can be shared with the cage ensemble a n d raise the effective temperature of the cage considerably above the ambient temperature of the solution. This would lead to a lower selectivity if indeed there is an appreciable E^ value for hydrogen a t o m abstraction. T h e temperature effects routinely observed in liquid-phase chlorinations d o suggest a higher AE^ value than in the gas phase, b u t this m a y reflect barriers to the orientation of the h y d r o c a r b o n molecules (in the cage walls surrounding the c r ) to form the nearly linear transition state depicted in 1.

3. Solvent

effects

and complexed

chlorine

atoms

The appreciable effect of certain solvents in liquid-phase photochlorination reactions is the result of the formation of complexes between the extremely electronegative Cl* and the solvent. These can be cr-complexes such as CS2Cr, S02Cr, PhlCr, CsHsNCl* or TT-complexes as observed for most aromatic molecules^"^"^^. As expected, the selectivity increases with the concentration of the complexing agent. Table 6 presents d a t a for the relative reactivity of the 3°- a n d T - h y d r o g e n a t o m s in 2,3-dimethylbutane (DMB) a n d the 2 ° - a n d T - h y d r o g e n atoms in heptane in CS2 a n d P h H solutions.


971

TABLE 6. Solvent effects in the photochlorinadon of 2,3-dimethylbutane^^''^ and n-heptane^^-"^ at 2 0 - 2 5 °C

n-Heptane

lk{2yk{r)Y

DMB Solvent

/c(3°)A(r: 4.2 15 105 225 11 20 49

Neat CS2,2M CS2,8M CS2,12M PhH,2M PhH,4M PhH,8M

C-2

C-3

C-4

3.0

2.9

2.8

27

8.1

35

9.6

31

9.1

"Per hydrogen atom.

The TT-complex of a chlorine atom with an aromatic molecule can approach the selectivity of a bromine atom. The observed selectivity of a chlorine a t o m in the presence of a complexing agent also depends upon the substrate c o n c e n t r a t i o n b e c a u s e the rate of the reaction of Cl* with the substrate a n d the complexing agent are of the same magnitude^ ^ Scheme 4 presents the absolute rate constants that have been deduced by a study of the chlorination of D M B by the laser flash photolysis technique^ ^

->

C|. -h

CgHg

1.3 X 10*^M~'s

MegCHCMeg

Cl-

4-

DMB-

IVIe2CHCH(Me)CH2*

7

4.6 X 1 0 ' M " ' s

4

+

Me2CHCMe2

DMB-

Me2CHCH(Me)CH2*

S C H E M E 4. Chlorination of 2,3-dimethylbutane (DMB) in benzene soluhon

The complex of 4 gives a K(3°)/K{R) selectivity of 126, considerably greater than the selectivity of ~ 50 observed in 8 M benzene where both the free chlorine atom a n d the complexed atom abstract hydrogen atoms from the alkane.

972

G. A. Russell

The selectivity of the chlorine a t o m in complexing aromatic solvents increases with a decrease in the ionization potential of the solvent u p to the point where the 7i-complex is so unreactive that most of the reaction occurs via the free Cl*. Thus, selectivity for attack o n D M B at 4 M aromatic concentration increases from P h N 0 2 t o P h C F j t o P h C l to P h F t o P h H a n d l,3-Me2C6H4. However, making the aromatic molecule a better complexing agent, e.g. l,3,5-Me3C6H3, l,2,4,5-Me4C6H2 or Me5C6H, results in a decrease in selectivity because a higher fraction of the hydrogen a t o m abstraction occurs by attack of the uncomplexed chlorine atom'^^ Pyridine forms a complex with c r , which is k n o w n to be a a-complex with the chlorine attached t o the nitrogen a t o m and in the plane of the pyridine ring"^^. Although the structure of this complex is quite different from the arene 7c-complex 4, photochlorination of D M B in CCI4 with 2 M pyridine gave about the same ratio of 3° t o 1° attack as observed with 2 M l,4-(t-Bu)2C6H4 forming the 3°- a n d l°-alkyl chlorides in a 8.0-8.5:1 ratio at r o o m t e m p e r a t u r e ' ^ U n d e r these conditions 2 M P h i gives a 371° ratio of chlorides of 23, /c(3°)//c(l°) = 138. Photochlorination of low concentrations of substrates such as D M B in inert solvents leads t o high percentages of di- a n d trichlorination products even at low conversions of the substrate^^. The polychlorination is drastically reduced by the presence of complexing solvents. Reaction in an inert solvent of an alkyl radical with molecular chlorine forms a molecule of the alkyl chloride a n d a chlorine atom with excess kinetic energy. U n d e r these conditions there is a high probability that the Cl* will react with abstraction of a hydrogen a t o m from the alkyl chloride in the wall of the cage of molecules surrounding the chlorine atom before the chlorine atom can diffuse o u t of the solvent cage. In the presence of solutes such as benzene, the cage walls will contain molecules which readily complex the chlorine atoms, thereby decreasing their reactivity and allowing them to escape from the molecule of alkyl chloride a n d thus decreasing the a m o u n t of polychlorination. Quantitative measurements of the effects of different aromatic solvents upon the ratio of m o n o - to polychlorinated neopentane in Cl2C(F)C(Cl)F2 has provided a measurement of the relative rates of complexation of c r by aromatic solvents'^. As would be expected for a process involving diffusion out of a cage, viscosity of the solvent can have an effect on the ratio of m o n o - t o polychlorination products'^^ 'Complexed chlorine atoms' can be generated directly by alkyl radical attack u p o n species such as PhICl2, SO2CI2 or PCI5. In the case of PhlCl* httle dissociation into P h i a n d free Cl* occurs a n d high selectivities are observed (Table 4). With SO2CI*, dissociation to the free chlorine atom occurs readhy. With reactive alkanes at low temperatures (e.g. 55 °C), SO2CI2 chlorinations are considerably more selective t h a n photochlorinations with C l i ^ ^ Thus, for D M B at 55 °C a k(3°)/k{r) reactivity of 10 is observed for SO2CI2 vs 3.7 for CI2. Addition of CgH^ gives rise t o the benzene-complexed chlorine atom and, if the SO2 is allowed t o escape, essentially the same selectivities are observed in chlorination by the two reagents. At higher temperatures, or with hydrocarbons with a low reactivity, there are only minor differences between the product ratios observed with SO2CI2 a n d Cl2^^. Photochlorination of octane by PCI5/BZ2O2 at ^ 100 °C, or with CI2/PCI3, gives a very high selectivity (approximately equivalent to that observed in CCl3- attack), indicating that the species PCI4* is capable of abstracting a hydrogen atom^^. The radical CI3CSO2* (formed by alkyl radical attack on CI3SO2CI) can dissociate into SO2 a n d 0013*"^^. In Table 7 the selectivities observed are identical for the benzoyl peroxide (BZ2O2) initiated chlorination of n-octane with CCI4 or CCI3SO2CI at 98 °C, suggesting that complete dissociation of CCI3SO2* to CCI3* occurred^^. F r o m Table 7 it is also obvious that N-chlorosuccinimide is reacting via a chlorine atom chain because of the facile reaction with HCI (reaction 10).


973

TABLE 7. Chorination of n-octane at 98 °C^^

Reagents'"

^CH3—

t-BuOCl, BZ2O2 CCU,BZ202 Cl3CS02Cl,BZ202 CI3SCUV PCl5,BZ202 NCS,BZ202 Cl2,/iv,20°C

8 2 2 5 2 15 14

% of monochlorides -^CH2—^CH2H« 40 42 42 32 28 31 30

28 30 30 33 35 29 28

25 26 26 31 35 25 27

"BZ202 = benzoyl peroxide; N C S = iV-chlorosuccinimide.

\N

4. Steric effects in radical

Cl +

attack

upon

(10)

;NH + C I 2

HCI

alkanes

The values of k(2°)/k{r) a n d /c(3°)//c(r) of Table 4 have been derived mainly from the simplest of alkanes. With highly branched alkanes steric effects become apparent even with the reactive Cl*. With sterically hindered radicals such as the amine radical cation derived from Ar-chloro-2,2,6,6-tetramethylpiperidinium ion, the reactivity of the 2position of pentane is 5 times that of the more hindered 3-position^^. In general, methylene hydrogen atoms near the end of a long alkane chain are more reactive towards radical attack t h a n methylene groups nearer to the center of the chain; e.g., see Table 7. With 2,3,4-trimethylpentane the two 3°-hydrogen atoms are quite different in reactivity towards Cl* a n d even the two kinds of methyl groups are differentiated by the hindered R S 0 2 N ( t - B u ) * radicals (Table 8)"^^ With the stericahy hindered amino radicals the 3°-hydrogen atom at the 3-position is a b o u t twice as reactive as the 3°-hydrogen at the

TABLE 8. Chlorinadon of 2,3,4-trimethylpentane at 85 °C Chlorinating system

SO2CI2, BZ2O2 MES02N(t-Bu)Cl, BZ2O2 PHS02N(t-Bu)Cl,BZ202 Cl3CS02Cl,BZ202

% of monochlorides [(Me^)2CH«]2CH^Me'^

40 52 64 5

24 19 15 71

26 19 13 24

10 9 8 —

G. A. Russell

974

2-position, possibly because of relief in strain in forming radical 5. However, the methylene hydrogen atoms in 2,2,4,4-tetramethylpentane d o not have an increased reactivity towards Cl', suggesting there is httie relief in strain in forming 6. Me

Me

\

/

HC.

/ Me

>Xy Me

M

Me

\

Me

I

Me

Me

Me

H (6)

(5)

Photochlorination at 40 °C of 2,4-dimethylpentane and 2,2,4-trimethylpentane actually give examples where the 2°-hydrogen atoms at C-3 are more reactive t h a n the 3°-hydrogen atoms at C-2 (Scheme 5)^"^. F o r 2,4-dimethylpentane a n d 2,2,4-trimethylpentane the 2°-hydrogen atoms have a normal reactivity relative t o the l°-hydrogen atoms whereas the reactivity of the 3°-hydrogen atoms are greatly reduced by the presence of isobutyl or neopentyl substituents at the 3°-position. These substituents apparently obstruct the approach of Cl' t o the 3°-position. Me Me-

Me -CH2

-CHg-

Me-

CHMe2

Me

2.4

-CMe,

rt

! 1t t

2.5

-CHo

Me-

H

Me

1.0

-Me

1.0

2.0

S C H E M E 5. Relative reactivities per hydrogen atom in photochlorination at 40 "C"^^ 1.0 the2.7 1.0 ratios of Table 4 are further The rather approximate values of r : 2 ° : 31.2 ° rate hlustrated by the reported selectivities for chlorine atom attack o n 2-methylheptane at 20 °C (Scheme 6)"^^. Again an isobutyl substituent appears t o reduce gready the reactivity of the methylene hydrogens at C-4. Me

-CHp

Me-

-CHo

-CHn

-CHc

-Me

1tt t ! t 0.8

2.5

2.2

1.5

2.1(average)

1.0

S C H E M E 6. Reladve reactivities of hydrogen atoms in 2-methylheptane towards Cl* at 20 °C^^

The reaction of t - B u O O ' with a series of alkanes in the liquid phase at 30 °C has been studied by the AIBN-initiated autoxidation of the alkane in the presence of 1-2 M t-BuOOH^^. Trapping of the alkyl radical by oxygen leads t o a peroxy radical which readily undergoes hydrogen a t o m transfer with t - B u O O H t o regenerate the hydrogenabstracting species t - B u O O ' . T h e results of co-autoxidation with 3-methyl pentane are given in Table 9, where absolute rate constants (per hydrogen atom) have been calculated from product analysis a n d a rate constant for tertiary attack o n 3methylpentane o f 7 x l 0 " ^ M " ^ s " ^

21. Radical reacdons of alkanes and cycloalkanes

975

TABLE 9. Reactivity of carbon-hydrogen bonds towards f-BuOO* at 30 °C^° Hydrocarbon

k{3y

k{2y

Me2CHCH2Me Me^CHCH^CH^Me

7 7

X X

10-3 10-3

MeCH2CH(Me)CH2Me MeCH2CH2CH2CH2Me

7

X

10-3

— 9.3

Me2CHCHMe2 Me3CCHMe2 Me2CHCH(Me)CH2Me

13

8.9 5.5 2.5 3.2 1.5

Me2CHCH2CHMe2 Me3CCH(Me)CH2Me Me3CCH2CHMe2 Cyclohexane Cyclopentane Methylcyclohexane Methylcyclopentane "Per hydrogen atom in M

1.4 X 1 0 - ^ 3.3 X 10-^(C-4) 1.0 X 10-''(C-3)

10-3 xlO-3

X

X 10-3 X 10-3 X

10-3

X

10-3

X

10-3

(C-3) (C-2)

— — 10X10-3

21 ^ s

X

10-3

3.5 X 10-'*(C-3) 4 . 4 x 10-^(C-2) — — — — — — — 2.6 X lO-'^ 8.7 X 1 0 - ^ — —

^

The most reactive secondary hydrogen atoms are nearly as reactive as the least reacdve tertiary hydrogen atoms, although in general a value of /c(3°)//c(2°) equal to 10-20 is observed. The low reactivity of the 3°-hydrogen atoms in M e 2 C H C H 2 C H M e 2 or M e 3 C C H 2 C H M e 2 is consistent with the chlorination results (Schemes 5 and 6) and reflects hindrance to radical attack as a 3°-carbon center containing an isobutyl or neopentyl substituent. The value for reaction of r-BuOO* with 3-methylpentane is 1603 ± 0.07 for 3°-attack and 17.4 + 0.8 kcal m o l " ^ for 2°-attack. Surprisingly, the intermolecular h y d r o g e n - d e u t e rium primary isotope effect is 2 4 - 2 8 (as measured with m e t h y l c y c l o h e x a n e - d i 4 or 3 - m e t h y l p e n t a n e - d i 4 ) and is much greater than the theoretical limit of ~ 10 for complete loss of the zero-point energies for c a r b o n - h y d r o g e n bonds in the transition state^^. 5. Reactivity

of

cycloalkanes

The methylene groups in cycloalkanes show only a small difference in relative reactivity towards Cl* for the C 4 - C 8 cycles (Table 10)^'^^. These differences are accenturated TABLE 10. Relative reactivities (per methylene group) of cycloalkanes towards Cl* Solvent, temperature Cycloalkane C3 C4 C5 Ce C7 C«

neat, 40 °C^^

1.0 1.0 1.1 1.6

12 M CS2,40 °C^^

1.1 1.0 2.0 3.8

5 M CCI4,0 °C3 0.05 0.84 0.95 1.0

976

G. A. Russell

by using the more selective complexed chlorine a t o m in 12 M €82^^. Cyclopropane is, of course, much less reactive than the other cycloalkanes because of the high c a r b o n - h y d r o g e n b o n d strength. T o w a r d s Br' at 60 °C the relative reactivities of cyclopentane and cyclohexane hydrogen atoms are - ' 9 : 1 ^ ^ while towards t-BuOO* at 30 °C (Table 9) the reactivity difference is 2 - 3 . 6. Radical

reactions

of

spiroalkanes

The radicals 1 (n= 1-4) are formed by t - B u O ' attack upon the hydrocarbons in the cavity of an E P R s p e c t r o m e t e r " ^ S i n c e 7 is a cyclopropylcarbinyl radical, ring opening to 8 can be expected. However, the spiro[2.2]pentyl radical (7, n=\) did not undergo ring opening u p to 110°C. The vapor-phase chlorination of spiropentane produces a mixture of products, but none appears to be derived from radical 8 (n = 1) or from the cyclopropyl radical 9 (Scheme 7)^^ Instead, the products are derived from radicals 7 (n = l), 10 and its cyclopropylcarbinyl ring-opening product 11. Lower temperatures favored the formation of 10 over 7 and reduced the a m o u n t of 10 converted to 11. In CCI4 solution at 20 °C the higher concentration of CI2 completely supressed the conversion of 10 to 11^^. P h o t o b r o m i n a t i o n or photoiodination of spiropentane at 20 °C produced the dibromide or dhodide expected from radical 10 with Br or I in place of C r ^ . Although spiropentane is not more reactive than cyclopropane in hydrogen abstraction by t-BuO* or CF3*, it is > 100 times as reactive as cyclopropane in S^2 attack at carbon by Br*^^. (CH2)„-1 (11)

(CH2), (8)

(7) Cl

(9)

(7)/7=1 CHgCl

.CH2CI CH2(10)

tx

'CH2 (11)

^CH2CI CHgCI

CICH2CH2C(=CH2)CH2CI -I-

CICH2CH2C(CI)(CH2CI)2 S C H E M E 7. Chlorination products of spiropentane^^

977

21. Radical reactions of alkanes and cycloalkanes

Both radicals 7 and 10 are cyclopropylcarbinyl radicals and are stabhized relative to simple alkyl radicals or to a cyclopropyl radical such as 9. The cyclopropylcarbinyl radical (12) exists in a preferred bisected conformation with an energy barrier for C — C bond rotation (interconversion of and Hg) of 2.8 kcal mol reflecting a cyclo propylcarbinyl resonance stabilization of 2.5 kcal mol

O ^ H p

(12)

The rate constant for ring opening of 7 (n = 1) cannot be greater t h a n 10"^s~ ^ at 25 °C (E^ > 12 kcal m o l " ^)^^. However, the radicals with n = 2 - 4 undergo facile ring opening. With n = 2 the ring opening occurs 1/10 as fast as for 12 whhe with w = 3 or 4 reaction 11 occurs more rapidly than reaction 3. Table 11 summarizes d a t a based on E P R measurements^^ P h o t o b r o m i n a t i o n of spirohexane produces only the products of 8^2 attack of Br* upon the cyclopropyl carbon a t o m (Scheme 8). However, in contrast to spiropentane, both the cycloalkylcarbinyl and cycloalkyl radicals are formed with the latter species predominating^^. -Br

Br

-Br

CHo

Br2

30Vo

hv,20°C

-Br

Br

Br 70

Vo

S C H E M E 8. Photobrominahon of spirohexane

In photochlorination of spirohexane, hydrogen a t o m abstraction from the cyclobutane ring gready predominated over reactions of the cyclopropyl ring (Scheme 9)^"^-

TABLE 11. Cyclopropylcarbinyl radical ring opening^ System

/c(25X)(s-i)

•CH2-

l,n = l l,n = 2 l,n = 3 7,n = 4 CH2-

£a (kcal m o l " 1)

1.3 X 10«

5.9

io«-^ 4.7 X 10^

G. A. Russell

978

-Cl

Cl

Cl

Cl

S C H E M E 9. Photochlorination of spirohexane^

7. Radical

reactions

of

bicyclolm.n.Ojalkanes

lodination of bicyclo[1.1.0]butane leads t o 1,3-diiodocyclobutane, b u t chlorination or bromination led t o complex product mixtures^^. Bicyclo[2.1.0]pentane reacts with c r or Br* to form products derived from the 3-halocyclopentyl radical as a result of reaction 12^^"^^. Trichloromethyl, t-butoxy or AT-succinimidyl radicals preferentially extract a hydrogen from the 2-position t o yield a cyclopropylcarbinyl-type radical which undergoes ring opening with a rate constant of 2 . 4 x l 0 ^ s " ^ at 37°C^^'^^. Bicyclo [2.1.0] pentane reacts with cytochrome P-450 t o produce a mixture of ~ 7 parts of the unrearranged alcohol t o 1 part of the ring-opened alcohol, whereas methyl cyclopropane yields only cyclopropylmethanoP^. These results are consistent with an oxygen rebound mechanism for P-450 oxidations of saturated hydrocarbons which can occur with retention of stereochemistry (Scheme 10), w h h /c(rebound) ^ 2 x 10^° s " ^ Interestingly, bicyclo[2.1.0]pentane reacts with P-450 by hydrogen abstraction a n d rebound only at the endo face^^.

+

+

RH

(X=CI,Br)

X'

I IV + :Fe

(12)

Ar(rebound)

OH R-

ROH

S C H E M E 10. Oxygen rebound mechanism for cytochrome P-450 oxidation

Oxidation of cis-decahydronaphthalene with chloro(5,10,15,20-tetraarylporphyrinato)iron(III) in the presence of the oxygen transfer agent P h I O , also gives a stereospecific


979

TABLE 12. Decomposidon of 9-carbo-t-butylperoxydecalins in the presence of O2 at 50 °C in 1,2-dimethoxyethane^^ Perester cis trans cis cis cis

O2 pressure (atm)

tr RCCI2CCI2* RCCI2CCI2* — > R C ( c i ) = c c i 2 + c r S C H E M E 19. Chlorovinylation of alkanes^^'

Simhar observations have been m a d e in the photocyanation of butane with C I C N (Scheme 2 0 ) ^ T h e extrapolated ratio of MeCH(CN)CH2Me/MeCH2CH2CH2CN at

21. Radical reactions of alkanes and cycloalkanes TABLE 15. Reladve hexane^

reactivities

per hydrogen

C H 3 ^ - CH2^—CH2^Reagent

atom

987

in

-C3H,

H«

Cl2,/iv,65 °C ds-C2H2Cl2,125°C'' C2HCl3,125°C^

C2Cl4,125°e

0.35 0.06 0.04 tr

1.15 2.0 1.7 4.2

1.0 1.0 1.0 1.0

"To give R C H = C H C 1 . "To give R C H = C C L 2 . '^To give R C ( C l ) = C C L 2 .

0% reaction was 2/1, consistent with the selectivity of a chlorine atom of /C(2°)//C(r) = 3. However, as HCI buht up in the solution the 271° product increased to 24/1 at 1% reaction and to 168/1 at 5% reaction^^^. Extensive hydrogen-deuterium exchange was observed for the cyanation of a mixture of C - C 6 H 1 2 and C-C6D12 a n d a d d h i o n of D C l resulted in the incorporation of D in unreacted alkanes such as cyclohexane or 2,3-dimethylbutane. The B Z 2 0 2 - i n i t i a t e d reaction of CICN w h h 2,3-dimethylbutane gave only the 3°-cyanide ( M E 2 C H C ( C N ) M E 2 ) in 9 5 % yield, although irreversible attack of cr upon M E 2 C H C H M E 2 actually produces more of the l°-alkyl radical ( ~ 12 parts 1° to 8 parts 3°). Reaction of methyl cyanoformate ( C H 3 0 C ( = 0 ) C N ) w h h M E 2 C H C H M E 2 fohowed a pathway simhar to CICN (Scheme 20) with jS-elimination of CH3CO2* from the adduct radical followed by decarboxylation and irreversible hydrogen atom abstraction by M e ' to yield up to 77% of M E 2 C H C ( C N ) M E 2 ^ ^ . With cyanogen (NCCN) 2,3-dimethylbutane in the presence of B Z 2 O 2 produced M E 2 C H C M E 2 C ( C N ) = N H in > 70% yield from the addition of M E 2 C H C M E 2 * to cyanogen followed by intermolecular hydrogen atom transfer (reaction 22)^°. cr

+ M E C H 2 C H 2 M E ^ H C l + n-Bu' + 5CC-Bu* R' +

C1CN-^RC(C1)=N'

R C ( C 1 ) = N ' ^ R C = N + cr S C H E M E 20. Photocyanation with C L C N ^ ^ o M E 2 C H C M E 2 C ( C N ) = N ' + R H ^ R' + M E 2 C H C M E 2 C ( C N ) = N H

(22)

Another example of the reversal of the hydrogen atom abstraction reaction with X' = c r is furnished by the reaction of HCI w h h B Z 2 O 2 in C H 3 C N at 98 °C in the presence of an a l k a n e ^ T h e reaction is presumed to yield C I 2 by reactions 23 and 24 and chlorination of the alkane is observed. Although the nature of the radical which attacks the alkane is uncertain, the reaction rate seems to be controlled by a slow reaction 23 fohowed by a fast reaction 24. With 0.3mol% B Z 2 O 2 the observed /C(2°)//C(l°) for butane was 400 decreasing to 60 at 3.5mol% B Z 2 O 2 , where the rate of formation and steady-state concentration of C I 2 would be much higher^^^ F o r isobutane, the values of /C(3°)//C(r) calculated from the ratio of the observed t-BuCl and /-BuCl decreased from 12,000 at 0.3mol% B Z 2 O 2 to 900 at 3.5mol% B Z 2 O 2 . Of course, the relative reactivities for cr attack in the absence of a reaction between R' a n d HCI (i.e. in the presence of signihcant amounts of C I 2 ) are much lower, /C(3°):/C(2°):/C(l°) = 4:3:1 at 98 °C. HCI + P h C ( 0 ) O C ( 0 ) P h -> P H C 0 2 H + P h C ( 0 ) O C l PhC(0)OCl

+ HCI ^ P H C 0 2 H + C I 2

(23) (24)

988

G. A. Russell

Because reversal in the hydrogen a t o m abstraction step can be observed in the absence of a good trapping agent for the alkyl radical, attention should be given to the nature of the hydrogen abstracting species for chlorinations using reagents other than CI2 or SO2CI2, for example with reagents such as PCI5 or R S 0 2 N ( t - B u ) C l (Tables 7 and 8)^^'"^^ The reversal of reaction 1 with X' = Br* should occur more readhy than for X* = Cl*. Thus, even in the presence of molecular bromine reversal can be observed (as reflected in the composition of the bromination product) if H B r is not rapidly removed from the system^^^'^^^. The reaction of alkyl radicals with H B r is, of course, weh k n o w n in the peroxide-initiated addition of H B r to alkenes. By use of Br2 for the reaction solvent the reversal can be effectively eliminated. Reversal of hydrogen abstraction with X* = Br* may even occur in the solvent cage before R* and H B r have diffused apart. Although trapping of R* that has escaped the solvent cage by H B r can be effectively eliminated by removal of the HBr, for example by using a large excess of an epoxide or of N B S to t r a p HBr^^"^'^^^, prevention of the cage reaction between R* and H B r is more difficult unless the trapping agent, e.g. Br2, is part of the cage wall and can effectively compete with HBr. Viscosity of the solvent will have an important effect on the lifetime of the cage and, with a lower viscosity, the probability is increased for R* to escape from the molecule of H B r formed in the hydrogen a t o m abstraction reaction. I m p o r t a n t viscosity effects have been demonstrated in the bromination of substituted toluenes even when good trapping agents for H B r (ethylene oxide, NBS) are e m p l o y e d ^ S i n c e viscosity varies with temperature, this introduces an uncertainty in the interpretation of temperature effects on relative reactivities observed in p h o t o b r o m i n a t i o n reactions. Cage return also explains the grossly different kinetic isotope effects observed in gas and hquid-phase photobrominations of PhCH2D: /c(H)//c(D) = 4.6 in CCI4 solution at 77 °C^2^; k{H)/k(D) = 6.5 vapor phase at 121 °C (8.2 calculated at 77 "C)^^"^. O n the other hand, photochlorination of P h C H 2 D in CCI4, both in solution and in the vapor phase, at 70 °C gives essentially identical values of /c(H)//c(D) = 1.99 and 2.08, respectively Competitive bromination of C-C6H12 and gas and liquid phases at 21 °C gave values of /c(H)//c(D) = 5.4 (vapor) and 4.3 (liquid, 0.07-3.6 M Br2). However, at 10-18 M Br2, /c(H)//c(D) was identical to the gas-phase result^^^. External exchange of R* and H B r is apparently prevented by a bromine concentration of 0.07 M or greater, but exchange within the solvent cage still occurs up to very high Br2 concentration. At 12-18 M, bromine molecules are an important part of the cage walls and the cage return is effectively quenched. P h o t o b r o m i n a t i o n s by ClsCBr can occur by mixed radical chains (Schemes 21 and 22)^^^, further comphcated by reversal of the hydrogen atom abstraction step in Scheme 22^^^. P h o t o b r o m i n a t i o n of toluene, ethylbenzene and cumene at high Br2 concentration with rapid removal of the H B r gives, for this benzylic series, /c(r):/c(2°):/c(3°) = 1:17:37 at 40 °C^^l A simhar result is observed for p h o t o b r o m i n a t i o n with NBS^^^. With BrCClg, a relative reactivity series of 1:50:260 is observed which suggests the occurrence of Scheme 21 with a greater selectivity for CCI3* than for Br*^^^. However, Scheme 22 is more susceptible to reversal of the hydrogen a t o m abstraction step than is bromination with molecular Br2 because of the lower reactivity of ClaCBr towards R*. W h e n the CCl3Br brominations are performed in the presence of efficient H B r traps such as K 2 C O 3 or ethylene oxide, a relative reactivity series towards CCI3* attack of 1:10:29 is observed and CCI3* is found to be slightly less selective t h a n Br'^^'^'^^^ In the absence of such HBr trapping agents the photolysis of BrCCl3 leads to the bromine a t o m chain of Scheme 22, but reversal of the hydrogen a t o m abstraction step dominates over the bromine atom transfer from BrCCl3. Photolysis of BrCClj with bicyclo[2.1.0]pentane yields a complex set of reaction products apparently formed by Br* attack (to yield the 3-bromocyclopentyl radical) and hydrogen atom abstraction by CCI3* (to yield the 3-cyclopentenyl radical)^^. Chlorinations with CCI4 do not give any evidence for a

c-C^T>i2


989

competing chlorine a t o m chain, presumably because HCl is much less reacdve t h a n H B r towards CC\^"'^. R' + ClaCBr

> RBr + CC\^'

CCls* + R H

> HCCI3 + R-

Br' + R H —

H B r + R'

R- + BrCCl3

> RBr + CCl3-

CCl3- + HBr

> HCCI3 + Br-

S C H E M E 21

S C H E M E 22

B. Halogenations Involving Mixed Radical Chains Alkane halogenations often occur by processes which do not involve halogen a t o m attack on the alkane (Scheme 23). Among the Z groups that have been previously mentioned, e.g. in Table 4, are t-BuO, CCI3, CIO, CCI3S, PCI4 a n d P h l C l . Similar reactions are observed with Z = (CU^)2lSiU^^^^-^^'^ or Et3N + ^ 3 ^ a n d alkane hydroxylations wih occur with Et2NHOH+ or Et3NOH'^ in the presence of Fe(II) in CF3C02H^^^ W h h Z = SO2CI hydrogen abstraction can occur by b o t h Cl* a n d S02Cr but S02Cr attack is observed only for the more reactive alkanes^^. A simhar situation exists for Cl3CS02'^CCl3- + S02'^^ (Attack of R' u p o n ZX to yield R Z and a halogen a t o m to continue the chain can also occur, for example w h h ZX = C I C O C O C I , vinyl halides or N C C l ; see Schemes 14, 19 and 20.) Z- + R H - ^ R - + H Z R' + Z - X ^ R - Z + X* S C H E M E 23. (X = halogen and Z not a halogen)

Mixed radical chains, where the attacking species are b o t h Z* a n d X', are sometimes observed when H X can readily generate X2 from reaction with the reagent ZX. Such processes have been identified in the reactions of r-BuOCl, N B S a n d CI2O. O n the other hand, AT-chlorosuccinimide seems to react always by a chlorine a t o m chain by virtue of reaction 10. With CI2O in the gas phase the /c(r):/c(2°):/c(3°) reactivities (Table 4) exclude Cl* as the chain carrying species and are consistent with hydrogen abstraction by CIO* fohowed by the reaction of R* w h h CI2O to form RCl (reaction 25)^^ In CCI4 a m u c h different selectivity is observed, i.e. /c(r):/c(2°):(3°) = 1:11.5:24, and the stoichiometry is closer to equation 26. This suggests that in solution reactions 27 a n d 28 occur a n d that a chlorine atom chain competes with hydrogen a t o m abstraction by CIO*. With H O C l in aqueous solution at 40 °C the reaction goes completely by the chlorine a t o m chain with k{r):k(2°):k(3°) the same as observed for photochlorination with Cl2^^^.

CI2O +

R H — > RCl + H O C l

(25)

2RH + CI2O — > 2RC1 + H2O

(26)

CI2O +

HCl — > HOCl +

CI2

H O C l + HCl — > H2O + CI2

(27) (28)

Photochemical reactions of t-BuOCl generally involve hydrogen a t o m abstraction by t-BuO*, a radical which is considerably more selective t h a n Cl*^^^. In the reaction of r-BuOCl with 2,3-dimethylbutane at 64 °C, there is a report of a selectivity identical to that of Cl* u p o n photolysis but a higher selectivity with initiation by Bz202^^. Photolysis of t-BuOCl may lead to chlorine atoms, hydrogen chloride and molecular chlorine whereas BZ2O2 leads to the t-BuO* radical chain. Reaction 29 will shift t-BuOCl

990

G. A. Russell

chlorination to a chlorine atom chain reaction. T h e occurrence of a chlorine a t o m chain will result in reduced selectivity a n d in an increase in the ratio of r-BuOH/Me2CO formed in the competitive reacdons of t - B u O ' (Scheme 24). r-BuOCl + H C l

> r-BuOH + C l ,

(29)

Me2C=0 + Me* ^BuO•fc^[RH]

. t - B u O H + RS C H E M E 24. Competidve reactions of t-BuG*

With aralkyl hydrocarbons there is considerable evidence that t-BuOCl prefers t o react by a chlorine atom c h a i n T h e chlorine atom chain also occurs more readhy for PhCH2CMe20Cl which, at 40 °C w h h hv or AIBN initiation, yields /c(3°):/c(l°) = 6 - 7 for D M B whereas r-BuOCl gives a value of 44 a n d CI2 a value of 4.5. With toluene the kjk^ ratios (Scheme 24) provide a diagnostic probe to the nature of the hydrogen-abstracting species (Table 16). Surprisingly, r-BuOBr reacts by a t-BuG* chain under condidons where ^ B u O C l gives a mixture of Cl* a n d t-BuO* chains (Table 16). The presence of an alkene [e.g. CH(Cl)=CCl2 in Table 16] in the photoinidated reaction of r-BuOCl traps Cl* and/or CI2 a n d allows the t-BuG* chain to dominate. Direct measurements of the relative reactivities of C-C6H12 a n d P h C H j (by disappearance of the reactants) and indirect measurements (from the kjk^ ratios observed in two separate experiments) gave the results summarized in Table 17^^^. Again the presence of CH(Cl)=CH2Cl2 stopped the chlorine atom chain for t-BuOCl a n d again r-BuOBr appeared to react w h h n o interference from a bromine atom chain. TABLE 16. Reaction of t-BuG' with toluene in CCL at 70°C^39

kJk,

Conditions

Radical precursor f-BuON=NOBu-t t-BuOBr t-BuOCl t-BuOCl r-BuOCl t-BuOCI

thermal hv hv hv plus 2% CI2 AIBN"

2.2 2.0 -10 150-450 2.4

/ z v p l u s O l M C2HCI3

2.5

"AIBN = azobisisobutyronitrile.

TABLE 17. Relative reactivities of cyclohexane and toluene at 40 °C^^^ Reagent

Solvent

t-BuOCI f-BuOCl f-BuOBr f-BuOBr [t-BuOC(O)^ [t-BuGN^

"From kjk^

Indirect"

Direct''

PhCl

1.8 6.0 4.7 5.4 5.3

6.5 6.2 4.2 4.3 5.2

PhCl

6.0

5.7

PhCl

C2HCI3 PhCl

C2HCI3

ratios.

''From disappearance of hydrocarbons.


991

With hydrocarbons which yield a resonance-stabhized benzylic radical, apparently the nature of the hydrogen atom abstracting species is determined by the competition between the benzyl radical a n d the possible chlorine atom donors. T h e reaction of PhCH2* with t-BuOCl is apparently slow enough that the benzyl radical wih preferentiahy react with traces of CI2 regenerated by reaction 29. With the more reactive r-BuOBr, apparently the benzyl radical reacts readhy to generate t-BuO* a n d a bromine atom chain does n o t ensue. A bromine atom chain is also less likely t o be observed than a c r or BuO* chain because Br* is a less reactive hydrogen a t o m abstracting agent. The results observed with t-BuOCI have considerable simharity to halogenations with iV-haloimides and, in particular, with N-halosuccinimides. With the iV-chloro c o m p o u n d s a chlorine atom chain is observed with all s u b s t r a t e s T h e AT-bromoimides are more reactive towards carbon radicals. F o r example, with Pr* N B S is 7.3 times as reactive as NCS^"^^ a n d T-alkyl radicals are reported t o react with iV-bromoimides or Br2 at a diffusion-controlled rate, /c-(1.3-2.2) x 10^° M " ^ s"^ at 15 °C in CH2Cl2^ although one report indicates that Br2 is much more reactive than N B S towards 3°-alkyl radicals^"^^. With reactive hydrocarbons, particularly with aralkyl hydrocarbons, N B S reacts by a bromine atom chain (Scheme 25)^"^^"^"^^. However, with less reactive hydrocarbons such as butane or neopentane which yield a more reactive alkyl radical, NBS reacts by an imidyl radical chain. The imidyl radical is relatively unselective a n d gives relative reactivhies closer t o Cl* than to Br*^'^^. Reaction of N B S with butane in the presence of C2H4 gives /c(2°)//c(r) ^ 4.6 vs - 3 for Cl* Br* + PhCHg

>

PhCH2* -h H B r

HBr + N B S —> BY2 + succinimide

PhCH2* + Br2 —> PhCH2Br + Br* S C H E M E 25. N B S brominaUon of toluene

Again, the nature of the chain is apparently controlled by the reaction of the alkyl radical with the halogenating agent. With iV-chloroimides, alkyl or benzyl radicals search out traces of molecular chlorine from reaction 10 and a chlorine atom chain predominates. With the more reactive NBS, l°-alkyl radicals can readily abstract a bromine atom a n d an imidyl chain results, particularly at high N B S concentrations a n d in the presence of alkenes, to trap Br* and/or Br2. However, as the radical becomes less reactive, such as a benzyl radical, the radical reacts more slowly with N B S b u t readhy with traces of Br2, and the bromine atom chain dominates. With radicals of intermediate reactivity such as cycloalkyl, both chains can occur s i m u l t a n e o u s l y A g a i n the presence of a n alkene traps Br* and/or Br2 a n d allows the imidyl radical chain t o dominate. Thus, the relative reactivities of C-C^HIQ-.C-CÛ^J are 9.2 towards Br* (bromination in liquid Br2) but only 0.82 towards the N-succinimidyl radical (NBS/CH2Cl2/CH2=CH2)'^''. With bicyclo[2.1.0]pentane N B S reacts to give about equal a m o u n t s of the products expected from bromine atom attack (1,3-dibromocyclopentane) and succinimidyl radical hydrogen atom abstraction (to yield 4-bromocyclopentene)^^. T h e occurrence of competing bromine atom a n d A^-succinimidyl radical chains has led to considerable confusion in the literature^^^'^'^^ The N-haloimide halogenations are also controhed partiahy by the fact that Cl* or the iV-succinimidyl radical are much more reactive t h a n Br* in hydrogen abstracting reactions and, towards a hydrocarbon of low reactivity such as neopentane, a bromine atom chain would be quite ineffective. With mixtures of N B S a n d CI2, halogenation occurs to form the alkyl bromides b u t with the selectivity expected for chlorine atom a t t a c k ^ A p p a r e n t l y ClBr is formed a n d reacts w h h the alkyl radical t o form RBr a n d a chlorine atom. A simhar situation exists for the bromination of alkanes using a mixture

992

G. A. Russell

of Br2 and CI2, at least for unreactive hydrocarbons^ In such a halogenation system the predominant species present will be BrCl and Br* because of the following equilibria^ Cl* + Br2

BrCl + Br*

Br* + C I 2 ^ = : ^ B r C l + Cl*

k, = 1.6 x 10^ k, = 1-3 x 1 0 " ^

With a hydrocarbon of low reactivity, hydrogen a t o m abstraction by Cl* dominates but, with a more reactive hydrocarbon, Br* can be the major hydrogen a t o m abstracting species. Thus, with P h C H 2 C H 3 /c(a)//c(j?) per hydrogen a t o m is 116, characteristic of Br* attack rather t h a n attack by Cl' or the complexed chlorine atom; the ratio of the a-halo c o m p o u n d s is about 10:1 in favor of the bromide^^^. Chain reactions involving halogen atoms are observed in several oxidation processes involving molecular oxygen. O n e example is the H B r - p r o m o t e d vapor-phase autoxidation of hydrocarbons such as isobutane^^^'^^^ Reaction of a 1:1 mixture of isobutane and O2 in the presence of 8 mol% of H B r at 163 °C gives up to 70% of t-butyl hydroperoxide by the mechanism of Scheme 26. Straight-chain hydrocarbons are oxidized to ketones^ and ethane to acetic acid^^^, products arising from further reactions of initially formed hydroperoxides. The side chains of aralkyl hydrocarbons are autoxidized in the presence of H B r in the liquid phase The two-step p r o p a g a t i o n sequence of Scheme 26 occurs more readily t h a n the one-step reaction involving attack of t-BuOO* upon M e 3 C H . The energy of activation for Br* attack on a 3°-carbon-hydrogen bond of 7.5 kcal mol is considerably lower than the value of ~ 16 kcal mol ~^ for t-BuOO*^^. Furthermore, the rapid conversion of t-BuOO* to Br* changes the termination mechanism. In particular, the formation of Br2 by the coupling of two bromine atoms is reversible at 163 °C whereas the t - B u O O ' termination process would be irreversible. The net effect is that the HBr-promoted reaction of Scheme 26 occurs more readily than autoxidation in the absence of H B r even though the two propagation steps have the same overall thermodynamics as the direct reaction of t-BuOO* with Me2CH. Br* + M c s C H M e 3 C * + O2 M e 3 C O O * + HBr

>HBr -h M e 3 C * > McsCOO* > M e 3 C O O H + Br*

S C H E M E 26. HBr-promoted autoxidation of isobutane

The reaction of alkanes with a mixture of SO2 and O2 also occurs more readily t h a n simple autoxidation of the hydrocarbon (reaction 30)^^^. Here the radical RSO2OO*, formed as shown in Scheme 27, is apparently less prone to termination reactions t h a n a simple alkylperoxy radical R H + SO2 + O2 R* + S 0 2

RSO2*

> RSO2OOH

(30)

>RS02*

>RS0200*

RSO2OO* + R H

> R S O 2 O O H + R*

R S O 2 O O H + H2O

^ R S 0 3 H + H2O2

S C H E M E 27. Sulfoxidation of hydrocarbons

Another intriguing reaction of molecular oxygen that involves a chlorine a t o m as the hydrogen abstraction species is the chlorophosphonation of alkanes (reaction 31)^^^"^^^. Reaction 31 and the competing reaction 32 spontaneously form chlorine atoms and

21. R a d i c a l r e a c t i o n s o f a l k a n e s a n d c y c l o a l k a n e s

993

p r o c e e d readily a t — 78 ° C w i t h a l k a n e s w i t h a l o w reactivity s u c h a s e t h a n e ^ E v i d e n c e that r e a c t i o n 31 i n v o l v e s Cl* attack o n t h e a l k a n e i n c l u d e s t h e o b s e r v a t i o n t h a t t h e i s o m e r d i s t r i b u t i o n in t h e c h l o r o p h o s p h o n a t i o n o f b u t a n e is t h e s a m e a s i n p h o t o c h l o r i n a t i o n . S c h e m e 28 s u m m a r i z e s t h e m o r e i m p o r t a n t r e a c t i o n s i n v o l v e d i n t h e o v e r a h r e a c t i o n 31^^"^. T h e relative reactivity o f R* = c-CÛ^^' t o w a r d s PCI3 a n d O2 is a b o u t 0 . 5 T h i s l e a d s t o S c h e m e 28 at h i g h PCI3 o r l o w o x y g e n c o n c e n t r a t i o n s . A t l o w PCI3 o r h i g h o x y g e n c o n c e n t r a t i o n s alkyl p h o s p h o r o d i c h l o r i d a t e s are f o r m e d (reaction 33). A s s h o w n i n S c h e m e 29, t r a p p i n g o f R* b y O2 l e a d s t o a p e r o x y / a l k o x y radical c h a i n . I n c o m p e t i t i o n w i t h S c h e m e s 28 a n d 29 are r e a c t i o n s i n v o l v i n g t h e t r a p p i n g of c r b y PCI 3 w i t h t h e r e g e n e r a t i o n of a Cl* ( S c h e m e 30). A t l o w o x y g e n pressures t h e relative reactivities o f PCI3 a n d C-C5H12 t o w a r d s Cl* are m e a s u r e d t o b e '^0.36. T h e c h l o r o p h o s p h o n a t i o n r e a c t i o n gives very p o o r yields w i t h aralkyl h y d r o c a r b o n s s u c h as P h C H 3 o r Ph2CH2, w h i l e P h 3 C H fails t o react^^^'^^^ W i t h m o r e s t a b l e alkyl radicals the i n t e r m e d i a t e RPCI3O* c a n d e c o m p o s e t o yield R* a n d POCI3 a n d t h e s u b s t i t u t i o n p r o c e s s is t h e r e b y s a b o t a g e d . T h e r e a c t i o n o c c u r s for o t h e r c h l o r o p h o s p h i n e s s u c h a s EtPCl2 (reaction 34)^^^.

O2 —> RPOCI2 +

R H + 2PCI3 +

POCI3 + H C l

(31)

PCI3+IO2—>POCl3

Cr

+ RH

(32)

. H C l + R*

R* + P C l 3

.PRCV

RPCV + O2—>RPCl300* RPCI3OO* + PCI3 — > R P C l 3 0 0 P C l 3 ' RPCI3OOPCI3* — . R P C I 3 O * + POCI3

RPCI3O*—>RPOCl2 + Cr S C H E M E 28. Chlorophosphonation mechanism R H + PCI3 +

O2 —

>

R O H + POCI3 — >

ROPOCI2 +

HCl

(33)

R* + 0 2 — ^ R O O * ROO* + PCI3 — > ROOPCI3* R O O P C 1 3 * — > RO* + POCI3 RO' + RH

^ R O H + R*

S C H E M E 29. Alkylphosphorodichloridadon mechanism Cl* + PCI3

> PCI4*

PCl4* + 0 2 — ^ P C U O O * p c u o o * + PCI3 — > PCUOOPCla*

PCU00PCI3* .PCI4O* + POCI3

pcuo*—>poci3 + cr S C H E M E 30. Autoxidadon of PCI3

EtPCl2 + C-C6H12 + O2 - > c - C 6 H i i P ( E t ) ( C l ) 0

(34)

T h e t r a p p i n g o f p e r o x y radicals b y PCI 3 t o yield a p h o s p h o r a n y l radical is k n o w n t o o c c u r readily^^^. I n t h e c a s e of P h 3 P , r e a c t i o n w i t h r-BuOO* o c c u r s w i t h a n e n e r g y o f a c t i v a t i o n o f o n l y 3 kcal m o l ' ^ m u c h less t h a n t h e e n e r g y o f a c t i v a t i o n for attack

994

G. A. Russell

of t-BuOO* u p o n 2°- or 3°-carbon hydrogen b o n d s , i.e. - 1 6 - 1 7 kcal m o l " One might expect the reaction of alkanes with PCI3 t o form RPCI2 a n d H C I t o occur readhy by Scheme 31. T h e reaction has been observed with m e t h a n e or ethane, b u t only in low yields at temperatures of 5 7 5 - 6 0 0 "C^"^^. T h e absence of a fache reaction m a y reflect the absence of a n initiation reaction, a n d in fact the reaction is reported t o occur m o r e readily in the presence of traces of oxygen. R- 4- PCI3 ^

RPC13-

Rpci3* — ^ RPCI2 + c r c r + RH

. R- + HCI

S C H E M E 31. Free radical alkylahon of PCI3

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21. Radical reacdons of alkanes and cycloalkanes 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170

997

C. Walling and J. A. McGuinness, J. Am. Chem. Soc., 91, 2053 (1969). J. Adam, R A. Grosselain and P. Goldfmger, Bull. Soc. Chim. Belg., 65, 533 (1956). A. G. Davies, B. P. Roberts and N. M. Smith, J. Chem. Soc, Perkin Trans. 2, 2221 (1972). P. S. Skell, D. L. Tuleen and P. D. Readio, J. Am. Chem. Soc, 85, 2850 (1963). G. A. Russell, C. DeBoer and K. M. Desmond, J. Am. Chem. Soc, 85, 365 (1963). R. E. Pearson and J. C. Mardn, J. Am. Chem. Soc, 85, 354, 3142 (1963). C. Waning, A. L. Rieger and D. D. Tanner, J. Am. Chem. Soc, 85, 3129 (1963). P. S. Skell, V. Liining, D . S. McBain and J. M. Tanko, J. Am. Chem. Soc, 108, 121 (1986). D. D. Tanner, C. P. Meintzer and S. L. Tan, J. Org. Chem., 50, 1534 (1985). D. D. Tanner, T. C.-S. Ruo, H. Takiguchi, A. Guillaume, D . W. Reed, B. P. Setiloane, S. L. Tan and C. P. Meintzer, J. Org. Chem., 48, 2743 (1983). D. D. Tanner, D. W. Reed, S. L. Tan, C. P. Meintzer, C. Walling and A. Sopchik, J. Am. Chem. Soc, 107, 6576 (1985). C. Walling, G. M. El-Taliawi and A. Sopchik, J. Org. Chem., 51, 736 (1986). J. L. Speier, J. Am. Chem. Soc, 73, 826 (1951). P. S. Skell, H. N. Baxter III and J. M. Tanko, Tetrahedron Lett., 27, 5181 (1986). F. F. Rust and W. E. Vaughan, Ind. Eng. Chem., 41, 2595 (1949). E. R. Bell, F. H. Dickey, J. H. Raley, F. F. Rust and W. E. Vaughan, Ind. Eng. Chem., 41, 2597 (1949). P. J. Nawrocki, J. H. Raley, F. F. Rust and W. E. Vaughan, Ind. Eng. Chem., 41,2604 (1949). E. R. Bell, G. E. Irish, J. H. Raley, F. F. Rust and W. E. Vaughan, Ind. Eng. Chem., 41, 2609 (1949). B. Barnett, E. R. Bell, F. H. Dickey, F. F. Rust and W. E. Vaughan, Ind. Eng. Chem., 41, 2612 (1949). R. Graf, Justus Liebigs Ann. Chem., 578, 50 (1952). G. A. Russell, J. Am. Chem. Soc, 79, 3871 (1957). J. O. Clayton and W. L. Jensen, J. Am. Chem. Soc, 70, 3880 (1948). L. Z. Soborovskii, Y. M. Zinov'ev and M. A. EngHn, Dokl. Akad. Nauk SSSR, 61,293 (1949). R. Graf, Chem. Ber., 85, 9 (1952). A. F. Isbell and F. T. Wadsworth, J. Am. Chem. Soc, 78, 6042 (1956). F. R. Mayo, L. J. Durham and K. S. Griggs, J. Am. Chem. Soc, 85, 3156 (1963). W. L. Jensen and C. R. Noller, J. Am. Chem. Soc, 71, 2384 (1949). P. Lesfauries and P. Rumpf, Bull. Soc Chim. Fr., 542 (1950). L. Z. Soborovskii and Y. M. Zinov'ev, Zh. Obshch. Khim., 24, 516 (1954). A. G. Davies and B. P. Roberts, Angew. Chem., Int. Ed. Engl, 10, 738 (1971). J. A. Howard, Free Radicals, Vol. II (Ed J. Kochi), Wiley, N e w York, 1973, p. 31. J. A. Pianfetd and L. D. Quin, J. Am. Chem. Soc, 84, 851 (1962).

Author index This author index is designed to enable the reader to locate an author's name and work with the aid of the reference numbers appearing in the text. The page numbers are printed in normal type in ascending numerical order, followed by the reference numbers in parentheses. The numbers in italics refer to the pages on which the references are actually listed.

Aarset, H. 918 (289), 925 Abakumov, G.A. 815, 822 (In), 886 Abdullah, C M . 903 (68), 920 Abe, E. 561 (45c), 601 Abe, H. 341 (112), 349 Abed, K.J. 376 (143), 392 Abel, E.W. 555 (2), 600 Abelt, C.J. 733 (137b), 741 Abernathy, R.N. 406 (79), 451 Abeywickrema, R.S. 478 (86), 527, 578 (131a), 604 Abraham, W. 907 (153), 922 Abryutina, N.N. 332, 336 (92), 348 Achiba, Y. 476, 477, 489, 502, 503, 507, 509 (32), Ackman, R.E. 909 (185), 923 Ackman, R.G. 294, 295 (10), 346, 907 (154), 922 Acton, N. 382 (186), 393, 595, 596 (204c),

525

607

Adam, J. 991 (140), 997 Adam, W. 682, 700, 701 (18b), 703 (79a), 708 (18b, 92c, 94a, 96a, 98), 709 (92c, 98), 710 (92c), 711 (18b, 109), 712 (96a, i l 5 d , 121b, 125a), 713 (115d), 716 (96a), 718 (121b), 719, 721 (125a), 722 (115d, 121b), 724, 725, 730 (79a), 736,

739-741

Adams, Adams, Adams, Adams,

A.A. 805 (81), 808 D.M. 540 (77), 549, 671 (68), 679 J.Q. 355 (17), 389 N.G. 406 (74, 81), 451, 537, 538 (53),

549

Adams, R.D. 564 (57a), 602, 931, 945 (44),

959

Ader, A.W. 918 (276), 925 Adler, P. 762, 763 (28), 779 Adlington, M.G. 562 (48), 573 (108a), 601,

603

Adriaens, P. 826 (76), 888 Aeiyach, S. 683 , 684 (23), 736 Aexel, R.T. 919 (292), 925 'Aglietto, M. 142, 143 (39), 182 Agosta, W.C. 562, 563 (51a), 601, 929, 930 (19), 931 (38), 933 (19, 38), 935, 940 (38), 944 (19, 97, 99), 945 (19, 100, 103), Agova, M. 871 (225), 892 Agrawal, V.P. 911 (201), 923 Ahmad, M. 374 (118), 391 Aigami, K. 593, 595 (203a), 607, 691 (53a,

959, 961

737

53f), Aizenshtat, Z. 321 (65), 333 (117), 334 (98), 336 (98, 100), 337 (100), 348, 349 Akhrem, I. 620 (45a), 650 Akhrem, I.S. 560 (42), 601 Akin, C. 916 (252), 924 Akopyan, M.E. 477 (63), 526 Aksnes, D.W. 377 (145, 146), 392 Akulov, G.P. 847 (125-130), 848 (127, 130),

889

Akutagawa, S. 558 (25b), 601 Alberti, R. 399 (16), 450 Alberty, R.A. 231, 232, 240, 247, 248, 255, 257 (29), Albrecht, J. 3 0 8 , 3 1 4 (38), 347 Albrecht, R 341 (111), 345, 346 (115), 349, 898 (19), 908 (169), 979, 923 Albro, P.W. 914 (227, 229), 924 Alcaide, B . 172 (130-132), 184

284, 286


1000

A u t h o r index

Alder, R . W . 109 ( 9 3 ) , 130, 6 9 1 ( 5 3 i , 5 3 j ) , 737, 9 3 0 , 9 3 1 ( 3 0 ) , 959 A l e i , M . , Jr. 8 1 2 ( 2 ) , 886 A l e m a n y , L . B . 3 5 2 ( 1 5 ) , 389 A l e x a n d e r , R. 3 0 7 , 3 0 9 ( 3 0 ) , 347 Alexandrov, Yu.A. 8 1 5 , 8 2 2 ( I m ) , 871 ( 2 3 3 - 2 3 5 ) , 886, 892 A l f a s s i , Z . B . 6 8 2 ( 2 0 b ) , 7 0 0 ( 7 4 ) , 736, A l f o r d , H.R. 8 0 4 ( 7 9 ) , 808 A l g r i m , D.J. 5 4 3 ( 1 3 4 ) , 550 AI Harbi, D . K . 8 9 7 ( 1 5 ) , 919 Aliprandi, B . 8 4 9 , 8 5 0 ( 1 3 1 ) , 889 Aljibury, A . L . 8 9 ( 5 4 ) , 94

738

A l - J o b o u r y , M . I . 4 8 7 ( 1 3 2 ) , 528 A l k e r , D . 6 4 3 ( 1 0 4 ) , 652 A l l e g r a , G. 171 ( 1 3 3 ) , 184 Allen, A.O. 7 6 2 (26), 779 A l l e n , C.F.H. 9 3 5 ( 7 4 ) , 960 A l l e n , F . H . 7 9 ( 3 ) , 8 0 ( 1 9 , 2 0 ) , 8 4 ( 2 0 ) , 93 A l l e n , G.R., Jr. 7 2 4 , 7 2 6 ( 1 2 9 c , 132a), 7 3 2 ( 1 2 9 c ) , 741 A l l e n , H . A . 8 5 8 , 8 8 1 ( 1 6 9 ) , 890 A l l e n , L . C . 15, 16 ( 1 6 ) , 7 7 , 9 3 3 ( 6 0 ) , 960 A l l e n , R . P . 5 6 9 ( 8 4 ) , 603 A l l e n , T . L . 2 3 5 , 2 4 1 ( 3 5 ) , 286 Allinger, N.L. 8 0 (17), 89 (50), 9 2 (17, 5 0 , 6 0 ) , 93, 94, 96 ( 2 ) , 9 7 ( 4 ) , 9 8 ( 4 , 2 1 ) , 9 9 (2, 2 6 , 2 7 , 2 8 b , 2 9 , 3 1 ) , 100 ( 2 7 , 2 8 b , 2 9 ) , 101 ( 4 0 , 4 2 ) , 109 ( 9 4 ) , 1 1 0 ( 2 9 , 4 2 ) , 118 ( 2 9 , 1 2 4 ) , 121 ( 1 5 3 , 1 5 6 ) , 122 ( 1 5 3 , 156, 1 6 8 ) , 123 ( 2 9 , 168, 187a, 187b), 125 ( 1 9 3 ) , 127 ( 2 9 , 3 1 , 1 9 3 , 2 0 6 , 2 1 0 ) ,

128 ( 2 1 4 , 2 2 0 ) , 128-133, 158, 159, 163, 166, 1 6 9 , 1 7 0 , 1 7 3 , 177 ( 9 9 ) , 183, 9 3 4 ( 7 0 ) , 960 A l l i s o n , J. 6 7 3 ( 8 3 ) , 6 7 4 ( 8 6 ) , 679 Allred, E . L . 5 9 0 , 5 9 1 ( 1 9 4 i ) , 5 9 5 , 5 9 6 ( 2 0 4 e ) ,

606, 607 A l m e n n i n g e n , A . 125 ( 1 9 3 ) , 127 ( 1 9 3 , 2 0 6 , 2 1 0 ) , 132, 133 A l p e r , H. 5 6 7 ( 7 4 ) , 602 A l - S a d e r , B . H . 8 7 8 ( 2 5 8 ) , 893 A l t e v o g t , R. 5 8 7 ( 1 8 0 ) , 606 A l t m a n , J. 9 2 9 ( 2 0 ) , 959 A l y a s s i n i , N . 6 9 1 ( 5 2 ) , 737 A m a i k e , M . 9 3 8 ( 8 2 ) , 960 A m d u r , M . O . 9 1 8 ( 2 8 4 ) , 925 A m i r - E b r a h i m i , V . 4 2 6 , 4 2 9 ( 1 7 7 ) , 453 A m o r e b i e t a , V . T . 4 0 7 ( 9 6 , 9 7 ) , 451 A m o s , R . D . 165 ( 1 1 5 ) , 184 A m o t o , S. 8 5 ( 3 7 ) , 94 A n a c h e r i k o , S . N . 5 5 9 ( 3 1 ) , 601 A n a h , D . A . 8 5 8 ( 1 7 5 a ) , 890 A n d e r s , D . E . 3 3 2 ( 8 9 ) , 348, 8 9 8 ( 2 5 ) , 9 0 8 ( 1 8 2 ) , 920, 923 A n d e r s e n , B . 9 3 3 ( 4 7 ) , 959 A n d e r s o n , F . E . , III 9 7 2 ( 7 3 ) , 995

A n d e r s o n , G.R. 8 5 0 ( 1 3 5 ) , 889 A n d e r s o n , H . W . 1 6 3 , 164 ( 1 1 0 ) , 184 A n d e r s o n , J.B.F. 6 8 5 ( 3 1 ) , 736 A n d e r s o n , J.E. 9 9 ( 2 5 ) , 102 ( 5 2 ) , 103 ( 5 5 , 5 7 ) , 104 ( 6 4 , 6 7 - 6 9 ) , 105 ( 6 7 ) , 106 ( 5 5 , 6 9 ) , 107 ( 5 5 ) , 109 ( 5 2 , 8 9 a , 9 0 ) , 1 1 0 ( 5 5 ) , 112 ( 5 2 , 5 5 , 8 9 a , 9 0 , 1 0 7 ) , 113 ( 5 2 , 5 7 , 6 4 , 8 9 a , 1 1 0 ) , 114 ( 5 7 , 6 4 , 6 9 , 8 9 a ) , 115 ( 5 2 , 6 7 - 6 9 ) , 1 1 6 ( 5 2 , 5 7 , 6 4 , 8 9 a , 9 0 , 1 1 3 ) , 117 ( 5 2 , 5 7 , 6 4 , 9 0 , 1 0 7 , 1 1 3 , 116, 1 1 7 ) , 1 2 0 ( 8 9 a , 1 4 8 ) , 123 ( 1 7 4 ) , 127

( 2 0 5 ) , 128-133, 2 2 3 (13), 285, 3 7 3 ( 1 1 2 , 113, Anderson, Anderson, Anderson, Anderson, Anderson,

115), 3 7 4 (115), i 9 / J.R. 6 8 4 ( 2 6 a ) , 736, 8 6 1 ( 1 9 9 ) , 891 P . C . 8 9 8 ( 2 5 ) , 920 P . H . 1 4 3 , 1 6 2 ( 5 3 ) , 182 R . C . 8 5 2 ( 1 3 7 ) , 889 S . D . 3 2 0 ( 5 6 ) , 347

A n d e r s o n , W . G . 1 0 3 , 1 0 4 ( 6 1 ) , 108 ( 8 2 , 8 3 ) , 113 ( 8 3 ) , 1 1 4 ( 6 1 ) , 116 ( 6 1 , 8 3 ) , 117 ( 6 1 , 8 2 , 8 3 ) , 7 2 9 , 130, 3 7 3 ( 1 0 8 , 114), 391 A n d o , E. 128 ( 2 2 4 ) , 133 A n d o , I. 3 5 2 ( 2 ) , 3 6 9 ( 7 3 - 7 7 ) , 3 7 6 ( 1 3 5 , 1 3 6 , 139), 389, 390, 392 A n d o n , R.J.L. 2 7 9 ( 9 0 ) , 287 A n d o s e , J . D . 9 9 ( 3 0 ) , 129, 6 9 1 , 6 9 2 ( 5 6 c ) , 738 A n d r a d e , J.G. 5 4 7 ( 1 5 5 ) , 551, 5 8 2 ( 1 5 6 ) , 605 A n d r e w , M . 9 0 4 ( 8 0 ) , 921 A n d r e w s , D . R . 5 8 9 ( 1 8 7 d ) , 606 A n d r e w s , G . C . 5 4 3 ( 1 2 9 ) , 550 A n d r e w s , G . D . 3 8 5 ( 2 1 5 ) , 393, 5 9 0 , 5 9 1 ( 1 9 4 a ) , 606, 7 1 2 , 7 1 3 ( 1 1 5 c ) , 740 A n e s h a n s l e y , D.J. 9 0 6 ( 1 2 3 ) , 922 A n e t , F . A . L . 9 8 ( 1 1 , 12), 9 9 , 1 0 0 ( 3 4 ) , 117 ( 1 1 8 ) , 118 ( 1 1 9 , 1 2 0 ) , 119 ( 1 3 3 ) , 1 2 0 ( 1 3 3 , 1 3 8 , 1 4 0 a , 140b), 121 ( 1 2 0 , 1 5 5 ) , 124 ( 3 4 ) , 126 ( 1 9 5 , 1 9 6 ) , 127 ( 1 2 , 3 4 , 195, 2 0 4 , 2 0 7 - 2 0 9 ) , 128 ( 2 1 5 , 2 1 9 , 2 2 0 ) ,

128-133, 3 7 3 ( 1 1 6 ) , 3 7 4 ( 1 1 8 , 1 1 9 , 1 2 1 , 128), 3 7 5 ( 1 3 0 - 1 3 3 ) , 3 7 7 ( 1 5 6 ) , 3 7 9 ( 1 6 9 ) , 391,392 A n e t , R. 1 2 6 , 127 ( 1 9 5 ) , 132 A n g y a l , S.J. 9 6 ( 2 ) , 9 7 , 9 8 ( 4 ) , 9 9 ( 2 ) , 121 ( 1 5 3 ) , 122 ( 1 5 3 , 1 6 8 ) , 123 ( 1 6 8 ) , J28,

131, 132 A n i c i c h , V . G . 4 0 6 ( 8 0 ) , 451 A n n i s , J.J. 3 3 0 ( 8 6 ) , 348 A n n u n z i a t a , R. 2 6 8 , 2 8 1 ( 8 4 ) , 287 A n p o , M . 6 8 2 ( 1 3 ) , 7 0 6 ( 8 8 0 , 735 , 739 A n s o n , P . C . 9 6 9 ( 3 7 ) , 994 A n s o r g e , W . 3 6 1 ( 4 6 ) , 390 A n t e u n i s , M.J.O. 123 ( 1 7 2 ) , 132 A n t h o n y , R . G . 6 8 2 , 6 8 3 ( 9 a ) , 735 A n t o n o v a , I.N. 8 5 9 , 8 8 4 ( 1 8 5 f ) , 891 Antunes Marques, J.C. 4 2 2 ( 1 5 4 , 155), 4 4 4 (233, 234), 4 4 5 (234), 4 4 6 , 4 4 7 ( 2 3 4 , 2 3 5 ) , 453, 454

A u t h o r index Anzenbacher, P. 917 (272), 925 Aparina, E.V. 407 (86, 87), 451 Apeloig, Y. 928, 930 (6), 958 Appell, J. 402, 404 (35), 450 Applequist, D.E. 543 (128), 550, 953 (125), 967, 964 (5), 976 (81), 977 (84), 983 (5),

994, 995

Appleton, W.R. 762, 763 (24), 779 Aquilanh, V. 535 (41), 548, 833 (95), 888 Aquino Neto, F.R. 308, 314 (38), 347 Arab, M. 377 (147), 392 Arai, H. 407 (90, 91), 451 Arai, T. 705 (83c, 83d), 739 Araki, T. 568 (77), 602 Arhart, R.J. 988 (131), 996 Arican, M.H. 969 (47), 995 Ariel, S. 104, 109 (66), 729 Arigoni, D. 143 (32), 182 Aristor, N. 541 (96, 98), 550 Armentrout, P.B. 541 (95, 96, 98-100, 102, 103, 105, 108), 542 (103), 550, 673 (84),

679

Armour, E.A. 733 (139), 741 Ameu, E.M. 544 (146), 557 Arnold, M.T. 905 (90), 906 (117), 927 Arpe, H.J. 644 (109a), 652 Arrieta, J.M. 724, 728, 733 (135), 741 Arsenyev, Yu.N. 826 (70a), 887 Arz, A.A. 301 (16), Asbrink, L. 475, 476 (28), 477 (52), 487 (28), 490 (52), 493, 502, 503 (28), 934 (68), Aschan, O. 538 (60), 549 Ashby, E.G. 559 (35, 36), 571 (36, 97, 98), 607, Ashfold, M.N.R. 687, 688 (37c), 736 Ashton, D.S. 789 (39a, 39b), 807 Asinger, F. 532, 538 (25), 548, 610 (1), 616 (31), Askani, R. 590, 591 (194b), 606 Askari, M. 122 (161), 131 Asmus, P. 477 (72), 478 (94, 101), 479 (94), 5 1 2 , 5 1 4 (72), 526, 527 Asselberghs, S. 826 (76), 888 Astik, R.R. 940 (93), 967 Aston, J.G. 99 (23), 109 (87), 128, 130 Asunta, T.A. 673 (82), 679 Atavin, E.G. 125, 127 (193), 132 Atkins, T.J. 540 (83), 549, 712, 713 (115a), 724, 726 (132c), 740, 741 Atkinson, J.G. 823 (54, 55, 56a, 56b),

346

960

525, 526,

603

649, 650

887

Atlas, R.M. 915 (241), 924 Atomi, H. 916 (246), 924 Attina, M. 430 (181), 453, 535 (45), 548 Audisio, G. (134), 184 Aue, D.H. 951 (118), 967

1001

Augustine, R.L. Augustynowicz, Ausloos, p. 407 425 (173),

555, 556 ( H i ) , 600 M. 905 (109), 927 (95), 417 (95, 143), 424 (162), 435 (199, 201), 437 (215),

451-454, 535 (40), 548, 687 (39e, 45), 688 (45), 689 (47), 736 , 737, 751, 752 ( l i b , 1 Ic), 755 (14), 756-758 (16), 763, 764 (31), 765 (34b), 778, 779, 867 (215),

892

Austel, V. 202 (40), 213 Auter, A.P. 857 (165), 890 Avato, p. 904 (78), 927 Averill, B.A. 858 (167), 890 Awasthi, A.K. 711 (108c), 740 Aydin, R. 377 (158, 159), 379 (161, 168), 380 (178), 381 (183), 382 (178, 183, 192), 383 (192), Ayer, W.A. 361 (50), 390 Ayre, G.L. 906 (121), 922 Ayrey, G. 826, 827 (77), 888 Azoulay, E. 854 (152d-f), 890 Azzena, U. 142 (43), 182

392,393

Baas, J.M.A. 119, 120 (130), 122 (159, 160), 123 (173), 7J7, 132 Babad, E. 929 (20), 959 Babemics, L. 851 (136), 889 Bachiri, M. 396 (2), 449 Back, T.G. 567 (75), 568 (79), 602 Bacon, B. 128 (220), 133 Bacon, E. 430 (184), 453 Bader, R.F.W. 2 (1-3), 6 (1, 3), 9 (2, 12, 13), 13 (14), 17 (18-20), 18 (2, 3), 26 (14, 24), 31 (24), 34 (2, 14, 26), 35 (26, 28, 29, 32, 33), 36 (3, 29, 34), 40 (33), 41 (14, 40), 43 (3), 45 (3, 40, 44), 48 (18), 52 (44), 54 (20), 56 (44), 61 (18), 68 (52), 70, 74 (20, 52), 92 (62), 96 (1), 101 (50), 933 (56, 57), 952 (57), Baer, T. 412, 425, 444 (123), 452 Baer, Y. 474 (26), 525 Baerends, E.J. 479 (112), 527 Baeyer, A. 928 (3), 958 Bafus, D.A. 542 (126), 550 Baggaley, A.J. 801 (66b), 807 Baggou, J.E. 259 (70), 287 Bagneres, A.G. 906 (137), 922 Bailey, A.L. 813, 852 (10b), 886 Bailey, D.S. 120-122 (144b), 131 Bailey, N.J. 909 (194), 923 Bailey, P.M. 657 (21), 677 Bailey, P.S. 637 (92, 94), 657 Bailey, W.F. 583 (165f, 166), 584 (165f), 589 (189, 190), 605, 606 Baird, N.C. 706, 707 (87a), 739

76, 77, 128, 129, 960

94,

1002

A u t h o r index

Baizer, M.M. 587 (182b), 606 Baker, A.D. 414 (131), 452, 471 (19), 476 (19, 39), 477 (19), 525 Baker, C. 4 7 1 , 476 (19), 477 (19, 51), 508, 509 (51), Baker, E A . 900, 902 (45), 920 Baker, E.B. 542 (124), 550 Baker, J.E. 905 (105, 112), 921 Baker, M.V. 663 (56), 678 Baker, R.B. 969 (41), 995 Bakker, M.G. 683 (22a), 736 Balaban, A.T. 189 (20), 272, 815 (14), 816 (21), 883 (272), 886, 893 Balaji, V. 711 (106a), 740 Balandin, A.A. 859 (186), 891 Balavoine, G. 802 (71, 72), 803 (73, 74), 808 Baldry, K.W. 379 (163), 392 Balduzzi, A.M. 906 (144), 922 Baldwin, J.E. 163 (105), 184, 385 (215), 393, 543 (130), 550, 590, 591 (194a), 606, 712 (115c, 116b, 120b), 713 (115c), 714 (116b), 717 (120b), 740, 741 Baldwin, M.A. 399, 406 (25), 424 (159), 450,

525, 526

453

Baldwin, R.R. 259 (66), 287, 969 (41), 995 Balestova, G.I. 560 (42), 607 Ballhausen, C.J. 460, 463 (12), 524 Bahs, D.M. 560, 561 (44c), 590, 591 (194f), 607, Bally, I. 815 (14), 816 (21), 886 Balogh, A. 620 (45b), 650 Balogh, D.M. 537, 538 (58), 549 Balogh, D.W. 382 (186), 393, 558 (28c), 592 (196b), 597 (213), 607, 606,

606

607

Bambaugh, K.J. 919 (298), 926 Ban, M. 698 (70), Bancroft, G.M. 476 (35), 525 Bandurski, E.L. 919 (300), 926 Bandy, J.A. 676 (93), 679 Banthorpe, D.V. 166 (122), 178 (137), 184, 904 (87, 88), 927 Baphst, J.N. 853 (147a), 855 (156), 889, 890 Barash, L. 165 (117), 184 Barbalas, M.P. 412 (125), 424, 434, 444 (163),

738

452, 453 Barber, H.N. 904 (75, 76), 927 Barber, T.R. 858 (178, 179), 890, 891 Barborak, J.C. 578, 579 (134c), 604 Barchi, J. 85 (38), 94 Barcicki, J. 812, 815, 822 (lb), 885 Bard, A.J. 794 (51), 807 Baresi, L. 897 (11), 979 Barfield, M. 352 (8), 380 (175, 176), 382 (187), 384 (194, 196), 386 (216), 387 (196), 389, 392, 393 Barger, H.J., Jr. 805 (81), 808

Barigelleui, F. 687 (39a, 39b, 40b), 736 Barlow, S.E. 542, 544, 547 (113), 550 Barnes, A.J. 314 (41), 347 Barnes, K.K. 782 (18a), 806 Barnett, B. 992 (157), 997 Bamier, J.-P. 479, 480 (115), 514 (115, 174), 527, Baron, M. 321 (59), 347 Barrett, A.G.M. 564 (58a, 58b), 565 (66d), 602 Barrett, J.W. 169 (126), 184 Barrick, R.C. 308 (37), 347 Barron, L.D. 140 (30), 163 (107, 108), 182,

529

184

Barrus, C A . 637, 640 (88), 657 Bartczak, W.M. 760, 762 (22a, 22b), 763 (30a), 771 (22a, 22b), 779 Bartell, L.S. 81 (27), 93, 97 (8), 102 (53), 103 (58, 59), 104 (8), 108 (81), 109 (8, 81,

91), 110, 114 (53), 128-130

Bartelt, R.J. 905 (96), 927 Bartlett, P.D. 637 (89), 657, 979 (91), 996 Bartmess, J.E. 302 (21), 346, 396, 397, 402, 408, 433 (3), 537, 538 (56), 543 (56, 140), 546 (56), Bartoli, J.F. 804 (75), 808 Bartolini, G. 85 (38), 94 Barton, D.H.R. 555 (1), 600, 564 (58a, 58b), 565 (64, 65c, 66a-e), 566 (64, 66a-c, 66e), 567 (69), 578 (130a, 130b, 135), 580 (130b, 136, 139), 581 (149a, 149b), 602, 604, 605, 643 (104), 652, 782 (17), 802 (71, 72), 803 (73, 74),

449, 549, 550

808

806,

Barz, W. 904 (89), 927 Barzaghi, M. 33 (25), 77 Basch, H. 477, 508, 509 (51), 526 Bashe, R.W. 820 (39), 887 Basilier, E. 474, 487, 493, 499 (27), 525 Basler, W.D. 369 (96), 391 Basson, I. 389 (229), 393 Bassova, G.I. 559 (30), 607 Bastian, E.W. 371 (98), 597 Bastiansen, O. 513, 514 (172), 529 Basu, D. 854 (152c), 890 Basus, V.J. 98 (11), 120 (138), 127 (207), 128, 131, 133, 375 (130), 391 Batalov, A.P. 871 (226-228), 892 Bates, G.S. 813, 852 (10b), 886 Bates, R.B. 542, 543 (117), 550 Batich, C. 477 (65), 526 Battioni, P. 804 (75), 808 Bathste, M.A. 535 (47), 548 Baudry, D. 661 (38), 663, 664 (38, 55a), 666, 668, 670 (55a), 678 Bauer, N. 402 (39), 450 Bauer, W. 928 (12), 959

A u t h o r index Baum, T. 707 (90), 708 (90, 97d), 739, 740 Baumann, H. 782 (3b), 806 Baumgart, K.-D. 949, 951 (112), 96J Baumgartel, O. 947, 951 (105), 961 Bauhsta, R.G. 122 (169), 132 Baxendale, J.H. 744 (4), 778 Baxter, B.M. 672 (76), 679 Baxter, H.N., III 966 (20), 971 (70), 972 (20), 992 (152), 994, 995, 997 Baxter, S.G. 374 (127), 391 Baxter, S.M. 654, 672 (2), 677 Beach, Y.J. 402 (39), 450 Beam, H.W. 915 (243), 924 Beatty, J.W. 838 (105), 888 Beauchamp, J.L. 259 (74), 287, 437 (213), 454, 541 (94, 101, 105, 106, 108), 550, 674 (85), 679 Becherer, J. 479 (110), 5 2 7 Beck, B.R. 590, 591 (194i), 595, 596 (204e),

606, 607 Beck, G. 763 (29c), 779 Beckelt, B.A. 574, 575 (113k), 604 Becker, E.D. 316 (48), 347 Becker, J.Y. 795 (54, 55), 807 Becker, L.W. 984 (111), 996 Becker, S. 567 (72), 602 Becker, W.G. 705, 706 (85b), 739 Beckerle, J.D. 686 (34b), 736 Beckey, H.D. 399 (22, 23, 26, 27), 400 (27), 406 (26), 450 Beckhaus, H.-D. 101 ( 4 4 ^ 9 ) , 103 (57), 109 (89a), 112 (49, 89a, 105, 106), 113 (44, 45, 57, 89a, 110), 114, 116 (57, 89a), 117 (57), 120 (89a), 729, 130, 373 (110), 391, , 583 (163), 585 (171), 605 Beckley, R.S. 540 (82), 549, 598, 599 (215b),

608 Becknell, A.F. 703, 724, 725, 730 (79b), 739 Beckwith, A.L.J. 589 (187c), 606 Beddall, P.M. 9 (13), 77 Bee, L.K. 593 (201c), 607 Beeby, J. 593 (201c), 607 Beeck, O. 538 (66, 67), 549, 612 (15), 649, 838 (102), 888 Beekman, W.J. 749 (8a), 778 Beeler, A.J. 376 (144), 392 Beenakker, C.I.M. 396, 4 0 1 , 402 (8), 450 Behl, M.H. 904 (79, 85), 927 Behrens, U. 514 (174), 529 Beierbeck, H. 368 (58), 371 (99, 100), 390,

391 Bekkum, H.van 122 (157, 158), 757, 361 (48),

390 Belanger, A. 576 (121a), 604 Belanger, P.C. 563 (56), 602 Beletskaya, I.P. 543 (137), 550 Bell, C S . 986, 987 (118), 996

1003

Bell, E.R. 992 (154, 156, 157), 997 Bell, O.F., Jr. 855 (160), 890 Bell, P. 101 (51), 729 Belyaeva, A.N. 916 (259), 925 Belzner, J. 479 (107), 527, 593, 594 (202c, 202e), 607, 953 (126), 954 (127-129, 132), 967 Benderskii, V.A. 235 (43), 286 Bendoraitis, J.G. 294 (5), 307, 310 (31), 323 (5), 346, 347 Benfield, F.W.S. 670 (67), 679 Ben Hadid, A. 615, 616 (25), 650, 785 (30),

806 Benneu, D.W. 940 (88), 960 Bennen, I.C. 916 (253), 924 Bensimon, M. 416, 421 (140), 424 (161), 435 (140, 209), 436 (140, 161), 442 (140), 4 4 4 ^ 4 6 (234), 447 (234, 237), 452-^54 Benson, S. 456 (5), 524 Benson, S.W. 3 (10), 77, 234 (31), 235 (31, 32, 46), 237 (32, 48), 238 (51), 239 (52), 241 (31, 32, 48), 251 (31, 32), 259 (56, 57, 62, 69, 73), 260 (32, 56), 261 (32), 267 (82), 269 (85), 286, 287, 429 (179), 453, 866 (214), 892, 966 (19), 985, 986 (116), 994, 996 Bentley, T.W. 368 (67), 390 Bercaw, J.E. 654 (2), 657 (15, 16), 658 (27), 672 (2, 74b), 677, 679 Berg, A. 385 (212), 393 Berg, U. 97, 98 (5), 101, 110, 111 (41), 117 (5), 128, 129 Berger, G. 813 (8, 9), 820 (40), 886, 887 Berger, R.G. 904 (89), 927 Berger, S. 352, 361, 368 (3), 377 (155), 380-382, 384, 385 (3), 387 (218, 221, 222), 388 (224), 389, 392, 393 Bergholz, R. 384 (198), 393 Bergman, R.G. 540 (91), 549, 661 (39, 42), 662 (43-46), 663 (51, 52), 670 (42), 678 Bergmark, T. 474 (26), 476 (37), 487, 489 (134), 525,528 Bergstrom, G. 820, 821 (45), 887, 906 (124, 136), 922 Bergstrom, S. 855 (158), 890 Berkert, U. 118 (124), 130 Berkowitz, J. 404, 409, 410 (48), 450, 542 (126), 550 Berlin, A.J. 374 (117), 391 Bernard, M. 120-122 (143), 131 Bemardi, B. 98, 111 (9), 128 Bernardi, F. 223 (11), 285, 371 (104), 391 Bemardi, R. 799 (60), 807 Bemardini, M.P. 906 (144), 922 Bernassau, J.M. 356 (23), 389 Bernays, E.A. 905 (99), 927 Beme, B.J. 98, 99 (19), 128

1004

A u t h o r index

Bemeu, W.A. 509 (165), 528 Bernhardt, P. 684 (29), 736 Bernier, P.P. 84 (33), 93 Bernstein, H.J. 110 (101), 130, 145 (68), 158 (100), 183, 228, 241, 244, 248, 275 (24), 285, 954 (134), 962 Bernstein, R.B. 435 (203), 453 Berrier, A.L. 635 (84), 651 Berson, J.A. 152 (82), 163 (104), 183, 184, 703 (79b), 710 (103), 724, 725, 730 (79b), 734 (140), Berthelot, M. 644 (108), 652 Bertini, F. 989 (132), 996 Bertram, J. 614 (23), 649, 782, 783 (19), 806 Bestmann, G. 108 (80), 130 Bethune, D.S. 84 (33), 93 Bettels, B.R. 102 (52), 109, 112 (52, 89a), 113 (52, 89a, 110), 114 (89a), 115 (52), 116 (52, 89a), 117 (52), 120 (89a), 129,

739-741

130

Bettels, R.E. 373, 374 (115), 391 Betteridge, D. 414 (131), 452, 476 (39), 525 Beveridge, D.L. 457, 460 (7), 524 Beynon, J.H. 405 (55), 415 (138), 451, 452 Bhacca, N.S. 479 (121, 122), 527 Bhaskar Rao, V. 562, 563 (51a), 601 Bhattacharya, D. 407 (92), 451, 773 (47), 779 Biali, S.E. 120 (137), 131, 556 (13b), 600 Bianchi, G. 904 (78), 927 Bickel, A.F. 539 (71), 549, 610 (5a, 5b), 612 (12), 613 (16), 623 (5a, 5b, 16), 982 (102), 996 Bickelhaupt, F. 703, 704, 712, 719 (80), 739 Bicker, R. 361 (40), 390 Bie, M.J.A. de 380 (177), 382 (177, 191), 384

649,

(177, 195), 392,393

Biellmann, J.-F. 122 (165), 132 Bienfait, C. 774 (57), 780 Bierbaum, V.M. 542 (113), 543 (142), 544 (113, 149, 152), 547 (113), 550, 551, 872 (241), 892 Bieri, G. 407, 408 (94), 451, 466 (18), 475, 476 (28, 29), 477 (29, 70), 478, 479 (29), 487 (28), 491 (18), 493 (28), 495 (18), 502, 503 (28), 507 (29), Biethan, U. 574 (113a), 603 Bigeleisen, J. 825 (67, 68), 879 (260), 887,

525, 526

893

Biggs, N.L. 188 (11), 272 Bigler, P. 940 (93), 967 Bijvoet, J.M. 141 (31), 182 Billeter, C. 128 (213), 133 Billingham, N.C. 565 (63a), 580 (137), 602,

604

Billups, W.E. 782, 797, 799 (8a), 806 Biltz, M. 816 (21), 886 Binder, H. 805 (82), 808

Bingel, W.A. 381 (182), 393 Binger, P. 479 (113), 527, 562 (46a-c), 601, 712, 717 (120a), 747 Bingham, R.C. 931 (40), 959 Binns, S.H. 827 (79), 888 Binsch, G. 118 (121), 120 (150, 151b), 121 (121, 151b), 131, 374 (120), 391, 560, 561 (44a), 601 Bioggi, R. 171 (133), 184 Birchard, J.P. 969 (35), 994 Bird, C W . 915 (238), 924 Bird, R.B. 226 (17), 227 (18), 266 (83), 285,

287 Birss, V.I. 568 (79), 602 Bischof, P. 477 (57, 58, 60, 65, 73, 75, 76), 478 (58, 60, 83, 84, 90, 9 1 , 104), 479 (118, 124, 126), 507 (57), 508 (162), 515 (57), 516, 519 (124), 731, 732 (137a), 747 Bishop, K.C., III 540 (85), 549, 672 (69), 679, 692 (62f), 696 (66b), 698 (62f), 712 (66b, 116a), 713 (66b), 714, 715 (66b, 116a), 716 (116a), 719 (66b), 738,

526-528,

740

Bishop, R.C. 540 (84), 549 Bittner, S. 384, 385 (204a), 393 Bjorklund, C. 582 (153), 605 Bjornstad, S.L. 128 (212, 221), 133 Black, T.M. 163 (108), 184 Blackburn, E.V. 582 (159b), 605, 988 (131),

996

Blackvall, J.E. 698 (69a), 738 Blades, A.T. 875 (250, 251, 253), 876, 881 (250), 893 Blair, C M . 188 (15), 272 Blanchard, E.P. 957 (145), 962 Blaustein, M.A. 734 (140), 747 Blazej, A. 706 (88d), 739 Blickle, P. 479 (114), 527 Blinder, S.M. 235 (41), 286 Blithe, D. 980 (98), 996 Blizzard, A.C. 384 (197), 393 Bloch, H.S. 610 (3), 649 Bloch, K. 853 (147c), 889 Bloch, M. 479 (114), 527 Blomberg, M.R.A. 698 (69a), 738 Blomquist, G.J. 905 (95, 98, 103), 906 (95, 116, 132, 133, 139), 914 (216-221), 927,

922, 924

Blount, J.F. 558 (28b), 601, 724, 728, 729 (136a), 747 Blouri, B. 970 (63), 995 Blum, J. 557 (15), 600 Blum, M.S. 905 (92), 906 (92, 121, 122, 129), 927, 922 Boand, G. 543 (141), 550 Boar, R.B. 564 (58a, 58b), 602

A u t h o r index Boates, T.L. 103 (58), 729 Bobilliart, F. 782 (18c, 20, 21), 784 (20),

806

Bodor, N. 303 (23), 347, 478, 514 (89), 527 Boehm, M.C. 479 (126, 127), 527, 528 Boelstler, H. 128 (226), 133 Boer, H. 637 (90), 657 Boerboom, A.J.H. 405 (59), 457 Boersma, J. 928 (12), 959 Boese, W.T. 666, 667 (61b), 678 Bogdanova, O.K. 859 (186), 891 Bogge, H. 942, 943 (94), 967 Boggs, J.E. 80 (15), 87 (42), 93, 94 Boggs, R.A. 540 (82), 549, 570 (89b), 598, 599 (215b), 603, 608 Bognor, A. 911 (204), 923 Bogomolov, A.I. 301 (17), 346 Bohan, S. 164, 180 (114), 184 Bohlen, H. 705 (84b), 739 Bohlman, F. 562 (52), 601 Bohm, H. 929 (18), 959 Bohm, M.C. 931 (41), 959 Bohme, D.K. 532 (13, 16), 535 (16), 537, 538 (55), 543 (144), 548, 549, 551 Boikess, R.S. 978 (86, 87), 980 (98), 995,

996

Boiron, F. 919 (295), 925 Boivin, J. 802 (71, 72), 803 (73, 74), 808 Boland, W. 590, 591 (194e), 606 Bolesov, I.G. 477 (62, 62), 526 Bolt, A.J.N. 639 (97), 657 Bolt, H.M. 917 (265, 266), 925 Bombach, R. 477 (66), 526 Bommel, A.J. van 141 (31), 182 Bonchev, D. 205 (46), 213 Bondarev, Y.M. 861 (201), 891 Bondi, A. 202, 203 (39), 2 7 i Bonnifay, R. 532 (21, 26), 548, 613 (17), 617 (17, 32a, 32b), Bonzo, R. 825, 826 (66), 887 Boojamra, C G . 675 (90d), 679 Booth, B.L. 632 (68), 657 Booth, H. 119, 120 (134), 131, 374 (123), 379 (164, 1 6 6 ) , i 9 7 , J92 Borchers, F. 447 (240), 454 Borcic, S. 116, 118 (112), 130 Borden, W.T. 711 (107, 108b, 114g), 740 Bordwell, E.G. 543 (132-134), 550 Borgen, G. 126 (198a, 198b), 128 (212, 221),

649, 650

132, 133 Borgstrom, B. 855 (158), 890 Bories, G.F. 855 (163), 890, 906 (142), 922 Borman, S.A. 329 (79), 348 Borowiecki, T. 812, 815, 822 (lb), 885 Bortha, R. 915 (241), 924 Bortz, J.T. 906 (145), 922 Bos, H.J.T. 705 (83a), 739

1005

Boschi, R. 476 (46), 478 (98), 525, 527 Bose, A.K. 564 (59), 602 Bose, P.K. 163 (107, 108), 184 Bosecker, K. 909 (195), 923 Bosnich, B. 555, 556 ( I l k ) , 600 Bosse, D. 560, 561 (44d), 593, 595 (203d), 601, 607, 712, 720, 722 (126), 741 Bostnott, J.K. 919 (302), 926 Botello, A.V. 900 (36), 920 Botha, D. 123 (179), 132 Bothe, H.K. 762, 763 (28), 779 Bothner-By, A.A. 85 (38), 94, 369 (97), 371 (98), Bottcher, E.-H. 683 (21b), 736 Botter, R. 410 (114), 452 Bouchard, D.A. 672 (78a), 679 Boucher, S. 136 (4), 181 Bouchet, P. 823 (53), 887 Bouma, W.J. 404, 408 (46), 425 (46, 166), 428 (46), Bouman, T.D. 164, 180 (114), 184 Bourn, A.J.R. 118, 121 (120), 131 Bourne, P.M. 169 (127), 7^, 41), 664 (37a-d, 59), 666, 667 (59), 668 (9), 669 (37c, 59), 670 (59, 66), 672 (6), 675 (90a-e, 91), 676 (92), 689 (48a, 48b),

283, 285, 286, 959

601, 606,

737

677-679,

Curl, R.F. 208 (59), 213 Curme, H.G. 137 (13), 181 Curran, D.P. 588, 589 (186a), 606 Curtis, E.G. 635 (83), 657 Curtis, J. 362, 364 (53), 390 Curtis, N.J. 568, 577 (78), 602 Curtiss, C F . 226 (17), 227 (18), 266 (83), 285,

886

287

Curtiss, L.A. 85, 87 (41), 94, 532, 534 (34), 930 (33), 959 Curvigny, T. 582 (151), 605 Cusumano, L. 954 (133), 967 Cvetanovic, R.J. 639 (98), 657, 674 (89), 679 Cygler, J. 773 (50b), 780

548,

Daage, M. 862 (204), 891 Dadok, J. 85 (38), 94 Dahl, L.E. 928 (14), 959 Dailey, W.P. 41 (38), 77, 478, 519 (82), 526, 933 (61), 934 (67), 954 (61, 67),

960

A u t h o r index Daino, A. 687 (46a), 737 Dais, P. 369 (79), 390 Dale, J. 125 (191, 192), 126 (198a, 198b), 127 (191, 199, 202), 128 (199, 212), Dalecki, T.M. 578 (132), 604 Dalling, D.K. 120, 121 (142), 123 (178), 131, 132, 360 (28), 362 (51, 52), 374 (125),

132, 133

389-391

Damrauer, R. 542 (113), 544 (113, 149, 152), 547 (113), 550, 551 Danen, W.C. 700, 703 (75a), 738 D'Angela, D. 858, 881 (172b), 890 D'Angelo, L.L. 387 (220), 393 Daniel, S.H. 841, 842 (113a), 889 Dannacher, J. 477 (66), 526 Dannenberg, H. 855 (161), 890 Danner, R.P. 208 (60), 213 Darriet, D. 907 (147-149), 914 (213, 214), 919 (296), 922, 924, 926 Das, M.L. 857 (164), 890 Das, N.C. 988 (131), 996 Date, T. 561 (45c), 601 Dauben, W.G. 570 (89a), 574, 575 (113j), 603, 604, 724, 726 (132d), 734 (141b), 741, 860 (197), 891, 944 (98), 961 Daughtney, W.C. 918 (276), 925 Daulemann, W. 916 (261), 925 Dauscher, A. 685 (32), 736 David, D.E. 711 (106a), 740 David, G.G. 815 (16), 886 Davidov, E.R. 853, 856 (144), 889 Davidson, E.R. 404 (47), 450, 933 (59), 960 Davidson, J.M. 659 (29), 677 Davidson, R.B. 514 (175), 529 Davies, A.G. 991 (141), 993 (168), 997 Davies, C.A. 228 (23), 259 (60), 285, 287 Davies, N.W. 906 (127), 922 Davis, B. 434 (198), 453 Davis, B.H. 816 (23), 886 Davis, B.R. 827 (78), 888 Davis, C C . 188 (16), 272 Davis, L.P. 544 (151), 557 Davis, S.C 673 (82), 679 Davis, S.K. 866, 867 (213), 892 Davis, T.C. 165 (117), 184 Davydov, L.G. 369 (95), 597 Deadman, W.D. 590 (195), 606 Dean, B.B. 902 (59), 920 Dearden, D.V. 437 (213), 454 DeBoer, C 988 (122), 991 (143), 996, 997 De Borger, R. 900 (31), 920 Debrencev, Yu.I. 865 (208, 209), 891 De Cesan, L. 916 (249), 924 Declercq, J.-P. 947 (105), 949 (109, 111), 951 (105, 121), Defay, N. 382 (185), 393 DeFrees, D.J. 532, 537, 538, 547 (33), 548

961

1011

Degani, I. 577, 578 (123a), 604 Degenhardt, C R . 479 (125), 527 Deguchi, K. 376 (135, 136), 592 deJongh, H.A.F. 120 (149), 757 De Lange, C.A. 479 (112), 527 Delavarnne, S. 633 (72b), 657 Delderick, J.M. 633, 635 (75), 657 De Leng, A . C 687 (40a), 756 Delia, E.W. 382 (187), 384 (204b, 231), 385 (204b), 387 (219), 595, 477 (69), 478 (86), 526, 527, 578 ( 1 3 l a - c ) , 604, 954 (134), 962 Dellonte, S. 687 (39a, 39b, 40b), 756 De Lucchi, O. 562, 563 (51b), 601, 708 (94a), 759 De Maleissye, J.T. 690 (51b), 757 Demanova, N.F. 853, 856 (144), 889 De Mayo, P. 706 (87a, 87c), 707 (87a), 759 DeMember, J.R. 619 (41), 624 (51, 52), 625 (54), Demny, J. 682 (12e), 755 Demuth, M. 590 (193a), 606 Denekas, M.O. 895 (3), 979 Denis, A. 812, 815, 822 (lb), 885 Denisov, L.K. 861 (201), 891 Deno, N . C 782 (8a, 15b), 797, 799 (8a), 806, 915 (230), 924, 969, 973 (56), 989 (134, 135), 995, 996 Depke, G. 376 (144), 592 Depp, M.R. 940 (88), 960 DePuy, C H . 507 (156), 528, 542 (113), 543 (142), 544 (113, 149, 150, 152), 547 (113), (241), Derbentser, Yu.I. 860 (188, 191), 891 Demiacheva, S.G. 916 (259), 925 Derrick, P.J. 399 (24, 25), 403, 405 (24), 406 (25), 414 (127, 128, 130), Derwish, G.A.W. 406 (64), 451 Desai, M . C 557 (23a), 601 De Sanctis, S.C. 81 (23), 95 Descei, V.R. 968 (32), 994 Deshayes, H. 564 (60a, 60b), 602 Deshpande, M.N. 88 (47), 94, 940 (88),

650

550, 551,^12

892

450, 452

960

Deslongchamps, P. 576 (121a), 604 Des Marais, D.J. 859 (184), 891 Desmond, K.M. 988 (130), 991 (143), 996, 997 Dessau, R.H. 614 (19), 649 Dessy, R.E. 543 (127), 550 Desty, D.H. 323 (69, 71), 348 DeTar, D.F. 109, 110 (97, 98), 130, 202 (36), 275 DeTar, M.B. 945 (102), 9 6 / Detty, M.R. 479 (117), 527 Deutsch-Wenzel, R. 916 (262), 925

1012

A u t h o r index

Devaprabhakara, D . 5 9 3 , 5 9 5 ( 2 0 3 c ) , D e v a u r e , J. 9 8 , 9 9 , 110 ( 1 7 ) , 128 D e v l i n , F. 140 ( 2 4 ) , 182

607

D o e h n e r , R.E., Jr. 5 9 5 , 5 9 6 ( 2 0 4 b ) , D o e p k e r , R . D . 6 8 9 ( 4 7 ) , 737

607

D o e n n g , W . v o n E. 1 6 3 , 164 ( 1 0 9 ) , 184, 2 5 9 (67), (25), 785 (29, 30), 795 (53), D o g g w e i l e r , H. 6 4 6 ( 1 1 0 ) , 6 5 2 D o l d o u r a s , G . A . 581 ( 1 4 6 ) , 605 D e w a r , M . J . S . 3 0 3 ( 2 3 ) , 347, 4 6 0 ( 1 1 ) , 4 7 6 D o l e , M . 7 7 7 , 7 7 8 ( 6 5 ) , 780 (30), 4 7 8 (89), 4 9 9 , 501 (144), 507 (11), D o l l , R.J. 7 8 2 ( 7 c ) , 806 514 (89), 5 3 6 ( 5 2D ) ,o m a i l l e , P.J. 6 5 7 ( 1 6 ) , 6 7 7 549, 7 2 4 , 7 2 5 , 7 3 0 ( 1 3 0 b ) , 741, 9 3 0 ( 3 5 ) , D o m a l s k i , E . S . 2 7 1 ( 8 9 ) , 284, 285, 287 931 (40), 959 D o m c k e , W . 4 8 9 , 4 9 0 ( 1 3 5 ) , 528 D o m n a s , A.J. 9 0 7 ( 1 6 3 ) , 923 D h e u , M . - L . 3 6 8 ( 6 9 ) , 390 D o m r a c h e v , G . A . 8 1 5 , 8 2 2 ( l o ) , 886 D i a n o , Y . 6 8 9 ( 4 6 b ) , 737 D o n a l d s o n , M . M . 6 9 1 , 6 9 2 , 6 9 4 ( 5 5 j ) , 737 D i a z , G . E . 5 8 2 ( 1 5 9 b ) , 605 D o n a t h , W . E . 123 ( 1 8 6 ) , 132 D i b e l e r , H. 4 0 4 ( 4 5 ) , 450 D o n c h i , K.F. 4 1 4 ( 1 3 0 ) , 452 D i b e l e r , V . H . 4 0 5 ( 5 2 ) , 450 Donnell, D.W. 907 (158), 922 D i c k e y , F.H. 9 9 2 ( 1 5 4 , 157), 9 9 7 D o n n e l l y , S.J. 5 6 9 ( 8 3 b ) , 603 D i c k s o n , R . S . 5 5 5 , 5 5 6 (1 Ij), 600 D ' O r , L. 3 0 7 ( 2 9 ) , D i C o s i m o , R. 6 6 3 ( 5 3 ) , 678 D o r a i s w a m y , K.K. 2 3 5 ( 4 4 ) , 286 D i e r c k s e n , G . H . F . 4 8 9 , 4 9 0 ( 1 3 5 ) , 528 D o r a n , M . A . 5 4 2 ( 1 2 4 ) , 550 D i e t r i c h , H. 9 2 8 ( 1 2 ) , 959 D o r i n g , E. 9 7 , 110 ( 6 ) , 128 D i l l , J . D . 9 2 8 , 9 3 0 ( 6 ) , 958 D o r o f e e v , Y.I. 7 0 8 ( 9 7 b ) , 739 D i l l , J.W. 4 6 6 , 4 9 1 , 4 9 5 ( 1 8 ) , 5 2 5 D o r o f e e v a , O . V . 127 ( 2 0 6 , 2 1 0 ) , 133, 284 Dillard, J.G. 4 5 6 , 4 5 7 ( 6 ) , 524, 5 4 3 ( 1 4 3 ) , 550, Dorr, M . 7 0 8 - 7 1 0 ( 9 2 c ) , 739 752 (12), Dorsselar, A . v a n 8 9 8 ( 1 9 ) , 9 7 9 D i l l e n , J . L . M . 9 2 ( 6 1 ) , 94, 9 9 , 100 ( 2 8 a ) , 122 D o u g h e r t y , D . A . 91 ( 5 8 ) , 94, 101 ( 4 3 ) , 106, ( 1 7 0 ) , 129, 132 D e v y n c k , J. 5 3 8 ( 6 2 ) , 5 4 9 , 6 1 5 ( 2 4 , 2 5 ) , 6 1 6

649, 650, 806, 807

287

524, 525, 527, 528,

347

778

D i l l w o r t h , J.W. 9 1 4 ( 2 1 9 ) , 924 D i n h - N g u y e n , N . 4 0 8 , 4 1 5 ( 1 0 1 ) , 451 Dinur, U. 8 0 ( 1 8 ) , 93 D i o n , R.P. 6 7 0 ( 6 6 ) , 6 7 9 Dirstine, P.H. 9 8 3 ( 1 0 9 ) , 9 9 6 D i s c h , R.L. 5 9 ( 5 1 ) , 7 7 , 9 3 3 ( 4 9 ) , 9 5 9 d i S i l v e s t r o , G. 123 ( 1 7 9 ) , 132 D i s k o , U. 3 3 6 , 3 3 8 , 3 3 9 ( 9 9 ) , 348 D i s t e f a n o , G. 4 7 6 ( 4 8 ) , 5 2 6 D i t t m a n , W . R . , Jr. 5 7 3 ( 1 0 8 a ) , 603 Dittmer, J.C. 9 1 4 ( 2 2 7 , 2 2 9 ) , 924 Dittmer, M. 120, 121 ( 1 5 1 a ) , 131 Dixon, D.A. 532 (36), 537 (36, 59), 538 (36), 929, 934 (23), 959 D i x o n , J.S. 85 ( 3 7 ) , 94

548, 549,

D i x o n , R . N . 4 8 7 , 4 8 9 ( 1 3 3 ) , 528 Djerassi, C. 137, 139 ( 1 4 ) , 181, 3 0 3 , 3 0 7 ( 2 0 ) ,

346

D j i g a s , S. 6 9 1 , 6 9 2 , 6 9 5 ( 5 5 h ) , 737 D o b i s , O. 2 5 9 ( 5 7 ) , 287, 9 8 5 , 9 8 6 ( 1 1 6 ) , 9 9 6 Dodd, C G . 895 (3), 9 / 9 D o d d r e l l , D. 3 8 6 ( 2 1 6 ) , 393 D o d o n o v , M . V . 5 5 9 ( 3 1 ) , 601 D o d s o n , R . W . 8 5 2 ( 1 3 7 ) , 889 D o d w e l l , C. 9 6 9 , 9 7 0 ( 5 1 ) , 9 9 5 D o d z i u k , H. 9 3 4 ( 7 0 ) , 9 3 5 ( 7 3 ) ,

960

D o e c k e , C. 4 7 9 , 4 8 0 ( 1 1 6 ) , 5 2 7 Doecke, C W . 4 7 9 (126), 527, 537, 538 (58), 549, 5 6 2 , 5 6 3 ( 5 1 b ) , 5 9 2 ( 1 9 6 a ) , 601,

606

129

112, 113, 115 ( 7 3 ) , D o u g l a s , A . G . 3 2 4 ( 7 2 ) , 348, 9 0 4 ( 8 2 ) , 9 2 / D o u l l , J. 9 1 8 ( 2 8 4 ) , 9 2 5 D o u s t e - B l a z y , L. 9 1 9 ( 3 0 3 ) , 9 2 6 D o w a t s h a s h i , H . A . 5 7 8 ( 1 3 5 ) , 604 D o w d , P. 5 9 0 , 5 9 1 ( 1 9 4 a ) , 606, 9 3 4 ( 7 1 ) , 960 D o w n e y , J.R., Jr. 2 2 8 ( 2 3 ) , 2 5 9 ( 6 0 ) , 285, 287 Downing, D.T. 9 0 0 (34), 906 (145), 907 (153) 9 1 9 ( 2 9 7 ) , 920, 922, 926 D o w n i n g , J.W. 3 7 6 ( 1 4 4 ) , 392 D o y l e , D.J. 6 8 7 , 6 8 8 ( 3 8 b ) , 736 D o y l e , M.J. 8 0 ( 1 9 ) , 93 D o y l e , M.P. 5 6 9 ( 8 3 a , 8 3 b ) , 602, 603 D o z o r o v , A . V . 8 1 5 , 8 2 2 ( I q ) , 886 Dragan, A. 5 3 2 ( 2 2 ) , 548, 6 1 5 ( 2 8 ) , 650 Drake, A . F . 152 ( 8 1 ) , 165 ( 1 1 5 ) , 183, 184 Draper, A . M . 7 0 6 ( 8 7 a , 8 7 c ) , 7 0 7 ( 8 7 a ) , 739 Drawert, F. 9 0 4 ( 8 9 ) , 921 Draxl, K. 4 1 0 , 4 1 4 ( 1 1 5 ) , 452, 4 5 6 , 4 5 7 ( 6 ) ,

524,

778

752 (12), Dreizler, H. 108 ( 7 8 , 8 0 ) , 130 D r e s s e l , J. 4 7 8 ( 1 0 4 ) , 5 2 7 D r e w , C M . 4 1 1 ( 1 1 9 ) , 452 Drew, M.G.B. 597, 598 (210d), 607 D r e w e r y , G.R. 2 5 9 ( 6 6 ) , 287 Dreyer, G . B . 9 3 9 , 9 4 2 ( 8 5 ) , 960 D r i s k o , R.L. 7 0 8 , 7 1 0 ( 1 0 1 a ) , 740 Droffen, G.H. 9 0 9 ( 1 9 1 ) , 923 Drotloff, H. 3 7 6 ( 1 4 0 , 141), 392 D r u d e , P. 152 ( 8 6 ) , 183

A u t h o r index D u b i n s k i i , Y u . D . 8 6 0 ( 1 8 9 ) , 891 D u b i n s k i i , Yu.G. 8 6 0 ( 1 9 0 , 191), 891 D u b i s , E. 9 0 6 ( 1 1 9 ) , 922 D u b o i s , J.E. 2 0 2 ( 3 5 ) , 213, 3 5 6 ( 2 1 ) , 389, 3 9 6 (2), D u b o u c h e r , C. 9 1 9 ( 3 0 3 ) , 926 D u b r o , D . W . 3 6 9 ( 8 3 ) , 391 D u B u s , R. 8 5 3 ( 1 4 7 d ) , 890 D u d d e c k , H. 116 ( 1 1 5 ) , 130, 3 6 8 ( 6 9 ) , 390 D u f r e s n e , C. 5 6 3 ( 5 6 ) , 602 D u g a s , H. 3 5 2 ( 4 ) , 389 D u m m e l , R.J. 8 7 8 ( 2 5 9 ) , 893 D u m o n , L. 8 2 6 ( 7 6 ) , 888 D u m o n t , O. 9 1 9 ( 2 9 5 ) , 925 D u n i t z , J . D . 15 ( 1 5 ) , 3 9 ( 3 6 , 3 7 ) , 4 0 ( 1 5 ) , 7 7 ,

449

5 7 4 ( 1 1 3 c ) , 603, 9 3 3 ( 5 5 ) , 9 3 4 ( 7 0 ) , 960 D u n n i n g , T.H. 17 ( 2 1 ) , 7 7 D u n o g u e s , J. I l l , 116 ( 1 0 3 ) , 130, 3 7 3 ( 1 1 1 ) ,

391

Duppel, W. 857 (165),

890

D u p u i s , M . 5 3 2 ( 3 7 ) , 548 Durand, B . 9 0 9 ( 1 8 8 ) , 923 D u r h a m , L.J. 9 9 3 ( 1 6 4 ) , 997 Durig, J.R. 9 8 ( 2 2 ) , 109, 117 ( 8 8 ) , 123 ( 1 8 3 , 184), D u r m a z , S. 9 3 0 ( 3 1 ) , 959 Durra, E. 9 1 6 ( 2 4 7 ) , 924 Durst, T. 5 4 2 ( 1 1 6 ) , 5 5 0 D u t h , R. 4 0 1 ( 3 8 ) , 450 Dutler, R. 163 ( 1 0 6 ) , 184, 6 9 1 , 6 9 2 ( 5 5 a ) ,

128, 130, 132

737 D v o r e t z k y , I. 2 9 4 ( 9 ) , 346 D y a c h k o v s k i i , F.S. 6 7 0 ( 6 4 a ) , 678 D y c z m o n s , V . 5 3 2 ( 2 7 , 3 1 ) , 548 D y k e , J. 4 7 6 ( 4 8 ) , 526 D z a n t i e v , B . G . 8 2 8 ( 8 0 , 8 1 a ) , 888

603-606, 608, 960

Eaton, P.J. 5 6 5 ( 6 1 ) , 602 E b e l , M . 188 ( 1 6 ) , 212 Eber, J. 5 9 0 ( 1 9 2 ) , 606 E b e r s o n , L. 5 7 2 ( 1 0 1 b ) , 603, E c h o l s , J.T. 9 6 9 ( 4 5 ) , 995

782 (18d),

806

E c k e r t - M a k s i c , M . 4 7 9 ( 1 2 8 ) , 528, 9 3 4 , 9 5 2 (69), E c k l i n g , R. 9 6 6 ( 1 7 ) , 994 E d e l s o n , E.H. 6 2 4 ( 5 0 a , 5 0 c ) , 650

960

E d e n , C. 7 8 2 ( 9 a ) , 806 E d l i n g t o n , M . A . 9 1 5 ( 2 3 9 ) , 924 E d m i s t o n , C. 4 6 4 , 5 0 9 ( 1 5 ) , 5 2 5 E d w a r d s , G.J. 4 7 7 , 4 7 8 , 4 8 0 ( 7 9 ) , 5 2 6 , 7 9 2 , 793 (48, 50), E d w a r d s , M . 5 6 8 ( 7 9 ) , 602 E g a w a , T. 123 ( 1 8 1 ) , 132 Egert, E. 120 ( 1 5 0 , 151a), 121 ( 1 5 1 a ) , 131 E g g e r s , S. 3 9 6 , 3 9 8 ( 1 0 ) , 450 E g g i n k , G. 9 1 6 ( 2 4 5 ) , 924 E g l i n t o n , C. 9 0 0 ( 4 2 , 4 6 ) , 9 0 2 ( 4 6 ) , 9 0 4 ( 8 1 ,

807

920, 921

82), E g l i n t o n , G. 3 2 1 , 3 2 3 ( 6 4 ) , 348,

8 9 6 (8), 898

( 2 1 , 2 4 ) , 9 0 8 ( 1 7 9 ) , 9 0 9 ( 1 7 9 , 190, 1 9 1 ) , 9 1 1 ( 1 9 7 ) , 9 1 3 ( 2 1 0 ) , 919, 920, 923, 924 Egolf, D . S . 123 ( 1 8 9 ) , 132 E g u c h i , T. 118 ( 1 2 3 ) , 131 E h m a n n , W.J. 5 6 0 ( 4 1 ) , 601 E i c h , C. 9 0 1 , 9 0 2 ( 5 5 ) , 920 E i d e , I. 9 1 8 ( 2 8 9 ) , 9 2 5 E i d e , M . O . 3 7 7 ( 1 4 5 ) , 392 E i d u s , Ya.T. 8 6 5 ( 2 0 7 , 2 0 9 , 2 1 0 ) , 891 Eilbracht, P. 6 7 0 ( 6 7 ) , 6 7 9 Eisenhardt, K. 9 8 9 ( 1 3 4 ) , 996 Eisner, T. 9 0 6 ( 1 2 3 ) , 9 2 2 Eland, J . H . D . 4 7 1 , 4 7 6 , 4 7 7 , 4 8 9 ( 2 1 ) , 5 2 5 Elbert, T. 8 1 3 ( 6 ) , 886 E l - F e k k y , T . A . 6 3 2 ( 6 8 ) , 651 Elian, M . 8 8 3 ( 2 7 2 ) , 893 Elias, B . M . 9 1 9 ( 2 9 1 ) , 9 2 5 E l i a s s o n , B . 6 8 2 ( 1 2 a , 12c), 735 Eliel, E.L. 9 6 ( 2 , 3 ) , 9 7 , 9 8 ( 4 ) , 9 9 ( 2 , 3 ) , 121 ( 1 5 3 ) , 122 ( 1 5 3 , 1 6 8 ) , 123 ( 1 6 8 ) , 128, 143 ( 3 2 ) , 186 ( 1 0 ) , 2 7 2 , 361 ( 3 4 ) , Elkind, J.L. 5 4 1 ( 1 0 0 ) , 550 Elliger, C A . 128 ( 2 1 1 ) , 133, 8 2 4 ( 6 4 ) , 887 Ellis, R . W . 6 4 6 , 6 4 8 ( 1 1 1 a ) , 6 5 2 E l l i s o n , P . O . 4 8 9 ( 1 3 8 ) , 528 Ellison, G.B. 5 4 3 (145), 5 5 7 , 9 2 8 (7), 9 3 0 (7, 34), 9 5 0 (7), E l l i s o n , S.L.R. 3 7 9 ( 1 6 5 ) , 392 E l l i s o n , S.R. 120 ( 1 3 9 ) , 131 E l l z e y , M . L . , Jr. 5 0 4 ( 1 5 0 ) , 528 E l s e n , Y . v a n 9 0 0 ( 3 1 ) , 920 E l s o m , L.F. 5 8 5 ( 1 6 9 c ) , 605 El-Taliawi, G . M . 9 9 1 ( 1 5 0 ) , 9 9 7 E m e i s , D . 3 7 6 ( 1 4 0 , 141), 3 9 2 E m s l e y , J.W. 3 8 0 ( 1 7 3 ) , 392 E n d e , C A . M . v a n den 7 6 2 ( 2 3 ) , 7 7 9 Enderer, K. 7 1 2 , 7 1 6 ( 1 1 7 ) , 7 4 0 E n d o , T. 5 6 8 ( 7 7 ) , 6 0 2 Engberts, J . B . R N . 81 ( 2 3 ) , 93 E n g e l , H. 9 1 6 ( 2 4 5 ) , 924 E n g e l , P. 5 9 7 ( 2 1 3 ) , 6 0 7 E n g e l , P . S . 7 0 8 ( 9 4 b , 9 5 ) , 7 1 6 ( 9 5 ) , 739 E n g e l , R. 5 7 3 ( 1 0 7 ) , 603

131, 132, 390

E a d o n , G. 4 3 0 ( 1 8 4 ) , 453 Earl, W . L . 3 7 6 ( 1 3 8 ) , 392 E a s t h a m , A . M . 3 5 2 ( 1 2 ) , 389 E a s t o n , B . C . 136, 138, 148 ( 7 ) , 181 Eaton, P.E. 4 7 9 , 5 1 6 , 5 1 9 ( 1 2 3 , 124), 5 2 7 , 5 4 0 ( 8 1 ) , 549, 5 7 0 ( 8 8 d ) , 5 7 4 , 5 7 5 ( 1 1 3 h ) , 5 7 6 ( 1 2 1 c ) , 5 7 8 , 5 7 9 ( 1 3 3 b , 134a, 134d), 5 8 3 (167a), 5 9 0 , 591 (194d), 5 9 8 , 5 9 9 (215a), 6 8 2 (8b), 6 9 2 ( 6 2 d ) , 7 1 1 ( 1 0 6 b , 108a, 112), 735, 738, 936 (81),

740,

1013

182,

958, 959

1014

A u t h o r index

Engelhardt, G. 120, 121 ( 1 4 6 ) , 131, 361 ( 3 2 ) , 3 7 4 ( 1 2 4 ) , 390, 391 Engelking, P.C. 5 4 3 (145), 557 E n g e n , D . v a n 6 9 2 , 6 9 4 ( 5 8 ) , 738 England, W. 4 6 4 , 509 (15), 5 2 5 Engler, E.M. 9 9 (30), 729, 597, 5 9 8 (210a),

607, 6 9 1

(53a, 56b, 56c), 6 9 2 (56b, 56c), 6 9 4 ( 5 6 b ) , 737, 738 E n g l e r , T . A . 5 5 7 ( 2 3 a ) , 601 Englin, M.A. 9 9 2 (161), 9 9 7 E n i k o p o p j a n , N . S . 6 7 0 ( 6 4 b ) , 679 E n n e n , L . W . 3 7 7 ( 1 4 8 ) , 392 E n r i q u e z , R . G . 3 6 9 ( 8 0 ) , 391 Ensminger, A.A. 898 (19), 979 E n t w i s t l e , I . D . 5 5 5 - 5 5 8 ( l l g ) , 600 Ephritikhine, M . 6 6 1 , 6 6 3 , 6 6 4 ( 3 8 ) , 6 6 6 , 6 6 8 , 6 7 0 ( 5 5 a ) , 678 Epiotis, N . D . 9 3 0 (29), 9 5 9 E p l i n g , G . A . 7 0 2 ( 7 7 c ) , 738,

101,

739

708 (90),

E w b a n k , J . D . 8 8 , 8 9 ( 4 6 ) , 94 Eyler, J.R. 4 3 7 ( 2 1 5 ) , 454 E y r i n g , H. 136 ( 6 ) , 181 Fabre, P.L. 5 3 8 ( 6 2 ) , 549, (25),

615 (24, 25), 616 (29, 30), 795 (53),

649, 650, 7 8 5 806, 807

F a c e l l i , J.C. 3 7 6 ( 1 4 4 ) , 3 8 2 ( 1 8 7 ) , 392, 393 F a e h l , L.G. 3 8 5 ( 2 1 0 ) , 393 Fair, C.K. 6 7 2 ( 7 5 ) , 6 7 9 Faisst, W . 120, 121 ( 1 4 1 ) , 122 ( 1 6 7 ) , 131,

132

Fajans, K. 2 3 3 ( 3 0 ) , 286 Fajula, F. 6 1 8 , 6 2 1 ( 3 6 a , 3 6 b ) , 650, 8 6 2 ( 2 0 4 , 205), F a k e s , H. 9 0 6 ( 1 2 9 ) , 9 2 2 F a l b e , J. 7 8 2 ( 3 b ) , 806 F a l c o n e r , W . E . 8 8 1 ( 2 6 4 ) , 893 Falick, A . - M . 3 9 9 , 4 0 3 , 4 0 5 ( 2 4 ) , 4 1 4 ( 1 2 7 ,

891

128), 4 2 5 ( 1 7 0 ) , 4 4 6 ( 2 3 5 ) , 4 4 7 ( 2 3 5 ,

E p s t e i n , S. 8 5 8 , 881 ( 1 6 9 ) , E r d m a n , J.E. 2 9 4 ( 4 ) , 346

236), 450, 452^54

890

Ermer, O. 101 ( 5 1 ) , 128 ( 2 1 6 ) , 7 2 9 , 133, 9 3 4 (70), Ernst, B . 5 6 4 ( 5 7 b ) , 602 Ernst, L. 361 ( 4 9 ) , 390 Ernst, T . D . 6 3 7 - 6 4 0 ( 8 7 b ) , 6 5 7 E m s t e r , L. 8 5 7 ( 1 6 4 ) , 890 E r s h o v , N . I . 8 6 5 ( 2 0 9 , 2 1 0 ) , 891 E s k o v a , V . V . 6 5 8 ( 2 3 a ) , 6 7 7 , 8 7 0 ( 2 2 1 ) , 892 E s p e l i c , K . E . 9 0 2 ( 6 0 ) , 9 0 5 ( 9 9 , 100), 920,

960

921

Fallis, A . G . 9 4 6 ( 1 0 4 ) , 9 6 7 Fanta, G.F. 9 7 6 ( 8 1 ) , 995 Farah, F. 9 6 6 ( 1 8 ) , 994 Farcasiu, D . 5 9 7 , 5 9 8 ( 2 1 0 a ) , 607 Farcasiu, M . 5 9 7 , 5 9 8 ( 2 1 0 b ) , 607,

691 (53a,

53h, 55e, 56b), 692 (55e, 56b), 6 9 4 ( 5 6 b ) , 6 9 5 ( 5 5 e ) , 737, 738 Farhat, M. 3 7 7 ( 1 4 7 ) , 392 Farhataziz 7 4 4 - 7 4 6 ( 2 ) , 778 Farina, M . 123 ( 1 7 9 ) , 132, 171 ( 1 3 3 ) , ( 1 3 4 ) ,

184

E s p i t a l i c , J. 9 0 9 ( 1 8 8 ) , 923 E s p l u g a s , S. 6 8 2 ( 1 5 b ) , 735 E s r a m , H. 6 8 2 ( 1 2 d , 12e), 735 E s s , C. 7 2 4 , 7 2 5 , 7 3 0 ( 1 3 0 c ) , 747 E s s e n , H. 3 4 , 35 ( 2 6 ) , 7 7 Estabrook, R . W . 8 5 5 ( 1 5 7 ) , 890 Ettinger, D . G . 3 1 5 , 3 2 9 ( 4 3 ) , 347 Ettre, L . S . 3 2 3 ( 7 0 ) , 348 E v a a n s , G . H . 9 1 6 ( 2 5 5 ) , 924 E v a n s , D . A . 5 4 3 ( 1 2 9 ) , 550, 5 5 7 ( 2 3 b ) , 601 E v a n s , E . A . 8 2 6 ( 7 3 ) , 888 E v a n s , E . D . 8 9 9 ( 2 6 , 2 7 ) , 9 0 8 ( 1 7 8 ) , 920,

923

Evans, G.T. 388 (228),

393

E v a n s , M . G . 9 6 7 ( 2 6 ) , 994 E v a n s , M . W . 4 0 2 ( 3 9 ) , 450 E v a n s , S. 4 7 7 ( 5 4 ) , 5 2 6 E v a n s , S.L. 9 0 6 ( 1 2 2 ) , 9 2 2 E v a n s , W . H . 2 7 1 ( 8 9 ) , 284, 287 E v e r e u , J.E. 3 7 9 ( 1 6 6 ) , 392 Everett, J.R. 1 1 9 , 1 2 0 ( 1 3 4 ) , 131, 379 (164), Everett, J.W. 5 9 3 ( 2 0 1 c ) , 607 E v e r s h e d , R.P. 3 2 9 ( 8 3 ) , 348 E v l e t h , E . M . 7 0 8 ( 9 7 a ) , 739

391,392

374 (123),

Farina, V . 5 6 8 , 5 7 7 ( 7 8 ) , 602 F a r k a c o v a , M . 6 9 0 ( 5 1 c ) , 737 Farley, F.F. 8 2 9 ( 8 1 c ) , 888 F a m e t h , W . 7 0 8 , 7 1 0 ( 1 0 1 b ) , 740 Fameth, W.E. 7 0 0 (75b, 76), 7 0 2 (75b), 703 (75b, 76), Farnham, W . B . 5 4 0 ( 8 2 ) , 549, 5 5 6 ( 1 3 e ) , 5 7 0 ( 8 9 b ) , 5 9 8 , 5 9 9 ( 2 1 5 b ) , 600, 603, 608 Famia, M. 6 4 3 - 6 4 5 (107a), 6 5 2 F a m i a , S . M . F . 6 1 9 ( 4 4 a ) , 650 Farooq, O. 6 1 9 ( 4 3 , 4 4 a ) , 6 2 0 ( 4 4 b ) , 6 2 7 ( 5 6 ) ,

738

6 3 3 , 6 3 5 ( 7 7 - 7 9 ) , 650, 651 Fatland, C L . 9 0 5 ( 1 0 5 ) , 9 0 6 ( 1 2 0 ) , 9 2 7 , 9 2 2 Fauconet, M. 6 3 3 (72b), 6 5 / Faulkner, T.R. 1 4 0 ( 2 3 ) , 182 F a w c e t t , A . H . 3 7 4 ( 1 2 6 ) , 391 F e d o r o v i c h , P . M . 9 0 6 ( 1 4 3 ) , 922 Fedtke, N. 917 (265, 266), 9 2 5 F e e n e y , J. 3 8 0 ( 1 7 3 ) , 392 Feher, F.J. 6 6 2 , 6 6 9 , 6 7 0 ( 5 0 ) , 678 Fehler, S . W . G . 9 1 4 ( 2 2 6 ) , 924 F e i b u s h , B . 2 9 4 ( 8 ) , 346 F e i g h a n , J.A. 8 1 6 ( 2 3 ) , 886 F e i n s t e i n , S. 3 3 6 , 3 3 7 ( 1 0 0 ) , 348 F e j e s , P. 861 ( 2 0 3 ) , 891

A u t h o r index F e k l i s o v , G.I. 8 5 9 ( 1 8 5 c , 185d, 185f), 8 8 3

Finn, R . D . 8 2 0 ( 4 1 ) , 887 F i n n e y , C D . 3 9 9 ( 1 8 ) , 450 Firestone, R . B . 8 1 3 , 8 3 0 , 8 5 2 ( 1 0 a ) , 886 Firth, W . C 5 7 8 ( 1 2 9 a ) , 604 Fischer, E.G. 2 9 3 , 3 0 0 , 3 0 4 ( 3 ) , 346 Fischer, J.W. 5 6 2 , 5 6 3 ( 5 1 b ) , 601 Fischer, W . F . , Jr. 8 2 0 ( 3 9 ) , 887 F i s h b e i n , R. 7 8 2 , 7 9 7 , 7 9 9 ( 8 a ) , 806, 9 8 9

( 1 8 5 c , 1 8 5 d ) , 8 8 4 ( 1 8 5 f ) , 891 Felberg, J.D. 6 3 0 ( 5 9 , 6 2 ) , 6 3 1 ( 6 2 ) , 6 4 3 - 6 4 5 ( 1 0 7 a ) , 6 4 6 ( 1 1 0 ) , 651, 652 Felkin, H. 5 5 7 ( 2 1 ) , 601, 6 6 1 ( 3 8 ) , 6 6 3 , 6 6 4 (38, 55a-d), 666 (55a-^), 668, 670 ( 5 5 a - d ) , 678 Fell, B . 9 7 0 - 9 7 3 , 9 8 8 , 9 8 9 ( 6 6 ) , 995 Feller, D . 4 0 4 ( 4 7 ) , 450, 9 3 3 ( 5 9 ) , 960 F e l l o w s , M . S . 120 ( 1 3 9 ) , 131 F e n g , J. 8 4 ( 3 5 ) , 93

( 1 3 4 ) , 996 Fisher, E.R. 5 4 1 , 5 4 2 ( 1 0 3 ) , 550 Fitger, L. 5 5 6 , 5 5 7 ( 1 3 j ) , 600 Fitjer, L. 120 ( 1 4 7 , 150, 151a, 1 5 1 b ) , 121

F e n g , W . 4 2 7 , 4 2 8 , 4 3 0 , 4 3 1 ( 1 7 8 ) , 453 F e n n y , P.P. 8 2 0 , 821 ( 4 6 ) , 887 F e r g u s o n , D . M . 100, 124, 127 ( 3 6 ) , 129 F e r g u s o n , E.E. 5 3 7 , 5 3 8 ( 5 3 , 5 4 ) , 549 F e r g u s o n , R.R. 6 7 5 ( 9 0 d , 9 0 e , 9 1 ) , 6 7 6 ( 9 2 ) ,

679

Fernandez, F. 169 ( 1 2 4 ) , 171 ( 1 2 8 ) , 172 ( 1 3 0 - 1 3 2 ) , 184 Ferrara, C. 9 1 6 ( 2 4 9 ) , 924 Ferrara, L. 9 0 5 ( 9 7 ) , 921 Ferraudi, G. 7 0 5 ( 8 5 a ) , 739 Ferry, M.J. 9 1 7 , 9 1 8 ( 2 6 9 ) , 925 F e s s e n d e n , R . W . 7 7 3 , 7 7 8 ( 5 2 ) , 780 Fessner, W . - D . 7 9 ( 7 ) , 93, 5 7 0 ( 9 0 a , 9 0 b ) , 5 7 6 ( 1 2 1 b ) , 5 9 2 ( 1 9 7 ) , 603, 604, 606, 6 2 0 ( 4 5 c ) , 650 F e h z o n , M . 3 5 6 ( 2 3 ) , 389 Fettis, G . C . 9 6 9 ( 3 6 ) , 994 Feuer, H. 5 8 2 ( 1 5 7 ) , 605 Feulmer, G.P. 3 2 5 , 3 2 6 ( 7 4 ) , 348 F e y n m a n , R.P. 4 2 ( 4 2 ) , 7 7 Fiaux, A . 3 9 7 ( 6 ) , 4 0 6 ( 7 1 ) , 4 3 5 ( 2 0 2 ) , 4 3 7 ( 2 1 4 ) , 4 3 8 (6, 2 1 4 ) , 4 3 9 ( 2 1 4 ) , 450,

453, 454

Flesch, G.D. 4 1 0 (111), 4 5 2 Fliszar, S. 2 1 2 ( 6 6 ) , 213, 2 5 9 ( 7 5 ) , 3 5 2 ( 4 - 6 ) , 389 F l o r e n z a n o , C. 9 0 7 ( 1 6 7 ) , 9 1 4 ( 2 2 5 ) ,

924

183

548,

346,

600

346,

600

(55b-d), 666 (55b, 55c), 668, 670 ( 5 5 b - d ) , 678 Filosa, J. 9 1 6 ( 2 5 4 ) , 924 Findlay, D . A . 1 6 3 , 1 6 4 ( 1 1 2 ) , 184 F i n g a s , M . 3 9 6 ( 1 ) , 449 F i n k e l m e i e r , H. 3 8 2 , 3 8 5 ( 1 9 0 ) , 393 F i n l a y s o n , O.E. 6 8 5 ( 3 0 ) , 736

( 1 6 3 ) , 5 8 5 ( 1 7 1 ) , 605 F l a s c h , G.W.Jr. 5 8 8 ( 1 8 3 ) , 606 Fleet, C.W.J. 5 7 5 ( 1 1 9 ) , 604, 8 5 8 ( 1 6 8 ) , 890 F l e i s c h m a n n , M . 6 1 4 ( 2 3 ) , 649, 7 8 2 , 7 8 3 ( 1 9 ) , 786 (33), 7 9 2 (33, 44, 45), 795 (52b),

Fickett, W . 145 ( 6 7 ) , 162 ( 1 0 3 ) , 164 ( 6 7 ) ,

524,

( 1 4 7 , 151a, 1 5 1 b ) , 131, 5 7 4 ( 1 1 3 d ) , 589 (187e), 593 (201a, 201b, 201e), 595 ( 2 0 7 ) , 603, 606, 607 Fitts, D . D . 137, 164 ( 1 2 ) , 181 Fitzer, L. 5 6 0 , 5 6 1 ( 4 4 a , 4 4 b ) , 601 Fitzwater, S. 81 ( 2 7 ) , 93, 109 ( 9 1 ) , 130 F l a m i g n i , L. 6 8 7 ( 3 9 a , 3 9 b , 4 0 b ) , 736 F l a m m a n g , R. 4 3 5 ( 2 0 7 ) , 454 F l a m m - t e r - M e e r , M . A . 1 0 1 , 1 1 2 ( 4 9 ) , 129, 5 8 3

806, 807

451,

Field, E. 9 1 6 ( 2 5 2 ) , 924 Field, F.H. 4 0 6 ( 6 3 , 6 5 , 6 6 , 6 8 ) , 451, 4 5 6 , 4 5 7 (6), 532 (2, 5), 7 5 2 (12), 8 4 7 ( 1 2 4 ) , 889 Field, L . D . 6 6 3 ( 5 6 ) , 678 Fieser, L.F. ( 5 7 ) , 182, 292, 2 9 3 ( 1 ) , 3 0 1 ( 1 5 ) , 555 (7), Fieser, M . ( 5 7 ) , 182, 2 9 2 , 2 9 3 ( 1 ) , 301 ( 1 5 ) , 555 (7), Fife, D.J. 7 0 5 ( 8 3 b ) , 739 F i g e y s , H.P. 3 8 2 ( 1 8 5 ) , 393 Fileppora, Z . O . 9 1 6 ( 2 5 9 ) , 9 2 5 F i l l e b e e n - K h a n , T. 5 5 7 ( 2 1 ) , 601, 6 6 3 , 6 6 4

1015

287, 923,

F o c h e m , H. 7 8 2 ( 3 b ) , 806 F o c h i , R. 5 7 7 , 5 7 8 ( 1 2 3 a ) , 604 F o l d , R.R. 3 6 9 ( 8 9 ) , 391 Foldiak, G. 6 8 7 , 6 8 8 ( 3 7 a , 3 8 a , 4 3 ) , 6 9 0 ( 4 9 ) , 7 4 4 (1), 7 6 6 (40), 769, 7 7 0 (42), F o n d , J. 85 ( 3 8 ) , 94 F o n g , L.K. 6 5 7 ( 1 5 ) , 6 7 7 F o n k e n , G . S . 7 8 2 ( 1 ) , 805 F o o n , R. 9 6 9 ( 3 3 , 3 4 ) , 994 Ford, B . 4 6 0 ( 1 0 ) , 4 7 6 ( 4 1 ) , 524, 525 Ford, R . A . 9 8 ( 2 1 ) , 128 Formanovskii, A.A. 477 (62), 5 2 6 F o r r o w , N.J. 6 6 3 , 6 6 4 , 6 6 6 , 6 6 8 , 6 7 0 ( 5 5 c ) ,

736 , 737, 778, 779

778,

678 Forster, T h . 5 0 8 ( 1 6 0 ) , 528 Fort, R . C . 6 9 1 ( 5 3 d ) , 737 Fort, R.C.Jr. 3 0 8 ( 3 3 , 3 4 ) , 347, 4 7 8 ( 1 0 2 ) , 6 1 9 ( 4 2 b ) , 650, 6 9 1 , 6 9 2 ( 5 5 c ) , 737 Fort, Y . 5 6 7 ( 7 2 ) , 602 F o s s e y , J. 9 6 9 , 9 7 9 ( 5 7 ) , 9 9 5 Foster, G. 8 8 2 ( 2 7 1 ) , 893 Foster, J.M. 4 6 4 , 5 0 4 , 5 0 9 , 5 1 6 , 5 1 8 ( 1 6 ) , 525 Foster, J.W. 9 1 5 ( 2 4 0 ) ,

924

527,

1016

A u t h o r index

Foster, R.F. 5 4 4 , 5 4 6 , 5 4 7 ( 1 4 7 , 1 4 8 ) , 551 F o u q u e t , G. 8 2 4 ( 6 1 ) , 887 Fourie, L. 5 7 4 , 5 7 5 ( 1 1 3 i ) , 604 F o w l e r , M . G . 3 3 6 , 3 3 7 ( 1 0 0 , 101), 348 F o w l e y , L . A . 5 9 0 ( 1 9 1 ) , 606 F o x , D.J. 8 5 , 87 ( 4 1 ) , F o x , M . A . 6 8 2 , 7 0 5 ( 1 7 a , 17d), 7 0 6 ( 8 8 a , 8 8 e ) ,

94

736, 739

Franke, W . 4 2 5 ( 1 7 4 ) , 4 2 6 ( 1 7 6 ) , 453 Franklin, J.L. 3 ( 9 ) , 7 7 , 4 0 6 ( 6 3 , 6 9 ) , 4 1 2 (126), 424 (164), 4 5 6 , 457 (6), 5 3 2 (5), 535 (43), 752 (12),

524, 778

451^53, 548,

F r a n k m o U e , W . 3 7 9 ( 1 6 1 ) , 392 Franz, L.H. 3 8 4 , 3 8 5 ( 1 9 9 ) , 393 Frasinski, L.J. 4 0 4 ( 4 3 ) , 450 Freas, R . B . 6 7 3 ( 8 3 ) , 6 7 4 ( 8 6 ) , 679 Freeh, D . 9 0 6 ( 1 3 5 ) , 922 Frechette, R.F. 5 6 7 ( 7 1 ) , 602 Fredricks, P.J. 9 6 9 ( 3 7 ) , 994 Fredricks, P.S. 9 6 4 , 9 7 5 , 9 8 3 ( 3 ) , 994 F r e e d m a n , T . B . 140 ( 2 9 ) , 163 ( 1 0 5 , 1 0 6 ) ,

184

F r e e m a n , G.R. 7 4 4 , 7 4 5 ( 3 ) , 7 6 2 ( 2 5 ) ,

779

182,

778,

F r e e m a n , K . H . 3 4 5 , 3 4 6 ( 1 1 5 , 116), 349 F r e e m a n , P.K. 5 6 0 , 5 6 1 ( 4 4 c ) , 5 9 0 , 5 9 1 ( 1 9 4 f ) , 601, 606, 9 5 6 ( 1 3 6 ) , 962, 9 8 0 ( 9 3 ) , 996 Frei, K. 9 5 4 ( 1 3 4 ) , 962 Freiberg, L . A . 1 2 1 , 122 ( 1 5 6 ) , 131 Freiser, B . S . 5 4 1 , 5 4 2 ( 1 0 4 ) , 550 Freitag, W . 109, 1 1 2 - 1 1 4 , 116, 120 ( 8 9 b ) , 130, 3 6 1 ( 3 3 ) , 3 7 1 , 3 7 2 ( 1 0 2 ) , 390, 391 French, M . 4 0 6 ( 7 2 ) , 451, 5 3 2 ( 1 2 ) , 548 Frenz, B . A . 6 5 9 ( 3 0 ) , 6 7 7 Frey, H . M . 9 3 3 ( 4 7 ) , 959 Fridh, C. 4 7 7 , 4 9 0 ( 5 2 ) , 5 2 6 , 9 3 4 ( 6 8 ) , 960 Friebolin, H. 1 2 0 , 121 ( 1 4 1 ) , 122 ( 1 6 6 , 167),

131,132

Friedkin, M . 8 2 0 ( 4 3 ) , 887 Friedman, N. 6 4 2 (100c), 657 Frieser, B . S . 5 4 1 ( 9 7 ) , 550 Fringuelli, F. 169 ( 1 2 4 ) , 184, 3 6 8 ( 6 4 ) , 390 Frisch, M . A . 1 2 2 ( 1 6 9 ) , 132 Fritz, H. 7 9 ( 7 ) , 93, 1 0 1 , 1 1 2 ( 4 9 ) , 7 2 9 , 3 7 4 ( 1 2 7 ) , 3 8 8 ( 2 2 5 ) , 5 9 7 , 393,

556 (13c),

5 8 5 ( 1 7 1 ) , 5 9 2 ( 1 9 7 ) , 600, 605, 606, 6 2 0 ( 4 5 c ) , 650 Fritz, H . - G . 5 7 0 ( 8 7 b ) , 603 Fritz, H . P . 7 8 6 ( 3 4 - 3 6 ) , 7 9 5 ( 3 4 , 3 5 ) , 807 F r o h l i c h , S. 6 4 6 ( 1 1 0 ) , 6 5 2 Frost, D . Z . 9 1 8 ( 2 7 6 ) , 9 2 5 Frurip, D.J. 2 2 8 ( 2 3 ) , 2 5 9 ( 6 0 ) , 285, 287 Fry, J.L. 5 6 2 ( 4 8 ) , 5 7 3 ( 1 0 8 a ) , 601, 603 Fu, T.-H. 5 5 8 (26), F u c h s , R. 4 0 1 ( 3 2 ) , 450 F u e k i , K. 6 8 3 ( 2 1 c ) , 736

601

F u e s s , H. 8 0 ( 2 1 ) , 93 Fujii, T. 6 6 6 , 6 6 7 ( 6 0 a ) , 678 Fujii, Y . 3 6 9 ( 7 7 ) , 390 Fujikura, Y . 5 9 3 , 5 9 5 ( 2 0 3 a ) , 5 9 7 ( 2 1 4 ) , 607, 691 (53a, 53e, 53f), F u j i m o t o , Y . 5 6 3 ( 5 4 a ) , 602 F u j i s e , Y . 9 3 8 ( 8 2 ) , 960 Fujita, S. 6 9 1 , 6 9 2 ( 5 5 b ) , 737 F u j i y a m a , S. 6 3 3 , 6 3 5 ( 7 4 ) , 6 5 7 F u j i y o s h i - Y o n e d a , T. 8 5 - 8 7 ( 4 0 ) , 94 Fukuhara, T. 6 3 3 ( 7 0 , 7 1 , 7 2 a ) , 6 5 7 Fukui, K. 155 ( 9 2 ) , 183 Fukui, S. 9 1 6 ( 2 5 7 ) , 9 2 5 F u k u s h i m a , T. 4 7 6 ( 4 9 ) , 5 2 6 F u k u y a m a , T. 123 ( 1 8 1 ) , 132 F u l c o , A.J. 7 8 2 ( 5 ) , 806, 8 5 3 ( 1 4 7 c ) , 889 Fuller, A . E . 9 7 2 - 9 7 4 , 9 8 8 ( 7 5 ) , 9 9 5 Fuller, D . L . 9 6 9 ( 4 5 ) , 9 9 5 F u n a b a s h i , T. 6 8 3 ( 2 1 c ) , 736 F u n g , F . N . 3 6 8 ( 6 8 ) , 390 F u n g , S. 361 ( 5 0 ) , 5 9 0

737

Furusaki, A . 5 9 7 , 5 9 8 ( 2 1 0 b ) , 607, 6 9 1 ( 5 3 h ) , 757 Futrell, J.H. 4 0 3 ( 4 0 ) , 4 0 5 ( 4 0 , 5 4 ) , 4 0 6 ( 7 1 ) , 409, 411, 413 (109), 435 (202), 754 (15),

450^53,

778

F u z e a u - B r a e s c h , S. 9 0 5 ( 1 1 1 ) , 9 2 7 G a a s b e e k , C.J. 5 3 8 ( 6 5 ) , 5 3 9 ( 7 1 ) , 549, 611 (9), 6 1 0 , 6 2 3 (5a), 6 1 3 , 6 2 3 (16),

649

Gabriel, M . W . 1 0 3 , 1 0 4 , 1 1 4 , 1 1 6 , 117 ( 6 1 ) , 729, 373 (114), 597 G a g n a i r e , D . 3 6 8 ( 6 9 ) , 390 G a g n i e r , R.P. 5 8 3 ( 1 6 6 ) , 605 G a j e w s k i , J.J. 6 8 2 , 7 1 1 ( 2 b ) , 7 5 5 , 8 7 7 ( 2 5 6 , 257), Gal, C. 6 4 3 ( 1 0 6 ) , 6 5 2 G a l , D . 8 5 9 , 8 8 4 ( 1 8 5 h ) , 891 Galiba, I. 9 6 9 ( 3 8 ) , 9 7 0 ( 6 1 ) , 9 9 5 G a l i m o v , E . M . 3 4 0 ( 1 0 5 ) , 349 G a l l a g h e r , A . 4 0 2 , 4 0 5 ( 3 3 ) , 450 G a l l e g o s , E.J. 3 3 3 ( 9 6 ) , 3 3 9 , 3 4 0 ( 1 1 8 ) , 348,

893

349

G a l l e g o s , J.E. 8 9 8 ( 2 2 ) , 9 7 9 G a l l i , A . 4 0 6 ( 6 4 ) , 451, (60),

807

Galli, R. 7 9 9 ( 6 0 ) ,

5 3 5 ( 4 1 ) , 548,

799

807

G a l l u c c i , J.C. 9 2 ( 6 0 ) , 94, 123 ( 1 8 7 b ) , 7 5 2 G a n e m , B . 5 5 9 , 5 7 1 ( 3 4 ) , 601 Gant, P.L. 8 3 2 ( 9 3 ) , 8 3 5 ( 9 7 , 9 8 ) , 888 Ganter, C. 5 6 4 ( 5 7 b ) , 5 7 4 , 5 7 5 ( 1 1 3 f , 1 1 3 g ) , 602, 603, 6 9 1 (55f, 5 5 g , 5 5 k ^ ) , 6 9 2 (55f, 5 5 g , 5 5 k ^ , 5 9 a ) , 6 9 3 ( 5 5 o - q , 6 5 ) , 6 9 4 (55f, 5 5 g , 551, 5 5 o - q , 5 9 a ) , 6 9 5 (55m, 55n), 757,

738

Gao, L 543 (138),

550

A u t h o r index Garatt, P J . 5 9 3 ( 2 0 1 c ) , 607 Garber, H.R. 3 2 0 ( 5 5 ) , 347 Garcia, A . R . 3 6 9 ( 9 4 ) , 39J Garcia, E . 7 9 4 ( 5 1 ) , 807 Gard, E . 8 1 6 ( 2 1 ) , 886 Gardini, G.P. 9 8 9 ( 1 3 2 ) , 996 Gardini-Guidoni, A. 535 (41), Gardner, P . M . 8 9 8 ( 2 5 ) , 920 Gareiss, G. 9 5 4 ( 1 2 8 ) , 961 Garibay, M . E . 3 7 7 ( 1 5 9 ) , 392

548

Garin, F. 6 8 3 ( 2 3 , 2 4 b , 2 4 c ) , 6 8 4 ( 2 3 , 2 4 b , 2 4 c , 2 9 ) , 6 8 5 ( 2 4 b , 2 4 c , 3 2 ) , 736 Garland, L.J. 2 6 9 ( 8 5 ) , 287 G a m e r , P. 9 3 4 ( 7 1 ) , 960 G a m e t , J.L. 871 ( 2 3 2 ) , 892 G a m e u , J.L. 6 5 7 , 6 5 8 ( 1 7 ) , 6 7 7 , 8 2 4 , 8 2 5 ( 6 5 ) ,

887 Garratt, P.J. 5 8 3 , 5 8 4 ( 1 6 5 g ) , 5 9 5 , 5 9 6 ( 2 0 4 d ) ,

605, 607 Garrou, P. 6 6 6 ( 6 2 ) , 678 G a r w o o d , R . F . 2 9 4 ( 7 ) , 346 Gaspar, P.P. 4 0 6 ( 8 3 ) , 45] Gassman, 583, 607, 712, 726

P.G. 3 6 8 ( 6 1 ) , 390, 5 4 0 ( 8 3 ) , 549, 5 8 4 ( 1 6 5 c ) , 5 9 5 , 5 9 6 ( 2 0 4 a ) , 605, 696, 698 (67c, 67d), 706, 707 (87d), 7 1 3 ( 1 1 5 a ) , 7 2 4 ( 1 2 8 , 1 3 2 c , 132f), ( 1 3 2 c ) , 7 2 7 (1321), 7 3 2 ( 1 2 8 ) , 7 3 3

( 1 3 9 ) , 738-741, 8 0 1 (67a, 6 7 b ) , 807, 9 2 9 , 9 3 4 (23), 9 5 0 (117), 951 (119), 957 ( 1 4 4 ) , 9 5 8 ( 1 4 7 ) , 959, 961, 962 Gat, J.R. 8 5 8 ( 1 7 5 a ) , 890 G a t h , C. 17 ( 2 0 ) , 3 3 ( 2 5 ) , 5 4 , 7 0 , 7 4 ( 2 0 ) , 7 7 Gaufres, R. 3 1 4 ( 4 1 ) , 347 Gault, E.G. 4 1 5 ( 1 3 7 ) , 4 2 6 , 4 2 9 ( 1 7 7 ) , 452, 453, 6 1 8 , 6 2 1 ( 3 6 a ) , 650, 6 8 4 , 6 8 5 ( 2 6 b ) , 736, 8 6 4 ( 2 0 6 ) , 891 Gault, Y . 6 6 3 , 6 6 4 , 6 6 6 , 6 6 8 , 6 7 0 ( 5 5 b ) , 678 G a u m a n n , T. 3 9 7 ( 6 ) , 4 0 0 ( 3 1 ) , 4 0 2 , 4 0 3 ( 3 4 ) , 4 0 6 (60, 73, 7 5 - 7 8 ) , 4 0 9 , 4 1 1 , 4 1 3 (34), 4 1 5 ( 3 1 , 139), 4 1 6 ( 1 4 0 ) , 4 1 8 ( 1 4 8 , 149), 4 1 9 ( 1 4 9 ) , 4 2 0 ( 1 5 1 ) , 4 2 1 ( 1 4 0 ) , 4 2 2 ( 1 5 1 , 1 5 4 , 155), 4 2 4 ( 1 6 0 , 1 6 1 ) , 4 2 7 (178), 4 2 8 (160, 178), 4 3 0 , 431 (178), 432, 433 (148), 434 (197), 435 (140, 209), 4 3 6 (76, 140, 161), 4 3 7 (73, 75, 77, 7 8 , 2 1 4 ) , 4 3 8 (6, 7 3 , 7 7 , 2 1 4 , 217-221), 439 (214, 218-220), 440 (221, 223, 224), 441 (148, 219, 224), 4 4 2 (31, 140, 1 4 8 , 1 4 9 , 2 2 1 ) , 4 4 3 ( 3 4 , 2 2 1 ) , 4 4 4 (229-234), 445 (234), 446 (234, 235), 4 4 7 ( 2 3 4 - 2 3 7 ) , 450^54, 5 4 3 ( 1 4 1 ) , 550, 765 (38), 779, 825, 826 (66), 867, 868 (217), 557, 592 Gaupset, G. 128 ( 2 2 1 ) , 133 Gauthier, J. 5 7 6 ( 1 2 1 a ) , 604 Gavezzotti, A. 56 (49), 77 G a y , I.D. 3 6 9 ( 8 2 ) ,

391

1017

Gazzarrini, F. 8 5 9 ( 1 8 3 ) , 5 9 7 G e c k l e , J.M. 7 1 2 , 7 1 9 ( 1 2 4 a ) , 741 G e d a n k e n , A . 139, 163 ( 1 9 ) , 7 5 2 G e e r l i n g s , P. 3 8 2 ( 1 8 5 ) , 393 Gehrig, C.A. 2 3 1 , 2 3 2 , 2 4 0 , 247, 2 4 8 , 2 5 5 , 2 5 7 ( 2 9 ) , 284, 286 G e i s e , H.J. 9 2 ( 6 0 ) , 94, 119 ( 1 2 7 ) , 123 ( 1 8 7 b ) , 7 J 7 , 132 G e l d e m , T . W . v o n 9 3 8 ( 8 4 ) , 960 Gelehi, Y.V. 658 (23b), 6 7 7 Gelius, U. 4 7 4 (26, 27), 4 8 7 , 4 9 3 , 4 9 9 (27),

525 G e n i n , E. 9 0 5 ( 1 1 1 ) , 9 2 7 G e n o n i , M . M . 3 9 9 ( 1 6 ) , 450 G e o r g e , C.F. 9 4 4 ( 9 9 ) , 9 4 5 ( 1 0 0 ) , 9 6 7 G e o r g e , K. 4 7 6 ( 3 6 ) , 5 2 5 G e o r g i a d i s , R. 5 4 1 ( 9 9 , 1 0 3 ) , 5 4 2 ( 1 0 3 ) , 550 Georgian, V. 9 2 9 (16), 9 5 9 Gerdil, R. 9 3 4 ( 7 0 ) , 960 Germain, A. 615 (26, 27), 6 1 6 (26), 618, 623 ( 2 7 ) , 650 G e r m a i n , G. 7 2 4 , 7 2 8 , 7 3 3 ( 1 3 5 ) , 741, 9 4 7 ( 1 0 5 ) , 9 4 9 ( 1 0 9 , 111), 9 5 1 ( 1 0 5 , 1 2 1 ) , 967 Gersdoft, W . A . 8 2 2 ( 5 0 ) , 5 5 7 G e r s o n , D.J. 3 1 4 ( 4 0 ) , 3 2 9 ( 8 2 ) , 347, 348, 7 1 1 ( 1 0 5 b ) , 740 G e r s o n , F. 7 9 ( 7 ) , 93, 7 2 4 , 7 2 5 , 7 3 0 ( 1 3 0 c ) , 747 G e s c h e i d t , G. 7 9 ( 7 ) , 93 Gestambide-Odier, M. 9 1 4 (228), 924 G e y e r , T.J. 123 ( 1 8 3 ) , 132 Geymer, D.O. 777 (64), 750 Ghatak, K . L . 6 9 2 , 6 9 4 ( 5 9 a ) , 738 G h o l s o n , R.K. 8 5 3 ( 1 4 7 a ) , 8 5 5 ( 1 5 6 ) , 5 5 9 ,

890 G h o s h , C.K. 6 6 2 ( 4 9 ) , 6 7 5 Ghosh, S.N. 637, 6 4 0 (88), 657 G i a c o m e l l i , G. 1 4 2 ( 4 2 ) , 7 5 2 G i a c o m e l l o , P. 5 3 5 ( 4 5 ) , 5 4 5 GianotU, C. 6 5 9 ( 3 5 ) , 6 7 7 Giardini-Guidioni, A. 4 0 6 (64), 457 G i b b o n i , D.J. 6 7 0 ( 6 6 ) , 6 7 9 G i b b s , J.W. 1 5 2 ( 8 5 ) , 183 G i e r s i g , M . 1 2 0 , 121 ( 1 5 1 a , 1 5 1 b ) , 131, 5 7 4 ( 1 1 3 d ) , 603 G i e s e , B . 5 8 8 , 5 8 9 ( 1 8 6 b ) , 606 G i e s e , C.F. 3 9 8 , 4 0 9 , 4 1 7 ( 1 5 ) , 450 Giger, U . 5 9 3 ( 2 0 0 b ) , 606 G i l - A v , G . E . 2 9 4 ( 8 ) , 346 Gilbert, R . G . 4 4 8 ( 2 4 3 ) , 4 5 4 Gilbert, T . D . 9 0 6 ( 1 2 7 ) , 922 G i l d e r s o n , P . W . 8 7 5 ( 2 5 1 , 2 5 3 ) , 893 Gill, G. 9 0 4 ( 8 4 ) , 9 2 7 G i l l e d , L.I. 9 0 6 ( 1 2 6 ) , 9 2 2 G i l l e s p i e , R.J. 35 ( 3 0 - 3 3 ) , 4 0 ( 3 3 ) , 7 7 , 5 3 8 (64), 539 (70), 5 4 9

1018

A u t h o r index

G i l h o m , L.R. 1 0 3 , 104, 114, 116, 117 ( 6 1 ) , 729, 373 (114), J97 Gilman, J.R 4 7 7 (59), 5 2 6 G i l m o u r , I. 341 ( 1 1 3 ) , 349 G i m a r c , B . M . 4 6 0 ( 1 0 ) , 524 G i n s b u r g , D . 4 5 6 ( 3 ) , 524, 7 3 3 ( 1 3 8 b ) , 929 (18, 20), 9 3 0 (24), 959 Girard, P. 5 7 0 ( 9 1 ) , 603, 6 8 6 (28),

736

741,

684 (28, 29), 685,

G i z y c k i , U . V . 5 7 4 ( 1 1 3 a , 1 1 3 c ) , 603 G l a d i a l i , S. 142 ( 4 3 ) , 182 G l a s s , T.L. 8 9 7 ( 1 1 ) , 9 7 9 G l a s s c o c k , K.G. 5 7 7 ( 1 2 2 ) , 604 G l a s s e r , L. 81 ( 2 3 ) , 93 G l a s s t o n e , S. 3 ( 4 a ) , 7 6 Glauser, W . A . 100, 124, 127 ( 3 6 ) , 7 2 9 G l a z e r , E . D . 127 ( 2 0 5 ) , 133 G l e g h o m , J.T. 7 0 8 ( 9 7 a ) , 739

G o l l n i c k , K. 165 ( 1 2 0 ) , 184 G o l o b o v , A . D . 8 5 3 , 8 5 6 ( 1 4 4 ) , 889 G o l o v n y a , R . V . 8 2 6 ( 7 0 a ) , 887 Gonfiantini, R. 8 5 8 ( 1 7 2 ) , 8 5 9 ( 1 8 3 ) , 8 8 1 ( 1 7 2 ) , 890, 891 G o n i n a , V . A . 8 1 5 , 8 2 2 ( I q ) , 886 Gonzales, A.G. 9 0 4 (81), 927 G o o d w i n , D . G . ( 5 5 ) , 182 G o o d w i n , R . D . 284 G o r d e n , B . 128 ( 2 1 4 ) , 133 G o r d e n , R., Jr. 5 3 5 ( 4 0 ) , 548 Gordon, A.S. 411 (119), 4 5 2 G o r d o n , B . E . 8 2 6 ( 7 4 ) , 888 Gordon, B.M. 295, 299 (14), 315 (44),

346,

347 Gordon, Gordon, Gordon, Gordon,

B.S. G.S., L.L. M.S.

8 2 9 ( 8 1 c ) , 888 III 141 ( 3 5 ) , 182 8 5 8 , 881 ( 1 7 1 ) , 8 9 0 544 (151), 557, 687, 688 (38b),

Gleiter, R. 4 7 6 ( 3 3 ) , 4 7 7 ( 3 3 , 5 8 , 6 7 , 6 8 , 7 4 - 7 6 ) , 478 (33, 58, 68, 74, 83, 84, 8 7 , 8 8 , 9 0 , 9 1 , 9 6 , 104, 105), 4 7 9 ( 3 3 , G o r d o n , R., Jr. 4 2 4 ( 1 6 2 ) , 453, 7 5 5 ( 1 4 ) , 778 6 7 , 7 4 , 107, 1 1 3 , 1 1 5 - 1 1 8 , 1 2 4 - 1 2 7 ) , G o r d o n , S. 2 3 1 ( 2 7 ) , 286, 8 5 8 ( 1 8 0 ) , 891 4 8 0 ( 3 3 , 115, 116, 129), 5 0 7 ( 1 5 3 ) , 5 0 8 Gordy, W. 637, 6 4 0 (88), 657 ( 3 3 , 162), 5 0 9 , 5 1 3 ( 3 3 ) , 5 1 4 ( 3 3 , 115), G o r e n , Z. 120 ( 1 3 7 ) , 7 5 7 , 5 5 6 ( 1 3 b ) , 600 5 1 6 ( 6 7 , 124), 5 1 9 ( 1 2 4 ) , 5 2 0 , 5 2 4 ( 6 7 ) , GorgeUi, A . 3 1 5 ( 4 5 ) , 347 5 9 0 , 591 ( 1 9 4 c ) , 7 3 1 , 7 3 2 G o r m a n , A . A . 7 0 5 ( 8 2 ) , 739 ( 1 3 7 a ) , 7 4 7 , 9 3 1 ( 4 1 ) , 9 5 6 ( 1 4 0 ) , 959, G o m e r , Ch. 8 1 9 ( 3 5 ) , 887

736

525-528,

606,

962

G o d b o l e , E . W . 5 3 2 ( 6 ) , 548 Goddard, W . A . 6 5 6 (11), 656, 657 (8a), 6 7 7 G o d e l m a n n , R. 9 0 4 ( 8 9 ) , 927 G o d f r e y , C . R . A . 5 6 4 ( 5 8 b ) , 602 G o d l e s k i , S.A. 5 9 7 ( 2 0 9 ) , 607, 691 ( 5 7 ) ,

738

G o e l , A . B . 5 7 1 ( 9 7 , 9 8 ) , 603 G o e t z , R . W . 109, 110 ( 9 6 ) , 130 G o l a n , O. 120 ( 1 3 7 ) , 131 G o l d b e r g , M. 3 3 6 , 3 3 7 ( 1 0 0 ) , 348 G o l d b e r g , M.J. 103, 104, 114, 116, 117 ( 6 1 ) , 7 2 9 , 3 7 3 ( 1 1 4 ) , 391 G o l d b e r g , P. 4 0 0 ( 2 9 ) , 450 G o l d e n , D . M . 3 ( 1 0 ) , 7 7 , 2 3 7 , 241 ( 4 8 ) , 2 5 9 (65, 71), 262 (65), (2),

994

284, 286, 287, 9 6 4

G o l ' d e n f e l ' d , I.V. 4 1 5 ( 1 3 6 ) , 452 G o l d f i n e , H. 9 0 7 ( 1 6 0 ) , 9 2 2 Goldfinger, R 9 6 6 ( 1 7 ) , 9 9 1 ( 1 4 0 ) ,

997

G o s n e l l , J.L., Jr. 1 2 0 - 1 2 2 ( 1 4 4 b ) , 7 5 7 G o s s e l a i n , P.A. 5 5 5 - 5 5 7 (1 I c ) , 600 G o t o , H. 8 9 ( 5 1 ) , 9 4 , 1 0 1 , 1 2 4 , 128 ( 3 9 ) , G o u g o u t a s , J.Z. 9 2 9 , 9 3 4 ( 2 3 ) , 9 5 9 G o u l d , K. 8 9 8 ( 1 7 ) , 9 7 9 G o u l d , L . D . 9 3 8 ( 8 3 ) , 960 G o u r s o t , A . 3 5 2 ( 4 ) , 389 Governa, M. 9 1 7 , 9 1 8 (264), 9 2 5 Graaf, B . van de 119, 1 2 0 ( 1 3 0 ) , 1 2 2 ( 1 5 8 - 1 6 0 ) , 123 ( 1 7 3 , 177), 7 5 7 ,

129

132

Graf, R. 9 9 2 ( 1 5 8 , 1 6 2 ) , 997 Graf, W . 5 8 0 ( 1 3 8 ) , 604 Graham, M.S. 907 (163), 9 2 5 Graham, W . A . G . 5 4 0 (92), 541 (93), 5 4 9 , 6 6 2 (47a, 47b, 4 8 , 49), G r a h a m , W . D . 3 6 8 ( 6 7 ) , 390, 5 9 7 , 5 9 8 ( 2 1 0 c ) ,

678

607 994,

G o l d m a n , A . S . 6 6 6 , 6 6 7 ( 6 1 b ) , 678 G o l d s c h l e g e r , N . F . 5 4 0 ( 8 8 ) , 549, 6 5 7 ( 1 8 ) , 6 5 8 ( 2 3 c ) , 6 7 7 , 6 5 9 ( 3 6 ) , 678, 8 6 8 ( 2 1 9 ) , 8 7 0 ( 2 1 9 , 2 2 1 ) , 871 ( 2 2 3 , 2 2 4 ) ,

892

G o l d s m i t h , B . 5 8 1 ( 1 4 5 ) , 605 G o l d s t e i n , M.J. 4 7 7 ( 7 0 , 7 8 ) , 5 2 6 G o l e m b e s k i , N . 5 6 4 ( 5 7 a ) , 602, 9 3 1 , 9 4 5 ( 4 4 ) , 959

Graham, W . H . 9 8 4 (113), 9 9 6 Granger, M . R . 143 ( 4 9 ) , 182 Granger, R. 165 ( 1 1 8 ) , 184 Grant, D . M . 120, 121 ( 1 4 2 ) , 123 ( 1 7 8 ) , 7 5 7 , 7 5 2 , 3 5 2 ( 1 , 10), 3 5 5 ( 1 6 ) , 3 6 0 ( 2 8 ) , 3 6 2 ( 5 1 - 5 3 ) , 364 (53), 374 (125), 376 (144), 388 (228),

389-393

Grant, G . E . Graselli, M . G r a s h e y , R. Grasselli, R

906 371 593 575

(135), 922 ( 1 0 1 ) , 391 ( 1 9 8 c ) , 606 ( 1 1 4 ) , 604

Gratzel, M. 6 8 2 ( 1 6 ) , 7 0 6 ( 8 8 b ) , 7 5 5 , 7 5 9

A u t h o r index Graul, S.T. 5 4 2 ( 1 1 0 - 1 1 2 ) , 5 4 3 ( 1 1 0 , 111), 545 (110-112), 546 (111), 547 (111, 112), 550 Gravel, D . 3 5 2 (6), 389 Gray, G . A . 3 1 6 ( 4 9 ) , 347 Gray, H . B . 4 6 0 , 4 6 3 ( 1 2 ) , 524 Gray, P. 9 6 8 , 9 6 9 ( 3 0 ) , 994 G r a y s o n , M . A . 3 2 9 ( 8 4 ) , 348 Grdina, M.J. 6 4 6 ( 1 1 0 ) , 652 Green, J.W. 3 3 3 ( 9 6 ) , 348 Green, K.E. 5 6 2 , 5 6 3 ( 5 1 b ) , 60J Green, M . A . 6 6 3 ( 5 4 ) , 678 Green, M . L . H . 6 5 5 ( 3 ) , 6 5 9 ( 3 5 ) , 6 7 0 ( 6 7 ) , 6 7 6 ( 9 3 ) , 677, 679 Green, N . 8 2 2 ( 5 0 ) , 887 Greenberg, A . 6 8 2 (2a, 4 ) , 6 9 1 (2a), 6 9 2 ( 6 2 g ) , 711 (2a, 114c, 114d), 735, 738, 740, 9 2 8 - 9 3 0 (4), 958 G r e e n l e e , M . L . 9 2 9 , 9 3 4 ( 2 3 ) , 959 G r e e n s h i e l d s , J.B. 2 3 5 ( 3 7 , 4 0 ) , 283, 286 G r e e n w o o d , M.R. 9 1 8 ( 2 7 6 ) , 9 2 5 Gref, A . 8 0 2 ( 7 1 , 7 2 ) , 8 0 3 ( 7 3 , 7 4 ) , 808 Greibrokk, T. 3 2 0 ( 5 7 a ) , 347 Greish, A . V . 8 6 0 ( 1 9 1 ) , 891 Gresham, W.F. 6 3 2 (67), 6 3 3 , 635 (76), 657 Gretz, E. 6 5 8 ( 2 8 a ) , 6 7 7 Grev, R . S . 1 0 1 , 110 ( 4 2 ) , 7 2 9 Grice, R.E. 9 0 2 ( 6 2 ) , 920 G r i e c o , P.A. 9 4 0 ( 9 2 ) , 967 Griffin, G . W . 7 9 (4), 93,682,711,722 ( 6 ) , 735 Griffin, J.W. 9 1 8 ( 2 7 7 ) , 9 2 5 Griffith, D . L . 127 ( 2 0 5 ) , 133 Griffiths, P.R. 3 1 5 ( 4 5 ) , 347 Grigg, R. 5 5 7 ( 1 7 ) , 600 G r i g g s , K . S . 9 9 3 ( 1 6 4 ) , 997 Grigoryan, E . A . 6 7 0 ( 6 4 a , 6 4 b ) , 678, 679, 8 7 1 ( 2 3 3 ) , 892 Griller, D . I l l , 112, 116 ( 1 0 4 ) , J30, 2 5 9 ( 6 4 ) , 287, 5 6 9 ( 8 6 ) , 603 G r i m e s , R . N . 9 2 8 ( 1 3 ) , 959 G r i m m , F . A . 4 7 6 ( 3 6 , 4 7 ) , 4 7 7 ( 5 6 ) , 525,

526 G r i m m , T . A . 5 0 8 ( 1 6 1 ) , 528 G r i m m e , W . 7 1 2 , 7 1 7 ( 1 1 9 b ) , 740 Grob, R.L. 3 2 9 ( 7 7 ) , 348 Grodelski, S.A. 3 6 8 ( 6 7 ) , 390 Gronert, S. 5 4 2 , 5 4 4 , 5 4 7 ( 1 1 3 ) , 550 Gronski, W . 3 7 6 ( 1 3 7 ) , 392 Grosjean, M. 140 ( 2 2 ) , 182 G r o s s , C. 136 ( 4 ) , 181 Grosselain, P . A . 9 9 1 ( 1 4 0 ) , 997 G r o s s m a n n , H.P. 128 ( 2 2 5 , 2 2 6 ) , 133 Groth, P. 128 ( 2 2 3 ) , 133 G r o v e s , J.T. 9 6 9 , 9 7 9 , 9 8 9 ( 5 9 ) , 995 Grubb, H . M . 4 3 2 ( 1 9 0 ) , 453 Gruber, G . W . 9 5 7 , 9 5 8 ( 1 4 3 ) , 9 6 2 Grubmuher, P. 6 9 2 , 6 9 4 ( 5 9 c ) , 738

1019

Gruner, H. 5 9 0 , 5 9 1 ( 1 9 4 b ) , 606 Gruse, W . A . 8 9 5 ( 1 ) , 9 7 9 Grushka, E. 3 3 4 , 3 3 6 ( 9 8 ) , 348 Grutzmacher, H.-Fr. 4 4 2 ( 2 2 6 b ) , 454 Guarino, A . 8 3 5 , 8 3 6 ( 1 0 0 ) , 8 3 8 , 8 3 9 ( 1 0 4 ) , 840 (111), 846 (122), 849 (131), 850 ( 1 3 1 , 134), 888, 889 Gubernator, K. 7 3 1 , 7 3 2 ( 1 3 7 a ) , 747 G u c z i , L. 6 8 4 ( 2 9 ) , 736 G u e l z , P.G. 9 0 1 , 9 0 2 ( 5 5 ) , 920 Guenat, C. 4 1 6 , 4 2 1 ( 1 4 0 ) , 4 3 5 ( 1 4 0 , 2 0 9 ) , 436 (140), 438, 439 (219), 4 4 0 (223), 4 4 1 ( 2 1 9 ) , 4 4 2 ( 1 4 0 ) , 452, 454 Guenther, E. 9 0 3 ( 6 6 ) , 920 Guenther, H. 4 7 7 ^ 7 9 ( 8 0 ) , 5 2 6 G u e r m o n t , J.P. 8 2 0 ( 3 6 ) , 887 Guida, W . C . 100, 124 ( 3 5 ) , 128 ( 3 5 , 2 1 8 ) , 7 2 9 , 133 G u i l d e m e i s t e r , F. 9 0 3 ( 6 9 ) , 920 G u i l l a u m e , A . 9 8 8 ( 1 2 5 ) , 9 9 1 ( 1 4 8 ) , 996, 997 G u i s h , G. 9 1 6 ( 2 6 0 ) , 925 Guittet, E. 6 6 3 , 6 6 4 , 6 6 6 , 6 6 8 , 6 7 0 ( 5 5 c ) , 678 Gulbransh, E . A . 3 4 1 ( 1 0 8 ) , 349 G u n d , P. 122 ( 1 7 1 ) , 132, 9 3 1 ( 4 5 ) , 9 5 9 G u n d , T . M . 122 ( 1 7 1 ) , 132, 9 3 1 ( 4 5 ) , 959 G u n s a l u s , I.C. 8 5 3 ( 1 4 7 d ) , 890 Gunthard, H. 128 ( 2 1 3 ) , 133 Gunthard, H . H . 1 4 0 ( 2 1 ) , 182, 4 4 8 ( 2 4 4 ) ,

454 Gunther, H. 3 6 8 ( 6 3 ) , 3 7 7 ( 1 5 7 - 1 5 9 ) , 3 7 9 ( 1 6 1 , 168), 3 8 0 ( 1 7 8 ) , 381 ( 1 8 3 ) , 3 8 2 ( 1 7 8 , 1 8 3 , 192), 3 8 3 ( 1 9 2 ) , 3 8 4 ( 2 0 2 ) ,

390, 392, 393 G u o , Q . - X . 7 1 2 , 7 1 3 ( 1 1 5 f ) , 740 Gupta, B . 6 4 3 - 6 4 5 ( 1 0 7 a ) , 6 5 2 G u r ' e v , M . V . 4 1 5 ( 1 3 5 ) , 452 Gurr, M.I. 9 0 6 ( 1 4 0 ) , 922 Gurtovaya, E.I. 6 7 0 ( 6 4 b ) , 6 7 9 G u r v i c h , L . V . 284 G u s e v a , I.V. 8 6 5 ( 2 1 0 ) , 891 G u s o w s k i , V . 3 7 3 ( 1 0 9 ) , 391 Gutert, I. 8 1 9 ( 3 5 ) , 887 Gutierrez, C G . 5 7 7 ( 1 2 2 ) , 604 G u t m a n , D . 2 5 9 ( 5 9 , 7 2 ) , 287, 9 6 6 ( 2 3 , 2 4 ) , 9 6 8 ( 2 3 , 2 9 ) , 994 G u y , J.T., Jr. 9 4 0 ( 8 8 ) , 960 G u y , R. 5 4 0 ( 7 7 ) , 549, 6 7 1 ( 6 8 ) , 6 7 9 G u z m a n , J., de 9 8 8 ( 1 2 7 ) , 996 G w i n n , W . D . 2 2 3 ( 1 4 ) , 285 G y o r g y , I. 7 5 1 , 7 5 4 , 7 5 5 , 7 6 5 , 7 6 7 ( 9 ) , 7 6 9 ( 9 , 4 2 ) , 7 7 0 ( 4 2 ) , 7 7 4 , 7 7 5 ( 9 ) , 778, 779 G y u l u m j a n , Kh.R. 6 7 0 ( 6 4 b ) , 6 7 9 G z e i m i e s , G. 7 2 4 , 7 2 8 , 7 3 3 ( 1 3 5 ) , 747 Ha, T.-K. 4 4 8 ( 2 4 4 ) , 4 5 4 Ha, Y . S . 284 Haag, W.O. 6 1 4 (19), 6 4 9

1020

A u t h o r index

H a a g e n - S m i t , W . 9 0 3 ( 6 7 ) , 920 H a a n , J.W. de 3 5 2 ( 1 3 ) , 3 6 9 ( 8 1 ) , 389,

960

391

H a a s , M . P . de 7 6 0 , 7 6 2 ( 2 2 b ) , 7 6 3 ( 2 9 c ) , 7 7 1 ( 2 2 b ) , 7 7 8 ( 6 9 ) , 779, 780 H a b a n o w s k a , E. 9 0 6 ( 1 1 9 ) , 922 Hackett, M . 6 6 3 ( 5 7 ) , 678 H a d d o n , R . C . 7 0 8 ( 1 0 0 ) , 740 H a d l e y , N . F . 9 0 5 ( 1 0 3 ) , 921 H a d s o n , R . A . 6 9 2 ( 6 2 d ) , 738 H a f e l i n g e r , G. 8 9 ( 5 2 ) , 94 Hafley, P.G. 9 7 4 ( 7 7 ) , 995 H a g a m a n , E . W . 3 6 8 ( 6 4 ) , 390, 5 9 7 , 5 9 8 ( 2 1 0 c ) , 607, 6 9 1 , 6 9 2 , 6 9 5 ( 5 5 e ) , 737 H a g e n , E.L. 5 3 5 ( 4 6 ) , 548 Hagler, A . T . 8 0 ( 1 8 ) , 93, 104, 109 ( 6 6 ) , 129 H a h n , E . H . 9 2 9 ( 1 8 ) , 959 Haider, R. 4 7 9 ( 1 1 0 , 115), 4 8 0 , 5 1 4 ( 1 1 5 ) , 5 2 7 H a k e n , J.K. 3 2 3 ( 6 8 ) , 3 3 3 ( 9 7 ) , 348 H a k k , H. 9 0 6 ( 1 2 0 ) , 9 2 2 H a k u s h i , T. 6 8 7 ( 4 6 a ) , 6 9 0 ( 5 0 ) , 737 Hala, S. 3 0 8 , 3 3 4 ( 3 5 ) , 347 Halarnkor, B . P . 9 1 4 ( 2 2 0 ) , 924 H a l g u n s e t , J. 9 1 8 ( 2 8 9 ) , 9 2 5 Hall, D . G . 4 2 4 , 4 2 5 ( 1 5 7 ) , 453 Hall, G . G . 4 6 0 ( 9 ) , 524 H a h , L . D . 3 7 4 ( 1 1 8 ) , 391 H a h , L . H . 186 ( 8 , 9 ) , 189 ( 8 , 9, 2 2 ) , 190 ( 8 , 9, 2 5 - 2 9 ) , 195 ( 9 ) , 196, 1 9 9 - 2 0 2 ( 8 , 9 ) , 2 0 4 , 2 0 5 ( 2 2 ) , 2 0 6 ( 8 , 9, 4 8 , 4 9 ) , 2 0 7 ( 8 , 9, 5 1 - 5 3 , 55), 208 (56, 57), 2 0 9 ( 6 1 - 6 5 ) ,

212, 213

H a l l a m , H . E . 3 1 4 ( 4 2 ) , 347 H a l l e , L.F. 5 4 1 ( 1 0 6 ) , 550, 6 7 4 ( 8 5 ) , 679 Haller, G.L. 7 0 6 ( 8 8 g ) , 739 H a l l e r e y , I. 8 0 3 ( 7 4 ) , 808 Halornker, B . P . 9 0 6 ( 1 3 2 ) , 922 Halpern, J. 5 4 0 ( 8 0 , 8 1 , 8 9 ) , 5 4 1 ( 8 9 , 107), 549, 550, 5 9 8 , 5 9 9 ( 2 1 5 a ) , 608, 6 5 6 ( 1 4 ) , 6 7 2 ( 7 0 ) , 677, 679, 6 9 2 ( 6 2 e ) , 738 Halpern, Y . 5 3 2 , 5 3 8 , 5 3 9 ( 1 8 , 19), 548, 6 1 2 , 6 1 3 ( 1 4 a ) , 6 2 4 ( 5 2 ) , 649, 650 H a m a n o n e , K. 7 7 3 ( 5 5 ) , 780 H a m b l e t t , I. 7 0 5 ( 8 2 ) , 739 Hamill, W.H. 773 (49), 779 Hamilton, D.G. 655 (3), 6 7 7 Hamilton, G.A. 639 (96), 657 H a m i l t o n , J.S. 3 3 6 , 3 3 7 ( 1 0 1 ) , 348 H a m i l t o n , R. 5 9 7 , 5 9 8 ( 2 1 0 e ) , 607, 6 9 1 ( 5 3 g ) ,

737 H a m i l t o n , R.J. 9 0 0 ( 4 2 , 4 6 ) , 9 0 2 ( 4 6 ) , 9 0 4 ( 8 0 , 81), H a m i l t o n , W . C . 9 2 8 , 9 5 1 ( 1 1 ) , 958 H a m m e r i c h , O. 7 8 2 ( 1 8 d ) , 806 H a m m o n d , G . S . 7 0 7 , 7 0 8 ( 9 1 ) , 739 Hamon, D.P.G. 9 4 8 (107), 967 H a m r i n , K. 4 7 4 ( 2 6 ) , 5 2 5 H a n , J. 9 0 7 ( 1 6 4 , 165), 9 1 4 ( 2 2 3 ) , 923, 924

920, 921

Han, W . C . 9 4 0 (87), Hanack, M. 121, 122 (152), 7 J 7 , 3 7 3 (109),

391

H a n c o c k , C.K. 2 0 2 ( 3 4 ) , 213 H a n c o c k , G. 6 8 2 ( 1 1 a ) , 735 H a n d y , N . C . 165 ( 1 1 5 ) , 184 H a n e d a , A . 5 6 8 ( 8 1 a ) , 602 H a n e y , M . A . 4 1 2 ( 1 2 6 ) , 452 H a n n a , R. 122 ( 1 6 5 ) , 132 Hanner, A . W . 4 0 6 ( 6 1 ) , 451 Hanotier, J. 7 8 2 ( 1 2 ) , 806 H a n o t i e r - B r i d o u x , M . 7 8 2 ( 1 2 ) , 806 H a n s e n , P.E. 3 7 7 ( 1 5 4 ) , 3 8 5 ( 2 1 1 , 2 1 2 ) ,

393

392,

H a n s o n , W . E . 2 9 4 ( 4 ) , 346 H a n s s k e , F. 5 6 5 , 5 6 6 ( 6 6 f ) , 602 Hapala, J. 6 9 2 , 6 9 5 ( 6 0 ) , 738 Hapner, L . S . 2 9 4 , 3 2 3 ( 5 ) , 346 Hara, T. 5 8 6 ( 1 7 7 ) , 606 Harada, N . 145 ( 6 5 ) , 183 Harborne, J.B. 9 0 6 ( 1 3 0 ) , 9 2 2 Harder, S. 9 2 8 ( 1 2 ) , 959 Harding, P.J.C. 5 7 5 ( 1 1 9 ) , 604 Harding, V.J. 8 5 4 ( 1 5 0 ) , 890 H a r d w i c k , T.J. 9 6 9 ( 4 0 ) , 995 H a r d w i d g e , E . A . 2 5 9 ( 7 6 ) , 287 H a r e n s n a p e , J.N. 3 2 3 ( 6 9 ) , 348 Harget, A.J. 4 5 7 , 4 6 0 ( 8 ) , 524 Hargittai, I. 7 9 ( 1 ) , 8 0 ( 1 1 , 12), 8 7 ( 1 2 ) , 92, 93 Hargittai, M. 8 0 ( 1 1 , 12), 87 ( 1 2 ) , 93 H a r g r e a v e s , M . K . 136, 138, 148 ( 7 ) , 181 Hariharan, P.C. 5 1 9 ( 1 7 9 ) , 5 2 9 , 5 3 2 ( 3 0 ) , ( 3 9 ) ,

548

Harlee, F . N . 4 0 4 ( 4 5 ) , 450 Harmony, M.D. 929, 9 3 4 (21), 959 Harnisch, H. 9 4 9 , 9 5 1 ( 1 1 0 , 1 1 2 ) , 9 6 7 H a r n i s c h , J. 7 2 4 , 7 2 8 , 7 3 3 ( 1 3 5 ) , 741, 9 4 7 (105), 9 4 9 (109, 110), 951 (105, 110),

961

Harriman, A . 6 8 2 ( 1 5 a ) , 735 Harris, G . M . 8 7 2 ( 2 3 6 , 2 3 7 ) ,

892

Harris, R . L . 9 0 6 ( 1 3 1 ) , 9 2 2 Harris, S.H. 142 ( 3 8 ) , 182 Harrison, A . G . 3 9 9 ( 1 8 ) , 4 3 5 ( 2 0 6 ) , 450,

454,

548

535 (42), Hart, E.J. 7 6 2 ( 2 7 ) , 7 7 9 Hart, J. 9 0 4 ( 8 6 ) , 9 2 7 Hart, R.R. 7 0 8 , 7 1 2 ( 9 6 f ) , 739 Hartley, F. 5 4 2 ( 1 1 9 ) , 550 Hartman, J.S. 127 ( 2 0 8 ) , 133, 3 7 4 ( 1 2 8 ) , 391 H a r t w i g , W . 5 6 5 ( 6 5 a , 6 6 e ) , 5 6 6 ( 6 6 e ) , 602 H a r w o o d , J.L. 9 0 2 , 9 0 7 ( 5 8 ) , 920 H a s e b e , M . 5 8 0 ( 1 4 3 ) , 604 H a s e g a w a , M . 81 ( 2 3 ) , 93 H a s e l b a c h , E. 4 7 7 ( 5 7 ) , 4 7 8 ( 8 5 ) , 4 7 9 ( 8 5 , 108), 5 0 7 ( 5 7 ) , 5 1 1 ( 1 7 0 ) , 5 1 5 ( 5 7 ) ,

527, 529

526,

A u t h o r index H a s h a , T.L. 118 ( 1 2 3 ) , 131 Hashiba, N. 597, 5 9 8 (210b), 6 0 7 , 691 (53h),

737

H a s h i m o t o , A . 9 0 5 ( 1 0 7 ) , 921 H a s h m a l l , J.A. 4 7 7 ( 7 3 ) , 5 0 8 ( 1 6 2 ) ,

528

526,

Hassenruck, K. 4 7 9 ( 1 0 9 ) , 5 2 7 , 5 7 2 ( 1 0 5 ) , 603, 6 8 2 , 6 9 1 ( 7 ) , 7 1 1 ( 7 , 106a), 7 1 2 , 7 1 9 ( 1 2 3 ) , 735, 740, 741, 9 6 4 ( 9 ) ,

994

Hata, K. 6 9 6 , 6 9 8 ( 6 7 a , 6 7 b ) , 738 Hata, Y . 7 1 2 , 7 1 7 ( 1 1 9 a ) , 740 Hatada, M . 4 0 7 ( 9 0 , 9 1 ) , 451 Hatano, Y. 765 (34a), 7 7 3 (48), 779 Hateren, A . v a n 9 2 8 ( 1 2 ) , 9 5 9 Hatherly, P . A . 4 0 4 ( 4 3 ) , 450 Haubrich, J.E. 7 3 4 ( 1 4 1 b ) , 741 286,

H e l l i n , J.M. 5 3 2 ( 2 1 , 2 6 ) , 548, 6 1 3 ( 1 7 ) , 6 1 7 (17, 32a, 32b), Hellin, L.C. 907 (155), 922 Hellman, T.M. 6 3 9 (96), 657 H e l l m a n n , F. 101 ( 4 7 ) , 7 2 9 H e l l m a n n , G. 1 1 2 ( 1 0 5 , 1 0 6 ) , 130, 3 7 4 ( 1 2 7 ) ,

649, 650

391 H e l l m a n n , S. 101 ( 4 7 , 4 8 ) , 1 0 6 ( 7 1 ) , 1 0 9 , 1 1 2

859 (184),

( 8 9 a ) , 113 ( 8 9 a , 1 1 0 ) , 1 1 4 , 116, 1 2 0 ( 8 9 a ) , 7 2 9 , 130 H e l m c h e n , G. 144 ( 5 6 ) , 7 8 2 , 5 7 4 ( 1 1 3 e ) , 603 H e l m k a m p , G.K. 143 ( 4 5 - 4 7 ) , 7 8 2 Helseth, A. 918 (289), 9 2 5 Hembrock, A. 7 8 6 (37), 7 8 9 (40a, 40b), 7 9 0 (40a, 40b, 41), 791 (41), 794, 795 (37), 7 9 6 (40a, 40b), 8 0 7 H e m m e r s b a c h , P. 4 7 7 , 4 7 8 ( 7 1 ) , 5 2 6 H e m p e l , J.C. 8 5 ( 3 7 ) , 94 Henchman, M. 4 0 6 (81), 457, 828 (81b), 8 8 8 H e n d e r s o n , W . 8 9 8 ( 2 4 ) , 9 0 8 , 9 0 9 ( 1 7 9 ) , 920,

287

923

H e n d r i c k s o n , J.B. 1 2 6 ( 1 9 7 ) , 127 ( 2 0 1 , 2 0 3 ) ,

132

H e d g e s , J.I. 3 0 8 ( 3 7 ) , 347 H e d m a n , J. 4 7 4 ( 2 6 ) , 5 2 5 H e e n a n , R.K. 1 0 2 , 1 1 0 , 114 ( 5 3 ) , 7 2 9 Heer, F.J. de 3 9 6 ( 8 , 9 ) , 4 0 1 , 4 0 2 ( 8 ) , 4 0 3 ( 9 ) , 7 4 6 (6), H e g e d u s , M . 6 8 5 , 6 8 6 ( 3 3 ) , 736 Hehre, W.J. 17 ( 1 7 ) , 7 7 , 8 0 , 8 8 ( 1 4 ) , 93,

450,

778

155 ( 9 3 ) , 183, 4 2 6 ( 1 7 6 ) , 453, (28, 29), 536 (51),

532

548, 549, 9 3 0

959 H e i d e m a , J. 8 5 7 ( 1 6 5 ) ,

890

H e i m b a c h , H. 4 1 8 , 4 4 2 , 4 4 6 ( 1 4 5 ) , 452 H e i m b r e c h t , J. 4 4 9 ( 2 4 5 ) , 454 H e i n e m a n n , U . 7 2 4 , 7 2 5 ( 1 3 1 a ) , 741 H e i n z e , J. 7 9 ( 7 ) , 93 H e j t m a n e k , V . 6 8 3 - 6 8 5 ( 2 4 a ) , 736 Helder, R. 9 3 5 ( 7 7 ) , 9 6 0 Heller, C. 4 7 9 ( 1 0 8 , 1 1 0 , 1 1 1 ) , 5 2 7 Heller, H. 9 6 4 ( 1 ) , 994 Heller, W . 137 ( 1 2 , 13), 1 6 4 ( 1 2 ) , 7 8 7

897 H a y e s , P . C . , Jr. 3 2 0 ( 5 6 ) , 347 Hayes, R.N. 544 (150), 557 H a y n e s , W . M . 284 H e a d - G o r d o n , M . 8 5 , 8 7 ( 4 1 ) , 94 Headlee, A.J.W. 895 (2), 9 7 9 H e a l y , E . A . 5 3 6 ( 5 2 ) , 549 Hearing, E . D . 2 7 1 ( 8 9 ) , 284, 285, H e a t l e y , F. 3 7 4 ( 1 2 6 ) , 5 9 7 H e c h t , L. 163 ( 1 0 7 , 1 0 8 ) , 184 Heckmann, M. 478 (88), 5 2 7 H e d b e r g , K. 9 5 4 ( 1 3 1 ) , 9 6 7 H e d b e r g , L. 9 5 4 ( 1 3 1 ) , 9 6 7 H e d e n , P.F. 4 7 4 ( 2 6 ) , 5 2 5

Heilbronner, E . 4 0 7 , 4 0 8 ( 9 4 ) , 451, 4 6 3 ( 1 3 ) , 4 6 4 ( 1 3 , 14), 4 6 6 ( 1 3 , 14, 18), 4 6 7 ( 1 4 ) , 4 7 1 ( 1 3 , 14, 2 2 ) , 4 7 5 , 4 7 6 ( 1 4 , 2 9 ) , 477 (29, 57, 60, 65, 70, 73, 74, 78, 80), 478 (29, 60, 74, 80, 82, 84, 85, 88, 95, 106), 4 7 9 (29, 7 4 , 80, 85, 123, 124), 4 8 0 ( 1 3 0 ) , 4 9 0 ( 1 4 ) , 4 9 1 ( 1 3 , 18), 4 9 5 (18), 4 9 7 (14, 143), 4 9 9 (145, 146), 5 0 2 ( 1 4 5 ) , 5 0 3 ( 1 4 ) , 5 0 4 ( 1 3 , 14), 5 0 5 (14, 152), 507 (29, 57, 155), 5 0 8 (162), 5 0 9 ( 1 6 6 - 1 6 8 ) , 511 (168, 169), 5 1 3 (167, 168), 5 1 4 (173), 515 (57, 176), 5 1 6 (106, 123, 124), 5 1 7 (106), 5 1 9 (82, 123, 124,

178), 525-529, 933, 954 (61), 960

H a u g e n , G.R. 3 ( 1 0 ) , 7 7 , 2 3 7 , 2 4 1 ( 4 8 ) , 8 6 6 ( 2 1 4 ) , 892 H a u g e n , O . A . 9 1 8 ( 2 8 9 ) , 925 Hauser, C.R. 8 2 3 ( 5 8 ) , 887 Havett, A . P . W . 1 2 0 ( 1 3 8 ) , 131 H a w k i n s , B . L . 116, 118 ( 1 1 2 ) , 130 Hawkins, D.R. 9 1 6 (263), 9 2 5 Hawthorne, S.B. 8 9 6 (9), 9 7 9 H a y a i s h i , O. 8 5 3 ( 1 4 7 b ) , 889 Hayakawa, N. 768 (41), 779 H a y a s h i , M . 5 7 4 ( 1 1 1 b ) , 603 Hayashi, N. 768 (41), 779 Haydon, D.A. 918 (282, 283), 925 H a y e s , J.M. 3 4 1 ( 1 1 0 , 1 1 1 ) , 3 4 5 , 3 4 6 ( 1 1 5 , 116), 349,

1021

(33),

Hendry, B.M. 918 (282, 283), 9 2 5 Hengartner, U . 5 6 7 ( 7 0 a ) , 6 0 2 H e n g l e i n , A . 5 3 2 ( 4 ) , 548 Henis, J.M.S. 4 0 6 (83, 84), 457 Henneker, W.H. 4 1 , 45 (40), 77 Henningsen, G.M. 917 ( 2 6 7 - 2 6 9 ) , 918 (269), 925 Henrikson, B.W. 9 7 6 (81), 9 9 5 H e n s l e y , J.L. 3 2 9 ( 7 8 ) , 348 H e n t z , R.R. 6 8 7 , 6 8 8 ( 4 2 ) , 736 H e n z e , H . R . 188 ( 1 5 ) , 2 7 2

1022

A u t h o r index

H e n z e l , R.P. 7 2 4 ( 1 2 9 b , 1 2 9 c , 132a, 1 3 2 b ) , 7 2 6 ( 1 2 9 c , 132a, 1 3 2 b ) , 7 3 2 ( 1 2 9 c ) , 741 Herbert, R. 361 ( 3 8 ) , 3 6 4 ( 5 4 ) , 381 ( 3 8 ) , 390 Herbin, G . A . 9 0 1 , 9 0 2 , 9 0 4 ( 4 9 ) , 920 Heriban, V . 9 1 6 ( 2 4 8 ) , 924 H e r i g , W . 3 6 8 ( 6 3 ) , 390 Herlan, A . ( 2 4 ) , 347, 4 3 2 ( 1 8 8 ) , 453 Herlem, M. 7 8 2 (18c, 2 0 - 2 3 ) , 783 (23), 7 8 4

806

(20), H e r m a n , Z. 4 0 6 ( 8 1 , 8 2 ) , 451 Hermann, R.B. 1 9 3 - 1 9 5 , 202 (30), 2 7 2 H e r n d o n , W . C . 4 6 0 ( 1 0 , 12), 4 6 3 ( 1 2 ) , 5 0 4

524,528

(150), H e r o d , A . A . 9 6 8 , 9 6 9 ( 3 0 ) , 994 Herrig, W . 3 8 4 ( 2 0 2 ) , 393 Herring, A . H . 6 5 8 ( 2 7 ) , 6 7 7 Herrmann, J.-M. 7 0 6 ( 8 8 c ) , 739 Herron, J.T. 4 1 0 , 4 1 4 ( 1 1 5 ) , 452,

524, 7 5 2

456, 4 5 7 (6),

778

(12), H e r s c h b a c h , D . R . 2 2 1 ( 4 ) , 285 Hertel, I. 3 9 9 , 4 0 0 ( 2 8 ) , 450 H e r t o g , H.J. den 9 7 0 ( 6 5 ) , 995 H e r z o g , C. 7 2 4 , 7 2 7 ( 1 3 3 ) , 7 4 7 , 9 5 7 , 9 5 8 ( 1 4 6 ) , 962 H e s s , D . C . 8 3 0 ( 8 4 ) , 8 5 0 ( 1 3 3 ) , 888, H e s s , J. 81 ( 2 3 ) , 93 Hesse, R.H. 643 (104), 652

889

H e u b e r g e r , C. 5 8 0 ( 1 3 8 ) , 604 H e u m a n , P. 5 8 1 ( 1 4 5 ) , 605 Heusler, A. 4 2 2 (154), 4 2 7 , 4 2 8 , 4 3 0 , 431 ( 1 7 8 ) , 4 4 6 ( 2 3 5 ) , 4 4 7 ( 2 3 5 , 2 3 6 ) , 453,

454

450

H e y , H. 3 9 9 , 4 0 0 ( 2 7 ) , H e y e r , D . 7 8 2 ( 7 b ) , 806 Hiatt, J.E. 9 2 9 , 9 5 0 ( 1 5 ) , 959 Hieri, P. 4 0 6 ( 8 2 ) , 451 H i g a s h i m u r a , T. 7 6 3 ( 3 0 d ) , 7 7 9 H i g g e n b o t t o m , W.J. 9 7 2 - 9 7 4 , 9 8 8 ( 7 5 ) , 9 9 5 Hikida, M . 9 1 6 ( 2 4 6 ) , 924 Hilaire, L. 6 8 3 ( 2 3 ) , 6 8 4 ( 2 3 , 2 8 ) , 6 8 5 , 6 8 6 (28), Hilderbrandt, R.L. 128 ( 2 1 7 ) , 133 H i l i n s k i , E.F. 6 7 2 ( 7 8 a ) , 6 7 9 Hill, C L . 6 7 2 ( 7 8 a ) , 6 7 9 , 6 8 2 ( l a , l b ) , 735 Hill, D . G . 8 2 3 ( 5 8 ) , 887 Hill, J.T. 3 9 9 , 4 0 6 ( 2 5 ) , 450 H i l l s , I.R. 8 9 8 ( 1 8 ) , 9 0 8 ( 1 8 2 ) , 919, 923 H i l s , D . 4 0 2 , 4 0 5 ( 3 3 ) , 450 H i n e , P.T. 3 8 2 ( 1 8 7 ) , 393 H i n k a m p , L. 7 8 2 ( 9 b ) , 806 Hirai, T. 3 6 9 ( 7 7 ) , 390 Hirai, Y . 6 8 3 ( 2 1 a ) , 736 Hirano, T. 8 0 ( 1 8 ) , 93 Hirao, K. 5 9 3 , 5 9 4 ( 2 0 2 g ) , 607 Hirao, K . A . 5 3 2 , 5 3 4 , 5 3 8 , 5 4 0 ( 3 8 ) , 548 Hirao, K.I. 5 6 1 ( 4 5 c ) , 601, 5 9 3 , 5 9 5 ( 2 0 3 f ) ,

736

607

Hiraoka, K. 4 3 7 ( 2 1 6 ) , 454, 5 3 2 ( 7 - 1 0 , 14), 5 3 3 , 5 3 4 ( 1 4 ) , 5 3 5 ( 1 0 , 14),

548

H i r a s h i m a , T. 8 0 1 ( 6 8 ) , 8 0 2 ( 7 0 ) , Hirata, Y . 5 7 4 (11 l a , 11 l b ) , 603 H i r a y a m a , F. 7 6 3 ( 2 9 a ) , 7 7 9 H i r a y a m a , K. 7 6 3 ( 3 0 d ) , 7 7 9

807

Hirota, H. 4 4 7 ( 2 3 6 ) , 454 Hirota, K. 4 0 8 ( 1 0 6 ) , 4 2 5 ( 1 7 1 ) , 452, 453 Hirsch, J.A. 118, 119 ( 1 2 6 ) , 123 ( 1 8 7 a ) , 7 i 7 ,

132

Hirschfelder, J.O. 2 2 6 ( 1 7 ) , 2 2 7 ( 1 8 ) , 2 6 6 ( 8 3 ) ,

285, 287

Hirsinger, F. 7 8 2 ( 3 b ) , 806 Hisanaga, N. 918 (285), 9 2 5 H i s h i d a , T. 9 1 6 ( 2 4 6 ) , 924 Hitchcock, C.H.S. 913 (209), Hixson, C J . 917 (267), 925 H i x s o n , S . S . 7 0 0 ( 7 3 ) , 738 H o , C.-K. 163 ( 1 0 6 ) , 184 H o , D.H. 931 (40), 9 5 9

923

601 806

Ho, K.M. 557 (20), H o , P.P. 7 8 2 ( 5 ) , Hobbs, P.D. 9 4 6 (104), 967 H o b e r g , J.O. 6 9 9 ( 7 2 ) , 738 Hobert, K. 7 8 2 ( 7 a ) , 806 Hobson, D.W. 917 (271), 925 H o c k e r , H. 3 7 6 ( 1 3 7 ) , 392 H o d a k o w s k i , L. 5 7 1 ( 9 4 ) , 603 H o d e k , P. 9 1 7 ( 2 7 2 ) , 9 2 5 H o d g e , C N . 5 3 9 ( 7 4 ) , 549 H o d g e s , R.J. 8 7 0 ( 2 2 2 ) , 892 H o d g e s , R.L. 6 5 7 , 6 5 8 ( 1 7 ) , 6 7 7 H o d g s o n , E. 9 1 6 ( 2 6 1 ) , 9 1 8 ( 2 8 0 , 2 8 6 ) , 9 2 5 Hoff, C D . 6 5 6 ( 1 3 ) , 6 6 2 ( 4 3 ) , 677, 678 H o f f m a n , H. 6 1 3 , 6 2 3 ( 1 6 ) , 649 H o f f m a n , N . E . 6 1 2 ( 1 3 ) , 649 H o f f m a n , R. 6 6 6 ( 6 3 ) , 678 H o f f m a n n , F. 9 0 3 ( 6 9 ) , 920 H o f f m a n n , H . M . R . 109, 1 1 2 ( 8 9 a ) , 113 ( 8 9 a , 110), 114, 116, 1 2 0 ( 8 9 a ) , 130 H o f f m a n n , R. 155 ( 9 3 ) , 183, 4 6 0 , 4 6 3 ( 1 2 ) , 5 0 5 ( 1 5 2 ) , 5 0 7 ( 1 5 3 ) , 5 1 4 ( 1 7 5 ) , 524, 6 5 6 ( 1 0 , 12), 6 7 7 , 9 3 0 , 9 3 1 (30), 933 (53), 945 (101),

528, 529,

959-961

Hoffmann, R.W. 4 7 9 (110), 5 2 7 Hofle, G . A . 5 4 3 ( 1 3 0 ) , 550 Hofner, D . 118, 121 ( 1 2 1 ) , 131,

391

374 (120),

H o g e n b i r k , M . 7 0 3 , 7 0 4 , 7 1 2 , 7 1 9 ( 8 0 ) , 739 H o g e v e e n , H. 5 3 8 ( 6 5 ) , 5 3 9 ( 7 1 ) , 5 4 0 ( 7 9 ) , 6 1 0 (5a, 5 b ) , 6 1 1 ( 9 ) , 6 1 2 ( 1 2 ) , 6 1 4 ( 2 0 ) , 6 2 3 (5a, 5 b , 4 9 ) , 6 3 2 ( 6 6 ) , 672 (69, 71), 679, 692 (62a),

549,

649-651, 738

H o g g , A . M . 3 4 0 ( 1 0 4 ) , 349 H o h a m , C.H. 3 4 5 , 3 4 6 ( 1 1 6 ) , H o h e n b e r g , P. 4 ( 1 1 ) , 7 7

349

A u t h o r index H o i g n e , J. 7 6 5 ( 3 8 ) , 7 7 9 H o i n e s s , C M . 5 9 3 ( 1 9 9 ) , 606 H o k e , D . 8 1 3 ( 7 ) , 886 H o l a k , T . A . 3 7 7 ( 1 4 6 ) , 392 Holder, R . W . 5 6 2 ( 5 3 b ) , 602 H o U i n s h e a d , D . M . 5 6 4 ( 5 8 b ) , 602 H o h o w o o d , F. 3 6 8 ( 6 9 ) , 390, 6 9 1 ( 5 3 g ) ,

737 H o l m , K . H . 6 9 2 , 6 9 4 ( 5 9 c ) , 738 H o l m e s , J.L. 3 0 2 ( 2 1 ) , 346, 3 9 6 ( 1 , 3 ) , 3 9 7 (3, 4), 4 0 2 (3), 407 (89), 4 0 8 (3, 98), 4 0 9 (108), 4 1 0 (116, 117), 411 (108, 116), 4 1 2 ( 1 1 6 , 124), 4 1 3 ( 1 0 8 , 116), 4 1 4 ( 1 1 6 ) , 4 1 5 ( 1 3 4 ) , 4 2 2 ( 1 3 4 , 152), 4 3 3 ( 3 ) , 4 3 5 ( 2 0 0 ) , 4 4 4 ( 1 1 6 , 1 3 4 ) , 449^53, 5 3 7 , 5 3 8 , 5 4 3 , 5 4 6 ( 5 6 ) , 549 H o l m e s - S m i t h , R. 6 6 3 , 6 6 4 ( 5 5 b , 5 5 d ) , 6 6 6 ( 5 5 b ) , 6 6 8 , 6 7 0 ( 5 5 b , 5 5 d ) , 678 H o i n e s s , N.J. 118, 119 ( 1 2 5 ) , J3J Holroyd, R.A. 687 (39c, 44), 688, 689 (44), 736, 737, 7 6 4 ( 3 3 ) , 7 6 5 ( 3 3 , 3 5 , 3 6 ) , 7 7 9 Holt, E . M . 6 5 6 , 6 6 8 ( 9 ) , 6 7 0 ( 6 6 ) , 677, 679 Holtzer, G. 2 9 5 ( 1 1 ) , 346 H o l z w a r t h , G. 140 ( 2 3 ) , 182 H o m e r , L. 6 3 7 ( 9 3 ) , 651 H o n , M . - Y . 6 8 2 ( 3 a ) , 735 H o n e g g e r , E. 4 6 3 ( 1 3 ) , 4 6 4 , 4 6 6 ( 1 3 , 14), 4 6 7 ( 1 4 ) , 4 7 1 ( 1 3 , 14), 4 7 5 , 4 7 6 ( 1 4 ) , 4 7 7 ( 8 0 ) , 4 7 8 ( 8 0 , 8 2 ) , 4 7 9 ( 8 0 , 123), 4 9 0 (14), 491 (13), 497, 503 (14), 504 (13, 14), 5 0 5 ( 1 4 ) , 5 0 9 ( 1 6 6 - 1 6 8 ) , 5 1 1 ( 1 6 8 ) , 5 1 3 ( 1 6 7 , 168), 5 1 4 ( 1 7 3 ) , 5 1 6 ( 1 2 3 ) ,

5 1 9 ( 8 2 , 123, 178), 525-527, 529, 9 3 3 , 9 5 4 ( 6 1 ) , 960 H o n n a , K. 6 9 1 , 6 9 2 , 6 9 4 ( 5 5 s ) , 737 H o o g , H. 621 ( 4 6 ) , 650 H o o g e n s t r a a t e n , W . 2 0 2 ( 3 7 ) , 213 H o o p e r , S . N . 2 9 4 , 2 9 5 ( 1 0 ) , 346, 9 0 9 ( 1 8 5 ) ,

923 H o p , C . E . C . A . 4 0 7 ( 8 9 ) , 451 Hopf, H. 4 7 8 ( 1 0 5 ) , 4 7 9 ( 1 1 4 ) , 527, 5 7 4 ( 1 1 3 b ) , 603 Hopkins, R.G. 9 3 3 (47), 9 5 9 H o p k i n s o n , J.A. 4 0 0 ( 2 9 ) , 450 H o p p e r , M.J. 7 7 1 , 7 7 2 ( 4 3 ) , 7 7 9 H o q , M . F . 8 7 2 ( 2 3 9 , 2 4 0 ) , 892 H o r i k a w a , T.T. 3 8 8 ( 2 2 6 ) , 393 Horiuchi, Y . 5 8 5 ( 1 7 0 ) , 605 H o m , D . H . S . 9 0 1 ( 4 8 ) , 920 H o m e r , L. 5 6 9 ( 8 2 ) , 5 7 2 ( 1 0 1 a ) , 602, 603 Hornish, R . E . 6 3 7 ( 9 4 ) , 651 Hornung, V. 4 7 7 (73, 78), 4 7 8 (84), 508 (162),

526, 528 Horton, W.J. 3 8 8 ( 2 2 8 ) , 393 H o s a k a , A . 8 4 2 ( 1 1 5 ) , 889 H o s a k a w a , K. 8 0 4 ( 8 0 ) , 808 H o s h i , T. 4 7 7 - 4 7 9 ( 7 4 ) , 526

1023

H o s o y a , H. 8 9 ( 5 1 ) , 94 H o s o y a , M . 7 2 4 , 7 2 5 ( 1 3 0 a ) , 741 H o s s e l , P. 7 0 8 - 7 1 0 ( 9 2 c ) , 739 H o u b e n - W e y l 5 5 5 ( 5 ) , 600 H o u k , K . N . 100, 1 2 4 , 128 ( 3 5 ) , 7 2 9 , 6 4 3 , 6 4 4 ( 1 0 7 c ) , 652, 9 3 4 ( 7 1 ) , 960 H o u l e , F . A . 2 5 9 ( 7 4 ) , 287 H o u n s h e l l , W . D . 1 0 3 , 105 ( 5 6 ) , 106 ( 7 3 ) , 108 ( 7 9 ) , 1 1 2 , 113 ( 7 3 ) , 114 ( 5 6 ) , 115 ( 7 3 ) , 116 ( 7 9 ) , 7 2 9 , 130 Houriet, R. 4 0 6 ( 7 3 , 7 5 , 7 6 , 7 8 ) , 4 1 8 , 4 1 9 ( 1 4 9 ) , 4 2 0 ( 1 5 1 ) , 4 2 2 ( 1 5 1 , 154, 1 5 5 ) , 4 3 6 (76), 437 (73, 75, 78), 438 (73, 217),

4 4 0 , 4 4 1 ( 2 2 4 ) , 4 4 2 ( 1 4 9 ) , 451-454, 5 4 3 ( 1 4 1 ) , 550, 6 7 4 ( 8 5 ) , 679 H o u s e , H . O . 8 2 0 ( 3 9 ) , 887, 9 4 5 ( 1 0 2 ) , 9 6 7 H o u s e m a n , T . H . 8 2 7 ( 7 8 , 7 9 ) , 888 H o u t m a n , J.P.W. 7 7 5 ( 6 0 ) , 780 H o w a r d , J.A. 9 9 3 ( 1 6 9 ) , 9 9 7 H o w a r d , J.J. 9 0 6 ( 1 2 8 ) , 9 2 2 Howard, R.W. 906 (139), 922 Howard, T.A. 969, 9 7 4 , 9 7 5 , 9 9 2 , 9 9 4 (60), 995 H o w b e r t , J.J. 9 3 9 , 9 4 2 ( 8 5 ) , 960 H o w e , I. 4 2 2 , 4 3 5 , 4 3 6 ( 1 5 3 ) , 453 H o y a n o , J.K. 5 4 0 ( 9 2 ) , 5 4 1 ( 9 3 ) , 549,

662

( 4 7 a , 4 8 ) , 678 H o z e n , S. 7 2 4 ( 1 2 7 ) , 747 Hrovat, D . A . 7 1 1 ( 1 0 7 , 1 0 8 b ) , 740 Hsiao, Y. 558 (25a), 607 H s i e h , T. 4 7 7 ( 5 9 ) , 5 2 6 H s u , E.G. 1 4 0 ( 2 3 ) , 182 H u , W.J. 3 6 ( 3 4 ) , 7 7 H u a n g , J.T. 4 8 9 ( 1 3 8 ) , 528 H u a n g , J.-T.J. 7 6 3 ( 3 0 b ) , 7 7 9 H u a n g , Y . 5 4 1 ( 9 7 , 104), 5 4 2 ( 1 0 4 ) , 550 Hubel, W. 928 (14), 9 5 9 Huber, H. 4 7 8 ( 8 2 ) , 5 1 9 ( 8 2 , 1 8 0 ) , 526, 529, 9 3 3 , 9 5 4 ( 6 1 ) , 960 Hubert, A.J. 6 7 3 ( 7 8 b ) , 6 7 9 H u b s c h e r , G. 8 5 4 ( 1 5 1 , 1 5 2 a ) , 890 H u c k e l , E. 4 5 6 , 4 6 0 ( 2 ) , 524 H u c k e l , W . 169 ( 1 2 5 ) , 184 H u d e c , J. 155 ( 9 5 ) , 183 H u d l i c k y , M . 5 5 5 - 5 5 8 ( l l f ) , 600 H u d l i c k y , T. 6 8 2 ( 3 a ) , 735 H u d s o n , C E . 4 4 4 ( 2 2 8 ) , 454 H u d s o n , H.R. ( 5 5 ) , 182 H u d s o n , R . A . 5 9 0 , 5 9 1 ( 1 9 4 d ) , 606 Huffman, H.M. 227 (19), 2 6 4 (80),

285,

287 H u f f m a n , J.C. 6 6 3 ( 5 4 ) , 678 H u g , P. 3 8 8 ( 2 2 5 ) , 393 H u g g i n s , C M . 2 0 8 ( 5 9 ) , 213 Huggins, M.L. 238, 2 5 1 , 271 (50), H u g h e s , M . T . 155 ( 9 5 ) , 183 H u i m i n , L. 6 8 3 , 6 8 4 ( 2 5 ) , 736

286

1024

A u t h o r index

H u i s g e n , R. 5 9 3 ( 1 9 8 c ) , 606 Hull, W . 9 8 ( 1 0 ) , 128, 3 7 1 , 3 7 3 ( 1 0 5 ) , H u l m e , R. 3 6 9 ( 9 4 ) , 391 Hulshof, L . A . 151 ( 7 3 , 7 4 ) , 183

391

H u m m e l , A . 6 8 7 ( 4 0 a ) , 736, 7 4 8 ( 7 ) , 7 5 9 ( 2 0 ) , 7 6 0 (22a, 22b), 761 (7), 7 6 2 (20, 22a, 22b, 23, 24), 763 (24, 29c, 30a), 7 7 0

(20), 771 (22a, 22b), 778 (69), 778-780

H u m m e l , J. 9 8 , 110 ( 1 5 ) , 128 H u n g , H.-K. 5 9 0 ( 1 9 2 ) , 606 H u n g e r , J. 9 7 2 ( 7 2 ) , 995 H u n i g , S. 5 5 8 ( 2 7 ) , 601 Hunkler, D . 7 9 ( 7 ) , 93, 5 9 0 , 5 9 1 ( 1 9 4 g ) , 5 9 2 ( 1 9 7 ) , 606, 6 2 0 ( 4 5 c ) , 650 Hunt, J.M. 9 0 0 ( 3 8 ) , 9 0 8 ( 1 7 0 ) , 920, 923 Hunt, L . M . 9 0 6 ( 1 3 8 ) , 922 Hunter, D . L . 6 5 9 ( 3 0 ) , 6 7 7 Hunter, T.F. 881 ( 2 6 4 ) , 893 H u n t r e s s , W . T . , Jr. 4 0 6 ( 7 0 , 8 0 , 8 5 ) , 451 Hurd, C O . 2 3 5 ( 4 2 ) , 2 3 7 ( 4 9 ) , 286 Husain, A. 6 1 0 (6), 6 2 4 ( 5 0 a - c ) , 6 4 3 - 6 4 5 ( 1 0 7 a ) , 649, 650, 652 H u t c h i n s , R . D . 8 1 3 ( 7 ) , 886 Hutchins, R.O. 571 (95), 575 (115), 581 (145),

603-605 H u t c h i n s o n , L.L. 9 5 6 ( 1 3 6 ) , 9 6 2 H u t m a c h e r , H . - M . 5 7 0 ( 8 7 b ) , 603 H u y b r e c h t s , G. 9 6 6 ( 1 7 ) , 994 H u y s e r , E . S . 9 7 2 ( 7 6 ) , 9 8 9 ( 1 3 6 ) , 995, 996 H u z i n a g a , S. 17 ( 2 2 ) , 7 7 H w a n g , D . R . 5 9 0 , 5 9 1 ( 1 9 4 d ) , 606, 6 9 2 ( 6 2 d ) ,

738

Hyman, A . S . 2 6 8 , 281 (84),

287

I m a s h i r o , F. 3 6 9 , 3 7 0 ( 9 0 ) , 391 Imirzi, A . 120 ( 1 3 6 ) , 131, 171 ( 1 3 3 ) , Inaba, S. 6 4 6 ( 1 1 0 ) , 6 5 2

184

I n a m o t o , Y . 5 9 3 , 5 9 5 ( 2 0 3 a ) , 5 9 7 ( 2 1 4 ) , 607, 691 (53a, 53e, 53f), Inanaga, J. 5 7 0 ( 9 2 ) , 603 Incremna, J.H. 9 8 4 ( 1 1 4 ) , 9 9 6 Inghram, M . G . 3 9 8 , 4 0 9 , 4 1 7 ( 1 5 ) , 450, 4 7 6

737

(43), 525 I n g o l d , C. 144 ( 5 6 ) , 182 I n g o l d , K . U . 9 8 ( 9 ) , 111 ( 9 , 1 0 3 , 1 0 4 ) , 1 1 2 ( 1 0 4 ) , 116 ( 1 0 3 , 1 0 4 ) , 128, 130, 2 2 3 ( 1 1 ) , 285, 371 ( 1 0 4 ) , 3 7 3 ( 1 1 1 ) , 391, 966, 971 (21), 9 7 2 (71), 9 7 6 (79), 978 (88, 89), 9 8 0 (88), 983 (79), 988 (88), 989 (133), I n o k u c h i , H. 4 7 6 ( 4 5 , 4 9 ) , 525, 526 I n o k u c h i , T. 801 ( 6 6 a ) , 807 I n o u e , M . 4 0 6 ( 6 7 ) , 451 I n o u e , S.-I. 5 5 8 ( 2 5 b ) , 601 I n o u e , Y . 3 6 9 ( 7 6 ) , 390, 6 8 7 ( 4 6 a ) , 6 8 9 ( 4 6 b ) ,

994-996

737

6 9 0 (50), I n o u y e , Y . 1 6 3 , 164 ( 1 1 1 ) , 184 l o n o v , S.P. 5 5 9 ( 3 1 ) , 601 Ip, W . M . 6 4 3 - 6 4 5 ( 1 0 7 a ) , 6 4 6 ( 1 1 0 ) , 6 5 2 Ipaktschi, J. 4 7 8 ( 9 5 ) , 5 2 7 Ireland, R . E . 5 6 7 ( 7 0 a ) , 602 Irish, G . E . 9 9 2 ( 1 5 6 ) , 9 9 7 Imgartinger, H. 5 9 0 , 5 9 1 ( 1 9 4 a ) , 606 Iroff, L . D . 103 ( 5 6 , 6 0 ) , 104 ( 6 0 ) , 105 ( 5 6 ) , 109 ( 6 0 ) , 114 ( 5 6 , 6 0 ) , 7 2 9 I s a g a w a , K. 5 8 7 ( 1 8 1 b ) , 606 Isagulyants, G . V . 8 5 9 ( 1 8 6 ) , 8 6 0 ( 1 8 8 - 1 9 1 ) , 865 (208, 209), Isbell, A . F . 9 9 2 , 9 9 3 ( 1 6 3 ) , 9 9 7 Ishida, T. 8 2 5 ( 6 8 ) , 887 Ishihara, Y . 6 8 6 ( 3 6 ) , 736 I s h i k a w a , M . 5 7 0 ( 9 2 ) , 603 Ishiwatori, M . 9 0 9 ( 1 9 2 ) , 923 I s h i w a t o n , R. 9 0 9 ( 1 9 2 ) , 923 Islam, T . S . A . 2 5 9 ( 7 3 ) , 287 Itao, S. 9 3 8 ( 8 2 ) , 960 Itier, J. 6 1 7 ( 3 3 ) , 650

891

Ibers, J.A. 6 6 3 ( 5 3 ) , 678 Ichihara, K. 8 5 4 ( 1 4 8 a , 154), 8 5 5 ( 1 5 4 , 155),

890

I d a c a v a g e , M.J. 5 8 7 ( 1 7 9 b ) , Igner, E . 5 5 6 ( 1 3 a ) , 600 lida, T. 9 1 5 ( 2 4 2 ) , 924

606

l i z u k a , T. 5 9 7 , 5 9 8 ( 2 1 0 a , 2 1 0 b ) , 607, 6 9 1 ( 5 3 h ) , 737 Ikeda, A . 8 0 2 ( 7 0 ) , 807 Ikeda, H. 5 9 3 , 5 9 5 ( 2 0 3 a ) , 607, 6 9 1 ( 5 3 f ) ,

737 Ikeda, S. 4 7 6 , 4 7 7 ( 4 4 ) , 5 2 5 Ikemura, T. 6 8 6 ( 3 6 ) , 736 Ikenben-y, D . 3 5 2 ( 1 0 ) , 389 I k e z a w a , H. 7 0 6 , 7 0 7 ( 8 7 b ) , 739 Ikuta, S. 4 7 6 , 4 7 7 ( 4 4 ) , 5 2 5 Ilinskii, V . V . 9 1 6 ( 2 5 9 ) , 9 2 5 Imai, K. 85 ( 3 9 , 4 0 ) , 8 6 ( 4 0 ) , 8 7 ( 3 9 , 4 0 ) ,

94

I m a m o t o , T. 5 6 8 ( 8 1 b ) , 602 I m a m u r a , A . 155 ( 9 2 , 9 3 ) , 183 I m a m u r a , P . M . 3 0 8 , 3 1 4 ( 3 9 ) , 347 Imanari, M . 3 7 6 ( 1 3 5 , 136), 392

Ito, T. 8 1 2 ( l a , I c , Id), 8 1 5 , 8 2 2 ( l a , I c , Id, Ih, Ik), Itoh, I. 5 5 6 ( 1 3 e ) , 600 Itoh, M . 871 ( 2 2 9 ) , 892 Ittel, S . D . 6 5 9 ( 3 1 ) , 6 7 7 Itzchaki, J. 9 2 9 ( 2 0 ) , 9 5 9 I v a n o v , P . M . 8 1 , 8 4 ( 2 5 ) , 93 I w a h a s h i , M . 3 8 8 ( 2 2 7 ) , 393 I w a k u m a , T. 5 6 1 ( 4 5 c ) , 601 I w a s a k i , M . 4 1 7 ( 1 4 2 ) , 4 2 5 ( 1 6 7 ) , 452, 453 Iwata, C. 6 8 6 ( 3 6 ) , 736 Iwata, S. 4 7 6 , 4 7 7 ( 3 2 ) , 4 8 9 ( 3 2 , 1 3 7 ) , 5 0 2 ,

885, 886

503, 507, 509 (32), Iyer, P . S . 3 8 4 ( 2 0 3 ) , 393

525, 528

A u t h o r index Jackman, L . M . 2 9 4 ( 6 , 7 ) , 346 Jacknow, B.B. 9 8 9 (138), 996 J a c k s o n , J.E. 15, 16 ( 1 6 ) , 7 7 , 9 3 3 ( 6 0 ) , 960 Jackson, L.L. 9 0 5 ( 9 0 , 9 6 , 108, 1 1 3 , 114), 9 0 6 (116, 117), 9 1 4 (216, 222), 927, Jackson, R . A . 5 6 5 ( 6 3 a , 6 3 b ) , 5 8 0 ( 1 3 7 ) , 602,

924

604

Jacob, E.J. 103 ( 5 9 ) , 7 2 9 Jacobi, P.A. 5 6 7 ( 7 1 ) , 602 Jacobs, P . W . M . 4 7 6 ( 3 5 ) , 525 J a c o b s , R . E . 3 6 9 , 3 7 0 ( 8 5 ) , 391 J a c o b s o n , D . B . 5 4 1 ( 9 7 ) , 550 J a c o b s o n , I.T. 5 5 6 ( 1 3 d ) , 600 J a c o b s o n , R . A . 9 3 6 ( 8 0 ) , 960 Jacques, J. 136 ( 4 ) , 174 ( 1 3 6 ) , 181, 184 Jacques, M . S t . 117 ( 1 1 8 ) , 1 2 0 - 1 2 2 ( 1 4 3 ) ,

130,

131

6 9 1 , 6 9 2 (55f,

5 5 g , 5 5 k ) , 6 9 3 ( 6 5 ) , 6 9 4 (55f, 5 5 g ) ,

738

Jahn, H . A . 4 8 7 ( 1 3 1 ) ,

737,

528

Jaime, C. 81 ( 2 6 ) , 8 5 - 8 7 ( 4 0 ) , 91 ( 2 6 ) , 93, 94, 99 (24), 223 (12), Jain, S. 9 1 9 ( 2 9 2 ) , 9 2 5 J a m e s , A . T . 9 0 6 ( 1 4 0 ) , 9 1 3 ( 2 0 9 ) , 922, 923 J a m e s , J.L. 6 4 3 ( 1 0 4 ) , 6 5 2 J a m i e s o n , C. 9 7 8 , 9 8 0 , 9 8 8 ( 8 8 ) , 9 9 5 Jamieson, G.W. 896 (4), 9 7 9 Jancke, H. 120, 121 ( 1 4 6 ) , 122 ( 1 6 4 ) , 131,

128,

Jering, D . M . 4 2 4 ( 1 5 9 ) , 453 Jesse, N . 5 3 2 ( 3 ) , 548 J e s s o n , J.P. 6 5 9 ( 3 1 ) , 6 7 7 Jiang, Z. 6 5 8 ( 2 8 a ) , 6 7 7 Jigajinni, V . B . 5 7 3 ( 1 0 6 ) , 603 Jin, P . W . 8 8 ( 4 7 ) , Jinno, M . 4 7 6 , 4 7 7 ( 4 4 ) , 5 2 5 J o a c h i m , P.J. 4 7 7 ( 5 4 ) , 5 2 6 J o b s o n , A . M . 9 0 9 ( 1 9 4 ) , 923 Joel, C D . 143 ( 4 5 ) , 182 Joffman, N . E . 5 3 2 ( 2 3 ) , 548, 6 1 6 ( 2 9 ) , 650 J o h a n s s o n , G. 4 7 4 ( 2 6 ) , 5 2 5 John, M . L . 9 0 0 ( 3 5 ) , 920 J o h n s o n , A . D . 6 8 6 ( 3 4 a , 3 4 b ) , 736 J o h n s o n , C P . 4 3 2 , 4 3 3 ( 1 8 9 ) , 453 J o h n s o n , D . E . 3 8 8 ( 2 2 6 ) , 393 J o h n s o n , L.F. 120, 121 ( 1 4 2 ) , 7 i 7 , 3 7 4 ( 1 2 5 ) ,

94

391

J a c q u e s y , J.C. 6 4 0 ( 9 9 a , 9 9 b ) , 6 5 7 J a c q u e s y , R. 6 4 0 ( 9 9 a ) , 6 5 7 J a e s c h k e , A . 122 ( 1 6 6 ) , 132 Jaggi, F.J. 5 7 4 , 5 7 5 ( 1 1 3 f ) , 603,

1025

285

132, 361 ( 3 2 ) , 3 7 4 ( 1 2 4 ) , 390, 391 Janco, G. 8 2 5 ( 6 9 c ) , 887 Jander, P. 8 1 9 ( 3 5 ) , 887 Janes, J.F. 9 0 3 ( 7 1 ) , 9 2 7 Jang, J.C. 7 0 0 , 7 0 3 ( 7 5 a ) , 738 Janik, B . 3 6 9 ( 8 6 ) , 391 Janku, J. 9 1 7 ( 2 7 2 ) , 9 2 5 J a n o w i c z , A . H . 5 4 0 ( 9 1 ) , 549, 6 6 1 ( 3 9 ) , 678 Janscak, P.J. 9 1 7 ( 2 7 2 ) , 9 2 5 Jarret, R . M . 9 5 4 ( 1 3 3 ) , 9 6 7 Jasinski, R. 7 8 5 ( 3 1 ) , 806 Javahery, G. 5 3 7 , 5 3 8 ( 5 3 , 5 4 ) , 549 J a w d o s i u k , M . 9 4 0 ( 8 8 ) , 960 Jednacak, M . 3 7 7 ( 1 4 9 ) , 392 Jedziniak, E.J. 7 8 2 ( 1 5 b ) , 806, 9 1 5 ( 2 3 0 ) ,

924 Jeffrey, G . A . 8 0 ( 2 1 ) , 93 Jeffs, P.W. 85 ( 3 7 ) , 94 J e m m i s , E . D . 8 9 ( 5 1 ) , 94, 9 2 8 ( 6 ) , 9 3 0 ( 6 , 3 6 ) ,

958, 959

Jenkins, J.A. 5 9 5 , 5 9 6 ( 2 0 4 b ) , 607 Jennings, P.W. 6 9 9 ( 7 1 , 7 2 ) , 738 Jensen, F. 6 4 3 , 6 4 4 ( 1 0 7 c ) , 6 5 2 Jensen, F.R. 119 ( 1 3 2 ) , 7 J 7 , 3 7 4 ( 1 1 7 ) , 391 Jensen, W . L . 9 9 2 ( 1 6 0 ) , 9 9 3 ( 1 6 5 ) , 9 9 7

J o h n s o n , O. 8 0 ( 1 9 ) , 93 J o h n s o n , P.L. 9 2 9 ( 2 2 ) , 9 5 9 J o h n s o n , R . A . 7 8 2 ( 1 ) , 805 J o h n s o n , T.H. 6 9 6 , 6 9 8 ( 6 7 c , 6 7 d ) , 738 J o h n s o n , W . H . 3 ( 8 ) , 7 7 , 2 3 6 ( 4 7 ) , 286 J o h n s o n , W . S . 1 2 2 ( 1 6 9 ) , 132 Johnston, H.J. 9 6 6 ( 1 7 ) , 994 Johnston, H . S . 2 2 1 ( 4 ) , 285, 8 8 1 ( 2 6 6 ) , 893 Johnston, R . A . W . 5 5 5 - 5 5 8 ( l l g ) , 600 Jonah, C D . 7 6 2 ( 2 7 ) , 7 7 9 Jonas, A . E . 4 7 6 ( 4 7 ) , 5 2 6 Jonas, J. 118 ( 1 2 3 ) , 7J7 Jonathan, N . 4 7 6 ( 4 8 ) , 5 2 6 J o n e s , A . 9 6 8 , 9 6 9 ( 3 0 ) , 994 J o n e s , C 8 5 , 8 7 ( 4 1 ) , 94 J o n e s , G., II 7 0 5 ( 8 3 g , 8 5 b ) , 7 0 6 ( 8 5 b ) , 739 J o n e s , J.G. 9 1 5 ( 2 3 9 ) , 924 Jones, K.H. 7 5 6 , 7 6 6 (18), 779 J o n e s , M . , Jr. 5 9 3 ( 1 9 8 a ) , 606, 6 8 2 ( 2 c ) , 735 J o n e s , N.J. 5 9 0 ( 1 9 5 ) , 606 J o n e s , P . M . 138 ( 1 7 ) , 181 J o n e s , S.H. 2 6 2 , 2 6 4 ( 7 9 ) , 287, 9 7 6 , 9 8 3 ( 8 2 ) , 995 J o n e s , S.R. 4 7 7 , 4 7 8 , 4 8 0 ( 7 9 ) , 5 2 6 , 7 8 2 ( 1 1 ) , 7 9 2 ( 4 8 - 5 0 ) , 7 9 3 ( 4 8 , 5 0 ) , 7 9 4 ( 4 9 ) , 806,

807

Jones, T.B. 4 7 8 (106), 4 7 9 (114, 124), 5 1 6 (106, 124), 517 (106), 5 1 9 (124), 5 2 7 J o n e s , T.H. 9 0 6 ( 1 2 3 ) , 922 J o n e s , W . D . 6 6 2 , 6 6 9 , 6 7 0 ( 5 0 ) , 678 Jonkers, G. 4 7 9 ( 1 1 2 ) , 5 2 7 J o n s s o n , B . - O . 5 0 5 ( 1 5 1 ) , 528 Jordan, J. 7 8 2 ( 2 2 ) , 806 Jorgensen, F . S . 5 0 7 ( 1 5 4 ) ,

528

Jorgensen, W . L . 9 8 , 9 9 ( 1 8 ) , 128, 5 4 3 (138, 139), Jorish, V . S . 284

183,

J o s e p h - N a t h a n , P. 3 7 7 ( 1 5 9 ) , Joshi, G . C . 3 2 9 ( 8 0 ) , 348

155 ( 9 4 ) ,

550 392

1026

A u t h o r index

Joshi, R . M . 2 3 5 ( 3 9 ) , 286 Joukhadar, L. 5 6 4 ( 5 8 a , 5 8 b ) , Joulain, D . 9 0 3 ( 6 8 ) , 920 JouHe, C. 9 0 6 ( 1 3 7 ) , 922 Juan, B . 5 4 3 ( 1 3 6 ) , 550 Juarish, E. 5 4 3 ( 1 3 1 ) , 5 5 0 J u d g e , W . A . 8 2 3 ( 5 8 ) , 887 Julg, A . 144 ( 5 9 ) , 182

Kanters, J.A. 9 2 8 ( 1 2 ) , Kantor, S . W . 8 2 3 ( 5 8 ) ,

602

Julliard, M . 7 0 8 ( 9 7 f ) , 740 Jullien, R. 9 0 5 ( 1 1 1 ) , 921 Jung, A . 5 7 3 ( 1 0 7 ) , 603 J u n g e n , M . 4 9 0 ( 1 4 1 ) , 528 Juniper, B . E . 9 0 4 ( 8 3 ) , 921 924

K a b a c h n i k , M.I. 8 1 5 , 8 2 2 (11), 886 Kabalka, G . W . 5 7 5 ( 1 1 6 , 118), 604 K a b u s s , S. 120, 121 ( 1 4 1 ) , 122 ( 1 6 6 , 1 6 7 ) ,

131, 132

740 600,

603 K a g i , R. 3 0 7 , 3 0 9 ( 3 0 ) , 347 Kahr, B . 81 ( 3 0 , 3 1 ) , 9 i Kaiser, G. 5 5 6 , 5 6 3 ( 1 3 g ) , 600 Kaithatu, M . 9 0 5 ( 9 4 ) , 921 Kaji, A . 5 8 2 ( 1 5 9 a , 160), 5 8 3 ( 1 6 0 ) , 605 K a j i y a m a , S. 6 3 3 , 6 3 5 ( 7 4 ) , 651 K a l a s i n s k i , V . F . 123 ( 1 8 3 ) , 132 Kalbfleisch, W . 2 0 2 ( 4 0 ) , 213 Kaldor, A . 6 7 3 ( 8 1 ) , 679 K a l e c h i t s , I.V. 8 6 0 ( 1 8 7 ) , 891 K a l e y a , R. 7 8 2 ( 7 c ) , 806 K a l i c h e v s k y , V . A . 2 9 5 ( 1 3 ) , 346 K a l i n o w s k i , H . O . 116 ( 1 1 4 ) , 130, 3 5 2 , 3 6 1 , 3 6 8 , 3 8 0 - 3 8 2 , 3 8 4 , 3 8 5 ( 3 ) , 389 K a l l i o , R . E . 9 1 5 ( 2 3 4 ) , 924 K a l l o , D . 6 8 2 , 6 8 3 ( 9 b ) , 735 K a m a n s a u s k a s , V . 7 7 3 ( 5 5 ) , 780 K a m b a r a , H. 123 ( 1 8 1 ) , 132 K a m i n s k y , M . 4 1 0 ( 1 1 2 ) , 452 K a m m e r e r , H. 5 6 9 ( 8 2 ) , 602 K a m p e r , F. 7 9 1 ( 4 3 ) , 7 9 7 ( 5 6 ) , 807 K a m p s c h i d t , L . W . E . 6 3 7 ( 9 0 ) , 651 Kan, T. 5 9 7 , 5 9 8 ( 2 1 0 a , 2 1 0 b ) , 607, 6 9 1 ( 5 3 h ) ,

737

K a s s a b , E. 7 0 8 ( 9 7 a ) , 739 K a s z y n s k i , P. 5 9 3 , 5 9 4 ( 2 0 2 c ) , 607, 9 5 6 ( 1 3 9 ) , 9 6 2 , 9 6 4 (8), Katagiri, M . 8 5 3 ( 1 4 7 b ) , 889 K a t c h e n k o v , S . M . 8 5 8 ( 1 8 2 ) , 891 K a t e s , M . 9 1 5 ( 2 3 5 ) , 924 K a t e s , M . R . 4 4 0 ( 2 2 2 ) , 454 K a t o , H. 155 ( 9 2 ) , 183 Katrib, A . 4 8 9 , 4 9 0 ( 1 4 0 ) , 528 Katsumata, S. 4 7 6 , 4 7 7 , 4 8 9 , 5 0 2 , 5 0 3 , 5 0 7 , 509 (32), Katsumura, Y . 7 6 8 ( 4 1 ) , 7 7 9 K a t s u s h i m a , T. 6 9 6 , 7 1 2 , 7 1 9 ( 6 6 a , 6 6 c , 6 6 d ) ,

994

525

738

Katsuura, K. 7 6 3 ( 3 0 d ) , 7 7 9 Kattner, R. 3 8 5 ( 2 1 0 ) , 393 Katz, T.J. 3 8 2 ( 1 8 6 ) , 393, 5 9 5 , 5 9 6 ( 2 0 4 c ) , 607, 7 0 3 ( 8 1 a ) , 7 1 2 , 7 1 8 , 7 2 1 ( 1 2 2 ) , 739,

741

K a u f m a n , R.L. 7 0 5 ( 8 3 e ) , 739 K a u f m a n n , E. 5 4 2 ( 1 2 5 ) , 550 K a u p p , G. 91 ( 5 8 ) , 94 K a u z m a n n , W . E . 136 ( 6 ) , 181, 166 ( 1 2 1 ) ,

184

K a w a b a t a , S. 7 0 5 ( 8 3 f ) , 739 K a w a m u r a , H. 9 1 6 ( 2 4 4 ) , 924 K a w a m u r a , T. 9 8 3 ( 1 0 5 , 106), 9 9 6 Kawanisi, M. 6 9 6 (66a, 66d), 6 9 8 (70), 7 1 2 ,

738,

K a n d a s a m y , D . 5 7 1 ( 9 5 ) , 603 K a n e , S . S . 9 8 0 ( 9 6 , 9 7 ) , 996 K a n e d a , T. 9 0 1 ( 5 1 ) , 9 1 1 ( 1 9 6 ) , 9 1 3 ( 2 1 1 ) ,

920, 923, 924

Kanehira, K. 801 ( 6 8 ) , 807 K a n e l , H.-R. 6 9 1 , 6 9 2 , 6 9 5 ( 5 5 m , 5 5 n ) , K a n o , K. 9 1 6 ( 2 4 4 ) , 924 K a n s k a , M . 8 5 9 , 8 8 3 ( 1 8 5 b ) , 891

K a o , L . C . 6 5 8 ( 2 8 b ) , 677 Kaplan, B . E . 9 8 3 ( 1 0 8 ) , 996 Kaplan, I.R. 9 0 9 ( 1 9 2 ) , 923 Kaplan, M . L . 1 2 0 - 1 2 2 ( 1 4 4 a ) , 131 K a p p e s , M . M . 6 7 4 ( 8 5 ) , 679 Karasek, F . W . 3 3 0 ( 8 7 ) , 348 Karcher, B . A . 9 3 6 ( 8 0 ) , 960 Karcher, M . 5 9 0 , 5 9 1 ( 1 9 4 c ) , 606 K a r l s s o n , L. 4 7 1 ( 2 0 ) , 4 7 6 ( 2 0 , 3 7 ) , 4 8 7 ( 1 3 4 ) , 4 8 9 ( 2 0 , 134), 5 2 5 , Karistrom, K.I. 8 2 0 ( 4 1 ) , 887 K a r p e l e s , R. 6 4 3 - 6 4 5 ( 1 0 7 a ) , 6 4 6 ( 1 1 0 ) , 6 5 2 Kartha, A . R . S . 9 0 2 ( 6 1 ) , 920 Kasahara, I. 5 5 8 ( 2 5 b ) , 601 K a s c h e r e , C M . 145 ( 6 0 ) , 182 K a s h i n , A . N . 5 4 3 ( 1 3 7 ) , 550 K a s p i , J. 6 1 8 ( 3 8 ) , 6 1 9 ( 4 0 ) , 650 K a s s , S.R. 3 9 ( 3 5 ) , 7 7 , 7 1 2 , 7 1 4 - 7 1 6 ( 1 1 6 a ) ,

528

Jurenka, R . A . 9 0 6 ( 1 3 2 ) , 9 1 4 ( 2 2 0 ) , 922, Jurs, P . C . 123 ( 1 8 9 ) , 132, 3 5 6 ( 2 2 ) , 389

Kafafi, Z . H . 6 7 4 ( 8 7 ) , 679 K a g a b u , S. 4 7 8 , 4 7 9 ( 9 3 ) , 5 2 7 K a g a n , H. 174 ( 1 3 6 ) , 184 K a g a n , H . B . 5 5 5 , 5 5 6 (111), 5 7 0 ( 9 1 ) ,

959 887

737

719 (66a, 66d), 935 (75), K a w a s a k i , M . 8 1 2 , 8 1 5 , 8 2 2 ( l a ) , 885 K a w a u c h i , H. 7 2 4 , 7 2 5 ( 1 3 0 a ) , 741 K a y s e r , S.G. 9 1 9 ( 2 9 4 ) , 9 2 5 K a z a n s k i i , B . A . 8 6 0 ( 1 8 9 - 1 9 2 ) , 891 K e a n , G. 3 5 2 ( 5 , 6 ) , 389 K e a r n e y , E.P. 9 1 4 ( 2 2 1 ) , 924 K e a r n e y , G.P. 9 0 5 ( 9 8 ) , 921

960

A u t h o r index Kebarle, P. 4 0 6 ( 7 2 ) , 4 3 7 ( 2 1 6 ) , 451, 454, 5 3 2 ( 6 - 1 2 , 14), 5 3 3 , 5 3 4 ( 1 4 ) , 5 3 5 ( 1 0 , 14), 537, 538 (57), K e e s e , R. 5 9 6 ( 2 0 8 b ) , 607, 9 2 8 ( 8 , 9 ) , 9 3 1 (42), 9 3 3 (8, 9, 50, 51), 9 4 0 ( 8 9 - 9 1 , 93),

548, 549

944, 945 (9, 50), 958-961

K e e t o n , M . 5 4 0 ( 7 8 ) , 549 K e i d e r l i n g , T A . 140 ( 2 5 ) , 182 Keller, A . 7 7 7 ( 6 7 ) , 780 Keller, J.W. 9 5 0 ( 1 1 7 ) , 961 Keller, P.R. 4 7 7 ( 5 6 ) , 5 0 8 ( 1 6 1 ) , 526, 528 Keller, T. 3 7 4 ( 1 2 2 ) , 3 7 5 ( 1 2 2 , 129), 391 K e l l e y , C.K. 7 0 5 ( 8 5 a , 8 5 c ) , 739 K e l l i e , G . M . 121 ( 1 5 4 ) , 131 K e l l y , K . W . 5 7 8 , 5 7 9 ( 1 3 4 b ) , 604 K e l l y , R . B . 5 7 4 , 5 7 5 ( 1 1 3 k ) , 5 9 0 ( 1 9 2 ) , 604,

606 K e l u s k y , E.G. 3 6 9 ( 9 3 ) , 391 K e m b a l l , C. 3 7 7 ( 1 5 3 ) , 392, 861 ( 1 9 9 ) ,

891

K e m m e r , P. 7 2 4 , 7 2 7 ( 1 3 3 ) ,

741

K e m p , N . P . 4 1 4 ( 1 3 1 ) , 452 K e m p , N . R . 4 7 6 ( 3 9 ) , 525 Kennard, Kennedy, Kennedy, Kennedy,

O. 8 0 ( 1 9 , 2 0 ) , 8 4 ( 2 0 ) , 93 A.J. 9 7 6 , 9 8 3 ( 7 9 ) , 995 J.W. 189 ( 2 0 ) , 212 R . M . 109 ( 8 7 ) , 130

K e n n y , G . S . 3 2 1 ( 5 8 ) , 347, 8 9 9 ( 2 6 ) , Kent, G.J. 5 9 7 , 5 9 8 ( 2 1 0 a ) , 607 K e n t g e n , G. 5 9 2 ( 1 9 6 b ) , 606 K e n y o n , J. 136 ( 8 ) , 181 K e o g h , J. 8 1 3 ( 7 ) , 886

920

994-996

780

K h a d k h o d a y a n , M . 6 7 2 ( 7 8 a ) , 679 Khan, A . A . 9 1 1 ( 2 0 3 ) , 923 Khanna, P.L. 7 8 2 ( 7 c ) , 806 Kharasch, M . S . 2 3 3 ( 3 0 ) , 286, 9 8 0 ( 9 4 - 9 7 ) , 986 (94), K h e n k i n , A . M . 8 0 4 ( 7 6 ) , 808 K h i d e k e l , M . L . 8 7 1 ( 2 2 3 ) , 892 K h o d a d a d i , G. 4 1 0 ( 1 1 4 ) , 452 K h o o , S . B . 7 9 2 ( 4 5 ) , 807 K h o s r o w s h a h i , J.S. 5 7 8 ( 1 3 2 ) , 604 Kidby, D.K. 907 (161), 922 K i e b o o m , A . P . G . 5 5 5 , 5 5 6 ( 1 1 a ) , 600 Kiel, W . A . 5 6 8 , 5 7 7 ( 7 8 ) , 602 Kielbania, A.J., Jr. 7 2 4 , 7 2 6 ( 1 3 2 d ) , 741 Kier, L . B . 186, 189 ( 8 , 9 ) , 190 ( 8 , 9, 2 3 , 2 5 - 2 9 ) , 195 ( 9 ) , 196, 199, 2 0 0

(8, 9), 201 (8, 9, 31), 4 1 - 4 3 ) , 205 (47), 206 4 9 ) , 2 0 7 ( 8 , 9, 5 1 - 5 3 , (31, 56, 57), 209 (31,

213

2 0 2 ( 8 , 9, (8, 9, 4 8 , 55), 208 6 1 - 6 5 ) , 212,

K i e s l i c h , K. 7 8 2 , 7 8 3 ( 2 a - c ) , 805 Kiji, J. 5 5 7 ( 1 9 ) , 601 K i k u c h i , E. 6 8 6 ( 3 5 ) , 736 K i l l o p s , S . D . 3 3 3 ( 9 3 ) , 348 Kilpatrick, J.E. 109, 117 ( 9 2 ) , 130,

285

K i m , J.K. 4 0 6 ( 8 0 ) ,

223 (14),

451

K i m b l e , B.J. 8 9 6 ( 8 ) , 9 0 8 ( 1 8 3 ) , 9 7 9 , K i m o t o , H. 81 ( 2 3 ) , 93 K i m o t o , K. 9 3 5 ( 7 5 ) , 960

923

Kimura, K. 4 7 6 , 4 7 7 , 4 8 9 , 5 0 2 , 5 0 3 , 5 0 7 , 5 0 9 (32), 5 2 5 Kimura, M . 119 ( 1 2 8 ) , 131 Kimura, T. 6 8 3 ( 2 1 a , 2 1 c ) , 736 Kindley, W.R. 9 8 0 (93), 9 9 6 K i n g , E.G. 9 0 6 ( 1 3 5 ) , 922 K i n g , R . W . 1 6 3 , 164 ( 1 1 2 ) , 184 K i n g m a , J. 9 1 6 ( 2 4 5 ) , 924 Kirby, R . E . 4 1 4 ( 1 3 1 ) , 452, 4 7 6 ( 3 9 ) , 525 Kirby, S.P. 2 3 5 , 2 4 1 , 2 4 3 , 2 5 0 , 2 5 4 , 2 5 6 , 2 5 7 ,

283, 286

Kerkut, G . A . 9 0 6 ( 1 2 6 ) , 922 Kerr, J.A. 9 6 7 ( 2 5 ) , 9 6 9 ( 4 6 ) , 9 7 0 ( 2 5 ) , 9 8 3 (110), 992 (25), Kertesz, M . 106, 107 ( 7 5 ) , 130 Kessler, H. 361 ( 4 0 ) , 3 7 3 ( 1 0 9 ) , 390, 391 K e s z e i , C S . 6 8 7 , 6 8 8 ( 4 3 ) , 737 K e u m i , T. 6 4 6 ( 1 1 0 ) , 652 K e v a n , L. 7 7 2 ( 4 5 ) , 7 7 5 , 7 7 8 ( 5 8 a , 5 8 b ) , 779,

996

1027

264, 265 (53), Kirchen, R.P. 4 3 0 ( 1 8 5 ) , 453 Kirk, A . W . 9 6 6 ( 1 6 ) , 994 Kirk, D . N . 139 ( 2 0 ) , 155, 157 ( 9 6 ) , 162 ( 1 0 2 ) ,

182-184

169 ( 1 0 2 , 124), 171 ( 1 2 8 ) , Kirkor, E . S . 7 0 7 ( 8 9 ) , 739 K i r k w o o d , J.G. 144 ( 5 8 ) , 145 ( 6 6 , 6 7 ) , 164

182, 183

(67), K i r m s e , W . 163, 164 ( 1 0 9 ) , 184, 7 1 2 , 7 1 7 , 7 1 9 , 7 2 1 ( 1 2 1 a ) , 747 Kirsch, P.A. 104 ( 6 7 , 6 8 ) , 105 ( 6 7 ) , 115 ( 6 7 , 6 8 ) , 117 ( 1 1 7 ) , 7 2 9 , 130 Kirschner, S. 7 2 4 , 7 2 5 , 7 3 0 ( 1 3 0 b ) , 747 K i r w a n , J.N. 5 6 6 ( 6 8 ) , 602 Kir'yakov, N.V. 4 0 7 (86, 87), 457 K i s s i n , Y . V . 3 2 5 , 3 2 6 ( 7 4 ) , 3 2 9 ( 8 1 ) , 348, 9 0 9 ( 1 8 9 ) , 923 K i s t e m a k e r , P.G. 4 0 5 ( 5 9 ) , 4 5 7 K i s h a k o v s k y , G . B . 8 7 3 ( 2 4 4 ) , 892 Kitamura, M . 5 5 8 ( 2 5 a ) , 601 Kitaoka, S. 9 0 5 ( 1 0 7 ) , 9 2 7 Kitaura, K. 6 5 6 ( 8 b ) , 6 7 7 Kitching, W . 5 4 3 ( 1 2 7 ) , 550 Kitoh, J. 9 1 8 ( 2 8 5 ) , 9 2 5 K i t s c h k e , B . 3 7 4 ( 1 2 7 ) , 391 K i y o n o , S. 4 7 6 ( 4 9 ) , 5 2 6 K l a b u n d e , K.J. 6 7 3 ( 7 9 , 8 2 ) , 6 7 9 , 8 7 2 ( 2 3 9 , 240),

892

K l a g e s , U . 120, 121 ( 1 5 1 b ) , 131, 5 6 0 , 5 6 1 ( 4 4 a ) , 601 K l a g e s , W . 120 ( 1 5 0 ) , 7J7 K l a m e r , F.-G. 7 1 2 , 7 1 7 ( 1 1 9 b ) , 740

1028

A u t h o r index

K l a s i n c , L. 4 7 8 ( 1 0 0 ) , 4 7 9 ( 1 2 1 , 122), 5 2 7 Klassen, C D . 918 (284), 925 K l a s s e n , N . V . 7 7 3 ( 5 0 a , 5 0 b , 5 1 ) , 780 K l a u s , R . O . 5 7 4 , 5 7 5 ( 1 1 3 g ) , 603 Klehr, M . 801 ( 6 5 a ) , 807 K l e i n , G. 4 7 9 , 4 8 0 ( 1 1 6 ) , 5 2 7 Klein, G.W. 765 (36), 779 K l e i n , H. 7 8 2 ( 7 a ) , 806 K l e i n , W . 9 0 2 ( 5 7 ) , 920 K l e i n p e t e r , E. 361 ( 2 9 ) ,

390

Klessinger, M. 3 8 4 (200, 2 0 6 - 2 0 8 ) , 385 (206, 2 0 7 ) , 3 8 6 ( 2 0 6 - 2 0 8 ) , 393, All ( 6 4 , 7 1 , 7 2 ) , 4 7 8 ( 7 1 , 9 2 , 9 4 , 101), 4 7 9 ( 9 4 ) , 509 (164), 512 (72), 513 (171), 514 (72),

526-529 Klester, A . M . 6 9 1 , 6 9 2 ( 5 5 g , 5 5 o - q ) , 6 9 3 ( 5 5 o - ^ ) , 6 9 4 ( 5 5 g , 5 5 o - ^ ) , 737 K l i m a s h e v s k a y a , V . A . 8 1 9 ( 3 2 ) , 886 K l i m k o w s k i , V.J. 8 0 ( 1 8 ) , 87 ( 4 3 ) , 8 8 ( 4 6 ) , 8 9 ( 4 6 , 4 9 ) , 93, 94 Klingauf, F. 9 0 2 ( 5 6 , 5 7 ) , 920 Klink, E . W . 7 8 5 ( 3 2 a ) , 806 K l o o s t e r z i e l , H. 9 6 9 ( 5 4 ) , 9 9 5 K l o p m a n , G. 4 6 0 , 4 6 3 ( 1 2 ) , 524, 6 1 1 ( 1 0 ) , 649, 8 3 7 ( 1 0 1 ) , 888, 9 3 0 ( 3 3 ) , 9 5 9 K l o s t e r - J e n s e n , E. 7 2 4 , 7 2 5 , 7 3 0 ( 1 3 0 c ) , 741 K l o t s , C E . 4 0 5 ( 5 6 , 5 7 ) , 451 Klumpp, G.W. 479 (112), 5 2 7 K l y n e , W . 136 ( 2 , 5 ) , 137 ( 1 5 ) , 138 ( 1 7 ) , 139 ( 1 5 ) , 155, 157 ( 9 6 ) , 169 ( 1 2 7 ) , 1 7 1 , 1 7 4 - 1 7 6 ( 1 2 9 ) , 181, 183, 184 K n i e z o , L. 6 9 2 , 6 9 5 ( 6 0 ) , 738 K n i g h t , D . L . 9 1 6 ( 2 5 3 ) , 924 K n i g h t , L . B . , Jr. 4 0 4 ( 4 7 ) , 450 Knorr, R. 127 ( 2 0 5 ) , 133 K n o t n e r u s , J. 9 8 2 ( 1 0 2 ) , 9 9 6 K n o x , J.H. 9 6 8 ( 3 1 ) , 9 6 9 ( 3 1 , 3 6 , 5 2 ) , 994,

995 K n o z i n g e r , H. 5 5 7 ( 1 8 ) , 601 K o b a y a s h i , H. 8 1 2 , 8 1 5 , 8 2 2 ( l a ) , 885 K o b a y a s h i , S. 6 3 3 , 6 3 5 ( 7 3 ) , 651 K o b a y a s h i , T. 4 7 7 ( 7 0 ) , 5 2 6 , 5 8 2 ( 1 5 5 ) , 605 K o c h , F. 6 8 7 ( 4 1 ) , 736 K o c h , R . O . 7 7 5 ( 6 0 ) , 780 K o c h , V . R . 7 9 2 ( 4 6 , 4 7 ) , 807 K o c h , W . 4 3 4 ( 1 9 6 ) , 453, 5 3 5 - 5 3 8 ( 4 9 ) , 549 K o c h i , J. 5 8 5 ( 1 6 9 a , 169b), 605, 8 2 4 ( 6 0 ) , 887 K o c h i , J.K. 5 7 8 ( 1 2 7 , 129b), 604, 7 1 1 ( 1 1 4 e ) ,

740 K o c h l o e f l , K. 5 5 7 ( 1 8 ) , 601 K o c o v s k y , P. 5 6 3 ( 5 4 b ) , 602 K o c s i s , W . P . 6 3 0 ( 5 8 ) , 650 K o d a m a , M . 5 5 9 ( 3 7 ) , 601 K o e m e r , M . 5 8 6 ( 1 7 5 a ) , 605 K o g a , K. 5 8 2 ( 1 5 0 ) , 605 K o g e l s c h a t z , U. 6 8 2 ( 1 2 a - e ) , K o h a r s k i , D . 8 1 3 ( 7 ) , 886

735

K o h l e r , H.J. 5 3 2 , 5 3 4 ( 3 5 ) , 5 3 6 ( 5 0 ) ,

548,

549 Kohling, A. 805 (82), Kohn, W. 4 (11), 77

808

K o k k e , W . C . M . C . 165 ( 1 1 6 ) , 184 K o l a t t u k u d y , P.E. 8 9 6 ( 5 ) , 9 0 0 ( 4 1 , 4 4 ) , 9 0 1 (44, 50), 902 (44, 59, 60), 9 1 1 , 907 ( 1 5 1 , 152), ( 1 9 8 - 2 0 0 , 2 0 2 - 2 0 5 ) , 9 1 2 (198, 205, 206), 913 (198), 914 (198, 2 1 2 ) , 9 1 6 ( 1 9 8 , 2 0 0 , 2 7 4 ) , 9 7 9 , 920,

922-925 K o l b , T . M . 7 1 2 , 7 1 3 ( 1 1 5 0 , 740 K o l l o n i t s c h , J. 5 8 1 ( 1 4 6 ) , 605 K o l o m n i k o v , I.S. 5 5 7 ( 1 6 ) , 600 K o l p i n , C.F. 7 8 5 ( 3 2 a ) , 806 K o l t e r m a n n , G . W . 120, 121 ( 1 5 1 a ) , 7 J 7 K o m a r e w s k y , V.I. 8 6 0 ( 1 9 6 ) , 891 Komarov, V.N. 398 (13), 4 0 4 (42), 425 (172),

450, 453 K o m a r o v a , T. 9 1 6 ( 2 5 9 ) , 9 2 5 K o m o m i c k i , A . 5 3 2 , 5 3 7 , 5 3 8 ( 3 6 ) , 548 K o m o t o , T. 128 ( 2 2 4 ) , 133, 3 7 6 ( 1 3 5 , 136, 139), 392 K o n a k a , S. 119 ( 1 2 8 ) , 131 K o n d o , M. 3 5 2 ( 2 ) , 3 6 9 ( 7 4 ) , 389, 390 K o n i n g s f e l d , H. van 122 ( 1 5 8 ) , 131 K o n i s h i , H. 5 5 7 ( 1 9 ) , 601 Koob, R.D. 687, 688 (38b, 38c),

736

K o o n , K . H . 109, 1 1 2 , 116, 117 ( 9 0 ) , 130, 3 7 3 ( 1 1 3 ) , 391 K o o p m a n s , T. 4 7 3 , 5 0 2 ( 2 3 ) , 5 2 5 K o o y m a n , E.G. 9 8 2 ( 1 0 0 , 1 0 2 ) , 9 9 6 Kopf, J. 5 9 3 ( 2 0 I d ) , 607 K o r a n y i , T. 4 7 6 ( 4 8 ) , 5 2 6 K o m b l u m , N . 5 8 2 ( 1 5 8 ) , 605 Koronelli, T.V. 9 1 6 (259), 925 K o r o s t y s h e v s k i i , I.Z. 4 1 5 ( 1 3 6 ) , 452 Korsakov, M.V. 847 (129, 130), 848 (130),

889 K o r s h u n o v , L A . 8 7 1 ( 2 2 6 ) , 892 Korte, F. 6 7 2 ( 7 7 ) , 6 7 9 K o s , A.J. 5 4 7 ( 1 5 4 ) , 5 5 7 K o s e r , G.F. 7 0 6 , 7 0 7 ( 8 7 d ) , 739 K o s e r , H.G. 7 1 2 , 7 1 7 ( 1 1 9 b ) , 740 Kostermans, G.B.M. 7 0 3 , 704, 712, 719 (80),

739 K o s u g i , H. 5 8 7 ( 1 8 1 b ) , 606 Kotera, K. 5 6 1 ( 4 5 c ) , 601 Kottirsch, G. 9 5 4 ( 1 3 0 ) , 967 K o u w e n h o v e n , A . P . 5 3 2 , 5 3 8 , 5 3 9 ( 2 0 ) , 548, 6 1 3 ( 1 8 a ) , 649 K o v a c , B . 4 7 8 ( 1 0 0 ) , 4 8 0 ( 1 3 0 ) , 527, 528 K o v a l e n k o , L.I. 8 6 0 ( 1 8 9 , 1 9 1 ) , 891 K o w a l e w s k i , J. 3 7 9 ( 1 7 0 ) , 392 K o w a r i , K. 7 4 9 ( 8 c ) , 778 Kozari, L. 6 8 7 , 6 8 8 ( 4 3 ) , 737 K o z a s a , M. 6 8 9 , 6 9 0 ( 4 8 c ) , 737

A u t h o r index K o z i n a , M . P . 3 7 9 ( 1 7 2 ) , 3 8 0 , 3 8 2 ( 1 7 9 ) , 392 K o z l o w s k i , J.A. 5 8 5 ( 1 7 2 b ) , 5 8 6 ( 1 7 2 b , 1 7 3 , 174a, 174b, 175b), 605 Krabbenhoft, H . O . 3 6 1 ( 4 5 ) , 390 Kraemer, W . P . 4 8 9 , 4 9 0 ( 1 3 5 ) , 528 Krafft, M . E . 5 6 2 ( 5 0 ) , 601 Kraka, E. 2 6 , 31 ( 2 4 ) , 7 7 Kramer, J.D. 5 9 9 ( 2 1 6 ) , 608 Kramer, P.A. 5 3 2 , 5 3 8 , 5 3 9 ( 2 0 ) , 548, 6 1 3 ( 1 8 a ) , 649 Krane, J. 127 ( 2 0 9 ) , J33 Krasutsky, P.A. 6 9 2 , 6 9 4 ( 5 8 ) , 738 Kraus, M. 4 0 4 ( 4 5 ) , 450 Krebs, A . 4 7 8 , 5 1 6 , 5 1 7 ( 1 0 6 ) , 5 2 7 Krebs, E.P. 5 7 6 ( 1 2 1 c ) , 604 Kreissl, F.R. 3 8 8 ( 2 2 4 ) , 393 K r e n m a y e r , P. 4 1 8 ( 1 4 6 ) , 452 Krennrich, G. 4 7 7 ( 6 8 ) , 4 7 8 ( 6 8 , 104), 4 7 9 ( 1 1 8 ) , 526,527 Kretzschmar, G. 5 8 0 ( 1 3 9 ) , 604 Krief, A . 5 7 7 ( 1 2 4 ) , 604 Krill, G. 6 8 4 - 6 8 6 ( 2 8 ) , 736 K r i m m , S. 8 0 ( 1 8 ) , 93 Krishna, M . V . 5 6 8 ( 7 9 ) , 602 Krishnamurthy, S. 5 6 2 ( 5 3 a ) , 5 7 1 ( 9 6 ) ,

602,

603 Krishnamurthy, V . V . 3 8 4 ( 2 0 3 ) , 393,

627 (56),

650 Kristof, W . 7 2 4 , 7 2 5 ( 1 3 1 a ) , 741 Kriz, J.F. 3 2 0 , 3 2 4 ( 5 7 b ) , 347, 3 6 9 ( 8 2 ) ,

1029

K u m a g a i , Y . 7 2 4 , 7 2 5 ( 1 3 0 a ) , 741 Kumar, B . 3 2 9 ( 8 0 ) , 348 K u m o b a y a s h i , H. 5 5 8 ( 2 5 b ) , 601 Kunt, S. 8 3 9 ( 1 1 0 ) , 889 Kuntz, P.J. 8 3 9 ( 1 0 7 ) , 888 K u n z e r , H. 5 6 2 , 5 6 3 ( 5 1 b ) , 601 Kuras, M . 3 0 8 ( 3 5 ) , 3 2 0 , 3 2 4 ( 5 7 b ) , 3 3 4 ( 3 5 ) ,

347 Kurisaki, K. 6 9 1 , 6 9 2 , 6 9 4 ( 5 5 s ) , 737 K u r s a n o v , D . N . 5 5 9 ( 2 9 , 3 0 ) , 5 6 0 ( 4 2 ) , 601 Kurz, H.R. 4 7 9 ( 1 1 0 ) , 5 2 7 K u s h i d a , K. 3 8 2 ( 1 8 4 ) , 393 K u s u m o t o , T. 5 6 8 ( 8 1 b ) , 602 K u s u n o s e , E. 8 5 3 ( 1 4 7 e ) , 8 5 4 ( 1 4 8 a , 152b, 154), 8 5 5 ( 1 5 4 , 1 5 5 ) , 890 K u s u n o s e , M . 8 5 3 ( I 4 7 e ) , 8 5 4 ( 1 4 8 a , 152b, 154), 8 5 5 ( 1 5 4 , 155), 890 Kutal, C. 7 0 5 ( 8 5 a , 8 5 c ) , 7 0 6 , 7 0 7 ( 8 7 b ) , 739 K u t s c h a n , R. 361 ( 4 9 ) , 390 Kutter, E. 2 0 2 ( 4 0 ) , 213 K u t z e l n i g g , W . 9 2 ( 6 3 ) , 94, 3 5 2 ( 7 ) , 389, 5 3 2 ( 2 7 , 3 1 ) , 548 K u w a h a r a , D . 3 6 9 , 3 7 0 ( 9 0 ) , 391 K u z m i n , V . A . 8 5 9 , 8 8 4 ( 1 8 5 0 , 891 Kuznetsov, B.N. 672 (72), 679 K u z n e t z o v a , N . V . 871 ( 2 3 3 , 2 3 4 ) , 892 K v a l h e i m , G . M . 3 7 7 ( 1 4 5 , 1 5 1 ) , 392 K v e n r o l d e n , K . A . 9 0 8 ( 1 6 8 ) , 923 Kwantes, A. 6 3 3 , 635 (75), 657 K w a s a n i , H. 6 9 6 , 7 1 2 , 7 1 9 ( 6 6 c ) , 738

391 K r o g h - J e s p e r s e n , M . - B . 9 3 0 ( 3 3 ) , 959 K r o g h - J e s p e r s o n , K. 9 7 2 ( 7 2 ) , 9 9 5 Krohn, K. 9 3 0 ( 2 7 ) , 9 5 9 Krug, L.H. 9 7 0 - 9 7 3 , 9 8 8 , 9 8 9 ( 6 6 ) , 9 9 5 K r u l w i c h , T . A . 9 1 5 ( 2 3 6 ) , 924 Krupp, H. 8 0 5 ( 8 2 ) , 808 Krushch, A . P . 6 5 8 ( 2 3 c ) , 6 7 7 K s i c a , F. 4 1 8 ( 1 4 6 ) , 452 K u b a c h , C. 4 0 2 , 4 0 4 ( 3 5 ) , 450 K u b a s , G.J. 6 5 5 , 6 7 2 ( 6 ) , 6 7 7 Kubat, P. 6 9 0 ( 5 1 c ) , 7 0 3 ( 7 8 ) , 737, 739 Kubiak, G. 5 5 6 ( 1 3 f ) , 600, 9 4 0 ( 8 8 ) , 960 K u c h h a l , R.K. 3 2 9 ( 8 0 ) , 348 Kuchitsu, K. 1 0 3 , 110, 114 ( 5 4 ) , 123 ( 1 8 1 ) , 7 2 9 , 132 Kuck, D . 4 4 2 ( 2 2 6 b ) , 454, (94), 967

942 (94, 95), 943

Kuebler, N . A . 4 7 7 , 5 0 8 , 5 0 9 ( 5 1 ) , 5 2 6 , 7 0 8 , 7 1 2 ( 9 6 0 , 739 K u h l e w i n d , H. 4 3 5 ( 2 0 4 ) , 454 Kuhn, A . T . 7 9 5 ( 5 2 a ) , 807 K u h n , S. 6 3 5 ( 8 0 ) , 6 5 7 Kuhn, W . 120 ( 1 5 0 ) , 131, 145 ( 6 1 - 6 4 ) ,

183 Kukla, M. 4 7 7 , 4 7 8 ( 5 8 ) , 5 2 6 K u k o l e v , V . P . 5 5 7 ( 1 6 ) , 600

182,

L a a h , K. 6 1 8 ( 3 7 ) , 6 2 7 ( 5 6 ) , 6 3 0 ( 5 8 , 6 1 ) , 6 3 1 ( 6 1 ) , 6 3 3 , 6 3 5 ( 7 8 ) , 650, 651 Laane, J. 123 ( 1 8 5 ) , 132 Labbauf, A . 283 Labinger, J.A. 6 5 8 ( 2 7 ) , 6 7 7 L a c h a n c e , P. 3 5 2 ( 1 2 ) , 389 Lack, R . E . 123 ( 1 7 6 ) , 132 L a c o m b e , L. 145 ( 6 0 ) , 182 L a d o n , L . H . 2 6 8 , 2 8 1 ( 8 4 ) , 287 L a g e r o n , A . 9 1 9 ( 3 0 3 ) , 926 Lahr, P. 7 1 2 , 7 1 7 ( 1 1 8 ) , 740 Lai, T . - W . 6 9 8 ( 6 8 ) , 738 L a i d i g , K . E . 6 8 , 7 0 , 7 4 ( 5 2 ) , 7 7 , 101 ( 5 0 ) , 7 2 9 Laidler, K.J. 2 3 5 , 2 5 1 , 2 7 1 ( 3 4 ) , 286 L a i n e , B . 9 1 6 ( 2 5 4 ) , 924 Lalli, C M . 9 1 6 ( 2 5 8 ) , 9 2 5 L a l o , C. 6 9 0 ( 5 1 b ) , 737 L a l o w s k i , W . 108 ( 8 0 ) , 130 L a m , A . Y . K . 5 3 5 ( 4 2 ) , 548 L a m a n d e , L. 6 4 0 ( 9 9 a ) , 6 5 7 L a m b , J. 9 7 ( 7 ) , 128 Lambert, J.B. 1 2 0 - 1 2 2 ( 1 4 4 b ) , 131 L a m m e r t s m a , K. 6 3 0 ( 5 9 , 6 2 ) , 6 3 1 ( 6 2 ) , 6 4 3 - 6 4 5 (107a), 646 (110), 657, 652 L a m o t t e , G. 5 8 1 ( 1 4 9 a , 1 4 9 b ) , 605 L a m p e , F . W . 4 0 6 ( 7 9 ) , 451, 8 4 7 ( 1 2 4 ) , 889

1030

A u t h o r index

Lampman, G.M. 978, 983 (85), 995 L a n c h e c , G. 9 7 0 ( 6 3 , 6 4 ) , 9 9 5 L a n d g r e b e , J.A. 9 7 7 ( 8 4 ) , 9 8 4 ( 1 1 1 ) , 9 9 5 , 9 9 6 L a n e , C.F. 8 2 2 ( 5 1 ) , 887 L a n g , C E . 8 2 1 ( 4 7 a , 4 7 b ) , 8 5 3 ( 1 4 0 ) , 887,

889

Lange, C 906 (137), 922 L a n g e , R. 9 5 7 , 9 5 8 ( 1 4 6 ) , 9 6 2 Langer, A . 4 3 2 , 4 3 3 ( 1 8 9 ) , 453 Langrish, J. 8 7 5 ( 2 5 4 ) , 893 L a n g s t r o m , B . 8 2 0 ( 3 7 ) , 887 L a n y j o v a , Z. 4 7 9 ( 1 0 8 ) , 5 2 7 L a p , B . V . 5 7 0 ( 8 7 a ) , 603 Lapcik, L. 7 0 6 ( 8 8 d ) , 739 L a Placa, S.J. 9 2 8 , 9 5 1 ( 1 1 ) ,

958

Lappert, M . F . 4 7 6 ( 4 6 ) , 5 2 5 L a r c h e q u e , M . 5 8 2 ( 1 5 1 ) , 605 Lardicci, L. 141 ( 3 3 ) , 142 ( 4 2 ) , 182 Larock, R . C . 5 5 5 ( 4 ) , 5 8 6 ( 1 7 6 ) , 600, 605 L a R o s e , R. 9 4 7 ( 1 0 6 ) , 9 6 7 L a r o u c h e , A. 17, 5 4 , 7 0 , 7 4 ( 2 0 ) , 7 7 Larrabee, R . B . 5 9 3 , 5 9 4 ( 2 0 2 d ) , 607 L a r r o u g u e r e - R e g n i e r , S. 9 1 9 ( 2 9 6 ) , 9 2 6 Larsen, A . 7 4 9 ( 8 b ) , 778 Larsen, J.W. 5 3 8 ( 6 8 ) , 5 3 9 ( 6 8 , 7 2 ) , 5 4 9 , 5 7 3 ( 1 0 8 b ) , 603 Larson, C W . 2 5 9 ( 7 6 ) , 287 L a s c o m b e , J. 9 8 , 9 9 , 110 ( 1 7 ) , 128 Lathan, W . A . 5 3 2 ( 2 8 - 3 0 ) , 548, 9 3 0 ( 3 3 ) , 9 5 9 Latore, F . B . 8 2 2 ( 5 0 ) , 887 Latypova, M.M. 477 (62), 5 2 6 Lau, C . D . H . 13 ( 1 4 ) , 17 ( 1 8 ) , 2 6 ( 1 4 , 2 4 ) , 31 ( 2 4 ) , 3 4 ( 1 4 ) , 3 5 , 3 6 ( 2 9 ) , 41 ( 1 4 ) , 4 8 , 61 (18), 77, 92 (62), 94, 9 6 (1), 933, 952 (57), Lau, C J . 7 2 4 , 7 2 8 , 7 2 9 ( 1 3 6 b ) , 747 L a u , C.K. 5 6 3 ( 5 6 ) , Lau, R . C . 6 9 1 , 6 9 2 , 6 9 4 (55r), 737 L a u d e n s l a g e r , J.B. 4 0 6 ( 7 0 ) , 4 5 7 Lauren, D . R . 5 6 5 ( 6 1 ) , 602 Lauterbur, P . C . 3 5 7 ( 2 7 ) , 389 Lavanchy, A. 4 1 8 , 4 1 9 (149), 4 2 0 (151), 4 2 2

128,

960

602

452,453

( 1 5 1 , 154), 4 4 2 ( 1 4 9 ) , L a v a n i s h , J. 9 7 8 , 9 8 3 ( 8 5 ) , 9 9 5 L a v e s , F. 3 2 1 ( 6 0 ) , 347 Lavin, M.E. 656, 668 (9), 6 7 7 Lavrik, P . B . 5 9 9 ( 2 1 6 ) , 608 Lavrushko, V.V. 658 (23c, 25), 6 7 7 L a w , J.H. 9 0 6 ( 1 2 5 ) , 9 2 2 L a w , R.L. 8 1 4 ( 1 1 ) , Lawrence, B.M. 295, 299 (14), 315 (44), L a w r e n c e , J.P. 6 9 6 , 6 9 8 ( 6 7 e ) , 738 L a z a r o , R. 8 2 3 ( 5 3 ) , 887 Lazier, R.J.D. 4 7 6 ( 3 5 ) , 5 2 5 L e a c h , D . R . 5 8 6 ( 1 7 6 ) , 605 L e b e d e v , S . A . 871 ( 2 3 3 , 2 3 4 ) , 892

L e e , E . K . C . 8 4 2 ( 1 1 4 , 117), 8 4 3 ( 1 1 7 ) , 8 4 4 ( 1 2 1 ) , 889 L e e , K. 9 1 6 ( 2 5 8 ) , 9 2 5 L e e , K . - S . 3 7 6 ( 1 4 1 ) , 392 L e e , N . S . 163 ( 1 0 6 ) , 184 L e e , P.G. 5 9 3 ( 2 0 0 b ) , 606 L e e , S.P. 5 6 7 ( 7 0 b ) , 602 Lee, Y.-S. 976, 982, 983 (78), 995 Lee, Y.T. 532, 534 (15), Lee-Ruff, E. 5 4 3 ( 1 4 4 ) , 5 5 7 L e e s , A.J. 661 ( 4 0 ) , 678 Le Fevre, R.J.W. 3 ( 5 ) , 76 Lefort, D . 9 6 9 , 9 7 9 ( 5 7 ) , 9 9 5 Legare, P. 6 8 3 , 6 8 4 ( 2 3 ) , 736 LeGoff, E. 5 9 0 ( 1 9 5 ) , 606 L e g o n , A . C . 123 ( 1 8 0 ) , 132 Legrand, M . 140 ( 2 2 ) , 182 Lehmann, D. 524 (181), 5 2 9 L e h n e , K. 4 7 9 ( 1 0 7 ) , 5 2 7 L e i g h , W.J. 7 0 8 ( 9 7 c ) , 7 3 4 ( 1 4 1 a ) , 740, 741 Leight, R.S. 4 7 7 (70), 5 2 6 L e i n i n g e r , H. 3 6 1 , 381 ( 3 8 ) , 390 L e i p z i g , B . D . 9 3 6 ( 8 1 ) , 960 L e m a l , D . M . 5 9 0 , 591 ( 1 9 4 b ) , 606, 7 1 2 , 7 2 0 ,

548

7 2 1 ( 1 2 5 c ) , 747 L e m p e r e u r , F. 6 9 0 ( 5 1 b ) , 737 L e m p k a , H. 4 7 8 ( 9 8 ) , 5 2 7 L e n g , F.J. 4 7 7 ( 5 5 ) , 5 2 6 L e n g , H . C . de 7 6 2 ( 2 3 , 2 4 ) , 7 6 3 ( 2 4 , 2 9 c ) , 7 7 9 L e n n a r d - J o n e s , J. 4 6 0 ( 9 ) , 5 2 4 Lennartz, H . - W . 6 9 3 ( 6 4 ) , 7 1 2 , 7 1 7 ( 1 1 9 b ) ,

738, 740 Lenoir, A . 9 0 6 ( 1 3 7 ) , 9 2 2 L e N o r m a n d , F. 6 1 8 , 6 2 1 ( 3 6 a , 3 6 b ) ,

886

347

L e b e d e v , V . S . 8 5 8 ( 1 8 1 ) , 891 Lebon, A.M. 917 (273), 925 Lebrilla, C B . 6 7 3 ( 8 0 ) , 6 7 9 Lechert, H. 3 6 9 ( 9 6 ) , 391 Leckta, T. 5 3 9 ( 7 3 , 7 4 ) , 5 4 9 L e C o u p a n e c , P. 8 0 3 ( 7 3 ) , 808 L e d , J.J. 3 8 5 ( 2 1 1 ) , 393 Lederer, E. 9 1 4 ( 2 2 8 ) , 9 2 4 Ledford, T.H. 5 3 8 , 5 3 9 ( 6 9 ) , 5 4 9 L e d u c , P. 8 0 4 ( 7 5 ) , 808 Lee, A. 4 0 6 (82), 457 L e e , E. 4 7 6 ( 4 8 ) , 5 2 6

346,

650,

6 8 4 - 6 8 6 ( 2 8 ) , 736, 8 6 2 ( 2 0 5 ) , 891 L e n z , D . H . 4 0 4 ( 4 1 ) , 450 Leonard, J.E. 7 0 7 , 7 0 8 ( 9 1 ) , 739 L e o n o v , M.R. 8 1 5 , 8 2 2 ( I p ) , 886 Lercker, G. 9 0 7 ( 1 6 7 ) , 9 1 4 ( 2 2 5 ) , 923, 924 L e r m o n t o v , S.A. 6 5 8 ( 2 5 ) , 6 7 7 L e s a g e , M . 5 6 9 ( 8 6 ) , 603 Lesfauries, P. 9 9 3 ( 1 6 6 ) , 9 9 7 L e s k o , S.A. 118, 121 ( 1 2 1 ) , 131, 3 7 4 ( 1 2 0 ) ,

391 Lester, D . E . 8 9 6 ( 6 ) , 9 7 9

A u t h o r index

1031

L e Terrier, F. 9 1 9 ( 2 9 5 ) , 9 2 5 Lethaeuser, D . 3 2 4 , 3 2 6 ( 7 3 ) , 348 L e T o u m e a l l , R. 3 3 3 ( 9 6 ) , 348 Letsinger, R.L. 141 ( 3 4 ) , 182 L e u n g , H . - W . 4 3 5 ( 2 0 6 ) , 454 Levachev, M.M. 906 (141), 922 L e v e n e , P.A. 136, 138, 141 ( 1 ) , 142 ( 1 , 3 8 ,

L i f s o n , S. 104, 109 ( 6 6 ) , 7 2 9

4 4 ) , 143, 144 ( 1 ) , Lever, J.R. 5 7 7 ( 1 2 3 b ) , 604 L e v e r , O . W . , Jr. 5 4 3 ( 1 3 0 ) , 550 L e v i n , R . D . 3 0 2 ( 2 1 ) , 346, 3 9 6 ( 3 ) , 3 9 7 ( 3 , 5 ) ,

L i k h o t v o n k , I.R. 6 9 2 , 6 9 4 ( 5 8 ) ,

181, 182

449, 450, 549

402, 4 0 8 , 4 3 3 (3), 4 7 6 (31), 525, 537, 538, 543, 546 (56), L e v i n , S. 8 5 5 ( 1 5 7 ) , 890 L e v i n e , B . H . 9 3 8 ( 8 4 ) , 960 L e v i n e , R . D . 4 3 5 ( 2 0 5 ) , 454 L e v i n s o n , S.R. 9 1 8 ( 2 8 2 , 2 8 3 ) , 9 2 5 Levron, J.C. 8 2 0 ( 3 6 ) , 887 L e v s e n , K. 3 9 9 , 4 0 0 ( 2 7 ) , 4 1 7 ( 1 4 4 ) , 4 1 8 ( 1 4 5 ) , 4 2 4 ( 1 5 8 ) , 4 4 2 ( 1 4 4 , 145), 4 4 6 ( 1 4 5 ) , 4 4 7 ( 2 4 0 ) , 4 4 9 ( 2 4 5 ) , 450,

452^54

L i g g e r o , S.H. 8 1 8 ( 2 7 ) , 8 1 9 ( 2 9 ) , 886 Light, R.J. 9 1 4 ( 2 2 6 ) , 924 Lightfoot, P . D . 2 5 9 ( 6 1 ) , 287 Lii, J.-H. 8 0 , 9 2 ( 1 7 ) , 9 9 ( 2 6 , 2 9 ) , 100, 110, 118, 1 2 3 , 127 ( 2 9 ) , 7 2 9 , 9 3 4 ( 7 0 ) ,

93,

960

738

L i m a s s e t , J. 5 9 3 ( 2 0 1 a ) , 607 Lin, C.-H. 8 1 2 ( l e ) , 8 1 5 , 8 2 2 ( l e , Ih, Ik),

885, 886

Lin, H . C . 6 4 1 ( 1 0 0 a ) , 6 5 7 Lin, J.J. 5 5 9 ( 3 5 , 3 6 ) , 5 7 1 ( 3 6 , 9 7 , 9 8 ) ,

603

601,

Lin, Y . 6 6 3 , 6 6 4 , 6 6 8 ( 5 5 d ) , 6 7 0 ( 5 5 d , 6 5 ) ,

678, 679

L i n d e m a n n , L.P. 3 3 0 ( 8 6 ) , 348,

389

355 (17),

L i n d e n , A . C . v a n der 9 1 5 ( 2 3 7 ) , 924 L i n d h o l m , C. 9 3 4 ( 6 8 ) , 960 L i n d h o l m , E. 4 7 7 , 4 9 0 ( 5 2 ) , 5 0 5 ( 1 5 1 ) ,

528

526,

L e v y , G . C . 8 7 ( 4 4 ) , 94 L e v y , J.B. 5 3 5 ( 4 4 ) , 548 L e v y , M . 139, 163 ( 1 9 ) , 182 L e w i s , G . N . 35 ( 2 7 ) , 7 7 , 2 1 6 ( 1 , 2 ) , 2 2 3 ( 1 5 ) ,

L i n d m a n , L.P. 3 3 3 ( 9 6 ) , 348 Lindner, H.J. 3 7 4 ( 1 2 7 ) , 391 Lindquist, R . H . 8 7 3 , 8 7 4 ( 2 4 6 ) , 892 L i n d s a y , D . 111 ( 1 0 3 , 104), 112 ( 1 0 4 ) , 116

2 2 6 ( 1 7 ) , 285, 6 4 9 ( 1 1 4 ) , 652 L e w i s , S.C. 9 8 6 , 9 8 8 , 9 8 9 ( 1 1 9 ) , 9 9 6 Li, J. 8 4 ( 3 5 ) , Li, J.C.M. 2 2 3 ( 1 4 ) , 285 Li, M . K . 5 6 7 ( 7 3 ) , Li, Y . 6 4 3 , 6 4 4 ( 1 0 7 c ) , 6 5 2 Liang, G. 3 6 8 ( 6 7 ) , 390

( 1 0 3 , 1 0 4 ) , 130, 3 7 3 ( 1 1 1 ) , 391 Lineberger, W . C . 5 4 3 ( 1 4 5 ) , 5 5 7 L i n l e y , J.R. 9 0 6 ( 1 3 4 ) , 9 2 2 Linstead, R.P. 169 ( 1 2 6 ) , 184 Lintas, C. 9 0 6 ( 1 4 4 ) , 9 2 2 L i p k o w i t z , K . B . 9 9 , 100 ( 2 8 b ) , 7 2 9 , 5 5 6 ( 1 3 e ) ,

Liardon, R. 4 0 0 ( 3 1 ) , 4 1 5 ( 3 1 , 139), 4 3 4 ( 1 9 7 ) , 4 4 2 (31), Lias, S.G. 3 0 2 ( 2 1 ) , 346, 3 9 6 ( 3 ) , 3 9 7 ( 3 , 5), 4 0 2 , 4 0 8 , 4 3 3 (3), 4 3 5 (201), 4 3 7 ( 2 1 5 ) , 449, 450, 453, 454, 4 7 6 ( 3 1 ) , 5 2 5 , 535 (40), 537 (56, 59), 538, 543, 546 (56), 687 (39e, 45), 688 (45), 7 5 1 , 7 5 2 ( l i b , 11c), 7 5 5 ( 1 4 ) , 7 5 6 - 7 5 8 (16), 763, 764 (31), 765 (34b),

Lipovich, V.G. 816 (24), 860 (187), 873 (24),

93

602

600

450, 452, 453

548, 549, 736 , 737,

778, 779

886, 891

L i p p , E . D . 140 ( 2 6 ) , 182 Lippmann, D.Z. 208 (59), 2 7 i Lipshutz, B . H . 5 8 5 ( 1 7 2 a , 1 7 2 b ) , 5 8 6 ( 1 7 2 a , 172b, 1 7 3 , 174a, 1 7 4 b , 175a, 1 7 5 b ) , 605 L i p s k y , S. 7 6 3 ( 2 9 a , 2 9 b ) , 7 7 9 Lipton, M . 100, 124 ( 3 5 , 3 7 ) , 127 ( 3 7 ) , 128 (35), 729 Lipton, M . S . 4 7 7 ( 7 0 ) , 5 2 6 L i s c h k a , H. 5 3 2 , 5 3 4 ( 3 5 ) , 5 3 6 ( 5 0 ) , 548,

Libby, W . F . 7 7 5 , 7 7 8 ( 5 8 a , 5 8 b ) , 780 Licini, G. 5 6 2 , 5 6 3 ( 5 1 b ) , 601 Lide, D.R. 108 ( 7 6 , 7 7 ) , 109 ( 8 4 ) , 130

Lishan, D.G. 7 0 7 , 708 (91),

L i d e , D.R., Jr. 109 ( 8 5 ) , 130 Liebelt, W . 5 5 7 ( 1 8 ) , 601

L i s i h k i n , G . V . 8 6 1 ( 2 0 1 ) , 891 Little, T . S . 123 ( 1 8 3 ) , 132

549

L i e b m a n , J.F. 2 6 8 , 2 8 1 ( 8 4 ) , 287, 3 0 2 ( 2 1 ) , 396, 397, 4 0 2 , 4 0 8 , 4 3 3 (3), 537, 538, 543, 546 (56), 656 (13), 6 7 7 , 6 8 2 (2a, 4 ) , 6 9 1 ( 2 a ) , 6 9 2 ( 6 2 g ) , 7 1 1 (2a, 1 1 4 c , 1 1 4 d ) , 735, 738, 740, 9 2 8 - 9 3 0 ( 4 ) , 958

346,

549,

449,

Lifshitz, C. 3 9 9 ( 1 9 - 2 1 ) , 4 4 8 ( 2 4 2 ) , 450,

Littlemore, L . A . 3 6 9 ( 8 4 ) , 391 L i t t l e w o o d , A . B . 8 4 9 ( 1 3 2 ) , 889 L i t v y n , A . L . 6 9 2 , 6 9 4 ( 5 8 ) , 738 Liu, B . 5 3 5 - 5 3 8 ( 4 9 ) , 549 Liu, H.J. 5 6 7 ( 7 0 b ) , 602 Liu, K . - C . 7 0 8 , 7 1 0 ( 1 0 2 a ) , Liu, K.-J. 3 6 9 ( 7 2 ) ,

390

Lien, T.R. 5 5 6 ( 1 2 ) , 600 Lietz, G. 861 ( 2 0 2 ) , 891

739

740

Liu, T.-Y.J. 9 1 6 ( 2 7 4 ) , 9 2 5 454

Livett, M . K . 4 7 7 ( 6 9 ) , 4 7 8 ( 8 6 ) , 5 2 6 , 5 2 7

1032

A u t h o r index

L l o y d , E.K. 188 ( 1 1 ) , 212 Lloyd, H.A. 906 (122), 922 Lo, D.H. 303 (23),

L u n i n , V . V . 861 ( 2 0 1 ) , 891 Luning, V. 991 (146), 9 9 7 L u n n , A . C . 189 ( 1 9 ) , 2 7 2

347

L o b b e r d i n g , A . 5 6 5 , 5 6 6 ( 6 6 b ) , 602 Lock, B.A. 917 (270), 925 L o c k e y , K . H . 9 0 5 ( 1 0 4 , 106), 927 L o c k s l e y , H . D . 9 0 2 ( 6 2 ) , 920 L o e h r , T . M . 8 5 8 ( 1 6 7 ) , 890 Loerzer, T. 3 8 4 , 3 8 5 ( 1 9 9 ) , 393 L o f q u i s t , J. 9 0 6 ( 1 2 4 ) , 9 2 2 L o f q v i s t , J. 8 2 0 , 8 2 1 ( 4 5 ) , 887 L o g e m a n n , E. 3 8 8 ( 2 2 5 ) , 393 L o i m , N . M . 5 5 9 ( 2 9 , 3 0 ) , 607 L o k e n s g a r d , J.P. 5 9 0 , 591 ( 1 9 4 b ) , 6 0 6 , 7 1 2 , 7 2 0 , 7 2 1 ( 1 2 5 c ) , 747 L o m a s , J.S. 104, 105, 115 ( 6 7 ) , 117 ( 1 1 7 ) ,

129, 130

L o m m e n , G . v a n 3 8 2 ( 1 8 5 ) , 393 L o n g , J. 4 4 2 ( 2 2 6 a ) , 454 L o n g , M . A . 871 ( 2 3 2 ) , 892 L o n g i n e h i , A . 8 5 8 , 8 8 1 ( 1 7 2 a , 172b), 890 L o o m e s , D.J. 122 ( 1 6 3 ) , 131, 361 ( 3 1 ) , 390 L o p e z , I. 9 1 7 ( 2 6 8 , 2 6 9 ) , 9 1 8 ( 2 6 9 ) , 9 2 5 Lorquet, J.C. 4 0 7 , 4 4 8 ( 9 3 ) , 4 4 9 ( 9 3 , 2 4 6 ) ,

451,454, 460 (10), 524

Lunsford, J.H. 8 1 2 ( l e , 10, 8 1 3 ( 1 0 , 8 1 5 , 8 2 2 ( l e - k ) , 885, 886 Luo, Y.-R. 2 5 9 (69), Lur'c, M . A . 8 1 6 , 8 7 3 ( 2 4 ) , 886 Luria, M . 2 3 8 ( 5 1 ) , 2 3 9 ( 5 2 ) , 2 6 7 ( 8 2 ) , 286,

287

287 Lurie, M . A . 8 6 0 ( 1 8 7 ) , 891 L u s z t y k , J. 9 6 6 , 9 7 1 ( 2 1 ) , 9 7 2 ( 7 1 ) , 9 7 8 ( 8 9 ) ,

994, 995

Luthjens, L . H . 6 8 7 ( 4 0 a ) , 736, 7 6 2 ( 2 3 , 2 4 ) , 763 (24, 29c), 779 Luttke, W . 1 0 3 , 114 ( 6 2 ) , 7 2 9 , 381 ( 1 8 2 ) , 3 8 2 (190), 3 8 4 (198, 199), 385 (190, 199), i 9 i , 513, 514 (172), 5 2 9 L u y t e n , M. 5 9 6 ( 2 0 8 b ) , 6 0 7 , 9 3 3 ( 5 1 ) , 9 4 0 (89, 91), Lyeria, J.R. 3 8 8 ( 2 2 6 ) , 393 L y n c h , J.M. 8 2 6 , 8 2 7 ( 7 7 ) , 888 L y n c h , V . M . 5 7 2 ( 1 0 5 ) , 603, 7 1 1 ( 1 0 6 a ) , 740,

959, 960

994

9 6 4 (9), L y u b i m o v a , A . L . 5 3 2 ( 1 ) , 548,

892

867 (216),

Lossing, p.p. 3 9 6 (1), 397 (4), 4 1 0 (117), 4 2 2 ( 1 5 2 ) , 449, 450, 452 L o u x , J.-P. 3 8 2 , 3 8 3 ( 1 9 2 ) , 393 L o v e l o c k , J.E. 9 0 8 , 9 0 9 ( 1 7 9 ) , 923 L o w , J.J. 6 5 6 , 6 5 7 ( 8 a ) , 6 7 7 L o w e , J.P. 9 8 , 113 ( 1 3 ) , 128 L o w r y , B.R. 5 7 8 ( 1 3 3 a ) , 604 L o w r y , T . M . 137 ( 1 1 ) , 181 Lu, D . H . 8 8 5 ( 2 7 5 ) , 893 Lu, T.T. 9 7 2 ( 7 4 ) , 9 9 5 Lu, X . 6 7 0 ( 6 5 ) , 6 7 9 L u c a s , J. 5 3 2 , 5 3 8 , 5 3 9 ( 2 0 ) , 548, 6 1 3 ( 1 8 a ) ,

649

L u c y k , A.I. 8 8 2 ( 2 7 0 ) , 893 Ludwig, W. 637 (93), 657 Lueder, U . 4 7 7 ( 7 6 ) , 5 2 6 Luef, W . 9 2 8 ( 8 , 9 ) , 9 3 3 ( 8 , 9, 5 0 ) , 9 4 4 , 9 4 5 (9, 50), Luftmann, H. 7 9 7 ( 5 6 ) , 807 Luh, T . - Y . 5 5 7 ( 2 0 ) , 5 6 7 ( 7 3 ) , Luisi, P.L. 142 ( 3 9 , 4 3 ) , 143 ( 3 9 ) , 157 ( 9 8 ) ,

958, 959

601, 602

182, 183

M a , P. 8 5 - 8 7 ( 4 0 ) , 94 M a c a u l a y , R. 3 5 2 ( 5 ) , 389 M a c c i a n t e l l i , D . 9 8 , 111 ( 9 ) , 128, 2 2 3 ( 1 1 ) , 285, 371 ( 1 0 4 ) , 391 M a c c o l l , A . 3 9 6 ( 1 1 ) , 3 9 8 ( 1 1 , 14), 4 1 0 ( 1 1 0 , 117), 4 2 5 ( 1 4 ) , 4 4 2 ( 1 1 ) , M a c C o r q u o d a l e , F. 9 7 7 , 9 8 2 , 9 8 3 ( 8 3 ) , 9 9 5 M a c D o n a l d , L. 9 0 6 ( 1 3 5 ) , 9 2 2 M a c d o n a l d , M . A . 4 0 4 ( 4 3 ) , 450 M a c D o u g a l l , P.J. 17 ( 2 0 ) , 2 6 , 31 ( 2 4 ) , 3 5 ( 2 9 , 32, 33), 36 (29), 4 0 (33), 54, 70, 74 (20), 77 M a c e y , M.J.K. 9 0 4 ( 7 5 , 7 6 ) , 9 2 7 M a c h i n e k , R. 3 8 4 ( 1 9 8 , 199), 3 8 5 ( 1 9 9 ) , 393 M a c h o c k i , A . 8 1 2 , 8 1 5 , 8 2 2 ( l b ) , 885 M a c i a r e l l o , M.J. 9 0 3 ( 7 0 ) , 9 2 7 M a c i e l , G.E. 3 5 2 ( 9 ) , 389 M a c K a y , C. 821 ( 4 8 a , 4 9 a ) , 887 M a c k a y , G.I. 5 3 2 ( 1 3 ) , 5 3 7 , 5 3 8 ( 5 5 ) , 548,

450, 452

549

L u k a s , J. 4 3 0 ( 1 8 2 ) , 453, 6 1 0 (4a, 4 b ) , 6 1 1 , 6 1 8 , 6 2 3 (7), L u k e , M . O . 8 2 3 ( 5 4 , 5 5 , 5 6 a , 5 6 b ) , 887 L u k o v n i k o v , A . F . 8 5 9 , 8 8 4 ( 1 8 5 e ) , 891 L u m b , J.T. 5 4 0 ( 8 3 ) , 549, 7 1 2 , 7 1 3 ( 1 1 5 a ) ,

649

740 L u n a z z i , L. 9 8 , 111 ( 9 ) , 128, 2 2 3 ( 1 1 ) , 3 7 1 ( 1 0 4 ) , 391 L u n d a n e s , E. 3 2 0 ( 5 7 a ) , 347 Lundin, A.G. 369 (95), i 9 7

Ma, D. 6 7 0 (65), 6 7 9

285,

Mackay, M. 9 8 0 (98), 9 9 6 Mackay, M.D. 978 (86, 87), 995 Mackenzie, A.S. 332 (91), 336 (91, 99), 338,

348

339 (99), M a c k e n z i e Peers, A . 4 0 5 ( 5 0 ) , M a c k o r , A . 7 0 5 ( 8 3 a ) , 739 M a c L e a n , C. 371 ( 9 8 ) , 391 M a c P h e e , J.A. 2 0 2 ( 3 5 ) , 213 M a g e e , J.L. 7 6 3 ( 3 0 b ) , 7 7 9 Maggini, M. 5 8 3 (167a), 6 0 5

450

A u t h o r index M a g n u s , P . D . 9 4 6 ( 1 0 4 ) , 961 Maguire, J.A. 6 6 6 , 6 6 7 ( 6 1 b ) , 678 Mah, R.A. 897 (11), M a h d i , W . 9 2 8 ( 1 2 ) , 959 M a h m u d , F. 8 9 7 ( 1 5 ) , 9 7 9 M a i a , E.R. 3 5 6 ( 2 3 ) , 389 M a i c u m , D . 6 8 3 , 6 8 4 ( 2 5 ) , 736

M a n n , G. 9 7 ( 6 ) , 110 ( 6 , 9 9 , 1 0 0 ) , 1 2 0 , 121 ( 1 3 5 , 145, 1 4 6 ) , 3 2 ) , 3 7 4 ( 1 2 4 ) , 390, 391 M a n n , R . S . 5 5 6 ( 1 2 ) , 600 M a n n i n g , J.P. 8 9 ( 4 9 ) , 94 Mansfield, K. 9 5 7 ( 1 4 4 ) , 9 5 8 ( 1 4 7 ) , 9 6 2

128, 130, 131, 3 6 1

919

Maier, G. 116 ( 1 1 4 ) , 130, 3 6 4 ( 5 6 ) , 3 8 4 , 3 8 5 ( 1 9 9 ) , 390, 393, 5 1 6 ( 1 7 7 ) , 5 2 9 , 5 9 5 ( 2 0 6 b , 2 0 6 c ) , 607, 6 8 2 ( 5 ) , 735 Maier, J.P. 4 0 7 , 4 0 8 ( 9 4 ) , 451, 4 7 1 ( 2 2 ) , 4 7 5 - ^ 7 9 , 507 (29), 5 2 5 Maier, W . F . 7 9 ( 7 ) , 93, 5 8 2 ( 1 5 6 ) , 5 9 2 ( 1 9 7 ) , 605, 606, 6 2 0 ( 4 5 c ) , 650, 6 7 3 ( 8 0 ) , 6 7 9 , 691 (55r), 6 9 2 , 6 9 4 (55r, 5 9 c ) , 737, 738

Maire, G. 6 8 3 ( 2 3 , 2 4 b , 2 4 c ) , 6 8 4 ( 2 3 , 2 4 b , 24c, 28, 29), 685 (24b, 24c, 28, 32), 686 (28),

736

M a i t h s , P.M. 6 5 7 ( 2 1 ) , 6 7 7 Majerski, Z. 3 6 8 ( 5 7 ) , 3 7 9 ( 1 6 0 ) , 390, 392, 4 7 9 ( 1 2 8 ) , 528, 5 8 5 ( 1 6 8 ) , 5 9 3 , 5 9 4 (202f, 2 0 2 h ) , 605, 607, 6 9 1 ( 5 3 a , 5 5 h ) , 6 9 2 , 6 9 5 ( 5 5 h ) , 737, 8 1 6 ( 2 6 ) , 8 1 8 ( 2 7 , 28), 819 (29, 30), 934 (69), 949, 9 5 0 ( 1 1 4 ) , 9 5 2 ( 6 9 , 1 2 2 - 1 2 4 ) , 960,

886,

961

604

602,

M a l i n o v i c h , Y . 3 9 9 ( 1 9 ) , 450 M a l i n s k i , E. 9 0 0 ( 3 2 ) , 9 0 5 ( 1 0 9 ) , 9 0 6 ( 1 1 9 ) ,

920-922

Mallard, G . W . 5 3 7 , 5 3 8 , 5 4 3 , 5 4 6 ( 5 6 ) , 549 Mallard, W . G . 3 0 2 ( 2 1 ) , 346, 3 9 6 , 3 9 7 , 4 0 2 , 4 0 8 , 4 3 3 (3), Mallory, T . B . 123 ( 1 8 2 ) , 132 M a l m q v i s t , P.-A. 4 7 4 , 4 8 7 , 4 9 3 , 4 9 9 ( 2 7 ) , 525 M a l o n , P. 140 ( 2 5 ) , 182 M a l o n e , J.F. 5 9 7 , 5 9 8 ( 2 1 0 e ) , 607 M a l o n e y , V . M . 7 0 7 ( 8 9 ) , 739 M a l s c h , K . D . 3 7 6 ( 1 4 4 ) , 3 8 4 , 3 8 5 ( 1 9 9 ) , 392,

449

i 9 J , 478, 516, 517 (106), 5 2 7 Malthur, H . S . 3 2 9 ( 8 0 ) , 348 M a n d e l k e m , L. 7 7 7 ( 6 6 ) , 780 M a n d e l l i , E.F. 9 0 0 ( 3 6 ) , 920 M a n d i c h , M . L . 541 ( 1 0 6 ) , 550 Mangiaracina, P. 5 6 4 ( 5 9 ) , 602 M a n g i n i , M . E . 8 5 8 ( 1 7 7 ) , 890 M a n i , J. 9 4 0 ( 9 3 ) , 967 Mann, B.E. 374 (125), i 9 7 M a n n , C.K. 7 8 2 ( 1 8 a ) , 806 M a n n , D . E . 109 ( 8 5 ) , 130

Mansfield, K.T. 5 9 5 , 5 9 6 ( 2 0 4 a ) , M a n s l a m a n i , D . 5 7 1 ( 9 5 ) , 603

607

M a n s u y , D . 7 8 2 ( 1 6 ) , 8 0 4 ( 7 5 ) , 806, M a n t i c a , E. 123 ( 1 7 9 ) , 132 Manukov, E.N. 477 (81), 5 2 6

808

M a n u s , M . M . 3 8 0 ( 1 8 0 ) , 392 M a p l e , J.R. 8 0 ( 1 8 ) , 93 M a q u e s t i a u , A . 4 3 5 ( 2 0 7 ) , 454 M a q u i n , F. 4 0 6 ( 6 0 ) , 451 Mar, A . 3 6 9 ( 7 9 ) ,

390

Maillard, B . 9 8 2 ( 1 0 4 ) , 9 9 6 Mailman, R.B. 918 (280), 925 M a i l m a n , R.P. 9 1 8 ( 2 8 6 ) , 9 2 5

M a k a b e , M . 871 ( 2 2 9 ) , 892 M a k a r o v , E.I. 8 1 5 , 8 2 2 ( I q ) , 886 M a l e k , F. 5 6 5 ( 6 3 a , 6 3 b ) , 5 8 0 ( 1 3 7 ) ,

1033

Maraioli, A.J. 3 0 8 , 3 1 4 ( 3 9 ) , 347 M a r a z a n o , C. 8 2 0 ( 4 0 ) , 887 Marcelli, M . 6 3 3 , 6 3 5 ( 7 9 ) , 6 5 7 March, J. 5 2 ( 4 8 ) , 7 7 , 5 5 5 ( 1 0 ) , 5 7 8 ( 1 2 8 b ) ,

600, 604

Marchand, A . P . 7 9 ( 4 ) , 8 8 ( 4 7 ) , 93, 94, 3 8 0 ( 1 7 5 ) , 392, 5 9 6 ( 2 0 8 a ) , 607, 6 8 2 ( 6 ) , 7 1 1 ( 6 , 105a), 7 2 2 ( 6 ) , 735, 740 Marchand, N . W . 3 8 0 ( 1 7 5 ) , 392 Maret, A . 9 1 9 ( 3 0 3 ) , 9 2 6 Margaretha, P. 5 9 0 ( 1 9 3 b ) , 606 Margitfalvi, J.L. 6 8 5 , 6 8 6 ( 3 3 ) , 736 M a r g o l i s , J. 9 1 9 ( 3 0 2 ) , 9 2 6 Margrave, J.L. 122 ( 1 6 9 ) , 132 Mark, J.E. 3 7 3 ( 1 0 6 ) , i 9 7 Marker, R.E. 142 ( 4 4 ) , 1 4 3 , 144 ( 5 4 ) , 182 Markin, M.I. 4 0 7 ( 8 6 ) , 4 5 7 Marks, T.J. 6 7 2 ( 7 5 ) , 6 7 9 Markwell, R.E. 6 4 3 (104), 6 5 2 Marlett, E . M . 2 9 4 ( 4 ) , 346 M a r m e t , P. 4 0 1 ( 3 8 ) , 450 M a r o n , F . W . 2 2 8 ( 2 6 ) , 286 M a r o n c e l l i , M . 8 2 4 ( 5 9 ) , 887 Marquard, C. 8 0 ( 1 6 ) , 93 Marshall, A . G . 5 3 7 , 5 3 8 ( 5 8 ) , 549 Marshall, J.A. 5 6 2 ( 5 3 c ) , 602 Marshall, J.L. 3 8 0 ( 1 7 5 ) , 3 8 4 ( 1 9 6 ) , 3 8 5 ( 2 1 0 , 2 1 4 ) , 3 8 7 ( 1 9 6 ) , 392, 393 Marshall, R . M . 2 5 9 ( 6 3 ) , 287 Marshall, S.J. 6 9 1 , 6 9 2 , 6 9 5 ( 5 5 i ) , 737 Martin, A.J.P. 3 2 2 ( 6 7 ) , 348 Martin, E . L . 5 7 4 ( l l O d ) , 603 Martin, H . - D . 5 0 7 ( 1 5 3 ) , 5 1 9 ( 1 7 8 ) , 528,

529,

6 8 2 , 691 ( 7 ) , 7 1 1 ( 7 , 106a), 7 1 2 , 7 1 9 ( 1 2 3 ) , 735, 740, 741 Martin, H . D . 4 7 7 ( 6 0 ) , 4 7 8 ( 6 0 , 8 8 , 9 3 ) , 4 7 9 (93, 1 0 8 - 1 1 1 , 119), 5 2 6 , 5 2 7 Martin, J.C. 9 9 1 ( 1 4 4 ) , 9 9 7 Martin, J.F. 2 7 9 ( 9 0 ) , 287 Martin, J.T. 9 0 4 ( 8 3 ) , 9 2 7 Martin, M.I. 4 0 7 ( 8 7 ) , 4 5 7

(29,

A u t h o r index

1034

Martin, R . O . 9 1 3 ( 2 0 8 ) , 923 Martins, F.J.C. 5 7 4 , 5 7 5 ( 1 1 3 i ) , 604 M a r u y a m a , K. 7 0 5 ( 8 3 f ) , 739 M a r x , D . E . 6 6 1 ( 4 0 ) , 678 M a r x , J.N. ( 1 3 5 ) , 184 Maryanoff, B . E . 5 7 1 ( 9 5 ) , 5 7 5 ( 1 1 5 ) ,

604

603,

Maryanoff, C . A . 5 7 1 ( 9 5 ) , 603 M a r z i o , A . di 4 3 0 ( 1 8 1 ) , 453 M a s a m u n e , S. 8 5 - 8 7 ( 4 0 ) , 94, 5 4 0 ( 8 6 ) , 549 M a s a n e t , J. 6 9 0 ( 5 1 b ) , 737 M a s c a r e l l a , S . W . 5 7 1 ( 9 9 ) , 603 M a s o n , J. 3 5 2 , 3 5 5 ( 1 1 ) , 389 M a s o n , R. 5 4 0 ( 7 8 ) , 549 M a s o n , S.F. 152 ( 8 1 , 8 9 ) , 163, 164 ( 1 1 2 ) , 183,

184

M a s s o u d i , M . 9 6 9 , 9 7 9 ( 5 7 ) , 995 M a s t e r s , C. 5 5 5 - 5 5 7 ( l i e ) , 600 M a s t r y u k o v , V . S . 125 ( 1 9 3 ) , 127 ( 1 9 3 , 2 0 6 , 2 1 0 ) , 132, 133, 3 7 9 ( 1 7 2 ) , 3 8 0 , 3 8 2 ( 1 7 9 ) , 392 M a t a g a , N . 6 8 7 ( 3 9 d ) , 736 M a t e e s c u , G . D . 4 7 8 ( 9 7 , 102), 5 2 7 Matheson, M.S. 762 (27), 779 M a t h i a s , A . 4 0 0 ( 2 9 ) , 450 M a t h i e u , D . 6 1 7 ( 3 3 ) , 650 Matsubara, Y . 801 ( 6 8 ) , 8 0 2 ( 7 0 ) , 807 M a t s u d a , K. 4 0 7 ( 9 0 , 9 1 ) , 451 M a t s u d a , T. 6 8 6 ( 3 5 ) , 736 M a t s u m o t o , T. 103, 112, 114, 116, 117 ( 6 3 ) , 7 2 9 , 5 9 7 , 5 9 8 ( 2 1 0 b ) , 607,

737

691 ( 5 3 h ) ,

M a t s u m u r a , Y . 791 ( 4 2 ) , 7 9 9 ( 6 3 ) , 8 0 0 ( 6 4 ) ,

807

M a y s , R. 321 ( 6 1 ) , 348 M a z a n e c , T.I. 8 0 5 ( 8 7 , 9 2 ) , 808 M a z i e r e , M . 8 2 0 ( 4 0 ) , 887 M a z l i a k , P. 9 0 0 ( 4 3 ) , 9 0 1 ( 4 7 ) , 9 0 4 ( 4 3 ) , 920 Mazur, R.H. 9 8 4 ( 1 1 2 , 1 1 3 ) , 9 9 6 Mazur, Y. 7 8 2 ( 1 5 c ) , 806 M c A d o o , D.J. 4 4 4 ( 2 2 8 ) , 454 M c A f f e e , A . M . 5 3 8 ( 6 1 ) , 549 M c A s k i l l , N . A . 9 6 9 ( 3 3 ) , 994 McBain, D.S. 991 (146), 9 9 7 M c B r i d e , B.J. 231 ( 2 7 ) , 286 M c C a f f r e y , J.G. 6 7 4 ( 8 8 ) , 6 7 9 M c C a r t h y , E . D . 8 9 8 ( 2 3 ) , 9 0 7 ( 1 6 5 ) , 920,

923

M c C a r t h y , K.E. 5 8 6 ( 1 7 4 a , 1 7 5 b ) , 605 M c C a r t h y , R . D . 8 5 4 ( 1 5 3 ) , 890 McClelland, R.E. 895 (2), 9 7 9 M c C l u s k y , J.V. 7 2 4 , 7 2 8 ( 1 3 4 ) , 741 M c C o m b i e , S.W. 5 6 5 , 5 6 6 ( 6 4 ) , 602 M c C o r m i c k , A . 3 2 1 , 3 2 3 ( 6 4 ) , 348 M c C r e a , J.M. 8 5 8 , 881 ( 1 6 9 ) , 890 McDaniel, C.A. 9 0 6 (139), 922 McDonald, G.A. 917 (267), 925 M c D o n a l d , R . A . 2 2 8 ( 2 3 ) , 2 5 9 ( 6 0 ) , 285, 287 M c E w e n , A . B . 5 9 2 ( 1 9 7 ) , 606, 6 2 0 ( 4 5 c ) , 650 M c E w e n , C N . 4 3 3 ( 1 9 1 - 1 9 5 ) , 453 M c F a d d e n , W . H . 4 1 1 ( 1 2 0 ) , 4 4 4 ( 2 2 7 ) , 452,

454

McFarland, C W . 4 7 8 (102), 5 2 7 M c G h e e , W . D . 6 6 2 ( 4 6 ) , 678 M c G h i e , J.F. 5 6 4 ( 5 8 a , 5 8 b ) , 602 M c G l y n n , S.P. 4 7 9 ( 1 2 1 ) , 5 2 7 McGrath, D.V. 6 6 4 , 6 6 6 , 6 6 7 , 6 6 9 (59), 6 7 0 (59, 66), M c G r a t h , M . P . 8 5 , 8 7 ( 4 1 ) , 94, 6 5 8 ( 2 2 ) , 677 M c G u i n n e s s , J.A. 9 9 0 ( 1 3 9 ) , 9 9 7 M c l n e m e y , E.J. 8 0 4 ( 7 8 ) , 808 M c l n n e s , A . G . 9 1 4 ( 2 2 4 ) , 924 M c l v e r , R.T. 5 4 3 ( 1 4 0 ) , 5 4 4 ( 1 4 6 ) , 550, 551 M c K e a n , D . C . 8 9 , 9 0 ( 5 5 ) , 94 M c K e e , M . L . 4 6 0 , 5 0 7 ( 1 1 ) , 524 M c K e e v e r , L . D . 5 4 2 ( 1 2 4 ) , 550

678, 679

M a t s u n a g a , M. 9 8 3 ( 1 0 5 ) , 9 9 6 Matsura, K. 4 2 5 ( 1 6 7 ) , 453 Matsuura, T. 6 8 2 ( 1 3 ) , 735 Mattay, J. 6 8 2 , 7 0 5 ( 1 7 c ) , 736 M a t t h e w s , C . S . 2 3 5 ( 4 2 ) , 2 3 7 ( 4 9 ) , 286 M a t t h e w s , D . E . 341 ( 1 1 0 ) , 349 M a t t h e w s , R . S . 361 ( 4 3 ) , 390 M a t t i c e , W . L . 128 ( 2 1 1 ) , 133 Matturro, M . G . 5 5 8 ( 2 8 a ) , 5 6 2 ( 5 3 b ) , 601, 602 , 7 1 1 , 7 3 3 ( 1 0 4 ) , 740 M a t u s c h , R. 3 6 4 ( 5 6 ) , 390, 5 9 5 ( 2 0 6 b ) , 6617 M a u n d e r , C M . 109 M a u r i c e , D . 8 8 5 ( 2 7 5 ) , 893 M a x w e l l , J.R. 2 9 4 , 2 9 5 ( 1 0 ) , 346, 8 9 6 ( 8 ) , 8 9 8

{93),. 130

( 2 1 ) , 9 0 0 ( 3 7 ) , 9 0 8 ( 1 8 3 ) , 9 0 9 ( 1 8 5 , 186),

919, 920, 923

Mayer, B. 4 7 9 (109), 507 (153), 5 2 7 . M a y e r , G. 4 7 8 , 5 1 6 , 5 1 7 ( 1 0 6 ) , 5 2 7 M a y n a r d , K.J. 6 8 6 ( 3 4 a ) , 736 M a y n e , C L . 3 8 8 ( 2 2 8 ) , 393 M a y n e s , G.G. 9 6 4 , 9 8 3 ( 5 ) , 994 M a y o , F.R. 9 9 3 ( 1 6 4 ) , 9 9 7 M a y o , P.de 7 1 1 ( 1 1 4 b ) , 740

528

M c K e n n a , E.J. 8 5 3 ( 1 4 3 ) , 889, 9 1 5 ( 2 3 4 ) , 924 M c K e r v e y , M . A . 116 ( 1 1 5 ) , 130, 3 6 8 ( 6 9 ) , 390, 5 9 7 ( 2 1 0 e , 2 1 1 , 2 1 2 ) , 5 9 8 ( 2 1 0 e ) ,

607,

737

691 ( 5 3 b , 5 3 c , 5 3 g ) , M c K i l l o p , A . 5 7 8 ( 1 2 9 c ) , 5 8 5 ( 1 6 9 c ) , 604, 605 M c K i n l e y , A.J. 7 1 1 ( 1 0 6 a ) , 740 M c K i n n e y , C R . 8 5 8 , 881 ( 1 6 9 ) , 890 McLafferty, F . W . 3 3 2 ( 9 0 ) , 348, 4 1 2 ( 1 2 5 ) , 4 2 4 ( 1 5 9 , 163), 4 3 4 , 4 4 4 ( 1 6 3 ) , 4 4 7 (238), McLafferty, W.J. 123 ( 1 8 2 ) , 132 M c L e a n , A . D . 5 3 2 , 5 3 7 , 5 3 8 , 5 4 7 ( 3 3 ) , 548 M c L u c k e y , S . A . 4 0 5 ( 5 9 ) , 451 M c M a h o n , R . E . 8 1 6 ( 2 2 ) , 886

452^54

A u t h o r index M c M a h o n , T . B . 5 3 7 , 5 3 8 ( 5 7 ) , 549 M c M a n u s , T.R. 3 1 9 ( 5 2 ) , 347 M c M a s t e r , A . D . 5 4 1 ( 9 3 ) , 549, 6 6 2 ( 4 8 ) , 678 M c M e e k i n g , J. 5 6 2 ( 4 6 b , 4 6 c ) , 601 M c M i l l e n , D . F . 2 5 9 , 2 6 2 ( 6 5 ) , 284, 287, 9 6 4 (2), 994 M c M u n y , J.E. 5 3 9 ( 7 3 , 7 4 ) , 549 M c M u n - y , T . B . H . 9 0 2 ( 6 3 ) , 920 M c N a i r , H . M . 3 2 9 ( 7 8 ) , 348 M c N e e n e y , S.P. 7 0 5 ( 8 2 ) , 739 M c O s k e r , C C . 5 6 9 ( 8 3 a , 8 3 b ) , 602, 603 M c W e e n y , D.J. 8 5 5 ( 1 5 9 ) , 890 M c W e n , A . B . 7 9 ( 7 ) , 93 M e a d , P.T. 4 1 4 ( 1 3 0 ) , 452 M e c k e , R. 1 2 2 ( 1 6 6 ) , 132 M e d r a n o , J.A. 9 3 3 ( 5 8 ) , 960 M e d v e d o v , F . A . 9 0 6 ( 1 4 1 ) , 922 M e e h a n , G . V . 6 9 1 , 6 9 2 , 6 9 5 ( 5 5 i ) , 737 M e e r w a l l , E . V . 3 8 9 ( 2 3 0 ) , 393 M e e s s c h a e r t , B . 8 2 6 ( 7 6 ) , 888 M e g e n , H. v o n 3 8 4 - 3 8 6 ( 2 0 7 ) , 393 Mehta, G. 5 7 0 ( 8 8 b , 8 8 c ) , 5 8 2 ( 1 5 2 ) , 603,

605 M e i , E. 8 8 1 , 8 8 2 ( 2 6 2 ) , 893 M e i b o o m , S. 3 6 1 , 3 8 1 , 3 8 2 , 3 8 4 ( 3 7 ) , 390 M e i c , Z. 3 6 8 ( 5 7 ) , 390 Meijer, G. 8 4 ( 3 3 ) , 93 Meijer, W . E . 9 1 6 ( 2 4 5 ) , 924 Meijere, A . d e 3 6 8 ( 6 2 , 6 3 ) , 390, 411 ( 7 4 , 7 6 , 7 7 ) , 4 7 8 ( 7 4 , 7 7 , 101), 4 7 9 ( 7 4 , 1 1 3 , 115, 1 2 7 ) , 4 8 0 ( 1 1 5 , 1 2 9 ) , 5 0 7 ( 1 5 7 ) ,

5 1 4 ( 1 1 5 , 174), 526-529, 5 6 0 , 5 6 1 (44d), 5 9 3 ( 2 0 1 d , 2 0 3 d ) , 5 9 5 ( 2 0 3 d ) , 601, 607, 7 1 2 , 7 2 0 , 7 2 2 ( 1 2 6 ) , 74J M e i n s c h e i n , W . G . 3 2 1 ( 5 8 ) , 347, 8 5 9 ( 1 8 4 ) , 89J, 8 9 7 ( 1 6 ) , 8 9 9 ( 1 6 , 2 6 ) , 9 0 8 ( 1 6 , 175, 176), 9J9, 920, 923 Meintzer, C P . 9 7 2 (74), 9 8 8 ( 1 2 5 , 126), 991 ( 1 4 7 - 1 4 9 ) , 995-997 M e i n w a l d , J. 9 0 6 ( 1 2 3 ) , 9 2 2 , 9 8 3 ( 1 0 8 ) , 996 M e i s e l s , G . G . 4 7 7 ( 5 9 ) , 526, 7 5 2 , 7 5 4 ( 1 3 ) ,

778 M e i s t e r s , A . 5 7 7 ( 1 2 6 ) , 604 Melhotra, A . K . 6 4 3 - 6 4 5 ( 1 0 7 a ) , 652 M e l l e a , M . F . 6 6 1 , 6 6 4 ( 3 7 b ) , 678 M e l l o r , J . M . 4 7 7 , 4 7 8 , 4 8 0 ( 7 9 ) , 526, 7 8 2 ( 1 1 ) , 7 9 2 ( 4 8 - 5 0 ) , 7 9 3 ( 4 8 , 5 0 ) , 7 9 4 ( 4 9 ) , 806,

807 M e l t o n , C E . 4 0 5 ( 5 1 ) , 450 M e n c h e n , S . M . 5 6 8 , 5 7 7 ( 7 8 ) , 602 M e n d e l h a l l , G . D . I l l , 1 1 2 , 1 1 6 ( 1 0 4 ) , 130 M e n g e r , F . M . 3 8 7 ( 2 2 0 ) , 393 M e n i c a g l i , R. 1 4 2 ( 4 2 ) , 182 M e n z i n g e r , M . 8 3 9 ( 1 0 9 ) , 889 Meot-Ner, M. 4 0 7 , 4 1 7 (95), 4 2 5 (173), 4 3 5

( 2 0 8 ) , 451,453, 454 M e r e s i , G . H . 3 6 9 ( 8 9 ) , 391

1035

Mergard, H. 6 7 2 ( 7 7 ) , 679 Merk, W . 6 9 2 ( 6 2 b ) , 738 Merrifield, D . L . 1 2 2 ( 1 6 1 ) , / J 7 M e s s e r , L . A . 7 8 2 ( 1 5 b ) , 806, 9 1 5 ( 2 3 0 ) , 924 M e s s m e r , R . F . 9 3 3 ( 6 2 ) , 960 M e s z a r o s , L. 5 8 3 ( 1 6 4 ) , 605 Metcalfe, N . B . 9 0 5 (104), 927 M e t e i k o , B . 3 7 9 ( 1 6 0 ) , 392 M e t z g e r , H. 9 1 9 ( 2 9 5 ) , 925 M e t z g e r , P. 3 6 1 ( 4 4 ) , 390 M e w , P . K . T . 9 3 6 ( 7 8 ) , 960 M e y e r , F . M . 128 ( 2 2 0 ) , 133 Meyer, L.U. 4 7 8 (101), 5 2 7 M e y e r , M . D . 7 8 2 ( 1 5 b ) , 806 M e y e r , T. 3 3 9 ( 1 0 3 ) , 349 Meyer, V. 9 4 0 (93), 967 M e y e r , W . 4 8 7 , 4 8 9 ( 1 3 4 ) , 528 M e y e r s , E . A . 2 0 2 ( 3 4 ) , 213 M e y e r s , L. 9 6 6 ( 1 7 ) , 994 M e y e r s o n , S. 3 0 6 ( 2 8 ) , 347, 4 0 0 ( 3 0 ) , 4 2 5 , 4 2 6 ( 1 6 9 ) , 4 3 2 ( 1 9 0 ) , 4 4 9 ( 2 4 7 ) , 450,

453, 454 Meyrant, P. 4 3 5 ( 2 0 7 ) , 454 M i c h e l s e n , K. 4 8 0 ( 1 2 9 ) , 528 M i c h l , E . 7 0 8 , 7 1 2 ( 9 6 e ) , 739 M i c h l , J. 3 7 6 ( 1 4 4 ) , 392, 5 7 2 ( 1 0 5 ) , 5 8 3 , 5 8 4 ( 1 6 5 b , 1 6 5 d ) , 5 9 3 , 5 9 4 ( 2 0 2 c ) , 603, 605, 607, 7 0 7 ( 8 9 ) , 7 1 1 ( 1 0 6 a ) , 739, 740, 9 3 3 , 9 5 2 ( 6 4 , 6 5 ) , 9 5 6 ( 1 3 9 ) , 960, 962, 9 6 4 (8, 9 ) , 994 Midland, M . M . 158, 159, 163, 166, 169, 170, 173, 177 ( 9 9 ) , 183 M i g d a l , A . 8 3 0 , 8 4 7 ( 8 3 ) , 888 Migita, T. 5 6 5 ( 6 2 a , 6 2 b ) , 602 Mihelcic, J.M. 6 6 0 (37a), 661 (37b), 6 6 4 (37a, 3 7 b ) , 678 Mijlhoff, F . C 1 1 9 ( 1 2 7 ) , 131 M i k h a i l , G. 5 9 0 ( 1 9 3 a ) , 606 Mikkelsen, J.D. 9 1 6 (275), 9 2 5 M i k k i l i n e n i , R. 9 8 , 9 9 ( 1 9 ) , 7 2 8 M i k n i s , F.P. 3 7 7 ( 1 4 8 ) , 392 M i l e w s k i , C . A . 5 7 5 ( 1 1 5 ) , 604 M i l h a u d , J. 4 0 5 ( 5 0 ) , 450 M i l l , S . G . 8 0 5 ( 8 8 ) , 808 Millar, M . 9 2 8 ( 1 2 ) , 9 5 9 Millard, B.J. 3 0 6 ( 2 7 ) , 3 3 0 ( 8 8 ) , 347, 348 Miller, B . 9 8 8 ( 1 2 8 ) , 9 9 6 Miller, D . E . 3 8 5 ( 2 1 4 ) , 393 Miller, D.J. 8 9 6 ( 9 ) , 919 Miller, J.R. 7 6 2 ( 2 7 ) , 7 7 9 Miller, J.S. 5 4 4 ( 1 4 6 ) , 5 5 7 Miller, L . L . 7 9 2 ( 4 6 , 4 7 ) , 7 9 5 ( 5 4 , 5 5 ) , 7 9 8 ( 5 9 ) , 7 9 9 ( 6 2 ) , 807 Miller, M . A . 123 ( 1 8 7 a ) , 132 Miller, R . W . 9 0 6 ( 1 3 1 ) , 922 Millership, J.S. 2 0 8 ( 5 8 ) , 2 7 i M i l l s , J . A . 136 ( 2 ) , 151 ( 7 8 ) , 181, 183

1036

A u t h o r index

M i l n e , C B . 9 0 9 ( 1 8 6 ) , 923 M i l n e , G . W . A . 4 1 8 , 4 4 2 , 4 4 6 ( 1 4 5 ) , 452, ( 4 9 b ) , 887

822

Mil'vitskaya, E.M. 379 (172), 380, 382 (179),

392 Minachev, K.M. 6 8 2 , 683 (9b), M i n i c h i n o , C. 2 5 9 ( 7 5 ) , 287

735

M i n i s c i , F. 7 9 9 ( 6 0 ) , 807, 9 8 9 ( 1 3 2 ) , M i n k i n , V.I. 9 3 0 ( 3 3 ) , 959 M i n y a e v , R . M . 9 3 0 ( 3 3 ) , 959

996

Miranda, D . S . de 3 0 8 , 3 1 4 ( 3 9 ) , 347 M i r b a c h , M . F . 7 0 7 ( 9 2 a ) , 7 0 8 ( 9 2 a , 102a, 1 0 2 b ) , 7 0 9 ( 9 2 a ) , 7 1 0 ( 9 2 a , 102a, 102b),

739, 740 M i r b a c h , M.J. 7 0 7 ( 9 2 a ) , 7 0 8 ( 9 2 a , 102a, 1 0 2 b ) , 7 0 9 ( 9 2 a ) , 7 1 0 ( 9 2 a , 102a, 102b),

739, 740 Mironov, D. 907 (159), 922 Mirov, N.V. 903 (67),

920

Misbah-ul-Hasan, A. 377 (147), Mishra, A . 8 7 8 ( 2 5 9 ) , 893 Mishra, P.K. 3 6 9 ( 9 7 ) , 391

392

M i s l o w , K. 81 ( 3 0 - 3 2 ) , 93, 101 ( 4 3 ) , 103 ( 5 6 , 6 0 , 6 1 ) , 104 ( 6 0 , 6 1 , 6 5 ) , 105 ( 5 6 , 6 5 ) , 1 0 6 ( 7 3 ) , 108 ( 7 9 ) , 109 ( 6 0 , 6 5 ) , 1 1 2 , 113 ( 7 3 ) , 114 ( 5 6 , 6 0 , 6 1 ) , 115 ( 6 5 , 7 3 ) , 116 ( 6 1 , 7 9 ) , 117 ( 6 1 ) , 129, 130, 3 7 3 ( 1 1 4 ) , 3 7 4 ( 1 2 7 ) , 391 Misra, S . C 5 6 4 ( 5 8 a , 5 8 b ) , 602 M i t c h e l l , J.J. 8 1 5 ( 2 0 ) , 886 M i t c h e l l , J.M. 8 5 9 ( 1 8 4 ) , 891 M i t c h e l l , M . P . 8 5 4 ( 1 5 1 , 152a), 890 Mitchell, T.R.B. 557 (17), 597 (212),

600,

607 M i t s c h k a , R. 9 3 9 ( 8 6 ) , 960 Miura, Y . 7 8 2 ( 4 ) , 806 Miyahara, Y . 5 9 2 ( 1 9 6 a ) , 606 M i y a k e , H. 5 8 2 ( 1 5 9 a ) , 605 M i y a s a k a , H. 6 8 7 ( 3 9 d ) , 736 M i y a s h i t a , Y . 3 5 6 ( 2 4 , 2 6 ) , 389 M i y a z a k i , T. 7 6 5 ( 3 7 ) , 7 7 9 M i z u g u c h i , Y . 5 8 2 ( 1 5 5 ) , 605 M l i n a r i c - M a j e r s k i , K. 3 6 8 ( 5 7 ) , 390, ( 1 2 8 ) , 528,

740 M o r i k a w a , A . 8 0 5 ( 8 9 ) , 808 Morita, K. 5 8 6 ( 1 7 7 ) , 606 Morita, T. 5 6 3 ( 5 5 ) , 602 Moritani, I. 5 7 2 ( 1 0 4 ) , 603 M o r i y a , K. 9 1 6 ( 2 4 4 ) , 9 2 4 M o r o k u m a , K. 6 5 6 ( 8 b ) , 6 7 7 M o r o k u m a , R. 155 ( 9 2 ) , 183 M o r o z o v a , O . E . 6 9 2 , 6 9 5 ( 6 1 ) , 738 Morris, A . 4 7 6 ( 4 8 ) , 5 2 6 Morris, D . F . C . 8 1 5 ( 1 6 , 17), 886 Morris, G.E. 5 5 7 ( 2 1 ) , 601 M o r r i s o n , G . A . 9 6 ( 2 ) , 9 7 , 9 8 ( 4 ) , 9 9 ( 2 ) , 121 ( 1 5 3 ) , 122 ( 1 5 3 , 1 6 8 ) , 123 ( 1 6 8 ) ,

128,

131, 132 479

9 3 4 ( 6 9 ) , 9 5 2 ( 6 9 , 1 2 2 , 123),

960, 961 Mlynek, C 478 (105), 5 2 7 M o , Y . K . 5 3 2 , 5 3 8 , 5 3 9 ( 1 8 , 19),

M o l l a h , M . Y . A . 4 1 5 , 4 2 2 , 4 4 4 ( 1 3 4 ) , 452 M o l l e r , M . 3 7 6 ( 1 3 7 , 1 4 0 , 141), 392 M o l l e r e , P . D . 5 0 5 ( 1 5 2 ) , 528 M o l o n e y , S.J. 9 1 8 ( 2 8 8 ) , 9 2 5 M o l t o n , P . M . 9 1 5 ( 2 3 8 ) , 924 M o m a n y , F . A . 8 0 ( 1 8 ) , 8 7 ( 4 3 ) , 93, 94 M o m i g n y , J. 3 0 7 ( 2 9 ) , 347 M o n a h a n , J.E. 4 1 7 ( 1 4 1 ) , 4 5 2 M o n k h o r s t , H. 9 3 0 ( 3 3 ) , 9 5 9 M o n t e r o , S. 109, 110 ( 9 5 ) , 130 M o n t g o m e r y , L.K. 128 ( 2 1 7 ) , 133 M o o r e , B.J. 8 9 7 ( 1 3 ) , 9 7 9 M o o r e , C B . 6 6 2 ( 4 5 ) , 678 M o o r e , J.W. 8 9 5 ( 3 ) , 9 7 9 M o o r e , R . E . 85 ( 3 8 ) , 9 4 M o o r e , W . M . 7 0 5 ( 8 3 b ) , 739 M o o r e , W . R . 1 6 3 , 164 ( 1 1 0 ) , 7 5 4 M o r a l e s , E. 8 1 5 , 8 2 2 ( I g ) , 885 M o r a n , T.F. 4 0 6 ( 6 1 ) , 4 0 7 ( 8 8 ) , 4 5 7 M o r a n d i , F. 123 ( 1 7 9 ) , J32 M o r e h o u s e , S.M. 6 5 6 , 6 6 8 ( 9 ) , 6 7 7 M o r e n o , L . N . 3 6 8 ( 6 4 ) , 390 Morf, J. 9 4 9 ( 1 1 3 ) , 9 6 7 M o r g a n , R.P. 3 9 9 , 4 0 6 ( 2 5 ) , 450 M o r i , T. 9 3 5 ( 7 5 ) , 960 M o r i , Y . 5 8 7 ( 1 8 1 a ) , 606 Moriarty, R . M . 5 7 8 ( 1 3 2 ) , 604, 7 1 1 ( 1 0 8 c ) ,

548,

612,

6 1 3 (14a), 625 (53), 6 4 2 (102a, 102b),

649-651 Moddeman, W.E. 4 7 6 (36), 5 2 5 Modelli, A. 4 7 6 (48), 5 2 6 M o d z e l e s k i , V . F . 9 1 9 ( 2 9 9 ) , 926 M o e l l e r , M . 128 ( 2 2 2 ) , 133 Moffitt, W . E . 5 2 ( 4 7 ) , 7 7 , 5 0 8 ( 1 5 9 ) , 528 M o i s e e v , I.I. 8 7 1 ( 2 2 3 ) , 892 M o l d o w a n , J.M. 3 3 9 , 3 4 0 ( 1 1 8 ) , 349 M o l e , T. 5 7 7 ( 1 2 6 ) , 604

M o r r i s o n , H. 9 3 9 , 9 4 2 ( 8 5 ) , 960 M o r r i s o n , J . D . 5 5 8 ( 2 4 ) , 66>7 M o r r i s o n , R.I. 9 0 0 ( 3 0 ) , 920 M o r r i s o n , R . T . 8 2 4 ( 6 3 ) , 887 Morrissey, M.M. 557 (23b), 607 M o r s e , K . W . 7 0 5 ( 8 3 b ) , 739 M o r t e n s e n , J. 7 9 ( 7 ) , 93 M o r t o n , T.H. 4 2 4 , 4 2 5 ( 1 5 7 ) , 453 M o s c o w i t z , A . 140 ( 2 3 ) , 152 ( 8 4 ) , 182, 183 M o s e l e y , K. 6 5 7 ( 2 1 ) , 6 7 7 M o s h e r , H . S . 140 ( 2 3 ) , 143 ( 5 1 - 5 3 ) , 1 6 2 ( 5 2 , 53),

182

M o s h k i n a , R.I. 8 5 9 , 8 8 4 ( 1 8 5 f ) , M o s k a u , D . 3 7 7 ( 1 5 7 ) , 392 M o s s , R . A . 5 9 3 ( 1 9 8 a ) , 606

891

A u t h o r index M o s s , S.J. 9 6 7 , 9 7 0 , 9 9 2 ( 2 5 ) , 994 M o t e l l , E.L. 9 6 5 ( 1 4 ) , 994 Motherwell, R.S.H. 565, 566 (66e), 581 (149a, 149b), 602, 605 Motherwell, W.B. 565 (65c, 66c, 66e), 566 ( 6 6 c , 6 6 e ) , 5 7 8 ( 1 3 0 a , 130b, 135), 5 8 0 ( 1 3 0 b , 136), 5 8 1 ( 1 4 9 a , 149b), 602, 604,

605

M o u s s e r o n , M . 165 ( 1 1 8 ) , 184 M o u v i e r , G. 3 9 6 ( 2 ) , 449 M o z u m d e r , A . 7 4 5 ( 5 ) , 778 M u c c i n i , G. 5 3 2 ( 4 ) , 548 M u c c i n o , R.R. 8 1 9 ( 3 1 ) , 886 Muccio, A.D. 906 (144), 922 M u c h m o r e , D . C . 5 6 7 ( 7 0 a ) , 602 M u e d a s , C . A . 6 7 5 ( 9 0 d , 9 0 e ) , 679 M u e l l e r , E. 4 7 8 ( 8 3 ) , 526 Mueller, R . H . 5 7 6 ( 1 2 1 c ) , 604 M u h l , J. 3 7 7 ( 1 4 9 ) , 392 Muhlstadt, M . 9 7 , 110 ( 6 ) , 120, 121 ( 1 3 5 ) ,

128, 131

1037

Murray, R . W . 1 2 0 - 1 2 2 ( 1 4 4 a ) , 131 Mun-ay, W.J. 190 ( 2 5 , 2 6 ) , 2 7 2 Murrell, J.N. 4 1 4 ( 1 3 2 ) , 452, 4 5 7 ( 8 ) , 4 6 0 ( 8 , 10), 4 7 6 , 5 0 3 ( 4 2 ) , 930 (31), 959 Murthy, G . S . 5 7 2 ( 1 0 5 ) , 603, 711 ( 1 0 6 a ) , 740, 9 6 4 (9), Murthy, P . S . 3 7 6 ( 1 4 4 ) , 392 Murty, B . A . R . C . 7 9 ( 7 ) , 93, 592 ( 1 9 7 ) , 606, 6 2 0 ( 4 5 c ) , 650 Musgrave, R.G. 9 6 9 (52), 9 9 5 M u s k a t i r o v i c , M . 1 4 3 , 162 ( 5 2 ) , 182 M u s k u l u s , B . 7 1 2 , 7 1 7 ( 1 1 9 b ) , 740 M u s s o , H. 9 9 , 120 ( 3 2 ) , 129, 4 7 8 ( 8 5 ) , 4 7 9 ( 8 5 , 124), 5 1 6 , 5 1 9 ( 1 2 4 ) , 526, 527, 5 5 6 ( 1 3 g - i ) , 5 5 7 ( 1 3 h , 13i), 5 6 1 ( 4 5 a , 4 5 b ) , 563 (13g), 570 (87b), 574 (113a-c), 5 8 0 (140), 590, 591 (194e),

524, 525,

994

600, 601,603,

604, 606

M y a l l , C.J. 7 8 4 , 7 8 5 , 7 9 7 ( 2 8 , 5 8 ) ,

807

Muir, G . D . 9 1 8 ( 2 8 1 ) , 9 2 5 M u k a i , T. 6 9 0 ( 5 0 ) , 737 M u l h e i m , L.J. 9 0 8 ( 1 8 4 ) , 923 M u l l a g a l i e v , I.R. 6 7 0 ( 6 4 a ) , 678 Muller, A . 3 1 4 ( 4 1 ) , 347 Muller, H.R. 5 5 8 ( 2 7 ) , 601 Muller, L. 85 ( 3 7 ) , 94, 9 0 7 ( 1 5 0 ) , 9 2 2 Muller, M . 6 1 8 ( 3 7 ) , 6 3 0 ( 5 8 , 6 1 ) , 6 3 1 ( 6 1 ) ,

650, 651 Muller, N . 5 1 , 6 3 ( 4 5 ) , 77, 3 1 6 ( 4 7 ) , 347, 3 8 0 ( 1 8 1 ) , 393 Muller, R. 6 9 1 ( 5 3 i , 5 3 j ) , 737 Muller, W . 5 0 3 ( 1 4 8 ) , 528, 7 8 2 ( 1 5 a ) , 806 Muller-Markgraf, W . 2 5 9 ( 7 1 ) , 287 Mullin, L.S. 9 1 8 (276), 925 M u l l i n e a u x , R . D . 861 ( 1 9 8 ) , 891 Munson, M.S.B. 406 (63, 65, 66, 68), 442 ( 2 2 6 a ) , 451, 454, 5 3 2 ( 2 , 5 ) , 548 Murahashi, S.-I. 5 7 2 ( 1 0 4 ) , 603 Murala, T. 9 0 5 ( 9 4 ) , 921 M u r a y a m a , A . 119 ( 1 2 8 ) , 131 M u r c k o , M . A . 8 1 , 8 4 ( 2 8 ) , 8 9 ( 2 8 , 5 3 ) , 93, 94, 9 8 , 110, 111 ( 1 6 ) , M u r p h y , M . E . 9 1 4 ( 2 1 5 ) , 924 Murphy, M.G. 907 (146), 922 Murphy, M.T.J. 3 2 1 , 3 2 3 ( 6 2 ) , 348 Murphy, R. 5 8 7 ( 1 7 9 c ) , 606 M u r p h y , S.M. 3 2 1 , 3 2 3 ( 6 4 ) , 348 Murphy, T.J. 5 9 5 , 5 9 6 ( 2 0 4 a ) , 607, 9 5 8 ( 1 4 7 ) ,

128

962 Murphy, W . F . 109 ( 9 5 ) , 110 ( 9 5 , 101), 130, 158 ( 1 0 0 ) , 183, 2 2 8 , 2 4 1 , 2 4 4 , 2 4 8 , 2 7 5 (24),

285

Mun-ay, A . 8 1 5 , 8 2 2 ( I r ) , 886 Murray, K.J. 5 5 9 ( 3 3 ) , 601 Murray, M.J. 8 6 0 ( 1 9 6 ) , 891

806,

N a c h b a r , R . D . 1 0 8 , 116 ( 7 9 ) , 130 Nafie, L . A . 140 ( 2 6 , 2 9 ) , 163 ( 1 0 5 ) , 182, Nafie, N . S . 163 ( 1 0 6 ) , 184 N a g a i , S. 4 0 7 ( 9 0 , 9 1 ) , 4 5 7 N a g a k u r a , S. 4 8 9 ( 1 3 7 ) , 528 Nagata, C. 155 ( 9 2 ) , 183 N a g e r , C. 5 0 3 ( 1 4 8 ) , 528 N a g y , B. 9 1 9 (299, 300), 9 2 6 N a i k , R.G. 5 5 7 ( 2 2 ) , 6 0 7 N a i k , U . R . 5 7 4 , 5 7 5 (1131), 604 N a k a g a w a , N . 3 6 9 ( 7 8 ) , 390 N a k a g a w a , Y . 7 9 9 ( 6 3 ) , 807 N a k a i , T. 3 6 9 , 3 7 0 ( 9 0 ) , J 9 7 N a k a j i m a , R. 5 8 6 ( 1 7 7 ) , 606 N a k a j u m a , K. 9 1 5 ( 2 4 2 ) , 924 Nakamura, Y. 7 7 3 (48), 779 N a k a n i s h i , K. 145 ( 6 5 ) , 183 N a k a y a m a , S. 8 7 1 ( 2 3 1 ) , 892 N a k a z a k i , M . 179 ( 1 3 8 ) , 184 N a l b a n d i a n , A . B . 8 5 9 , 8 8 4 (185f, 1 8 5 g ) ,

891

N a m b a , H. 7 7 3 ( 4 8 ) , 7 7 9 N a m y , J.L. 5 7 0 ( 9 1 ) , 603 N a n b u , H. 6 8 6 ( 3 6 ) ,

736

N a r a s i m h u l u , S. 8 5 5 ( 1 5 7 ) , Narayan, B. 4 7 6 (38), 5 2 5

890

N a r a y - S z a b o , G. 4 7 6 ( 4 8 ) , 5 2 6 N a r b o n n e , C. 6 4 0 ( 9 9 a ) , 6 5 7 Natalis, P. 3 0 7 ( 2 9 ) , 347 Natiello, M.A. 379 (171),

392

N a t o w s k y , S. 4 7 7 ( 7 8 ) , 5 2 6 Natta, G. 171 ( 1 3 3 ) , 184 N a v a , D . F . 2 5 9 ( 7 2 ) , 287 N a w r o c k i , P.J. 9 9 2 ( 1 5 5 ) , 9 9 7 N a w r o t , J. 9 0 5 ( 1 0 9 ) , 9 0 6 ( 1 1 9 ) , 9 2 7 , 9 2 2

184

1038

A u t h o r index

Naylor, R.D. 235, 2 4 1 , 243, 250, 254, 256, 257, 264, 265 (53), N e b e n z a h l , L.L. 5 4 3 ( 1 3 1 ) , 550 N e c h v a t a l , A . 7 8 9 ( 3 9 b ) , 807, 9 6 8 ( 3 2 ) , 994 N e c s o i u , I. 8 8 3 ( 2 7 2 ) , 893 N e d e l e c , J.-Y. 9 6 9 , 9 7 9 ( 5 7 ) , 995 N e f e d o v , V . D . 8 4 7 ( 1 2 5 - 1 3 0 ) , 8 4 8 ( 1 2 7 , 130),

283, 286

889 N e g i s h i , E.-I. 5 8 7 ( 1 7 9 b ) , 606, N e g r e , A . 9 1 9 ( 3 0 3 ) , 926

698 (69b),

738

N e i m a n , M . B . 8 5 9 ( 1 8 5 a , 1 8 5 c - f , 185h, 186), 8 8 3 ( 1 8 5 a , 1 8 5 c , 185d), 8 8 4 ( 1 8 5 e , 185f, 1 8 5 h ) , 891 N e i s s , M . A . 7 7 3 ( 5 3 ) , 780 N e l s e n , S.F. 3 6 1 ( 4 7 ) , 390, 7 1 2 , 7 1 3 ( 1 1 5 f ) ,

740

N e l s e n , T.R. 5 7 2 ( 1 0 3 ) ,

603

N e l s o n , D . R . 9 0 5 ( 9 1 , 9 3 , 105, 1 1 5 ) , 9 0 6 ( 9 1 , 120, 133), 9 1 4 ( 2 1 8 , 2 1 9 ) ,

921, 922,

924

N e l s o n , G. 9 2 9 , 9 3 4 ( 2 1 ) , 959 N e l s o n , J.H. 9 1 4 ( 2 1 9 ) , 924 N e l s o n , R.L. 9 6 8 , 9 6 9 ( 3 1 ) , 994 N e m e t h , E . M . 8 3 9 ( 1 0 7 ) , 888 N e m o , T . E . 9 6 9 , 9 7 9 , 9 8 9 ( 5 9 ) , 995 N e n i t z e s c u , C D . 5 3 2 ( 2 2 , 2 4 ) , 548, 6 1 5 ( 2 8 ) , 6 1 6 ( 3 0 ) , 650, 8 8 3 ( 2 7 2 ) , 893 N e s b y , J.R. 4 1 1 ( 1 1 9 ) , 4 5 2 N e s m e y a n o v , A . N . 8 2 8 ( 8 1 a ) , 888 N e s t r i c k , T.J. 5 5 8 ( 2 6 ) , 601 N e t h , J.M. 119, 120 ( 1 3 1 ) , / j y N e t z e l , D . A . 3 7 7 ( 1 4 8 ) , 392 N e u b e l l e r , J. 9 0 1 , 9 0 2 , 9 0 4 ( 5 3 ) , 920 N e u m a n n , W . P . 5 6 5 ( 6 5 d ) , 602 N e u n e r t , D . 7 8 2 ( 7 a ) , 806 N e u s s e r , H.J. 4 3 5 ( 2 0 4 ) , 454 N e v i t t , T . D . 3 0 6 ( 2 8 ) , 347,425,426 (169),453 N e v i t z , T . D . 4 4 9 ( 2 4 7 ) , 454 N e w m a n , L.J. 6 6 2 ( 4 3 ) , 678 N e w s a m , J.M. 3 6 9 ( 9 4 ) , 391 N e w t o n , M . 9 3 4 , 9 5 4 ( 6 7 ) , 960 N e w t o n , M . D . 41 (38), 77, 3 8 0 (180), 385 ( 2 0 9 ) , 392,

393,

928 (11), 930 (29), 933

(52), 951 (11), 958-960

N e w t o n , S.Q. 87 ( 4 3 ) , 94 N g , F.T.T. 5 4 1 ( 1 0 7 ) , 5 5 0 N g u y e n , S.L. 5 8 6 ( 1 7 4 a , 1 7 4 b , 1 7 5 b ) , 605 N g u y e n - B a , N . 123 ( 1 7 5 ) , 132 N g u y e n - D a n g , T.T. 2 ( 1 , 2 ) , 6 ( 1 ) , 9 ( 2 , 12),

N i e l s e n , A . T . 5 8 2 ( 1 5 7 ) , 605 N i e r , A . G . 3 4 1 ( 1 0 8 ) , 349 N i e s s e n , W . v o n 4 8 9 , 4 9 0 ( 1 3 5 ) , 528 N i k k i , K. 3 6 8 ( 7 1 ) , 3 6 9 ( 7 8 ) , 390 Nilsen, A.G. 918 (289), 925 N i s h i d a , S. 4 7 9 ( 1 1 8 ) , 5 2 7 N i s h i g u c h i , I. 8 0 1 ( 6 8 ) , 8 0 2 ( 7 0 ) , 807 N i s h i m o t o , K. 4 0 8 ( 1 0 6 , 1 0 7 ) , 452 N i s h i m u r a , J. 5 8 5 ( 1 7 0 ) , 605 N i s h i m u r a , N . 6 8 9 , 6 9 0 ( 4 8 c ) , 737 N i s h i m u r a , Y . 7 0 5 ( 8 3 c ) , 739 Nishioka, A. 352 (2), 369 ( 7 3 - 7 5 , 77),

390

389,

N i s h i s h i t a , T. 4 4 7 ( 2 3 8 ) , 454 N i t a s a k a , T. 5 7 7 ( 1 2 2 ) , 604 N i w a , Y . 4 2 5 ( 1 7 1 ) , 453 N i z n i k , G.E. 5 8 1 ( 1 4 8 ) , 605 Nizova, G.V. 658 (26), 6 7 7 N j a m i l a , M . S . 9 0 2 ( 6 3 ) , 920 N o b l e , R. 3 0 7 , 3 0 9 ( 3 0 ) , 347 N o e c k e r - W e n z e l , K. 9 0 2 ( 5 6 , 5 7 ) , Noel, A.F. 673 (78b), 6 7 9 Nolan, M.C. 654, 6 7 2 (2), 6 7 7 N o l a n , S.P. 6 6 2 ( 4 3 ) , 678 Noller, C R . 9 9 3 (165), 9 9 7 N o l t e m e y e r , M . 1 2 0 ( 1 5 0 ) , 131 N o m u r a , K. 6 6 6 , 6 6 7 ( 6 0 b , 6 0 c ) , N o m u r a , M . P . 301 ( 1 6 ) , 346

920

678

N o r d l i n g , C. 4 7 4 ( 2 6 ) , 5 2 5 N o r m a n t , H. 5 8 2 ( 1 5 1 ) , 605 N o v o s e l ' t s e v , A . M . 3 9 8 ( 1 3 ) , 450 N o w b a h a r i , E. 9 0 6 ( 1 3 7 ) , 9 2 2 N o y c e , D . S . 3 7 4 ( 1 1 7 ) , 391 N o y o r i , R. 5 5 8 ( 2 5 a , 2 5 b ) , 601, 7 1 2 , 7 1 3 ( 1 1 5 b ) , 7 2 4 , 7 2 5 ( 1 3 0 a ) , 740, 741 N o z a k i , H. 9 3 5 ( 7 5 ) , 960 N o z a k i , K. 5 6 6 ( 6 7 ) , 602 N u n o m e , K. 4 1 7 ( 1 4 2 ) , 4 2 5 ( 1 6 7 ) , 452, 453 N u r m i , T.T. 5 8 9 ( 1 8 9 ) , 606 N u r s t e n , H . E . 9 0 2 , 9 0 3 ( 6 4 ) , 920 N u s s e , B.J. 6 7 2 ( 7 1 ) , 6 7 9 N u s s e , R.J. 5 4 0 ( 7 9 ) , 549 N u h , S. 8 5 8 , 881 ( 1 7 2 a ) , 890 N y b e r g , G.L. 4 7 7 ( 5 5 ) , 5 2 6 N y b e r g , K. 7 8 2 ( 1 8 c ) , 806 Nychka, N. 989 (137), 996 N y h o l m , R.S. 35 (30), 77 N y i , K. 5 7 8 , 5 7 9 ( 1 3 4 a ) , 604 N y s t r o m , R.F. 8 1 9 ( 3 3 ) , 887

76, 77

18 ( 2 ) , 2 6 , 31 ( 2 4 ) , 3 4 ( 2 ) , N i c h o l a s , H.J. 9 1 9 ( 2 9 2 , 2 9 8 ) , 925, 926 N i c k o n , A . 5 9 3 , 5 9 5 ( 2 0 3 b ) , 607, 9 2 9 ( 1 7 ) ,

959 N i c o l a i d e s , N . 3 2 1 ( 6 0 ) , 347,

922

N i e d r a c h , L . W . 8 0 4 ( 7 9 ) , 808 N i e d z i e l s k i , J. 9 6 6 ( 1 8 ) , 994

9 0 7 (150, 151),

Obara, S. 6 5 6 ( 8 b ) , 6 7 7 O'Brien, D.F. 543 (128),

550

O'Brien, M.E. 724, 728, 729 (136b), O c c e l l i , M . L . 6 8 2 , 6 8 3 ( 9 a ) , 735 O c h i a i , T. 9 8 8 ( 1 2 9 ) , 9 9 6 O c h s , M . 3 8 7 ( 2 2 2 , 2 2 3 ) , 393 O ' C o n n o r , A . W . 5 6 5 ( 6 1 ) , 602

741

A u t h o r index

604

Oda, M . 5 8 0 ( 1 4 1 , 142), Odaira, Y . 6 9 2 , 6 9 4 , 6 9 5 ( 5 9 b ) , 738 O ' D o n n e l l , G . W . 1 4 2 ( 3 7 ) , 182 O ' D o n n e l l , M.J. 9 3 6 ( 7 9 ) , 960 O ' D o n o g h u e , J.L. 9 1 8 ( 2 7 8 ) , 925 Oehldrich, J. 9 3 9 ( 8 6 ) , 960 Oelderick, J.M. 6 1 0 , 6 2 3 ( 5 a ) , 649 O e s s e l m a n n , J. 8 5 8 , 8 8 1 ( 1 7 2 c ) , 890 Ofstead, E . A . 6 9 6 , 6 9 8 ( 6 7 e ) , 738 Ogata, M . 5 6 5 ( 6 2 a ) , 602 O g d e n , M . W . 3 2 9 ( 7 8 ) , 348 O g l e , C.A. 5 4 2 , 5 4 3 ( 1 1 7 ) , 550 O g u c h i , T. 7 0 5 ( 8 3 c ) , 739

111a, 1 1 1 b ) , 6 4 8 ( 4 8 , 111a, 1 1 1 b ) , 6 4 9 (11a), 837 (101), 9 3 0 (33),

959

649-652,

888,

Olah, J.A. 6 1 9 ( 4 2 c ) , 6 2 5 ( 5 3 ) , 6 3 0 ( 5 8 ) , 6 3 2 ( 6 5 ) , 6 3 3 , 6 3 5 ( 7 3 ) , 6 4 6 , 6 4 8 (11 l a ) ,

650-652

O ' L e a r y , D.J. 1 2 0 ( 1 4 0 a , 1 4 0 b ) , 131, ( 1 5 6 ) , 3 7 9 ( 1 6 9 ) , 392 Oliver, G . D . 2 6 4 ( 8 0 ) , 287 Oliver, J.A. 3 7 7 ( 1 5 3 ) , 392

377

Oliver, T.F. 6 5 8 ( 2 8 a ) , 6 7 7 Olivieri, A . C . 3 7 1 ( 1 0 1 ) , 391

Ogura, Y . 3 8 8 ( 2 2 7 ) , 393 O ' H a r e , D . 6 7 6 ( 9 3 ) , 679 O h b a y a s h i , A . 5 8 5 ( 1 7 0 ) , 605 O h m i c h i , N . 3 9 9 ( 1 9 , 2 0 ) , 4 3 5 ( 2 0 5 ) , 450, Ohnishi, T. 8 0 1 ( 6 8 ) , 807 O h n o , K. 5 9 5 ( 2 0 5 ) ,

1039

O l l e r e n s h a w , J. 7 1 2 ( 1 1 6 b , 1 2 0 b ) , 7 1 4 ( 1 1 6 b ) , 7 1 7 ( 1 2 0 b ) , 740, 741

454

607

Olli, L.K. 5 6 4 ( 5 7 a ) , 602, 9 3 1 , 9 4 5 ( 4 4 ) , 9 5 9 O l l i s , W . D . 5 5 5 ( 1 ) , 600 O l s o n , C T . 9 1 7 ( 2 7 1 ) , 925 Olson, K.D. 724, 727 ( 1 3 2 0 , Omar, S.H. 9 1 6 ( 2 5 6 ) , 925

741

O h n o , S. 7 5 1 - 7 5 3 ( 1 1 a ) , 778 O h s a k o , H. 3 5 6 ( 2 4 , 2 6 ) , 389

O'Neal, H.E. 3 (10), 77, 237, 241 (48), 259, 260 (56),

O h s a w a , T. 5 6 8 ( 8 1 a ) , 5 8 2 ( 1 5 5 ) , 602, 605 Ohta, O. 5 5 8 ( 2 5 a ) , 601 Ohta, T. 5 5 8 ( 2 5 a , 2 5 b ) , 601 O h u c h i , Y. 5 9 3 ( 2 0 2 g , 2 0 3 f ) , 5 9 4 ( 2 0 2 g ) , 5 9 5 ( 2 0 3 0 , 607

Ono, N. 5 8 2 (159a, 160), 5 8 3 (160), Ono, Y. 918 (285), 925 Onuki, Y. 81 ( 3 2 ) , 93 Opitz, K. 9 5 3 ( 1 2 6 ) , 9 6 7

O i s h i , S. 7 0 5 ( 8 3 c ) , 739 Oishi, T. 5 6 8 ( 8 1 a ) , 5 8 2 ( 1 5 5 ) , 602, Oka, T. 6 1 2 , 6 4 9 ( l i b ) , 649 O k a b e , N . 6 8 3 ( 2 1 c ) , 736 Okada, K. 5 8 0 ( 1 4 1 , 142), 604

286, 287

605

O k a m o t o , K. 5 8 0 ( 1 4 2 ) , 604 O k a m o t o , Y . 5 6 3 ( 5 5 ) , 602 O k a n o , T. 5 5 7 ( 1 9 ) , 601 Okazaki, K. 7 5 1 - 7 5 3 (1 l a ) , 778 Okazaki, M . 3 7 6 ( 1 4 2 ) , 392, 4 2 5 ( 1 6 7 ) , 453 O ' K e e f e , J.H. 8 2 4 , 8 2 5 ( 6 5 ) , 887 O k o m o t o , T. 801 ( 6 5 b ) , 807 O k u , A . 5 8 5 ( 1 7 0 ) , 605 O k u b o , K. 5 8 0 ( 1 4 1 ) , 604 O k u y a m a , F. 3 9 9 , 4 0 6 ( 2 6 ) , 450 O k u y a m a , T. 3 5 6 ( 2 4 ) , 389 Olah, G . A . 7 9 ( 9 ) , 93, 3 8 4 ( 2 0 3 ) , 393, 4 3 0 ( 1 8 2 ) , 4 3 6 ( 2 1 2 ) , 453, 454, 5 3 2 , 5 3 8 , 5 3 9 ( 1 7 - 1 9 ) , 548, 6 1 0 (2a, 2 b , 4 a , 4 b , 6 ) , 6 1 1 ( 7 , 8, 10), 6 1 2 ( 1 1 a , 14a, 14b), 6 1 3 ( 1 4 a , 14b), 6 1 4 (2a, 8 ) , 6 1 8 ( 7 , 3 4 , 3 5 , 38, 39), 619 (40, 4 1 , 42c, 4 3 , 44a), 620 (44b), 623 (7, 48), 6 2 4 ( 5 0 a ^ , 5 1 , 52), 625 (48, 53, 54), 626 (48, 55), 627 (56), 629 (57), 6 3 0 ( 5 7 - 5 9 , 62), 631 (62), 6 3 2 (65), 633 (73, 78, 79), 635 (73, 7 8 - 8 0 , 82, 84, 85), 636 (85, 86), 6 3 7 - 6 3 9 (87a, 8 7 b ) , 6 4 0 ( 8 2 , 8 7 a , 8 7 b ) , 6 4 1 ( 9 9 c , 100a, 100b), 6 4 2 ( 1 0 0 c , lOOd, 102a, 1 0 2 b ) , 6 4 3 ( 1 0 3 , 1 0 7 a - c ) , 6 4 4 ( 1 0 7 a - ^ , 109b), 6 4 5 ( 1 0 7 a , 1 0 7 b , 109b), 6 4 6 ( 1 0 9 b , 1 1 0 ,

605

O p p e n l a n d e r , T. 6 8 2 , 7 0 0 , 7 0 1 ( 1 8 b ) , 7 0 3 (79a), 708 (18b, 9 3 , 96a, 98), 709 (93, 98), 7 1 0 (93), 711 (18b, 109, 113), 7 1 2 (96a, 115d), 7 1 3 (115d), 7 1 6 (96a), 7 2 2 (115d), 7 2 4 , 7 2 5 , 7 3 0 (79a),

736, 739,740

Or, Y . S . 5 7 8 , 5 7 9 ( 1 3 4 d ) , 604 O r b a n o p o u l o s , M . 5 6 2 ( 4 8 ) , 601 Orchard, A . F . 4 7 7 ( 5 4 ) , 5 2 6 Ore, A . 7 4 9 ( 8 b ) , Ore, J. 2 9 5 ( 1 1 ) , Orendt, A . M . 3 7 6 ( 1 4 4 ) , 392 O r f a n o p o u l o s , M . 5 7 3 ( 1 0 8 a ) , 603 Orhalmi, O. 8 6 1 ( 2 0 3 ) , 891 Orlandi, G. 6 8 7 ( 3 9 a , 3 9 b , 4 0 b ) , 736 O r l i n k o v , A . 6 2 0 ( 4 5 a ) , 650 Orpen, A . G . 8 0 , 8 4 ( 2 0 ) , 93, 109 ( 9 3 ) , 130 Orrenius, S. 8 5 7 ( 1 6 4 ) , 890 Ors, J.A. 7 0 2 ( 7 7 a ) , 7 0 8 ( 9 7 d , 9 7 e ) , 738, 740 Ortega, P. 6 1 5 , 6 1 6 ( 2 6 ) , 650 Ortis de M o n t e l l a n o , P.R. 9 7 8 , 9 8 6 ( 9 0 ) , 9 9 6 O r v i l l e - T h o m a s , W.J. 3 1 4 ( 4 1 ) , 347

778 346

O s a w a , E. 7 9 ( 1 0 ) , 8 0 ( 1 6 , 18), 81 ( 2 5 , 2 6 , 3 2 ) , 8 4 ( 2 5 , 3 4 ) , 85 ( 3 9 , 4 0 ) , 8 6 ( 4 0 ) , 8 7 ( 3 9 , 4 0 ) , 8 9 ( 5 1 ) , 91 ( 2 6 , 5 8 ) , ( 2 4 , 3 2 ) , 101 ( 3 9 ) , 103 ( 6 3 ) , 110, 111 ( 1 0 2 ) , 1 1 2 , 1 1 4 , 116, 117 ( 6 3 ) , 119 ( 1 0 2 ) , 1 2 0 ( 3 2 , 1 0 2 ) , 1 2 4 , 128 ( 3 9 ) ,

94, 99

93,

128-130, 223 (12), 285, 561 (45a, 45b),

585 (168), 597 (209, 210a, 210b, 2 l 0 d ) , 5 9 8 ( 2 1 0 a , 2 1 0 b , 2 1 0 d ) , 6 0 7 , 605, 607, 691 (53a, 53h, 57), 696, 7 1 2 , 7 1 9 (66a, 66c), 818 (28),

737, 738,

886

1040 O s b e r g h a u s , O. 4 3 6 ( 2 1 0 ) , 454 O s b o r n e , A . D . 4 3 5 ( 2 0 0 ) , 453 O s b y , J.O. 5 5 9 , 571 ( 3 4 ) , 601 Osetskii, A.S. 658 (24), 6 7 7 O s h i m a , K. 5 6 6 ( 6 7 ) , 602 O s k a y , E. 2 9 4 ( 7 ) , 346 O s m a n , R. 3 6 ( 3 4 ) , 7 7 O s t l u n d , N . S . 4 5 7 , 4 6 0 ( 7 ) , 524 O s u k a , A . 5 8 2 ( 1 6 1 ) , 605 Otsuji, Y . 5 8 7 ( 1 8 l b ) , 606 O t s u k a , K. 8 0 4 ( 8 0 ) , 8 0 5 ( 8 9 , 9 0 ) , 808 Otten, J. 9 1 6 ( 2 4 5 ) , 924 Otterbach, A . 5 5 6 , 5 5 7 ( 1 3 h ) , 5 8 0 ( 1 4 0 ) ,

A u t h o r index Paquette, L . A . 7 9 ( 8 ) , 9 2 ( 6 0 ) , 93, 94, 123 ( 1 8 7 b ) , 132, 3 8 2 ( 1 8 6 ) , 393, All ( 5 8 , 7 5 ) , 4 7 8 ( 5 8 , 9 1 , 1 0 3 , 104), 4 7 9 ( 1 1 6 , 117, 125, 1 2 6 ) , 4 8 0 ( 1 1 6 ) , 526, 527, 5 3 7 , 5 3 8 ( 5 8 ) , 5 4 9 , 6 2 0 ( 4 5 b ) , 650, 5 4 0 ( 8 2 , 87), 549, 556 (13e), 558 (28b, 28c), 562, 563 (51b), 5 7 0 (89b), 5 8 9 (187d), 5 9 2 (196a, 196b), 5 9 3 (203e), 595 ( 2 0 3 e , 204b), 596 (204b), 597 (213), 598 ( 2 1 5 b ) , 5 9 9 ( 2 1 5 b , 2 1 6 ) , 600, 601, 603,

606-608, 6 8 2 (8a), 6 9 1 ( 5 5 i ) , 6 9 2 ( 5 5 i , 600,

604 Ottinger, C . 3 9 9 , 4 0 0 ( 2 8 ) , 4 0 5 ( 5 3 ) , 4 3 6 ( 2 1 0 ,

211), 450, 451,454

6 2 c ) , 6 9 3 ( 6 3 ) , 6 9 5 (551), 7 1 2 , 7 1 9 ( 1 2 4 a , 124b), 7 2 4 ( 1 2 9 a ^ , 132a, 1 3 2 b , 136a, 136b), 7 2 6 ( 1 2 9 c , 132a, 1 3 2 b ) , 7 2 8 , 7 2 9 ( 1 3 6 a , 136b), 7 3 2 ( 1 2 9 c ) , 735 , 737, 738, 741, 9 5 6 ( 1 4 2 ) , 9 6 2

O t v o s , J.W. 5 3 8 ( 6 6 , 6 7 ) , 5 4 9 , 6 1 2 ( 1 5 ) , 6 4 9 ,

Paraszcak, J. 7 7 3 ( 4 6 ) , 7 7 9

8 3 8 ( 1 0 2 ) , 888 O u c h i , A . 6 8 7 ( 4 6 a ) , 6 8 9 ( 4 6 b , 4 6 c ) , 737 O u d e n , B . d e n 7 0 5 ( 8 3 a ) , 739 O u m a r - M a h a m a t , H. 9 7 2 ( 7 4 ) , 9 8 8 ( 1 2 6 ) ,

Parisod, G. 4 0 6 , 4 3 7 ( 7 5 , 7 7 ) , 4 3 8 ( 7 7 ) , 4 5 7 Parker, A . C . 137, 139 ( 1 5 , 16), 1 4 0 ( 1 6 ) ,

181 995,

996 O u r i s s o n , G. 122 ( 1 6 5 ) , 132, 174 ( 1 3 6 ) , 184, 3 0 8 , 3 1 4 ( 3 8 ) , 347, 8 9 8 ( 1 9 ) , 9 0 8 ( 1 6 9 , 1 8 3 ) , 9 7 9 . 923 Ouwerkerk, C.E.D. 4 0 5 (59), 457 O v e r m a r s , J . D . 2 3 5 ( 4 1 ) , 286 Ozbalik, N. 7 8 2 (17), 802 (71, 72), 803 (73, 7 4 ) , 806, 808 Ozin, G.A. 674 (88), 679 O z r e t i c h , T . M . 1 6 3 , 164 ( 1 1 0 ) , 184 Paal, Z. 6 8 4 , 6 8 6 ( 2 7 ) , 736, 8 6 0 ( 1 9 3 - 1 9 5 ) , 8 6 1 ( 1 9 4 , 195), 891 Paatz, R. 6 3 2 ( 6 9 ) , 6 5 7 P a c a n s k y , J. 2 6 1 ( 7 7 , 7 8 ) , 2 7 1 ( 8 7 , 8 8 ) , 287 P a c e , T. 9 8 8 ( 1 2 9 ) , 9 9 6 P a c e y , P . D . 2 5 9 ( 5 8 ) , 287 P a c i e l l o , R . A . 6 5 7 ( 1 5 , 16), 6 7 7 Paddon-Row, M.N. 479 (120), 507 (154), 527, 528, 5 7 0 ( 8 7 a ) , 603, 9 3 4 ( 7 1 ) , 960 P a d m a , S. 5 7 0 ( 8 8 b , 8 8 c ) , 603 P a g a n o , E.P. 4 1 2 ( 1 2 5 ) , 4 5 2 Pagni, R.M. 5 3 9 (72), 5 4 9 P a l i n o , G.F. 8 4 2 ( 1 1 6 ) , 889 Palis, J. 21 ( 2 3 ) , 7 7 Paliyath, E. 9 1 1 ( 2 0 4 ) , 923 Palmieri, P. 165 ( 1 1 5 ) , 184 P a l m o , K. 8 0 ( 1 8 ) , 93 P a m i d i m u k k a l a , K . M . 284 P a n a y e , A . 2 0 2 ( 3 5 ) , 213 Pandit, G . D . 5 9 3 , 5 9 5 ( 2 0 3 b ) , 607 Pansegrau, P.D. 4 7 8 (104), 5 2 7 Paoletti, C. 9 0 7 ( 1 6 7 ) , 9 1 4 ( 2 2 5 ) , 923,

924 P a o l u c c i , G. 5 7 5 ( 1 1 7 ) , 604 P a p a d a k i s , K. 9 0 7 ( 1 5 0 ) , 9 2 2

Parker, D . 5 8 6 ( 1 7 3 ) , 605 Parker, D . A . 5 8 6 ( 1 7 4 a , 1 7 4 b , 175a, 1 7 5 b ) ,

605 Parker, D . G . 6 3 5 ( 8 2 , 8 5 ) , 6 3 6 ( 8 5 , 8 6 ) , 6 3 7 - 6 3 9 (87a), 6 4 0 (82, 87a), 657 Parker, D . H . 4 3 5 ( 2 0 3 ) , 453 Parker, G. 6 7 6 ( 9 3 ) , 6 7 9 Parkin, G. 6 7 2 ( 7 4 b ) , 6 7 9 Parkin, J.E. (113), Parmar, S.S. Pamell, C P .

109, 1 1 2 , 116, 117 ( 9 0 ) , 130, 3 7 3 i97 2 5 9 ( 6 2 ) , 287, 9 6 6 ( 1 9 ) , 9 9 4 661, 664 (37c, 37d), 669 (37c),

678 P a m e l l , M.J. 9 1 7 ( 2 6 7 ) , 9 2 5 Pames, Z.N. 559 (29, 30), 5 6 0 (42), 569 (85),

601, 603 P a m i s , J.M. 6 7 4 ( 8 8 ) , 6 7 9 Parrish, J.H. 6 3 9 ( 9 7 ) , 6 5 7 Parshall, G . W . 5 5 5 - 5 5 7 ( l i d ) , 600, 677 P a r s o n a g e , M.J. 9 6 9 ( 4 6 ) , 9 9 5 P a r s o n s , T.R. 9 1 6 ( 2 5 8 ) , 9 2 5 Partney, H.K. 5 0 7 ( 1 5 4 ) , 528 Partridge, R . H . 7 7 8 ( 6 8 ) , 780

659 (34),

Pascard, C. 5 1 4 ( 1 7 4 ) , 5 2 9 Pascaru, I. 8 8 3 ( 2 7 2 ) ,

893

P a s c u a l , C. 3 9 9 ( 1 6 ) , 450 Pasquali, M . 6 8 2 ( l b ) , 735 Pasquato, L. 5 6 2 , 5 6 3 ( 5 1 b ) , 6 0 7 P a s s , G. 8 4 9 ( 1 3 2 ) , 889 Passut, C . A . 2 0 8 ( 6 0 ) , 213 P a s t e e l s , J.M. 9 0 6 ( 1 2 9 ) , 9 2 2 Patai, S. 5 4 2 ( 1 1 9 ) , 550, 5 9 3 ( 1 9 8 b ) , Paterlini, M . G . 163 ( 1 0 6 ) , 184 Paterson, E . S . 5 8 9 ( 1 8 8 ) , 606 P a t i e n c e , R.L. 9 0 0 ( 3 7 ) , 920 P a u l , B . B . 9 4 0 (90). 960

606

A u t h o r index Patney, H.K. 3 8 2 ( 1 8 7 ) , 393, 4 7 9 ( 1 2 0 ) , 527 Patoiseau, J.F. 6 4 0 ( 9 9 a , 9 9 b ) , 651 P a t n c i a , J.J. 5 8 9 ( 1 8 9 ) , 606 Patrikeev, S . V . 8 1 5 , 8 2 2 ( I p ) , 886 Pattengill, M . D . 8 3 9 ( 1 0 6 ) , 888 Patterson, D . R . 5 7 4 , 5 7 5 ( 1 1 3 h ) , 603 Patton, S. 9 1 9 ( 2 9 4 ) , 9 2 5 Paul, E.G. 3 5 5 ( 1 6 ) , 3 6 2 ( 5 1 ) , 389, Pauling, L. 4 5 6 ( 1 , 4 ) , 524 P a u l s o n , J.F. 4 0 6 ( 8 1 ) , 451

Peter, R. 5 8 6 ( 1 7 8 ) , 606 Peters, E . M . 9 5 7 , 9 5 8 ( 1 4 6 ) , 9 6 2 Peters, K. 1 0 1 , 1 1 2 ( 4 9 ) , 7 2 9 , 5 8 3 ( 1 6 3 ) , 5 8 5 ( 1 7 1 ) , 605, 9 5 7 , 9 5 8 ( 1 4 6 ) , 9 6 2 Peters, K . S . 6 6 2 ( 4 3 ) , 678 Petersen, D . E . 2 0 8 ( 5 9 ) , 213 Petersil'e, I.A. 8 5 8 ( 1 8 1 ) , 891 Peterson, A.J. 8 5 4 ( 1 5 2 c ) , 890 Peterson, P.E. 5 6 2 ( 4 9 ) , 601 Petrov, A . A . 3 3 2 , 3 3 6 ( 9 2 ) , 348, 6 9 2 , 6 9 5

390

738

Pauluth, D . 109, 1 1 2 ( 8 9 a ) , 113 ( 8 9 a , 110), 114, 116, 120 ( 8 9 a ) , 130 P a u n c z , R. 4 9 9 ( 1 4 7 ) , 528 Paynter, O.I. 5 5 6 ( 1 3 a ) , 600 Payzant, J.D. 3 4 0 ( 1 0 4 ) , 349 P e a c o c k , V . E . 361 (41), 390 Pean, M . 9 0 4 ( 8 4 ) , 927 Pearlman, R . S . 2 0 2 , 2 0 4 ( 3 8 ) , 213 Pearson, D . E . 5 5 5 ( 3 ) , 600 Pearson, H. 9 9 ( 2 5 ) , 112 ( 1 0 7 ) , 116 ( 1 1 3 ) , 117 ( 1 0 7 , 1 1 3 , 116),

285

128, 130,

223 (13),

Pearson, R . E . 9 9 1 ( 1 4 4 ) , 9 9 7 Pechet, M.M. 6 4 3 (104), 6 5 2 P e d e r s e n , E . E . 145 ( 6 8 ) , 183 Pedersen, L . D . 163 ( 1 0 4 ) , 184 P e d l e y , J.B. 2 3 5 , 2 4 1 , 2 4 3 , 2 5 0 , 2 5 4 , 2 5 6 , 257, 264, 265 (53), 4 7 6 (46), 525,930 (30,959 Peel, J.B. 4 7 7 ( 6 9 ) , 4 7 8 ( 8 6 ) , 5 0 7 ( 1 5 4 ) ,

283, 286,

526-528 Peel, T.E. 5 3 8 ( 6 4 ) , 549 P e e r d e m a n , A . F . 141 ( 3 1 ) , 182 P e g , S.A. 8 9 7 ( 1 5 ) , 9 7 9 Peitila, L . - O . 8 0 ( 1 8 ) , 93 P e l i z z a , F. 6 3 3 , 6 3 5 ( 7 3 ) , 6 3 6 ( 8 6 ) , 651 Pelizzetti, E. 6 8 2 ( 1 4 ) , 735 Pellerite, M.J. 5 4 4 , 5 4 6 , 5 4 7 ( 1 4 7 ) , 5 5 7 P e l l i c c i o n e , N.J. 9 1 5 ( 2 3 6 ) , 924 Pendalwar, S.L. 5 5 7 ( 1 4 ) , 600 P e n g , C.T. 871 ( 2 3 0 ) , 892 Penmasta, R. 711 ( 1 0 8 c ) , 740 P e n t o n e y , S.L., Jr. 3 1 5 ( 4 5 ) , 347 Perez, F. 9 0 5 ( 1 1 1 ) , 927 Periana, R . A . 6 6 3 ( 5 1 ) , 678 Periasamy, M . 5 5 9 ( 3 9 ) , 601 Perichon, J. 7 8 2 ( 1 8 c ) , 806 Perkin, W . H . , Jr. 9 2 7 ( 1 ) , 9 2 8 ( 2 ) , 958 Pen-y, D . 188 ( 1 7 ) , 2 7 2 P e n y , J.J. 9 1 5 ( 2 4 3 ) , 924 Person, W . B . 2 4 4 , 2 8 3 ( 5 4 ) , 287 Pestana, A . X . 8 0 3 ( 7 3 ) , 808 Pestana, J.A. 8 0 3 ( 7 4 ) , 808 Pesti, J. 9 4 4 ( 9 8 ) , 967 Pete, J.-P. 5 6 4 ( 6 0 a , 6 0 b ) , 602 Peter, J.A. 361 ( 4 8 ) , 390

1041

(61), Pettit, G.R. 5 7 6 ( 1 2 0 a ) , 604 Pettit, R. 5 7 8 , 5 7 9 ( 1 3 4 c ) , 604,

6 9 2 (62b),

738 Peyerimhoff, S . D . 4 8 9 , 4 9 0 ( 1 3 9 ) , 5 0 3 ( 1 4 9 ) ,

528

P e z , G.P. 5 3 9 ( 7 0 ) ,

549

Pfeifer, K . - H . 4 7 7 , 4 7 9 , 5 1 6 , 5 2 0 , 5 2 4 ( 6 7 ) , 479 (107), 526, 527, 956 (140), 962 Pfenninger, A. 931 (42), 9 5 9 P f e n n i n g e r , J. 5 8 0 ( 1 3 8 ) , 604 Pfriem, S. 3 6 4 ( 5 6 ) , 390, 5 9 5 ( 2 0 6 b ) , 607 Phan Tan L u u , R. 6 1 7 ( 3 3 ) , 650 Phillipi, G.T. 9 0 9 ( 1 8 7 ) , 923 Phillips, D . 6 8 7 , 6 8 8 ( 3 7 b ) , 736 Phillips, K. 8 2 7 ( 7 9 ) , 888 P h i l o p s b o m , W . v . 3 6 8 ( 7 0 ) , 390 Philp, R.P. 3 0 5 - 3 0 7 , 3 0 9 , 3 1 0 , 3 1 4 ( 2 6 ) , 347, 8 9 6 (8), 9 0 6 (127), 979, 922 P h o t i n o s , D.J. 3 6 9 ( 8 7 ) , 391 Pianfetd, J.A. 9 9 4 ( 1 7 0 ) , 9 9 7 Piatak, D . M . 9 0 4 ( 7 7 ) , 927 Pichat, L. 8 2 0 ( 3 6 ) , 887 Pichat, P. 7 0 6 ( 8 8 a , 8 8 c ) , 739 Pierini, A . B . 9 3 3 ( 5 8 ) , 960 Pierre, C. 8 5 8 ( 1 7 5 b ) , 890 Pierson, C. 7 8 2 , 7 9 7 , 7 9 9 ( 8 a ) , 806, 9 8 9 ( 1 3 4 ) , 996 Pietre, S. 5 6 3 ( 5 6 ) , 602 P i e t r u s i e w i c z , K . M . 3 6 1 ( 3 4 ) , 390 P i g n o l e t , L . H . 5 5 5 , 5 5 6 (1 I m ) , 600 P i g o u , P.E. 3 8 2 ( 1 8 7 ) , 3 8 4 ( 2 0 4 b , 2 3 1 ) , 3 8 5 ( 2 0 4 b ) , 3 8 7 ( 2 1 9 ) , 393, 411 ( 6 9 ) , 5 2 6 , 478 (86), 527, 9 5 4 (134), 962 Pihlaja, K. 9 0 0 ( 3 2 ) , 9 0 6 ( 1 1 9 ) , 920, 922 Pilcher, G. 2 2 7 ( 2 1 ) , 2 2 8 ( 2 1 , 2 5 ) , 2 3 3 ( 2 1 ) ,

283, 285, 286

235 ( 2 1 , 33), 241 (21), Pilling, M.J. 2 5 9 ( 6 1 , 7 0 ) , 287 Pillinger, C.T. 341 ( 1 1 3 ) , 349, 8 9 8 ( 2 1 ) , 979 P i m e n t e l , G . C . 2 4 4 , 2 8 3 ( 5 4 ) , 287,

678

662 (45),

P i n c o c k , P.E. 5 8 3 , 5 8 4 ( 1 6 5 e ) , 605 P i n c o c k , R . E . 3 6 8 ( 6 8 ) , 390, 9 5 0 ( 1 1 5 ) , 979 (91), 996 Pinczewski, W.V. 333 (97), Pinder, A . R . 5 6 8 ( 8 0 ) , 602

348

961,

1042

A u t h o r index

P i n e s , H. 5 3 2 ( 2 3 ) , 548, 6 1 0 ( 3 ) , 6 1 2 ( 1 3 ) , 6 1 6 (29), 621 (47), 8 1 5 ( 1 8 , 19), 816 (18), P i n i z z o t t o , R.F., Jr. 4 0 6 ( 7 0 ) , 4 5 7 P i n o , P. 141 ( 3 3 ) , 1 4 2 , 143 ( 3 9 ) , 182 Piper, S.H. 9 0 0 ( 3 3 ) , 920 Pireaux, J.J. 4 7 4 , 4 8 7 , 4 9 3 , 4 9 9 ( 2 7 ) , 5 2 5 P i m i c , M . P . 8 5 3 ( 1 4 2 ) , 889 Pirnik, M . P . 9 1 5 ( 2 4 1 ) , 9 2 4 Pisareva, N . 9 0 6 ( 1 4 1 ) , 9 2 2 Pittam, D . A . 2 2 8 ( 2 5 ) , 285 Pitti, C. 7 8 2 ( 2 1 , 2 2 , 2 3 ) , 806 Pitzer, K . S . 109 ( 8 6 , 9 2 ) , 117 ( 9 2 ) , 123 ( 1 8 6 ) ,

649, 650, 886

130, 132, 2 0 8 ( 5 9 ) , 213, 2 2 1 ( 1 4 ) , 2 8 3 ( 9 1 ) , 285, 287

(4), 2 2 3

347,

548, 549, 958, 959

P o p o v , E.I. 8 5 9 ( 1 8 6 ) , 891 P o p o v i c , M . 8 5 5 ( 1 6 2 ) , 890 P o p p , B . N . 3 4 5 , 3 4 6 ( 1 1 6 ) , 349 Poppinger, D. 4 0 4 , 4 0 8 (46), 4 2 5 (46, 166), 4 2 8 ( 4 6 ) , 450, 453, 5 9 5 ( 2 0 6 a ) , 607 P o r e t h , M . 4 2 4 , 4 2 8 ( 1 6 0 ) , 453 Porter, A . E . A . 5 8 1 ( 1 4 9 a ) , 605 Porter, R . N . 8 3 9 ( 1 0 8 , 1 1 0 ) , 889 P o s n e r , G . H . 5 8 5 , 5 8 6 ( 1 7 2 c ) , 605,

887

Possagno, E. 8 3 8 , 8 3 9 (104), Potter, E. 9 6 9 ( 4 7 ) , 9 9 5

820 (38),

888

Potts, A . W . 4 1 4 ( 1 3 3 ) , 4 5 2 , 4 7 4 , 4 7 5 ( 2 4 , 2 5 ) ,

286

4 7 6 (25, 34, 40), 477 (40, 50), 4 9 3 , 4 9 6 (25),

525, 526

P l a t t e u w , J.C. 6 1 0 , 6 2 3 ( 5 a ) , 649 P l a t z m a n , R.L. 3 9 6 ( 7 ) , 450, 7 5 1 ( 1 0 ) ,

Potts, F.E. 6 3 7 ( 9 4 ) , 6 5 7 P o u e t , M.J. 3 6 1 ( 4 4 ) , 390 P o u l s e n , O.K. 3 8 5 ( 2 1 2 ) , 393

778

P l e a s o n t o n , F. 8 4 7 ( 1 2 3 ) , 889 Plechter, D . 6 1 4 ( 2 3 ) , 649 Plemenkov, V.V. 477 (62, 62), 526

Poupart, J. 5 7 6 ( 1 2 1 a ) , 604 P o u t a n e n , E.L. 9 0 0 ( 3 2 ) , 920

P l e s s i s , P. 4 0 1 ( 3 8 ) , 450 Pletcher, D . 7 8 2 ( 1 9 ) , 7 8 3 ( 1 9 , 2 4 ) , 7 8 4 ( 2 4 , 2 6 - 2 8 ) , 785 (26-28), 786 (33), 7 9 2 (33, 4 4 ) , 7 9 5 ( 5 2 b ) , 7 9 7 ( 2 6 - 2 8 , 5 7 , 5 8 ) , 806,

807

P o c k l i n g t o n , J. 4 7 8 , 5 1 6 , 5 1 7 ( 1 0 6 ) , 5 2 7 P o d o l s k a y a , N . I . 8 1 5 , 8 2 2 ( I q ) , 886 Pogna, N. 9 0 4 (78), 927 Poh, B.-L. 356 (20), Pohl, D.G. 9 6 9 , 9 7 3 (56), 9 8 9 (134, 135),

389

996

995,

P o l a , J. 6 9 0 ( 5 1 a , 5 1 c ) , 7 0 3 ( 7 8 ) , 737, 739 P o l a n y i , J.C. 8 3 9 ( 1 0 7 ) , 888 Polanyi, M. 967 (26, 27), 994 P o l a v a r a p u , P.L. 1 4 0 ( 2 7 ) , 163 ( 1 0 7 , 1 0 8 ) ,

182, 184

P o l b o r n , K. 5 6 8 ( 7 6 ) , 5 9 8 , 5 9 9 ( 2 1 5 c ) , 602, 608, 9 5 4 ( 1 2 8 , 1 3 0 ) , 9 5 6 ( 1 3 8 ) , 9 6 7 , 962 286

Poutsma, M.L. 6 4 2 (101), 657, 9 7 0 (62), 9 8 4 ( 1 1 5 ) , 995, 996 P o v i n e c , P. 8 1 2 ( 3 ) , 886 P o w e l l , G.P. 155 ( 9 5 ) , 183 P o w e l l , R . E . 2 2 1 ( 4 ) , 285 P o z d e e v , V . V . 8 2 8 ( 8 1 a ) , 888 P o z d n k i n a , S.G. 6 9 2 , 6 9 5 ( 6 1 ) , 738 Prager, R . H . 5 8 7 ( 1 7 9 c ) , 606 Prahlad, J.R. 5 7 4 , 5 7 5 (1131), 604 Prakash, G . K . S . 5 3 2 , 5 3 8 , 5 3 9 ( 1 7 ) , 548, 6 1 0 (2b, 6), 6 1 2 , 6 1 3 (14b), 6 2 0 (44b), 627 (56), 633 (79), 635 (79, 84), 6 3 7 6 4 0 (87b), 641 (99c), 646, 648 (111a),

649-652

Prange, T. 5 1 4 ( 1 7 4 ) , 5 2 9 Pratt, T . H . 8 3 2 ( 9 4 a ) , 8 3 3 ( 9 4 b ) , 888 Pratt, W . E . 5 8 3 , 5 8 4 ( 1 6 5 f ) , 605, 9 3 3 , 9 5 2 (64), Pratt, W . R . 5 8 3 , 5 8 4 ( 1 6 5 b ) , 605

960

Prausnitz, J.M. 2 3 5 ( 4 5 ) , 286 Prelog, V. 142 (40), 144 (56),

P o l o n o v s k i i , J. 9 1 9 ( 3 0 3 ) , 9 2 6 P o l y a , G. 188, 189 ( 1 3 , 14), 2 7 2 P o m e r a n t z , M . 3 8 4 , 3 8 5 ( 2 0 4 a ) , 393, (143), 962 P o m o n i s , G.J. 9 0 6 ( 1 1 8 ) , 9 2 2 P o m o n i s , J.E. 9 1 4 ( 2 1 9 ) , 9 2 4 P o m o n i s , J.G. 9 0 6 ( 1 2 0 ) , 9 2 2 P o n s , S. 7 9 2 ( 4 5 ) , 807 P o n t y , A . 7 8 2 ( 7 a ) , 806 P o p e , J.M. 3 6 9 ( 8 3 , 8 4 ) , 391

93, 94,

Poshparaj, B . 9 1 4 ( 2 2 5 ) , 9 2 4

Pitzer, R . M . 2 2 3 ( 6 ) , 285 P i z e y , J.S. 5 7 6 ( 1 2 0 b ) , 604 Plant, W . D . 9 0 6 ( 1 2 7 ) , 9 2 2 Piatt, B . C . 136 ( 8 ) , 181 Piatt, J.R. 186, 1 9 0 ( 3 , 4 ) , 2 7 2 , 2 3 5 ( 3 6 ) ,

Poling, B.E. 235 (45),

P o p l e , J.A. 17 ( 1 7 ) , 7 7 , 8 0 ( 1 4 ) , 8 5 , 8 7 ( 4 1 ) , 88 (14), 303 (22), 457, 460 ( 7 ) , 5 1 9 ( 1 7 9 ) , 524, 529, 5 3 2 ( 2 8 - 3 0 , 32, 34), 533 (32), 534 (32, 34), 5 3 6 (51), (39), 928 (6), 9 3 0 (6, 33), 931 (43),

957, 958

182

Prenant, C. 8 1 3 ( 8 , 9 ) , 886 P r e s s e s , J.M. 6 8 7 ( 3 9 c ) , 736 P r e u s s , H. 7 8 9 ( 3 8 ) , 807 P r e u s s , T. 4 7 9 ( 1 2 7 ) , 528 Price, J.M. 5 3 2 , 5 3 4 ( 1 5 ) ,

548

Price, R. 3 7 4 ( 1 2 2 ) , 3 7 5 ( 1 2 2 , 1 2 9 ) , 391 Price, W . C . 4 7 4 , 4 7 5 ( 2 4 , 2 5 ) , 4 7 6 ( 2 5 , 3 4 ) , 477 (50), 4 9 3 , 4 9 6 (25), Prince, T.L. 5 6 7 ( 7 4 ) , 602

525, 526

A u t h o r index Prinzbach, H. 7 9 ( 7 ) , 93, 4 7 7 , 4 7 8 ( 6 0 ) , 4 8 0 ( 1 3 0 ) , 526, 528, 5 7 0 ( 9 0 a , 9 0 b ) , 5 9 0 , 591 ( 1 9 4 g ) , 5 9 2 ( 1 9 7 ) , 603, 606, 6 2 0 ( 4 5 c ) ,

650 Prinzbach, M . 5 7 6 ( 1 2 1 b ) , 604 Pritchard, D . E . 5 1 , 6 3 ( 4 5 ) , 7 7 , 3 8 0 ( 1 8 1 ) , Pritchard, H . O . 881 ( 2 6 5 ) , 893 Pritchard, O. 8 7 5 ( 2 5 4 ) , 893

393

Proehl, G . S . 3 6 8 ( 6 1 ) , 390, 5 8 3 , 5 8 4 ( 1 6 5 c ) , 605, 9 5 1 ( 1 1 9 ) , 96J Profeta, S. Jr. 122 ( 1 6 2 ) , 128 ( 2 1 4 ) , 13], 133 P r o k o p i o u , P.A. 5 6 4 ( 5 8 b ) , 5 6 5 ( 6 6 d ) , 602 Proksch, P. 9 0 4 ( 7 9 , 8 5 ) , 921 Pronpiou, P.A. 5 6 4 ( 5 8 a ) , 602 Prosen, E.J. 3 ( 8 ) , 7 7 , 2 2 8 ( 2 6 ) , 2 3 6 ( 4 7 ) , 286 Prout, K. 6 7 6 ( 9 3 ) , 679 Pryde, A . W . H . 137 ( 1 0 ) , 181 Pryor, W . A . 9 6 9 ( 4 2 , 4 5 ) , 995 Psan-as, T. 5 4 3 ( 1 2 7 ) , 550 Pucci, S. 142, 143 ( 3 9 ) , 182 P u g e s , P.E. 6 8 4 ( 2 9 ) , 736 P u g m i r e , R.J. 3 6 2 , 3 6 4 ( 5 3 ) , 390 Puippe, N . 5 2 4 ( 1 8 1 ) , 5 2 9 Pujare, N . U . 8 0 5 ( 9 1 ) , 808 Pullen, B . P . 4 7 6 ( 3 6 ) , 5 2 5 P u l l m a n , A . 4 9 6 ( 1 4 2 ) , 528 P u l l m a n , B . 4 9 6 ( 1 4 2 ) , 528 Pun-ington, S.T. 5 7 7 ( 1 2 3 b ) , 604 Pushparaj, B . 9 0 7 ( 1 6 7 ) , 923 Puttemans, J.P. 4 7 7 ( 6 1 ) , 5 2 6 P y c k h o u t , W . 9 2 ( 6 0 ) , 94, 123 ( 1 8 7 b ) , 132 Qi, S.P. 8 2 4 ( 5 9 ) ,

887

Q i n , X . - Z . 7 2 4 , 7 2 5 , 7 3 0 ( 1 3 0 c ) , 741 Q u a b e c k , Q. 5 9 5 ( 2 0 7 ) , 607 Quin, L.D. 9 9 4 (170), 9 9 7 Quinn, M. 6 9 1 ( 5 2 ) , 737 Quintas, L . V . 189 ( 2 0 ) , 2 / 2 Quirk, J.M. 6 6 0 ( 3 7 a ) , 6 6 1 ( 3 7 b ) , 6 6 4 ( 3 7 a , 3 7 b ) , 678 Quirk, M . M . 9 0 0 ( 3 7 ) , 920 Raadschelders-Buijze, C.A. 8 1 4 (12), 8 3 0 (86),

886, 888 R a a s c h , M . S . 9 4 3 ( 9 6 ) , 967 Rabaa, H. 6 5 6 ( 7 ) , 6 7 7 Rabaa, S. 6 5 6 ( 1 2 ) , 6 7 7 Rabalais, J.W. 4 7 6 ( 3 7 ) , 4 8 7 ( 1 3 4 ) , 4 8 9 ( 1 3 4 , 140), 4 9 0 ( 1 4 0 ) , 525,

528

Raber, D.J. 100, 124, 127 ( 3 6 ) , 7 2 9 R a b i n o v i t c h , B . S . 2 5 9 ( 7 6 ) , 287, 8 7 4 ( 2 4 9 ) , 8 7 5 ( 2 5 1 , 2 5 2 ) , 8 7 6 , 8 7 7 ( 2 5 5 ) , 881 ( 2 6 3 ) , 892, 893 Rabitz, H. 143 ( 5 0 ) , 182 Rabjohn, N . 3 5 2 ( 1 4 ) , 389, 5 8 8 ( 1 8 3 ) , 606 Rabolt, J.F. 9 8 , 110 ( 1 5 ) , 128 Rack, E.P. 821 ( 4 7 a ) , 8 5 3 ( 1 4 0 ) , 887, 889

1043

R a d e g l i a , R. 1 2 0 , 121 ( 1 4 6 ) , 131,

361 ( 3 2 ) ,

390 R a d e m a c h e r , P. 5 0 9 ( 1 6 4 ) , 528 Radin, D . N . 9 0 4 ( 8 5 ) , 9 2 7 R a d k e , M . 3 2 0 ( 5 3 ) , 347 Radler, F. 9 0 1 ( 4 8 ) , 9 0 4 ( 7 3 ) , 920, 921 R a d o m , L. 17 ( 1 7 ) , 7 7 , 8 0 ( 1 4 ) , 8 5 , 8 7 ( 4 1 ) , 8 8 ( 1 4 ) , 93, 94, 3 0 3 ( 2 2 ) , 347, 4 0 4 ( 4 6 ) , 4 0 6 (62), 407 (89), 408 (46), 425 (46, 1 6 6 ) , 4 2 8 ( 4 6 ) , 450, 451, 453, 5 3 6 ( 5 1 ) ,

549 R a d z i s e w s k i , J.G. 7 1 1 ( 1 0 6 a ) , 740 R a e y m a e k e r s , P. 3 8 2 ( 1 8 5 ) , 393 Raghavachari, K. 8 5 , 87 ( 4 1 ) , 8 9 ( 5 3 , 5 4 ) , 94, 4 3 4 ( 1 9 6 ) , 453,

5 3 2 - 5 3 4 (32), 542

( 1 2 5 ) , 548, 550, 7 0 8 ( 1 0 0 ) , 7 1 2 , 7 2 0 , 7 2 1 ( 1 2 5 b ) , 740, 741 R a g h u v e e r , K . S . 5 0 4 ( 1 5 0 ) , 528 R a h i m i , P . M . 9 6 4 , 9 6 9 , 9 8 7 ( 1 0 ) , 994 R a h m a n , L. 2 5 9 ( 6 3 ) , 287 Rainwater, D . L . 9 1 1 ( 2 0 2 ) , 923 R a j z m a n n , M . 6 8 3 ( 2 2 b ) , 736 Rakvin, B. 9 5 2 (123), 967 R a l e y , J.H. 8 6 1 ( 1 9 8 ) , 891, 992 ( 1 5 4 - 1 5 6 ) , 997 R a m a c h a n d r a n , V . 7 9 8 ( 5 9 ) , 807 Ramaiah, M. 565 (65b), 588, 5 8 9 (186c),

602,

606 Ramamurthy, V. 7 0 3 (81a), 7 0 8 , 7 1 0 (101b, 1 0 2 b ) , 739, 740 R a m a n o v e r , V . S . 5 6 9 ( 8 5 ) , 603 Ramsey, R.B. 919 (292), 925 Randall, M . 2 1 6 ( 1 , 2 ) , 2 2 3 ( 1 5 ) , 2 2 6 ( 1 7 ) ,

285 R a n d i c , M . 189 ( 2 1 ) , 1 9 0 ( 2 4 - 2 6 ) , 2 0 4 ( 2 1 ) , 2 7 2 , 3 5 6 ( 2 5 , 2 6 ) , 389 Raner, K . D . 9 6 6 , 9 7 1 ( 2 1 ) , 9 7 2 ( 7 1 ) , 994, 995 R a n g u n a t h a n , N . 163 ( 1 0 5 ) , 184 Rantwijk, F. van 5 5 5 , 5 5 6 ( 1 1 a ) , 600 Rao, C B . 6 3 7 - 6 4 0 (87b), 657 Rao, V.B. 9 4 4 (97, 99), 967 Raphael, R.A. 9 0 4 (81), 927 Rapin, J. 4 0 2 , 4 0 3 , 4 0 9 , 4 1 1 , 4 1 3 ( 3 4 ) , 4 2 4 (160, 161), 4 2 8 (160), 4 3 6 (161), 4 4 3 ( 3 4 ) , 4 4 7 ( 2 3 7 ) , 450, 453, 454 R a p p o l i , B.J. 5 5 9 ( 3 2 ) , 601 Rappoport, Z. 7 1 1 ( 1 1 4 a ) , 740 R a s m u s s e n , K. 8 0 ( 1 3 ) , 93, 9 9 , 101 ( 3 3 ) , 7 2 9 Rathray, J . B . M . 9 0 7 ( 1 6 1 ) , 9 2 2 R a t l e d g e , C. 9 1 5 ( 2 3 2 ) , 924 Rau, H. 7 0 8 , 7 1 2 ( 9 6 d ) , 739 Rauk, A . 163 ( 1 0 6 ) , 184, 6 9 1 , 6 9 2 ( 5 5 a ) , 737 Rauscher, G. 5 9 5 ( 2 0 6 a ) , 607 R a v e t , M . F . 6 8 4 - 6 8 6 ( 2 8 ) , 736 R a v i Shankar, B . K . 4 7 9 , 5 1 6 , 5 1 9 ( 1 2 3 ) , 5 2 7 R a w d a h , T . N . 128 ( 2 1 9 ) , 133 R a w s o n , D.I. 9 9 ( 2 5 ) , 128

1044

A u t h o r index

R a y , T. 163 ( 1 0 6 ) , 184 R a y m o n d , F.A. 9 8 0 (93), 9 9 6 R e a d , R . C . 188, 189 ( 1 4 ) , 212 Readio, P.D. 991 (142), 9 9 7 R e a l e , H . F . 9 3 3 ( 5 8 ) , 960 Rebbert, R . E . 4 3 5 ( 2 0 1 ) , 453, 6 8 7 , 6 8 8 ( 4 5 ) , 737, 7 5 6 - 7 5 8 ( 1 6 ) , 7 6 5 ( 3 4 b ) , 778, 779 R e c h k a , J. 8 9 6 ( 7 ) , 9 7 9 Redchenko, V.V. 477 (62), 5 2 6 R e d d y , K . V . 7 0 7 , 7 0 8 ( 9 1 ) , 739 R e d e m a n n , P. 9 0 3 ( 6 7 ) , 920 Redfield, J.H. 189 ( 1 8 ) , 2 7 2 R e d v a n l y , C . S . 8 1 8 ( 2 7 ) , 886 R e e d , A . E . 5 4 2 ( 1 2 5 ) , 550 Reed, C.R.V. 766 (39), 771 (39, 43), 7 7 2 (43), 779 R e e d , D . W . 9 8 8 ( 1 2 5 ) , 9 9 1 ( 1 4 8 , 149), 9 9 6 . 997 R e e d , R . C . 5 7 2 ( 1 0 2 ) , 603 R e e d y , G . T . 3 1 5 , 3 2 9 ( 4 3 ) , 347 R e e s e , R . M . 4 0 4 ( 4 5 ) , 450 R e e t z , M . T . 5 7 7 ( 1 2 5 a , 125b), 5 8 6 ( 1 7 8 ) , 604,

606 R e g e l m a n n , C U . 8 9 ( 5 2 ) , 94 R e g n i e r , F.E. 9 0 6 ( 1 1 7 , 125), 9 2 7 , 9 2 2 R e h m , H.J. 9 1 5 ( 2 3 1 ) , 9 1 6 ( 2 5 6 ) , 924, 925 R e i c h , H.J. 361 ( 3 5 ) , 390 R e i d , G.P. 9 6 9 ( 3 4 ) , 994 R e i d , R . C . 2 3 5 ( 4 5 ) , 286 Reiff, I. 9 1 5 ( 2 3 1 ) , 924 Reinhardt, S . B . 8 5 8 ( 1 7 7 ) , 890 R e j , R . N . 4 3 0 ( 1 8 4 ) , 453 R e m a n i c k , A . 152 ( 8 2 ) , 183 R e m b e r g , E. 4 2 3 ( 1 5 6 ) , 453 R e m b e r g , G. 4 2 3 ( 1 5 6 ) , 453 R e m i c k , R.J. 6 7 3 ( 8 2 ) , 6 7 9 R e m i n s j e , J.D. 122 ( 1 5 7 ) , 131 R e m p e l , G.L. 5 4 1 ( 1 0 7 ) , 550 R e n k , E. 9 8 4 ( 1 1 3 ) , 9 9 6 R e n k i n , T.L. 9 5 3 ( 1 2 5 ) , 967 R e n n e k e , R.F. 6 7 2 ( 7 8 a ) , 6 7 9 , 6 8 2 ( l b ) , 735 Renner, R. 6 4 2 ( 1 0 2 b ) , 6 5 7 R e n o b a l e s , M . de 9 0 5 , 9 0 6 ( 9 5 ) , 9 2 7 R e p i c , O. 5 9 3 ( 2 0 0 a , 2 0 0 b ) , 606 Requera, J. 9 1 8 ( 2 8 2 , 2 8 3 ) , 9 2 5 R e s a s c o , D . E . 7 0 6 ( 8 8 g ) , 739 Rest, A.J. 541 ( 9 3 ) , 549 R e s t l e , F.R. 3 0 8 , 3 1 4 ( 3 8 ) , 347 R e u t o v , G . A . 5 4 3 ( 1 3 7 ) , 550 Reynhardt, E.G. 3 8 9 ( 2 2 9 ) , 393 R e y n o l d s , R . N . 9 5 1 ( 1 1 8 ) , 967 R e y n o l d s , W . F . 3 6 9 ( 7 9 , 8 0 ) , 390, 391 R e y n o l d s - W a m h o f f , P. 152 ( 8 2 ) , 183 R h e a d , M . M . 9 0 9 ( 1 9 1 ) , 923 R i c h a r d s , W . G . 2 2 3 ( 9 ) , 285 R i c h a r d s o n , D . B . 2 9 4 ( 9 ) , 346 Richartz, A . 4 8 9 , 4 9 0 ( 1 3 9 ) , 5 0 3 ( 1 4 9 ) , 528

R i c h a u d , R. 165 ( 1 1 8 ) , 184 Richter, K. 8 0 5 ( 8 2 ) , 808 Richter, R. 8 5 5 ( 1 6 1 ) ,

890

R i c h t s m e i e r , S. 9 2 9 , 9 3 4 ( 2 3 ) , 9 5 9 R i c k , W . 9 0 0 ( 3 0 ) , 920 R i c k b o r n , B . F . 143 ( 4 6 ) , 7 5 2 R i d d e l l , E.G. 121 ( 1 5 4 ) , 131 Ridge, D.P. 673 (83), 6 7 4 (86), 6 7 9 R i d g e w a y , J.A. 9 1 6 ( 2 5 2 ) , 924 Ridyard, J . N . A . 4 7 8 ( 9 8 ) , 5 2 7 Rieger, A . L . 9 9 1 ( 1 4 5 ) , 9 9 7 Rieker, A . 81 ( 2 9 ) , 93 R i g o , A . 8 0 2 ( 6 9 ) , 8 0 4 ( 7 7 ) , 807, R i g o l l i e r , P. 5 9 0 ( 1 9 1 ) , 606 R i h s , G. 5 7 0 ( 9 0 b ) ,

808

603

R i l e y , J.R. 8 9 7 ( 1 2 ) , 9 7 9 Ringsdorf, H. 85 ( 3 6 ) , 93 R i p o l l , J.L. 5 9 3 ( 2 0 1 a ) , 607 Ritter, W . 9 8 ( 1 0 ) , 128, 3 7 1 , 3 7 3 ( 1 0 5 ) , 391 R i v i e r e , H. 8 0 2 ( 7 1 , 7 2 ) , 8 0 3 ( 7 3 , 7 4 ) , 808 Roberts, B . P . 5 6 6 ( 6 8 ) , 5 6 9 ( 8 4 ) , 602, 603, 991 (141), 9 9 3 (168), 9 9 7 Roberts, C. 9 7 6 , 9 7 7 ( 8 0 ) , 9 7 9 , 9 8 0 ( 9 2 ) , 9 9 5 , 996 Roberts, D . H . 5 8 9 ( 1 8 7 c ) , 606 Roberts, D . T . , Jr. 6 3 0 ( 5 8 ) , 6 3 1 ( 6 3 ) , 6 3 2 ( 6 4 ) ,

650, 651 R o b e r t s , J. 9 1 7 ( 2 6 8 , 2 6 9 ) , 9 1 8 ( 2 6 9 ) , 9 2 5 Roberts, J . D . 116, 118 ( 1 1 2 ) , 123 ( 1 7 6 ) , 127 ( 2 0 0 , 2 0 5 ) , 130, 132, 133, 361 ( 3 0 , 3 5 ) , 3 8 5 ( 2 1 3 ) , 3 8 8 ( 2 2 4 ) , 390, 393, 9 8 3 ( 1 0 9 ) , 9 8 4 ( 1 1 2 , 113), 9 9 6 R o b e r t s o n , R. 4 0 2 , 4 0 5 ( 3 3 ) , 450 R o b i n , M . B . 138, 1 3 9 , 163 ( 1 8 ) , 181, All, 508, 509 (51), 5 2 6 , 708 (96b, 96c, 96f), 7 1 1 ( 1 1 0 ) , 7 1 2 ( 9 6 b , 9 6 c , 9 6 f ) , 739, 740 R o b i n s , M . Y . 5 6 5 , 5 6 6 ( 6 6 f ) , 602 R o b i n s , P.A. 9 0 1 , 9 0 2 , 9 0 4 ( 4 9 ) , 920 R o b i n s o n , M.J.T. 1 2 0 ( 1 3 9 ) , 122 ( 1 6 3 ) , 131, 361 ( 3 1 ) , 3 7 9 ( 1 6 3 , 165), 390, 392 Robinson, N. 8 9 6 (7), 9 7 9 R o b i n s o n , R. 9 0 8 ( 1 7 3 , 174), 923 R o b i n s o n , W . E . 3 3 2 ( 8 9 ) , 348, 8 9 8 ( 2 5 ) , 9 0 8 ( 1 8 2 ) , 920, 923 R o c c h i c c i o l i , F. 9 1 9 ( 3 0 3 ) , 9 2 6 R o c k e r , E. 116 ( 1 1 4 ) , 130 Roder, A . 7 2 4 , 7 2 8 , 7 3 3 ( 1 3 5 ) , 747 R o d e r , H. 5 7 2 ( 1 0 1 a ) , 603 R o d e r i c k , H.R. 8 2 7 ( 7 8 ) , 888 R o d g e r s , A . S . 3 ( 1 0 ) , 7 7 , 2 3 7 , 241 ( 4 8 ) ,

286 R o d g e r s , M . A . J . 7 4 4 - 7 4 6 ( 2 ) , 778 R o d r i g u e z , E. 9 0 4 ( 7 9 , 8 5 ) , 9 2 7 Roe, D.M. 657 (21), 6 7 7 R o e , M . E . 3 3 0 ( 8 5 ) , 348 R o e d a , D . 8 2 0 ( 4 2 ) , 887 Roesle, A. 931 (42), 9 5 9

A u t h o r index R o e u g e r , V . 9 0 2 ( 5 6 ) , 920 R o g e r s , D . 284 R o g e r s , L. 911 ( 2 0 4 ) , 923 R o g e r s , L . M . 9 0 7 ( 1 5 1 ) , 922 R o g e r s , M . A . 9 0 9 ( 1 9 4 ) , 923 R o g i n s k i , S.Z. 8 7 2 ( 2 3 8 ) , 892 Rohrback, R.G. 9 0 9 ( 1 9 2 ) , 923 Rolla, F. 5 7 0 ( 9 3 ) , 603

R o w l a n d , F.S. 831 ( 9 0 ) , 8 4 2 ( 1 1 3 b , 1 1 4 - 1 1 7 ) , 8 4 3 ( 1 1 7 - 1 2 0 ) , 8 4 4 ( 1 1 8 , 121), 8 4 5 ( 1 1 8 ) , 888, 889 R o y , U. 9 5 7 , 9 5 8 ( 1 4 3 ) , 9 6 2 R o z e n , S. 6 4 3 ( 1 0 4 , 106), 6 5 2 Rozengart, M.I. 8 6 0 ( 1 8 9 - 1 9 1 ) , 891 R o z h k o w , I.N. 7 8 5 ( 3 2 b ) , 807 Rozinkov, B.V. 916 (259), 925 Roznyatovsky, V.A. 384 (205), R u b i n , B . H . 128 ( 2 2 0 ) , 133 Rubinstein, I. 3 4 0 ( 1 0 4 ) , 349

R o l l e f s o n , G.K. 8 7 3 , 8 7 4 ( 2 4 6 ) , 892 R o l l g e n , F . W . 3 9 9 , 4 0 6 ( 2 6 ) , 450 Rolstan, J.R. 9 7 9 ( 9 1 ) , 996 R o m e r , R. 7 2 4 , 7 2 8 , 7 3 3 ( 1 3 5 ) , 741, 9 4 9 , 951 ( 1 0 8 ) , 961 R o n a l d , C . S . 8 6 6 , 8 6 7 ( 2 1 3 ) , 892 Rontani, J.F. 9 1 6 ( 2 6 0 ) , 925 R o o n e y , J.J. 5 9 7 ( 2 1 0 e , 2 1 1 , 2 1 2 ) , 5 9 8 ( 2 1 0 e ) , 607,

6 8 4 ( 2 6 c ) , 6 8 5 ( 3 0 ) , 691 ( 5 3 g ) ,

Rucker, C. 9 5 6 ( 1 3 6 ) , 9 6 2 R u d a k o v , E . S . 6 5 8 ( 2 4 ) , 6 7 7 , 8 8 2 ( 2 7 0 ) , 893 R u d a k o v , I.S. 8 8 3 ( 2 7 3 , 2 7 4 ) , 893 Rudat, M . A . 4 3 3 ( 1 9 1 - 1 9 4 ) , 453 R u d e n , R . A . 5 6 2 ( 5 3 c ) , 602 Rudler, H. 5 8 2 ( 1 5 3 ) , 605 Rudzinski, J.M. 81 ( 2 5 ) , 8 4 ( 2 5 , 3 4 ) , 91 ( 5 8 ) ,

R o s a s , R.L. 123 ( 1 8 5 ) , 132 R o s e n b e r g , R . E . 9 3 4 ( 7 2 ) , 960 Rosenberg, R.O. 98, 9 9 (19),

128

130

R o s e n f e l d , J. 4 3 0 ( 1 8 3 ) , 453, 5 3 5 ( 4 6 ) , Rosenstock, H.M. 4 0 5 (51, 52), 4 1 0 (113-115), 4 1 4 (115), 448 (241), 4 5 7 (6),

452, 454, 4 5 6 , 778

548

Rosenthal, L. 9 8 , 110 ( 1 5 ) , 128 Rosenthal, O. 8 5 5 ( 1 5 7 ) , 890 R o s i n s k i , M . 9 0 1 , 9 0 2 ( 5 5 ) , 920 R o s m u s , P. 5 0 3 ( 1 4 8 ) , 528 R o s s , B . D . 118. 121 ( 1 2 2 ) , 131 R o s s , C.L. 8 3 0 ( 8 6 ) , 888 R o s s , J.R.H. 8 6 5 ( 2 1 1 ) , 891 R o s s , P. 8 3 0 ( 8 6 ) , 888 R o s s e l l , J.B. 9 0 4 ( 8 0 ) , 921 R o s s i , A . R . 7 0 2 ( 7 7 c ) , 738 R o s s i , K. 5 8 9 ( 1 9 0 ) , 606 R o s s i , M.J. 2 5 9 ( 7 1 ) , 287 R o s s i , U. 171 ( 1 3 3 ) , 184 R o s s i n i , D . 8 9 7 ( 1 4 ) , 919 R o s s i n i , F . D . 3 ( 6 - 8 ) , 76. 7 7 , 2 2 8 ( 2 6 ) , 2 3 5 (37, 40), 236 (47), Roth, H . D . 7 0 8 ( 1 0 0 ) , 7 1 2 , 7 2 0 , 721 ( 1 2 5 b ) , 7 3 3 ( 1 3 7 b ) , 740, 741 Roth, R.J. 7 1 2 , 7 1 8 , 721 ( 1 2 2 ) , 741 Roth, W . D . 7 9 ( 7 ) , 93, 5 9 2 ( 1 9 7 ) , 606 Roth, W . R . 6 2 0 ( 4 5 c ) , 650, 6 9 3 ( 6 4 ) , 7 1 2

283, 286

( 1 1 7 , 119b), 7 1 6 ( 1 1 7 ) , 7 1 7 ( 1 1 9 b ) ,

740

Rothen, A . 136, 138, 1 4 1 - 1 4 4 ( 1 ) ,

181

Rothkopf, H . - W . 7 0 5 ( 8 4 b ) , 739 Rothman, W. 7 6 3 (29a), 779 R o t m a n , A . 7 8 2 ( 1 5 c ) , 806 Rouser, E. 9 1 9 ( 2 9 3 ) , 9 2 5 R o u v i e r e , J. 8 2 3 ( 5 3 ) , 887 Rouvray, D . H . 186, 188, 2 0 6 ( 5 , 6 ) , 212

93, 94

450,

524, 7 5 2

738,

393

Ruchardt, C. 101 ( 4 4 - 4 9 ) , 103 ( 5 7 ) , 109 ( 8 9 a ) , 112 ( 4 9 , 8 9 a , 105, 106), 113 ( 4 4 , 4 5 , 5 7 , 8 9 a , 110), 1 1 4 , 116 ( 5 7 , 8 9 a ) , 117 ( 5 7 ) , 120 ( 8 9 a ) , 7 2 9 , 130, 3 7 3 ( 1 1 0 ) , 3 7 4 ( 1 2 7 ) , 391, 5 8 1 ( 1 4 7 ) , 5 8 3 ( 1 6 3 ) , 5 8 5 ( 1 7 1 ) , 605

736,

737

Rosenblum, D. 1 1 6 ( 1 1 5 ) ,

1045

(12),

R u e d e n b e r g , K. 4 6 4 , 5 0 9 ( 1 5 ) , 5 2 5 Ruf, A . 8 6 7 , 8 6 8 ( 2 1 7 ) , 892 R u i z , J.M. 5 3 6 ( 5 2 ) , 549 R u l e , H . G . 137 ( 9 , 10), 181 Rullkotter, J. 3 3 6 , 3 3 8 , 3 3 9 ( 9 9 ) , Rumpf, P. 9 9 3 ( 1 6 6 ) , 9 9 7 Rumyancev, Yu.M. 828 (81a),

348

888

Ruo, T.C.-S. 9 8 8 (125), 991 (148), 996, 9 9 7 Ruscic, B. 4 7 9 (121), 5 2 7 R u s s e l l , C.G. 5 6 8 , 5 7 7 ( 7 8 ) , 602 R u s s e l l , D.R. 5 4 0 ( 7 8 ) , 549 Russell, G.A. 9 6 4 , 9 6 6 (12), 9 6 9 (12, 39, 4 4 , 58), 9 7 0 ( 6 7 - 6 9 ) , 971 (68), 9 7 2 (58), 974 (77), 975, 976 (69), 986 (12), 988 (122, 130), 991 (143), 9 9 2 (159),

994-997

R u s s e l l , J.J. 2 5 9 ( 5 9 , 7 2 ) , 287,

994

966, 968 (23),

R u s s e l l , N.J. 7 8 2 ( 3 a ) , 805, 9 0 2 , 9 0 7 ( 5 8 ) , 920 Rust, F.F. 9 6 4 ( 1 1 ) , 9 8 6 , 9 8 7 ( 1 1 8 ) , 9 9 2 ( 1 5 3 - 1 5 7 ) , 994, 996, 997 Ruth, E.G. 9 0 7 ( 1 5 0 ) , 9 2 2 R u v e d a , E . A . 3 0 8 , 3 1 4 ( 3 9 ) , 347 R u z i c k a , L. 163, 164 ( 1 1 3 ) , 184 Ryback, G. 9 0 8 ( 1 8 4 ) , 923 Rydberg, J. 831 ( 9 1 ) , 888 R y e , R . T . B . 4 0 9 , 4 1 1 , 4 1 3 ( 1 0 8 ) , 452 R y h a g e , R. 4 0 8 , 4 1 5 ( 1 0 1 ) , 451 Rylander, P.N. 3 0 6 ( 2 8 ) , 347, 4 2 5 , 4 2 6 ( 1 6 9 ) , 4 4 9 ( 2 4 7 ) , 453,

600

454,

R z a d , S.J. 6 8 7 , 6 8 8 ( 4 2 ) ,

5 5 5 , 5 5 6 (1 l b , 1 Ih), 736

1046

A u t h o r index

Sabet, Z. 6 9 1 ( 5 2 ) , 737 Sabio, M.L. 9 3 3 (49), 959 Sachse, H.P.E. 8 8 1 , 8 8 2 (262), m S a c k e u , W . M . 8 5 3 ( 1 4 6 ) , 8 5 8 ( 1 7 6 , 177),

S a t o , F. 5 5 9 ( 3 7 ) , 5 8 7 ( 1 8 1 a ) , 601, 606 S a t o , H . . 1 2 8 ( 2 2 4 ) , 133, 3 7 6 ( 1 3 5 , 136), 889,

890 S a c k w i l d , V . 2 2 3 ( 9 ) , 285 S a d e k , N . Z . 9 0 2 ( 6 0 ) , 920 Sadler, I.H. 3 7 7 ( 1 5 3 ) , 392 Saethre, L.J. 5 4 7 ( 1 5 3 ) , 551 S a i g o , K. 81 ( 2 3 ) , 93 Saillard, J.Y. 6 5 5 (5), 6 5 6 (7, 10), 6 7 7 S a i t o , H. 3 7 6 ( 1 3 4 ) , 392 S a i t o , O. 7 7 6 ( 6 3 ) , 780 S a i t o , Y . 6 6 6 , 6 6 7 ( 6 0 a - c ) , 678 S a i t o h , T. 5 8 2 ( 1 5 5 ) , 605 Sajbidor, S. 9 1 6 ( 2 4 8 ) , 924

392,

5 5 9 ( 3 7 ) , 601, 6 3 3 ( 7 1 ) , 651 S a t o , M . 5 8 7 ( 1 8 1 a ) , 606 S a t o , S. 5 5 9 ( 3 7 ) , 601, 7 4 9 ( 8 c ) , 7 5 1 - 7 5 3 ( 1 1 a ) , 778 S a t o h , S. 3 8 2 ( 1 8 4 ) , 393 Satyanarayana, N . 5 5 9 ( 3 9 ) , 601 Sauer, J. 85 ( 3 6 ) , 93, 5 9 3 ( I 9 8 c ) , 606 Sauers, R.R. 5 7 8 , 5 7 9 ( 1 3 4 b ) , 604 Saunders, J.K. 3 6 8 ( 5 8 ) , 3 7 1 ( 9 9 , 100),

390,

391

Sakakura, T. 6 6 6 , 6 6 7 ( 6 1 a ) ,

678

S a u n d e r s , M . 100 ( 3 5 , 3 8 ) , 120 ( 1 3 8 ) , 124 ( 3 5 , 3 8 ) , 128 ( 3 5 ) , 7 2 9 , 131, 4 2 6 ( 1 7 6 ) , 4 3 0 ( 1 8 3 ) , 4 4 0 ( 2 2 2 ) , 453, 454, 5 3 5 ( 4 6 ) , 548 Sauter, H. 3 8 8 ( 2 2 5 ) , 393 S a u v a g e , J.-P. 7 9 ( 6 ) , 93 S a v o i a , D . 5 8 2 ( 1 5 4 ) , 605 S a y o , N . 5 5 8 ( 2 5 b ) , 601

Sakuragi, H. 7 0 5 ( 8 3 c , 8 3 d ) , Sakurai, H. 5 6 3 ( 5 5 ) , 602 S a l a u n , J. 6 8 2 ( 3 b ) , 735

739

Scanlon, R.S. 899 (28),

Sakai, M . 5 4 0 ( 8 6 ) , 549 Sakai, Y . 6 9 2 , 6 9 4 , 6 9 5 ( 5 9 b ) ,

738

920

Scarsdale, J.N. 88 ( 4 8 ) , 94 S c h a d e , G. 165 ( 1 2 0 ) ,

184

S a l e m , G. 6 4 6 ( 1 1 0 , 112), 6 4 8 ( 1 1 2 ) , 6 5 2 S a l e m , J.R. 8 4 ( 3 3 ) , 93 S a l e m , L. 155 ( 9 4 ) , 183 S a l i n g e r , R. 5 4 3 ( 1 2 7 ) , 550 Salmon, L.S. 464, 509 (15), 5 2 5 S a l v a d o r i , P. 141 ( 3 3 ) , 182

Schaefer, Schaefer, Schaefer, Schaefer, Schaefer, Schaefer,

S a l v a y r e , S. 9 1 9 ( 3 0 3 ) , 9 2 6 S a l v i n i , E. 9 0 5 ( 9 7 ) , 9 1 6 ( 2 4 9 ) , 921, 924 Salzman, M. 9 2 9 (16), 9 5 9 S a m m e l l s , A . F . 8 0 5 ( 9 1 ) , 808 S a m u l s k i , E.T. 3 6 9 ( 8 6 , 8 7 ) , 391 Sander, W . 4 7 8 ( 9 6 ) , 5 2 7 S a n d e r m a n n , W . 9 0 3 ( 6 5 ) , 920 S a n d e r s - L o e h r , J. 8 5 8 ( 1 6 6 , 167), 890 S a n d e r s o n , W . A . 143 ( 5 1 ) , 182 Sandorfy, C. 154, 155 ( 9 1 ) , 183 Sandris, C. 122 ( 1 6 5 ) , 132 S a n d s t e d e , G. 8 0 5 ( 8 2 - 8 4 ) , 808 S a n d s t r o m , J. 9 7 ( 5 ) , 9 8 ( 5 , 14), 1 0 1 , 110, 111 ( 4 1 ) , 117 ( 5 ) , 128, 129 S a n F i l i p p o , J. 8 2 0 ( 3 9 ) , 887 S a n o , H. 5 6 5 ( 6 2 a , 6 2 b ) , 602 S a n o , M. 341 ( 1 1 2 ) , 349 Santamaria, J. 7 0 6 ( 8 6 ) , 739 Santarsiero, B . 6 5 4 , 6 7 2 ( 2 ) , 6 7 7 S a m i U a n , R.L. 3 7 7 ( 1 5 9 ) , 392 S a n t o s , E.G. 9 0 7 ( 1 5 0 ) , 9 2 2 S a n t o s , I. 5 3 7 , 5 3 8 ( 5 8 ) , 549 Santry, D . P . 3 8 4 ( 1 9 7 ) , 393 S a s a k i , K. 6 6 6 , 6 6 7 ( 6 1 a ) , 678 Sasaki, S. 341 ( 1 1 2 ) , 349, 3 5 6 ( 2 4 , 2 6 ) , 389 S a s s , V . P . 8 4 7 ( 1 2 8 ) , 889 S a s s o n , Y . 5 5 7 ( 1 5 ) , 600 Sastre, J. 8 1 3 ( 8 , 9 ) , 886 S a t o , A . 9 1 5 ( 2 4 2 ) , 924

S c h a e f e r , T. 3 8 2 ( 1 8 9 ) , 3 8 4 ( 1 8 9 , 193), 393 Schaeffer, W . D . 143 ( 4 8 ) , 182 Schafer, H.J. 5 8 7 ( 1 8 2 a , 1 8 2 c ) , 6 0 6 , 7 8 2 ( 8 b , 14), 7 8 6 ( 3 7 ) , 7 8 9 , 7 9 0 ( 4 0 a , 40b), 794, 795 (37), 796 (40a, 40b), 7 9 7 ( 8 b , 5 6 ) , 7 9 9 ( 8 b ) , 801 ( 6 5 a ) , 806,807 Schafer, J. 101 ( 5 1 ) , 7 2 9 , 5 8 3 ( 1 6 7 b ) , 5 9 8 , 5 9 9 ( 2 1 5 c ) , 6 0 5 . 608 Schafer, L. 8 0 ( 1 8 ) , 8 7 ( 4 3 ) , 8 8 ( 4 5 ^ 8 ) , 8 9 ( 4 6 , 4 9 , 5 1 ) , 93, 94 Schafer, P.R. 9 8 4 ( 1 1 3 ) , 9 9 6 Schafer, U. 3 6 4 ( 5 6 ) , 390 Schafer, U . 5 9 5 ( 2 0 6 b ) , 6 0 7 Schafer, W . 5 9 0 , 591 ( 1 9 4 b ) , 6 0 6 Schallner, O. 3 6 8 ( 6 2 ) , 390 S c h a n g , P. 9 3 1 ( 4 1 ) , 9 5 9

H. 6 3 7 ( 9 3 ) , 6 5 7 H.F., III 1 0 1 , 110 ( 4 2 ) , 7 2 9 J.P. 9 2 9 ( 2 2 ) , 9 5 9 L. 122 ( 1 6 1 ) , 131 P. 6 5 4 , 6 7 2 ( 2 ) , 6 7 7 R.G. 3 2 4 , 3 2 6 ( 7 3 ) , 348

Schappert, R. 9 3 4 ( 7 1 ) , 9 6 0 S c h a y , Z. 6 8 4 ( 2 9 ) , 736 Scheers, W. 903 (65), 920 S c h e i g e t z , J. 5 6 3 ( 5 6 ) , 6 0 2 S c h e i n m a n n , F. 9 0 2 ( 6 2 ) , 9 2 0 S c h e r a g a , H . A . 81 ( 2 3 ) , 93 Schertler, P. 9 7 8 , 9 8 3 ( 8 5 ) , 9 9 5 S c h e u r m a n n , H.-J. 120, 121 ( 1 4 7 ) , 131, 561 ( 4 4 a , 4 4 b ) , 6 0 7

560,

Schibeci, A. 907 (161), 922 S c h i e s s e r , C.H. 5 8 9 ( 1 8 7 c ) , 6 0 6 Schiff, H.I. 5 3 2 ( 1 3 ) , 5 3 7 , 5 3 8 ( 5 5 ) , 548, S c h i l l , G. 5 5 6 ( 1 3 c ) , 6 0 0

549

Author index

S c h i l h n g , F . C . 3 7 3 ( 1 0 7 ) , 3 7 7 ( 1 5 2 ) , 391,

392 S c h i l l i n g , J . B . 5 4 1 ( 1 0 1 ) , 550 S c h i l l i n g , M . L . M . 7 3 3 ( 1 3 7 b ) , 741 S c h i l l i n g , P. 6 4 2 ( 1 0 2 b ) , 6 4 3 ( 1 0 3 ) , 651, 652 S c h i m k e , H. 9 8 9 ( 1 3 6 ) , 996 S c h i n d e l , W . G . 9 7 9 ( 9 1 ) , 996 Schindler, M . 3 5 2 ( 7 ) , 389 Schinkel, W.R.T. 9 0 6 (123), 9 2 2 S c h i m i e r , J. 4 8 9 , 4 9 0 ( 1 3 5 ) , 528 Schlafer, L. 5 6 9 ( 8 2 ) , 602 S c h l a g , E . W . 4 3 5 ( 2 0 4 ) , 454, 8 7 4 ( 2 4 9 ) , 8 8 1 ( 2 6 3 ) , 892, 893 Schlarb, B . 8 5 ( 3 6 ) , 93 S c h l e n c k , W . 3 6 9 ( 8 8 ) , 391 S c h l e n k , W . 3 2 1 ( 6 3 ) , 348 S c h l e y e r , P.v.R. 17 ( 1 7 ) , 7 7 , 7 9 ( 7 ) , 8 0 , 8 8 ( 1 4 ) , 93, 9 9 ( 3 0 ) , 1 1 0 , 1 1 1 , 1 1 9 , 1 2 0 ( 1 0 2 ) , 7 2 9 , 130, 3 0 1 ( 1 6 ) , 3 0 3 ( 2 2 ) , 3 0 8 ( 3 3 ) , 346, 347, 3 6 8 ( 6 7 ) , 390, 4 2 5 ( 1 7 4 ) , 4 2 6 ( 1 7 6 ) , 4 3 4 ( 1 9 6 ) , 453, 532-534 (32), 535 (49), 536 (49, 51), 5 3 7 , 5 3 8 (49), 5 4 2 (109, 125), 546 (109), 547 (109, 154-156), 548-551, 5 8 2 ( 1 5 6 ) , 5 8 5 ( 1 6 8 ) , 5 9 0 , 5 9 1 (194h), 5 9 2 (197), 595 (206a), 597 (209, 2 1 0 a - d , 21 Of), 5 9 8 ( 2 1 0 a - d , 21 Of), 605-607, 6 1 9 ( 4 2 a ) , 6 2 0 ( 4 5 c ) , 650, 691 (53a, 53d, 53h, 5 4 , 5 5 e , 55j, 56b, 56c, 57), 6 9 2 (54, 55e, 55j, 56b, 56c, 59c), 6 9 4 (54, 55j, 56b, 59c), 6 9 5 ( 5 5 e ) , 737, 738, 8 1 6 ( 2 6 ) , 8 1 8 ( 2 7 , 2 8 ) , 8 1 9 ( 2 9 , 3 0 ) , 886, 9 2 8 ( 6 , 12), 9 3 0 ( 6 , 3 3 , 3 6 ) , 9 3 1 ( 3 9 ) , 958,

959 S c h l o s b e r g , R . H . 6 1 1 ( 8 , 10), 6 1 2 ( 1 1 a ) , 6 1 4 ( 8 ) , 6 2 4 ( 5 1 , 5 2 ) , 6 3 0 ( 5 8 ) , 6 4 9 (I l a ) , 649, 650, 8 3 7 ( 1 0 1 ) , 888 S c h l o s s e r , M . 8 2 4 ( 6 1 ) , 887 S c h l u n e g g e r , L. 9 1 9 ( 3 0 1 ) , 926 Schluter, A . - D . 9 4 9 ( 1 1 0 ) , 9 5 1 ( 1 1 0 , 1 2 0 ) , 9 5 3 (126), 967 Schluter, W . - D . 9 3 3 ( 5 5 ) , 960 S c h m a l z , D . 3 7 9 ( 1 6 1 ) , 392 Schmelzer, A. 4 6 6 (18), 4 7 7 (70), 4 7 8 ( 8 5 , 106), 4 7 9 ( 8 5 , 124), 4 9 1 , 495 (18), 507 (155), 509 (166, 167), 5 1 1 ( 1 6 9 ) , 5 1 3 ( 1 6 7 ) , 5 1 6 (106, 124), 5 1 7 (106), 5 1 9 (124),

525-529 S c h m e r l i n g , L. 6 1 0 ( 3 ) , 649, 9 8 6 ( 1 1 7 ) , 996 Schmid, Schmid, Schmidt, Schmidt, Schmidt,

H . G . 1 2 2 ( 1 6 7 ) , 132 W. 9 5 4 (128), 967 G. 123 ( 1 8 8 ) , 132 H. 1 2 0 , 121 ( 1 4 1 ) , 7 i 7 H . G . 1 2 2 ( 1 6 6 ) , 132

1047

S c h m i d t , H.J. 7 8 2 ( 1 4 ) , 806 S c h m i d t , J. 5 8 3 , 5 8 4 ( 1 6 5 e ) , 605, 9 5 0 ( 1 1 5 ) , 967 Schmidt, J.A. 6 7 2 (78a), 6 7 9 S c h m i d t , L. 8 1 9 ( 3 4 ) , 887 S c h m i d t , W . 4 1 4 ( 1 3 2 ) , 452, 4 6 0 ( 1 0 ) , 4 7 6 ( 4 2 , 4 6 ) , 4 7 8 ( 9 8 , 9 9 ) , 5 0 3 ( 4 2 ) , 524,

525, 527 S c h m i d t , W . F . 6 8 3 ( 2 1 b ) , 736 Schmitt, P. 4 7 7 ^ 7 9 ( 8 0 ) , 5 2 6 Schnautz, N . 143 ( 4 7 ) , 182 S c h n e i d e r , F . W . 8 7 5 ( 2 5 2 ) , 893 S c h n e i d e r , H.-J. 1 0 9 , 1 1 2 - 1 1 4 , 1 1 6 , 1 2 0 ( 8 9 b ) , 1 2 3 ( 1 7 5 , 1 8 8 ) , 130, 132, 3 6 1 (33, 4 1 , 46), 3 7 1 , 3 7 2 (102), 3 7 4 (122), 3 7 5 ( 1 2 2 , 1 2 9 ) , 390, 391, 7 8 2 ( 1 5 a ) ,

806 S c h n e i d e r , I. 5 6 1 ( 4 5 b ) , 601 S c h n e i d e r , J.F. 3 1 5 , 3 2 9 ( 4 3 ) , 347 S c h n e p p , O . 1 3 9 , 1 6 3 ( 1 9 ) , 182 Schnering, H.G.von 101, 112 ( 4 9 ) , 7 2 9 , 5 8 3 ( 1 6 3 ) , 5 8 5 ( 1 7 1 ) , 605, 9 5 7 , 9 5 8 ( 1 4 6 ) , 962 S c h n o e s , H . K . 3 0 6 , 3 0 7 , 3 3 0 ( 2 5 ) , 347 S c h o e l l , M . 3 4 1 ( 1 0 9 ) , 349 Schoffer, A . 7 2 4 , 7 2 8 , 7 3 3 ( 1 3 5 ) , 7 4 7 , 9 4 9 , 951 (108), 967 S c h o l z , B . P . 7 1 2 , 7 1 7 ( 1 1 9 b ) , 740 Schori, H. 9 4 0 ( 9 0 ) , 960 S c h o m i a n n , N . 1 2 0 , 121 ( 1 5 1 b ) , 131, 5 5 6 , 5 5 7 ( 1 3 j ) , 5 7 4 ( 1 1 3 d ) , 600, 603 S c h o r m a n n , W . 1 2 0 , 121 ( 1 5 1 a ) , 131 Schrader, B . 2 7 1 ( 8 7 ) , 287, 3 6 8 ( 6 3 ) , 390 Schriver, G . W . 7 1 1 ( 1 0 5 b ) , 740 Schroder, G. 5 0 8 ( 1 6 2 ) , 528 Schrodinger, E . 4 2 ( 4 1 ) , 7 7 Schroeder, G. 4 7 8 ( 8 4 ) , 5 2 6 Schroth, G. 5 6 2 ( 4 6 b ) , 6 0 7 Schubert, U . 6 5 6 ( 7 ) , 6 7 7 Schuchardt, U . 5 6 2 ( 4 6 a , 4 6 c ) , 6 0 7 S c h u c h m a n n , H . P . 7 0 2 ( 7 7 b ) , 738 Schug, J.C. 3 9 6 , 3 9 9 , 4 0 0 ( 1 2 ) , 4 1 2 (122),

450, 452 Schuh, G.C. 621 (46), 6 5 0 Schuler, R . H . 7 7 3 , 7 7 8 ( 5 2 ) , 780 Schulman, J.M. 5 9 ( 5 1 ) , 77, 3 8 0 (180), 3 8 5 ( 2 0 9 ) , 392, 393, 9 3 3 ( 4 9 , 5 2 ) , 959, 960 S c h u l t e - F r o h l i n d e , D . 7 0 2 ( 7 7 b ) , 738 S c h u l t z , J . C . 2 5 9 ( 7 4 ) , 287 Schultz, P.A. 9 3 3 ( 6 2 ) , 9 6 0 S c h u l z , A.J. 6 7 2 ( 7 5 ) , 6 7 9 Schulz, R.H. 541 (100), 5 5 0 S c h u m a n n , S . C . 1 0 9 ( 8 7 ) , 130 Schuster, A . 9 4 2 ( 9 5 ) , 9 6 7 S c h w a b , J . M . 1 6 3 ( 1 0 6 ) , 184 S c h w a g e r , I. 1 4 3 ( 5 0 ) , 182 S c h w a g e r , L. 7 3 1 , 7 3 2 ( 1 3 7 a ) , 741

1048

A u t h o r index

S c h w a r t z , J. 6 7 2 ( 7 3 ) , 6 7 9 Schwarz, R P . 687 (39e), 7 i 6 , 7 5 6 - 7 5 8 (16), 7 6 3 , 7 6 4 ( 3 1 ) , 7 6 5 ( 3 4 b ) , 778, 779 S c h w a r z , H. 4 0 6 ( 6 0 ) , 4 2 4 ( 1 6 5 ) , 4 2 5 ( 1 7 4 ) , 426 (176), 430 (180), 447 (240),

453, 454

S c h w a r z , J. 5 4 3 ( 1 3 6 ) ,

451,

550

S c h w a r z , R . M . 3 5 2 ( 1 4 ) , 389 S c h w e i c k e r t , N . 5 5 6 ( 1 3 c ) , 600 S c h w e i g , A . 4 7 7 ( 5 3 ) , 4 8 9 ( 1 3 6 ) , 526, 528 S c h w e i t z e r , G.K. 4 7 6 ( 3 6 , 4 7 ) , 525, 526 S c h w e s i n g e r , R. 4 7 8 ( 9 3 ) , 4 7 9 ( 9 3 , 1 1 9 ) , 5 2 7 S c h w i n g e r , J. 4 2 ( 4 3 ) , 7 7 S c o p e s , M . 171 ( 1 2 8 ) , 184 S c o p e s , R M . 163, 164 ( 1 1 2 ) , 169 ( 1 2 4 ) , 184 S c o n , A.I. 152 ( 7 9 , 8 0 ) , 183 S c o U , D . R . 3 3 3 ( 9 5 ) , 348 S c o u , D . W . 2 5 5 ( 5 5 ) , 283, 287 Scott, L . T . 6 8 2 ( 2 c ) , 735 Scott, W . B . 5 8 3 , 5 8 4 ( 1 6 5 e ) , 605, 9 5 0 ( 1 1 5 ) ,

961

Seshadri, S.J. 9 6 4 , 9 8 3 , 9 9 1 ( 4 ) , 994 Sehloane, B.P. 988 (125), 991 (148),

997

Setser, D . W . 8 7 5 ( 2 5 2 ) , 8 7 6 , 8 7 7 ( 2 5 5 ) , S e v e n a i r , J.R 1 0 9 , 110 ( 9 6 ) , 130 S e v e r i n , A . V . 8 7 1 ( 2 2 8 ) , 892 Sevin, A. 691, 692, 6 9 4 (56b), S e v r i n , M . 5 7 7 ( 1 2 4 ) , 604 Shacklady, C.A. 9 1 6 (251), Shafer, K.H. 3 1 5 ( 4 5 ) , 347 S h a k e d , Z. 7 8 2 ( 9 a ) , 806

994

893

738

924

Shal, C. 9 0 6 ( 1 3 2 ) , 9 1 4 ( 2 2 0 ) , 922, 924 Shankar, B . K . R . 5 7 8 , 5 7 9 ( 1 3 4 d ) , 604 S h a n n o n , C.E. 2 0 5 ( 4 4 ) , 213 S h a n n o n , R V . R . 168 ( 1 2 3 ) , 184 S h a n n o n , V . L . 128 ( 2 1 1 ) , 133 Sharman, H. 143 ( 4 5 ) , 182 S h a w , A . W . 8 1 5 ( 1 9 ) , 886 Shaw, B.L. 655, 666, 6 6 9 (4b), 6 7 7 S h a w , D . F . 3 0 6 ( 2 7 ) , 347 S h a w , G.J. 4 1 8 , 4 4 2 , 4 4 6 ( 1 4 5 ) , 452,

Scott, W . M . 9 1 9 ( 2 9 9 ) , 9 2 6 S c u s e r i a , G. 3 7 9 ( 1 7 1 ) , 392 Searle, C.E. 9 1 8 ( 2 9 0 ) , 9 2 5 S e a r l e s , S.K. 4 1 7 ( 1 4 3 ) , 452 S e a s e , J.W. 5 7 2 ( 1 0 2 ) , 603 S e d e l m e i e r , G. 5 7 0 ( 9 0 b ) , 603 S e d e r h o l m , C.H. 3 7 4 ( 1 1 7 ) , 391 S e d l e t s k a y a , I.S. 8 1 9 ( 3 2 ) , 886 S e e g e r , R. 9 2 8 , 9 3 0 ( 6 ) , 958 S e e l , H. 3 6 8 ( 6 3 ) , 390 S e e t u l a , J.A. 2 5 9 ( 5 9 , 7 2 ) , 287, 9 6 6 ( 2 3 , 2 4 ) , 968 (23), S e f c i k , M . D . 4 0 6 ( 8 3 ) , 451 S e g u c h i , T. 7 6 8 ( 4 1 ) , 7 7 9 S e i d m a n , K. 3 5 2 ( 9 ) , 389 Seifert, W . K . 3 3 9 , 3 4 0 ( 1 1 8 ) , 349 Seller, R 15 ( 1 5 ) , 3 9 ( 3 7 ) , 4 0 ( 1 5 ) , 7 7 , 9 3 3 ( 5 5 ) , 9 5 4 ( 1 3 2 ) , 960, 961 S e i p , R. 125, 127 ( 1 9 3 ) , 132 Seitz, L . M . 5 4 2 ( 1 2 2 ) , 550 S e k i , K. 4 7 6 ( 4 5 , 4 9 ) , 525, 526 S e l l e r s , R 2 3 6 ( 4 7 ) , 286 S e m m l e r , K. 5 9 3 , 5 9 4 ( 2 0 2 c ) , 607, 9 5 3 ( 1 2 6 ) , 9 5 4 ( 1 2 8 ) , 967 S e n , A . 6 5 8 ( 2 8 a ) , 6 7 7 , 6 9 8 ( 6 8 ) , 738 S e n e z , J.C. 8 5 4 ( 1 5 2 d - 0 , 890 Senior, J.K. 189 ( 1 9 ) , 2 7 2 S e n k a n , S . M . 2 5 9 ( 5 9 ) , 287 Serber, R. 8 3 0 ( 8 2 b ) , 888 S e r g e , A . L . 3 8 0 ( 1 7 5 ) , 392 Sergeev, Y.L. 477 (63), 5 2 6 S e r g e y e v , N . M . 3 8 2 ( 1 8 8 ) , 3 8 4 ( 1 8 8 , 2 0 5 ) , 393 S e r p o n e , N . 6 8 2 ( 1 4 ) , 735 Serve, M . R 917 ( 2 6 7 - 2 6 9 , 271), 918 (269), 925 S e r v e d i o , P.M. 6 8 7 - 6 8 9 ( 4 4 ) , 737

996,

822

( 4 9 b ) , 8 2 4 ( 6 2 ) , 887 S h a w , R. 3 ( 1 0 ) , 7 7 , 2 3 7 , 2 4 1 ( 4 8 ) , 2 6 6 ( 8 1 ) , 989 (55), 995 S h c h e g l o v a , A . R 8 5 9 ( 1 8 6 ) , 891 Shchetakaturina, T.L. 9 0 7 ( 1 5 7 , 1 5 9 ) , 9 2 2 S h e a , K.J. 9 6 4 , 9 8 3 - 9 8 5 ( 6 ) , 994 S h e l d o n , J.C. 5 4 4 ( 1 5 0 ) , 5 5 7 S h e l d o n , R . A . 5 7 8 ( 1 2 7 ) , 604 Sheldrick, G . M . 120 ( 1 5 0 ) , 131 Sheley, C R 478 (102), 5 2 7 S h e n , J. 5 3 2 , 5 3 8 , 5 3 9 ( 1 8 , 19), 548, 6 1 2 ( 1 1 a , 14a), 6 1 3 ( 1 4 a ) , 6 1 9 ( 4 1 ) , 6 2 5 ( 5 4 ) , 6 4 9 ( 1 1 a ) , 649, 650 S h e n , K . - W . 9 2 8 , 9 5 1 ( 1 1 ) , 958

286, 287, 969,

Shepard, N . 6 7 1 ( 6 8 ) , 6 7 9 Sheppard, N . 5 4 0 ( 7 7 ) , 549 Sheridan, R . S . 118 ( 1 1 9 ) , 121 ( 1 5 5 ) , 130, 131 Sherk, J.A. 3 9 9 ( 1 8 ) , 450 Sherry, A . E . 6 6 3 ( 5 8 ) , 678 S h e s t a k o v , A . R 871 ( 2 3 3 ) , 892 S h e v l y a k o v a , L.I. 8 1 6 , 8 7 3 ( 2 4 ) , 886 Shida, S. 7 6 5 ( 3 4 a , 3 7 ) , 7 7 9 Shida, T. 7 1 2 , 7 1 3 ( 1 1 5 e ) , 740 S h i e l d s , G . C . 4 0 7 ( 8 8 ) , 451 S h i e m k e , A . K . 8 5 8 ( 1 6 7 ) , 890 Shikata, M . 9 0 5 ( 9 4 ) , 927 S h i l o v , A . E . 5 4 0 ( 8 8 ) , 549, 6 5 7 ( 1 8 , 19), 6 5 8 (23a, 23b, 25, 26, 28b), 6 5 9 (36), 804 (76), 868 (218, 219), 869 ( 2 2 0 ) , 8 7 0 ( 2 1 9 , 2 2 1 ) , 8 7 1 ( 2 2 4 ) , 892 S h i m i z u , N . 6 9 1 , 6 9 2 , 6 9 4 ( 5 5 s ) , 737 S h i n s a k a , K. 7 6 5 ( 3 7 ) , 7 7 3 ( 4 8 ) , 7 7 9 S h i o k a w a , T. 4 7 6 , 4 7 7 ( 4 4 ) , 5 2 5 Shirahama, H. 1 0 3 , 112, 114, 116, 117 ( 6 3 ) , 729 Shirley, I.M. 1 6 3 , 164 ( 1 1 2 ) , 184

678,

808,

677,

A u t h o r index S h m i d t , O.I. 8 6 0 ( 1 8 7 ) , 891 S h m y r e v a , R.K. 9 0 6 ( 1 4 3 ) , 922 Shoji, A . 3 6 9 ( 7 7 ) , 390 S h o l d , D . M . 4 3 5 ( 1 9 9 ) , 453 S h o n o , T. 7 9 1 ( 4 2 ) , 7 9 9 ( 6 3 ) , 8 0 0 ( 6 4 ) , S h o o l e r y , J.N. 5 1 , 6 3 ( 4 5 ) , 7 7 Short, E.L. 8 1 5 ( 1 6 ) , 886

807

892

451-453

(162), Sieflcen, M . W . 6 9 1 , 6 9 2 , 6 9 5 ( 5 6 a ) , 738 S i e g b a h n , H. 4 7 1 , 4 7 6 , 4 8 9 ( 2 0 ) , 5 2 5 S i e g b a h n , K. 4 7 4 ( 2 6 , 2 7 ) , 4 7 6 ( 3 7 ) , 4 8 7 ( 2 7 , 134), 4 8 9 ( 1 3 4 ) , 4 9 3 , 4 9 9 ( 2 7 ) , 5 2 5 ,

528

738

S i e g e l , M . G . 5 8 9 ( 1 8 7 a ) , 606 S i e g e l , S. 165 ( 1 1 9 ) , 184 S i e g e l , T . M . 7 9 9 ( 6 2 ) , 807 S i e g e r m a n n , H. 7 8 2 ( 1 8 b ) , 806 S i e h l , H . - U . 3 7 9 ( 1 6 2 ) , 392 S i e m i o n , I.Z. 8 7 3 ( 2 4 2 ) ,

892

S i e n a , M . G . 3 0 8 , 3 1 4 ( 3 9 ) , 347 Siggel, M.R.F. 547 (153), 557 Sigler, S. 8 9 7 ( 1 3 ) , 9 7 9 S i g o i l l o t , J.C. 9 0 4 ( 8 4 ) , 927 Silberlied, R . E . 9 0 6 ( 1 2 3 ) , 922 Silbernagel, B . G . 3 6 9 ( 9 4 ) , 391 Silberstein, J. 4 3 5 ( 2 0 5 ) , 4 5 4 S i l v e r m a n , J. 7 7 3 ( 5 4 , 5 5 ) , 780 S i l v e r m a n , S . B . 5 7 3 ( 1 0 8 a ) , 603 S i l v e r s m i t h , E.F. 9 2 9 ( 1 7 ) , 9 5 9 Silverton, J.V. 9 3 9 ( 8 6 ) , 9 4 0 ( 8 7 ) , 960 S i m m o n d s , D.J. 5 5 6 ( 1 3 a ) , 600 S i m m o n d s , P. 9 0 8 , 9 0 9 ( 1 7 9 ) , 923 S i m m o n s , H . E . 5 9 3 ( 1 9 9 ) , 606 S i m m o n s , M . C . 2 9 4 ( 9 ) , 346 S i m o n , I. 81 ( 2 3 ) , 93 Simon, M. 6 3 3 (72b), 657 Simonetta, M. 33 (25), 77 S i m s , L . B . 8 7 7 ( 2 6 1 ) , 881 ( 2 6 1 , 2 6 2 ) , 8 8 2 (261, 262, 269), Singer, L . A . 8 5 0 ( 1 3 5 ) , 889, 9 7 9 ( 9 1 ) , 9 9 6 S i n g h , A . 5 6 8 , 5 7 7 ( 7 8 ) , 602 S i n g h , S.P. 9 0 2 ( 6 1 ) , 920 S i n g h , V . 5 9 7 , 5 9 8 ( 2 1 0 b ) , 607, 6 9 1 ( 5 3 h ) ,

893

737

Sinke, G.C. 227 (20, 22), 228, 2 3 0 , 2 3 5 , 2 4 4 , 247, 250, 255, 257, 264, 276 (22), S i n k e , G.F. 283 S i n n e m a , A . 122 ( 1 5 8 ) , 131 S i n o t o v a , E . N . 8 4 7 ( 1 2 5 - 1 3 0 ) , 8 4 8 ( 1 2 7 , 130),

285

Shteinman, A.A. 5 4 0 (88), 5 4 9 , 657 (18), 658 (23a, 23c), 6 5 9 (36), 6 7 7 , 6 7 8 , 868 (218, 2 1 9 ) , 8 6 9 ( 2 2 0 ) , 8 7 0 ( 2 1 9 , 2 2 1 ) , 871 (223, 224), Shugaev, B.B. 918 (279), 925 Shulpin, G . B . 6 5 8 ( 2 6 ) , 6 7 7 S h u n d o u , R. 8 0 2 ( 7 0 ) , 807 S i a m , K. 8 8 ( 4 6 , 4 7 ) , 8 9 ( 4 6 , 5 1 ) , 9 4 S i c k l e s , B.R. 5 7 8 , 5 7 9 ( 1 3 4 b ) , 604 Sidebottom, H.W. 9 6 9 (48), 995 S i d o r o v a , I.P. 9 0 6 ( 1 4 3 ) , 9 2 2 S i e c k , L . W . 4 0 7 ( 9 5 ) , 4 1 7 ( 9 5 , 143), 4 2 4

Siegbahn, P.E.M. 698 (69a),

1049

889

Sironi, G. 8 5 9 ( 1 8 3 ) ,

891

S i s k i n , M . 6 3 0 ( 5 8 , 6 0 ) , 650, 651 S i x m a , E.L.J. 6 3 7 ( 9 0 , 9 1 ) , 651 Sjoberg, S. 8 2 0 ( 3 7 ) , 887 Skattebol, L. 5 9 3 , 5 9 4 ( 2 0 2 a ) , 607,

692, 694

( 5 9 c ) , 738, 9 3 1 ( 4 6 ) , 9 3 3 ( 4 7 ) , 9 5 9 S k e l l , P.S. 6 7 3 ( 8 2 ) , 6 7 9 , 8 2 3 ( 5 8 ) , 887, 9 6 4 (4, 6), 9 6 6 (20), 971 (70), 9 7 2 (20), 983 ( 4 , 6 ) , 9 8 4 , 9 8 5 ( 6 ) , 9 9 1 ( 4 , 1 4 2 , 146), 992 (152), 994, 995, 997 Skinner, G . B . 8 6 6 , 8 6 7 ( 2 1 3 , 2 8 4 ) , 892 Skinner, H . A . 2 3 5 ( 4 0 ) , 286 Skuballa, N . 5 9 0 , 5 9 1 ( 1 9 4 e ) , 606 Skuballa, W . 5 6 2 ( 5 2 ) , 6 0 7 Skurat, V . E . 7 0 8 ( 9 7 b ) , 739 Slanina, Z. 8 4 ( 3 4 ) , 93 Slater, N . B . 8 7 4 , 8 7 9 ( 2 4 8 b ) , 892 S l a u g h , L.H. 9 8 8 ( 1 2 3 ) , 9 9 6 S l e e , T . S . 2 6 , 31 ( 2 4 ) , 7 7 , 7 9 ( 2 ) , 93 Slessor, K.N. 9 0 6 (135), 922 Sletten, E. 3 7 7 ( 1 4 5 , 151), 392 S l i a m , E. 8 8 3 ( 2 7 2 ) , 893 S m a l l , T. 8 4 3 ( 1 1 9 , 120), 889 S m a l e , S. 21 ( 2 3 ) , 7 7 Small, L.E. 5 4 4 (146), 557 S m i t , P. 9 7 0 ( 6 5 ) , 9 9 5 S m i t h , B . E . 3 7 7 ( 1 5 0 ) , 392 S m i t h , C.Z. 7 8 4 , 7 8 5 ( 2 6 ) , 7 9 7 ( 2 6 , 5 7 , 5 8 ) ,

806, 807 Smith, D. 4 0 6 (74, 81), 4 5 7 , 537, 538 (53), 5 4 9 , 6 8 7 ( 3 9 e ) , 736, 7 6 3 , 7 6 4 ( 3 1 ) , 779 S m i t h , D . H . 3 5 6 ( 2 2 ) , 389 S m i t h , D . L . 4 0 6 ( 7 1 ) , 4 3 5 ( 2 0 2 ) , 4 5 7 , 453 Smith, G.M. 6 7 2 (75), 6 7 9 S m i t h , G . V . 165 ( 1 1 9 ) , 7 8 4 Smith, G.W. 898 (18), 9 7 9 , 9 8 3 (107), 9 9 6 S m i t h , H. 9 8 3 ( 1 1 0 ) , 9 9 6 S m i t h , J.C. 8 2 6 ( 7 5 ) , 8 8 8 S m i t h , J.E. 8 9 9 ( 2 8 ) , 9 2 0 S m i t h , J.G. 4 0 2 ( 3 7 ) , 4 5 0 S m i t h , J.W. 8 9 8 ( 1 7 ) , 9 7 9 S m i t h , K. 9 6 9 ( 4 5 ) , 9 9 5 Smith, N . M . 991 (141), 9 9 7 Smith, P.M. 9 0 4 (72), 9 2 / Smith, P.V. 9 0 8 (177),

923

Smith, R.D. 4 0 5 (54), 4 0 9 , 4 1 1 , 4 1 3 (109),

451, 452

Smith, R.G. 5 8 2 (158), 6 0 5 S m i t h , R.R. 8 5 5 ( 1 6 0 ) , 8 9 0 Smith, S.C. 4 4 8 (243), 4 5 4

1050

Author index

S m h h , W . B . 3 6 4 ( 5 5 ) , 390 S m h h , Z . 9 3 3 ( 4 7 ) , 959 S n e e d e n , R . P . A . 8 2 3 ( 5 7 ) , 887 Snell, A . H . 8 4 7 (123), 5 5 9 S n e h i n g , R.R. 9 0 6 ( 1 2 2 ) , 9 2 2 Snider, B . B . 7 8 2 ( 6 a , 7 c ) , 806 Snow, R.A. 4 7 9 (126), 5 2 7 S n o w d o n , L.R. 3 2 6 - 3 2 8 ( 7 6 ) , 3 3 6 , 3 3 7 ( 1 0 0 , 1 0 1 ) , 348 S n y d e r , C . H . 5 8 7 ( 1 7 9 a ) , 606 S n y d e r , H. 8 3 0 ( 8 2 b ) , 5 5 5 S n y d e r , J.P. 9 3 0 ( 3 2 ) , 9 5 9 S n y d e r , L . C . 3 6 1 , 3 8 1 , 3 8 2 , 3 8 4 ( 3 7 ) , 390 S n y d e r , R . G . 8 9 ( 5 4 ) , 94, 128 ( 2 1 1 ) , 133, 3 6 9 (92), 3 9 7 , 8 2 4 (59), 5 5 7 S o , Y . - H . 7 9 5 ( 5 5 ) , 807 Soborovskii, L.Z. 9 9 2 (161), 9 9 3 (167), 9 9 7 Soderquist, J.A. 5 4 4 (152), 5 5 7 S o d e y a m a , T. 6 6 6 , 6 6 7 ( 6 1 a ) , 6 7 5 S o k o l o v , Yu.I. 8 5 3 , 8 5 6 ( 1 4 4 ) , 5 5 9 Soliday, C L . 9 0 6 (116), 927 S o l k a , B . H . 4 0 5 ( 5 5 ) , 451, 5 3 5 ( 4 2 ) , 548 S o l l a d i e , G. 1 4 3 , 1 6 2 ( 5 2 ) , 7 5 2 Sollomon, R.A. 917 (268), 925 Sollomon, R.O. 9 1 7 , 918 (269), 925 S o l o m o n , D . R . 3 2 9 ( 8 2 ) , 348 S o l o m o n , P.R. 3 1 4 ( 4 0 ) , 347 Solov'yova, G.V. 815, 822 (Ip), 556 S o l u m , M . S . 3 7 6 ( 1 4 4 ) , 392 S o m a y a j u l u , G . R . 2 0 7 ( 5 0 ) , 213, 2 3 5 ( 3 8 ) , 2 5 6 S o m m e r , J. 5 3 2 ( 1 7 ) , 5 3 8 , 5 3 9 ( 1 7 , 6 3 ) , 548, 549, 6 1 0 ( 2 b ) , 6 1 3 ( 1 8 b ) , 6 1 8 ( 3 6 a , 3 6 b , 37), 621 (36a, 36b), 6 3 0 (58, 61), 631 ( 6 1 ) , 6 3 3 ( 7 2 b ) , 649-651 Sonnet, P.E. 9 0 6 (131), 9 2 2 S o n n t a g , C . v o n 7 0 2 ( 7 7 b ) , 738 S o n n t a g , E.L 9 8 1 ( 9 9 ) , 9 9 6 S o n n t a g , F.J. 9 8 2 ( 1 0 1 ) , 9 9 6 Sopchik, A. 991 ( 1 4 9 , 150), 9 9 7 Sorensen, J.S. 9 0 7 (156), 9 2 2 Sorensen, N . A . 9 0 7 (156), 9 2 2 Sorensen, P.D. 9 0 4 (77), 927 S o r e n s e n , T . S . 4 3 0 ( 1 8 5 ) , 453, 6 9 1 , 6 9 2 ( 5 5 a ) ,

737 Sorita, T. 128 ( 2 2 4 ) , 133, 3 7 6 ( 1 3 5 , 1 3 6 , 1 3 9 ) ,

392 S o r m , F. 9 0 1 ( 5 2 ) , 9 0 5 ( 1 0 2 ) , 920, 921 S e n d e r s , M.Jr. 2 3 5 ( 4 2 ) , 2 3 7 ( 4 9 ) , 2 5 6 S o v o c o l , G . W . 9 0 7 ( 1 6 3 ) , 923 S o w a , H. 1 6 9 ( 1 2 5 ) , 184 S o w d e n , R . G . 8 8 1 ( 2 6 5 ) , 893 S o w i n s k i , A . F . 5 6 0 ( 4 0 ) , 601 S p a n g e t - L a r s e n , J. 4 7 8 ( 8 7 , 1 0 5 ) , 4 7 9 ( 1 1 3 , 116, 1 1 7 , 1 2 5 ) , 4 8 0 ( 1 1 6 , 129), 5 2 7 , 525 S p a n s w i c k , J. 9 8 9 ( 1 3 3 ) , 9 9 6 S p e e r s , G . C . 3 1 8 , 3 1 9 ( 5 1 ) , 347

Speier, G. 8 5 4 ( 1 4 8 b ) , 890 S p e i e r , J.L. 9 9 2 ( 1 5 1 ) , 9 9 7 Spence, M.W. 9 0 7 (146), 9 1 4 (215), 9 2 2 ,

924 S p e n c e r , J.F.T. 9 1 6 ( 2 5 0 ) , 924 S p e n c e r , K . M . 163 ( 1 0 5 ) , 184 Spenser, R.B. 189, 2 0 4 ( 2 1 ) , 2 7 2 Speranza, M . 8 3 5 , 8 3 6 ( 1 0 0 ) , 8 4 0 ( 1 1 1 ) , 5 5 5 , 559 S p i e l m a n n , W . 3 6 8 ( 6 2 ) , 390 S p i n e l l i , H. 9 8 9 ( 1 3 4 ) , 9 9 6 S p i n e l l i , H.J. 9 6 9 , 9 7 3 ( 5 6 ) , 9 9 5 Spiteller, G. 3 9 6 , 3 9 8 ( 1 0 ) , 4 2 3 ( 1 5 6 ) ,

450,

453 Spiteller-Friedmann, M . 3 9 6 , 3 9 8 ( 1 0 ) , 4 2 3 ( 1 5 6 ) , 450, 453 Spitzer, U . A . 7 8 2 ( 1 3 ) , 5 0 6 Spitznagel, G.W. 5 4 2 , 5 4 6 (109), 5 4 7 ( 1 0 9 , 1 5 6 ) , 550, 551 Sponsler, M . B . 6 6 2 (44), 6 7 5 S p o o r m a k e r , T. 3 8 0 ( 1 7 7 ) , 3 8 2 ( 1 7 7 , 1 9 1 ) , 3 8 4

( 1 7 7 , 195),

392,393

Spurr, P.R. 7 9 ( 7 ) , 93 Spyckerelle, C. 8 9 8 (19), 9 7 9 Squillacote, M.E. 1 1 8 ( 1 1 9 ) , 1 1 9 ( 1 2 9 , 131, 133), 1 2 0 ( 1 3 1 , 1 3 3 ) , 121 ( 1 5 5 ) ,

J30,

131 S q u i r e s , R.R. 5 4 2 ( 1 1 0 - 1 1 2 ) , 5 4 3 ( 1 1 0 , 1 1 1 ) , 545 (110-112), 5 4 6 (111), 547 ( 1 1 1 , 112), 550 Srica, V . 3 7 7 ( 1 4 9 ) , 392 Sridar, V . 5 8 9 ( 1 8 7 a , 1 8 7 b ) , 606 Srikrishna, A . 5 8 2 ( 1 5 2 ) , 605 Srinivasan, R. 6 8 2 ( 1 0 a , 1 0 b ) , 7 0 2 ( 7 7 a , 7 7 c ) , 703 (79b), 7 0 7 (90), 7 0 8 (90, 9 7 c - ^ ) , 7 2 4 , 7 2 5 , 7 3 0 ( 7 9 b ) , 735, 738-740, 9 8 1 (99), 9 8 2 (101), 9 9 6 Srisukh, D . 3 2 3 ( 6 8 ) , 348 Staddon, B . W . 9 0 5 (101), 927 S t a d e l m a n n , J.P. 4 7 7 ( 6 6 ) , 5 2 6 Staemler, V. 5 3 2 ( 2 7 ) , 5 4 5 Staffeldt, J. 5 6 2 ( 5 2 ) , 601 Stagner, B . A . 2 9 5 ( 1 3 ) , 346 Stahl, D . 4 0 6 ( 6 0 ) , 4 1 6 , 4 2 1 ( 1 4 0 ) , 4 3 5 ( 1 4 0 , 209), 4 3 6 (140), 438 (218-221), 4 3 9 (218-220), 440 (221, 223, 224), 441 (219, 224), 4 4 2 (140, 221), 4 4 3 (221), 444 (229-234), 4 4 5 (234), 4 4 6 (234, 2 3 5 ) , 4 4 7 ( 2 3 4 - 2 3 6 ) , 451, 452, 454 Stahl, W . J . 3 4 0 ( 1 0 6 , 1 0 7 ) , 349 Staiger, G. 5 7 4 ( 1 1 3 e ) , 603 Staley, R.H. 6 7 4 ( 8 5 ) , 6 7 9 Stallberg, G. 5 8 3 ( 1 6 2 ) , 605 S t a l l b e r g - S t e n h a g e n , S. 141 ( 3 6 ) , 7 5 2 , 4 0 8 , 4 1 5 ( 1 0 1 ) , 4 5 7 , 5 8 3 ( 1 6 2 ) , 605 Stamm, E. 9 4 0 ( 9 3 ) , 967 S t a n g e , A . 5 6 5 , 5 6 6 ( 6 6 c , 6 6 e ) , 602

A u t h o r index Stangl, R. 9 5 7 , 9 5 8 ( 1 4 6 ) , 9 6 2 Staniland, P A . 168 ( 1 2 3 ) , 184 Stanislowski, A.G. 657 (20), 6 7 7 S t a n k i e w i c z , M . 4 0 4 ( 4 3 ) , 450 Stanley, J.P. 9 6 9 ( 4 2 ) , 9 9 5 Stanton, H . E . 4 1 7 ( 1 4 1 ) , 452 Stapersma, J. 4 7 9 ( 1 1 2 ) , 5 2 7 Starck, B . 113 ( 1 0 8 ) , 130 Staudinger, H. 1 6 3 , 164 ( 1 1 3 ) , 184 S t e a c i e , E . W . R . 9 6 9 ( 3 5 ) , 994 S t e a d m a n , J. 4 0 4 ( 4 7 ) , 450 Steams, R.A. 978, 9 8 6 (90), 996 Steel, C. 7 0 8 , 7 1 6 ( 9 5 ) , 739 Steel, M . C . F . 8 6 5 ( 2 1 1 ) , 891 S t e i g e r w a l d , M. 6 5 6 ( 1 1 ) , 6 7 7 Stein, H.J. 6 8 2 ( 1 2 a ) , 735 Stein, M . 81 ( 2 9 ) , 93 Steinbach, R. 5 7 7 ( 1 2 5 b ) , 5 8 6 ( 1 7 8 ) ,

Stocker, M . 3 7 7 ( 1 4 6 ) , 3 8 4 ( 2 0 0 , 2 0 1 , 2 0 6 ) , 3 8 5 , 3 8 6 ( 2 0 6 ) , 392, 393 S t o c k l i n , G. 831 ( 8 9 ) , 8 5 3 ( 8 9 , 1 3 9 ) , 888,

889 Stoddart, C . T . H . 8 4 9 ( 1 3 2 ) , Stoddart, I.K. 7 8 9 ( 3 9 b ) , Stohrer, W . - D . 9 3 3 ( 5 3 ) , Stoler, A . 3 3 4 , 3 3 6 ( 9 8 ) ,

889

807 960 348

S t o n e , F . G . A . 5 5 5 ( 2 ) , 600 Storch, W.J. 9 2 8 ( 1 2 ) , 9 5 9 Stothers, J.B. 361 ( 3 9 , 4 2 , 5 0 ) , 3 6 2 ( 3 9 ) , 3 6 8 ( 6 5 , 6 6 ) , 390 Stoutland, P . O . 6 6 2 ( 4 3 , 4 4 ) , 678 Stover, P . M . 9 0 7 ( 1 5 3 ) , 9 2 2 S t o w e l l , J.C. 5 4 2 , 5 4 3 ( 1 1 8 ) , 550, 6 9 2 ( 6 2 c ) ,

738 604,

606 Steiner, B . 3 9 8 , 4 0 9 , 4 1 7 ( 1 5 ) , 450 Steiner, B . W . 4 1 0 , 4 1 4 ( 1 1 5 ) , 452 Steinmetz, M.G. 6 8 2 , 7 0 0 (18a), 711 (18a, 111), 7 3 0 ( 1 8 a ) , 736, 740 S t e n h a g e n , E. 141 ( 3 6 ) , 182, 4 0 8 , 4 1 5 ( 1 0 1 ) , 4 5 7 , 5 8 3 ( 1 6 2 ) , 605 Stephens, M.E. 35 (28), 7 7 S t e p h e n s , P.J. 140 ( 2 8 ) , 182 S t e p h e n s o n , B . 1 4 3 , 162 ( 5 3 ) , 182 S t e p h e n s o n , D . S . 120 ( 1 5 0 , 1 5 1 b ) , 121 ( 1 5 1 b ) , 131, 5 6 0 , 5 6 1 ( 4 4 a ) , 6 0 7 S t e p h e n s o n , M . 6 1 9 ( 4 4 a ) , 650 S t e m , P.S. 104, 109 ( 6 6 ) , 7 2 9 S t e m h e h , S. 113 ( 1 0 9 ) , 130 Stetten, D . W . , Jr. 8 5 4 ( 1 4 9 ) , 890 Steu, J. 7 1 2 , 7 1 7 , 7 1 9 , 7 2 1 ( 1 2 1 a ) , 741 Stevens, D.R. 895 (1), 9 7 9 S t e v e n s , N . P . 9 0 8 ( 1 7 8 ) , 923 S t e v e n s , P.J. 140 ( 2 4 ) , 182 Stevenson, D.P. 399 (17), 411 (118), 425 ( 1 6 8 ) , 4 3 7 ( 1 7 , 1 6 8 ) , 450, 452, 453, 5 3 8 ( 6 6 , 6 7 ) , 549, 6 1 2 ( 1 5 ) , 649, 8 3 8 ( 1 0 2 ) ,

888 Stewart, J.J.P. 91 ( 5 7 , 5 9 ) , 94 Stewart, R. 5 4 3 ( 1 3 5 ) , 550, 7 8 2 ( 1 3 ) , Stieglitz, J. 4 3 2 ( 1 8 6 ) , 453 Shies, M. 6 3 7 (89), 657

1051

806

Straatmann, M . G . 8 2 0 ( 4 4 ) , 887 Strain, P . M . 8 5 8 ( 1 7 4 ) , 890 Stransky, K. 9 0 5 ( 1 0 2 ) , 9 2 7 Strasser, J. 9 1 7 ( 2 7 0 ) , 9 2 5 Strauss, H.L. 8 9 ( 5 4 ) , 94, 128 ( 2 1 1 ) , 133,

25), 476 (25, 40), 477 (40, 50), 493, 496 (25), 525, 5 2 6 Streibl, M . 9 0 1 ( 5 2 ) , 9 0 5 ( 1 0 2 ) , 920, 921 Streitwieser, A . , Jr. 143 ( 4 8 - 5 0 ) , 151 ( 7 2 ) , 182, 183, 5 4 3 ( 1 3 1 ) , 550 S t n d h , G. 2 3 6 ( 4 7 ) , 286 Stringham, R . A . 5 7 7 ( 1 2 2 ) , 604 Strobel, H . W . 8 5 7 ( 1 6 5 ) , 890 Strong, A . B . 3 5 2 ( 1 0 ) , 389 Stroud, S.G. 7 8 2 ( 1 5 b ) , 806 Stryker, J.M. 6 6 1 , 6 7 0 ( 4 2 ) , 678 Stuart, R . S . 8 2 3 ( 5 4 , 5 5 , 5 6 b ) , 887 Smll, D.R. 227 (20, 22), 2 2 8 , 230, 235, 244, 2 4 7 , 2 5 0 , 2 5 5 , 2 5 7 , 2 6 4 , 2 7 6 ( 2 2 ) , 283,

285 Stumpf, R K . 9 1 1 ( 2 0 1 ) , 9 1 3 ( 2 0 7 , 2 0 8 ) , Suatoni, J.C. 3 2 0 ( 5 4 , 5 5 ) , 347 Subramanian, R. 5 6 5 , 5 6 6 ( 6 6 a ) , 602 S u c k , S.H. 4 9 9 , 5 0 1 ( 1 4 4 ) , 528 S u e i s h i , Y . 6 8 9 , 6 9 0 ( 4 8 c ) , 737 Suffolk,-LR. 4 7 8 (98), 5 2 7 S u g a , K. 8 0 5 ( 9 0 ) , 808

Still, P.C. 158, 159, 1 6 3 , 166, 169, 170, 173, 177 ( 9 9 ) , 183 Still, W . C . 100, 124 ( 3 5 , 3 7 ) , 127 ( 3 7 ) , 128

Sugimoto, M. 6 9 1 , 692, 6 9 4 (55s), S u g i n o m e , H. 7 9 9 ( 6 1 ) , 807 Sugita, K. 4 7 6 ( 4 9 ) , 5 2 6

( 3 5 , 2 1 8 ) , 7 2 9 , 133 Stille, J.R. 5 9 0 ( 1 9 1 ) , 606 St.Jacques, M . 3 7 3 ( 1 1 6 ) , 391 St.John M a n l e y , R. 81 ( 2 3 ) , 93 S h u k a , C. 3 6 9 ( 9 7 ) , 391

Sugita, T. 1 6 3 , 164 ( 1 1 1 ) , 184 Sugiura, Y . 9 1 8 ( 2 8 5 ) , 9 2 5

Stober, R. 4 7 9 , 5 1 6 , 5 1 9 ( 1 2 4 ) , 5 2 7 , 5 6 1 ( 4 5 a ) ,

601 Stockbauer, R. 4 7 6 ( 4 3 ) , 5 2 5

224

( 1 6 ) , 285, 3 6 9 ( 9 2 ) , 391, 8 2 4 ( 5 9 ) , 887 Straustz, O.P. 3 4 0 ( 1 0 4 ) , 349 Streets, D . G . 4 1 4 ( 1 3 3 ) , 452, 414, 415 ( 2 4 ,

S u k h D e v 5 7 4 , 5 7 5 (1131),

737

604

Sukkestad, D . 9 0 5 (115), 927 S u l y a , L.L. 8 5 5 ( 1 6 0 ) , 890 S u m m e r s , S.T. 5 7 5 ( 1 1 8 ) , 604 Sunderiand, J.G. 7 9 5 ( 5 2 a ) , 807 Sunderiin, L . S . 5 4 1 ( 9 5 , 9 6 , 102),

550

923

1052

A u t h o r index

Sunner, J. 4 1 4 ( 1 2 9 ) , Sunner, S. 2 3 6 ( 4 7 ) ,

452

Taft, R . W . , Jr. 2 0 2 , 2 0 8 ( 3 2 ) , 2 7 2 Tagliarento, G. 9 1 7 , 9 1 8 ( 2 6 4 ) , 9 2 5 Tagliavini, E. 5 8 2 ( 1 5 4 ) , 605 Tahara, Y. 5 9 7 , 5 9 8 ( 2 1 0 a , 2 1 0 b ) , 607,

286

S u o m a l a i n e n , H. 9 1 6 ( 2 4 7 ) , 924 Surba, J. 9 6 9 , 9 7 9 ( 5 7 ) , 995 Suri, S . C . 5 8 2 ( 1 5 2 ) , 605 S u r m i n a , I.G. 4 7 7 ( 6 2 ) , 526 S u s h i n s k i i , M . M . 2 2 3 ( 1 0 ) , 285 S u s t m a n n , R. 5 8 7 ( 1 8 0 ) , 606 Sutcliffe, L.H. 3 8 0 ( 1 7 3 ) , 392 Suter, U . W . 142 ( 4 3 ) , 157 ( 9 8 ) , 182, Sutherland, M . D . 1 4 2 ( 3 7 ) , 182 Sutter, E. 9 0 1 , 9 0 2 ( 5 4 ) , 920 Sutton, J.C. 9 8 0 ( 9 3 ) , 996 Sutton, J.R. 801 ( 6 6 b ) , 807 Suzuki, Suzuki, Suzuki, Suzuki,

A. H. M. S.

633 (70, 71, 72a), 5 8 2 ( 1 6 1 ) , 605 3 8 8 ( 2 2 7 ) , 393 152 ( 8 2 ) , 183

183

651

607,

6 9 1 ( 5 3 a , 5 3 e , 5 3 0 , 737 Takaoka, K. 5 8 2 ( 1 6 1 ) , 605 Takaya, H. 5 5 8 ( 2 5 a , 2 5 b ) , 6 0 7 , 7 1 2 , 7 1 3

S u z u k i , T. 7 1 2 , 7 1 3 ( 1 1 5 b ) , 7 2 4 , 7 2 5 ( 1 3 0 a ) ,

740, 741 S v e c , H.J. 4 1 0 ( 1 1 1 ) , 4 5 2 Svensson, B.E. 906 (136), 922 S v e n s s o n , S. 4 7 4 , 4 8 7 , 4 9 3 , 4 9 9 ( 2 7 ) , 5 2 5 S w a b , R . E . 3 2 0 ( 5 4 ) , 347 S w a b y , R.J. 9 0 0 ( 3 4 ) , 920 S w a i n , F . W . 9 0 8 ( 1 8 1 ) , 923 Swart, P.K. 3 4 1 ( 1 1 3 ) , 349 S y n a k , E. 9 0 6 ( 1 1 9 ) , 9 2 2 S y n g e , R . L . M . 3 2 2 ( 6 7 ) , 348 S y r e y s h c h i k o v , V . A . 8 4 7 ( 1 2 5 , 126), 889 S y v e r u d , A . N . 2 2 8 ( 2 3 ) , 2 5 9 ( 6 0 ) , 285, 287 S z a b o , A . 4 5 7 , 4 6 0 ( 7 ) , 524 S z a b o , I. 4 1 4 ( 1 2 9 ) , 452 Szafranek, J. 9 0 5 ( 1 0 9 ) , 9 2 7 Szafranell, J. 9 0 6 ( 1 1 9 ) , 9 2 2 S z e i m i e s , G. 41 ( 3 9 ) , 7 7 , 101 ( 5 1 ) , 7 2 9 , 4 7 7 ( 6 7 ) , 4 7 9 ( 6 7 , 107), 5 1 6 , 5 2 0 , 5 2 4 ( 6 7 ) , 526, 527, 5 6 8 ( 7 6 ) , 5 8 3 ( 1 6 7 b ) , 5 9 3 , 5 9 4 ( 2 0 2 b , 2 0 2 c , 2 0 2 e ) , 5 9 8 , 5 9 9 ( 2 1 5 c ) , 602, 605, 607, 608, 9 3 3 ( 5 5 ) , 9 4 7 ( 1 0 5 ) , 9 4 9 ( 1 0 8 - 1 1 0 , 1 1 2 , 113), 9 5 1 ( 1 0 5 , 1 0 8 , 1 1 0 , 1 1 2 , 120, 121), 9 5 3 ( 1 2 6 ) , 9 5 4 ( 1 2 7 - 1 3 0 ,

132), 9 5 6 ( 1 3 7 , 138, 140, 141), 960-962

( 1 1 5 b ) , 7 2 4 , 7 2 5 ( 1 3 0 a ) , 740, 741 Takeda, T. 5 6 5 ( 6 2 b ) , 602 Takeshita, K. 4 8 7 , 4 8 9 ( 1 3 4 ) , 528 Takeshita, M . 128 ( 2 2 0 ) , 133 Takeshita, T. 6 4 3 ( 1 0 4 ) , 6 5 2 T a k e s u e , T. 6 8 6 ( 3 6 ) , 736 T a k e u c h i , T. 4 0 8 ( 1 0 6 , 1 0 7 ) , 452 Takeuchi, Y. 9 1 8 (285), 9 2 5 T a k e y a m a , T. 5 6 8 ( 8 1 b ) , 602 T a k e y u , G. 8 7 1 ( 2 2 9 ) , 892 Takigku, R. 341 ( 1 1 1 ) , 349 T a k i g u c h i , H. 9 8 8 ( 1 2 5 ) , 9 9 1 ( 1 4 8 ) , 996, Tal, Y . 9 ( 1 2 ) , 7 7 Talas, E. 6 8 5 , 6 8 6 ( 3 3 ) , 736 Talroze, V . L . 4 0 7 ( 8 6 , 8 7 ) , 4 5 7 , 5 3 2 ( 1 ) ,

Tamiaki, H. 7 0 5 ( 8 3 0 , 739 Tamura, M . 5 8 5 ( 1 6 9 a , 1 6 9 b ) , 605,

824 (60),

Tamura, N . 7 6 8 ( 4 1 ) , 7 7 9

Tan, E.G. 8 5 8 ( 1 7 3 , 174), 890

Tabata, Y . 7 6 8 ( 4 1 ) , 7 7 3 ( 5 5 ) , 779, 780 Tabet, G . E . 6 3 2 ( 6 7 ) , 6 3 3 , 6 3 5 ( 7 6 ) , 6 5 7 Tabor, D . C . 6 4 6 ( 1 1 0 ) , 6 5 2 T a c h i k a w a , E . 8 4 2 , 8 4 3 ( 1 1 7 ) , 889 Tachiya, M. 7 6 3 (30a), 779 Tadanier, J. ( 4 1 ) , 182 Taft, R . W . 5 4 3 ( 1 3 3 ) , 550

604,

887

S z e k e r e s - B u r s i c s , E. 6 9 0 ( 4 9 ) , S z e p e s , L. 4 7 6 ( 4 8 ) , 5 2 6 603

548,

605

Tamura, R. 5 8 2 ( 1 5 9 a , 1 6 0 ) , 5 8 3 ( 1 6 0 ) , Tan, C T . 361 ( 3 9 , 4 2 ) , 3 6 2 ( 3 9 ) , 390

737

997

8 6 7 ( 2 1 6 ) , 892 Tam, W. 657 (15), 6 7 7 Tambarulo, R. 6 3 7 , 6 4 0 ( 8 8 ) , 6 5 7 T a m b u n a n , U . S . F . 9 3 8 ( 8 2 ) , 960 T a m e l e n , E.E. v a n 5 7 6 ( 1 2 0 a ) , 5 8 2 ( 1 5 3 ) ,

S z e i m i e s - S e e b a c h , U . 9 4 9 ( 1 0 8 - 1 1 0 , 112), 9 5 1 ( 1 0 8 , 110, 112, 121), 967

Szmant, H.H. 5 7 4 (110c), S z o n d y , T. 6 9 0 ( 4 9 ) , 737

691

( 5 3 h ) , 737 Takagaki, T. 5 6 8 ( 8 1 a ) , 602 T a k a g a w a , M. 6 3 3 , 6 3 5 ( 7 4 ) , 6 5 7 Takagi, M . 9 1 6 ( 2 4 4 ) , 924 Takahara, Y. 9 1 5 ( 2 4 2 ) , 924 Takahashi, K. 9 3 9 ( 8 6 ) , 9 4 0 ( 8 7 ) , 960 Takahashi, N . 801 ( 6 6 a ) , 807 Takahashi, Y . 6 3 3 ( 7 0 , 7 1 , 7 2 a ) , 6 5 7 Takahayashi, F. 123 ( 1 8 1 ) , 7 i 2 Takaishi, K. 3 5 2 ( 2 ) , 389 Takaishi, N . 5 9 3 , 5 9 5 ( 2 0 3 a ) , 5 9 7 ( 2 1 4 ) ,

Tan, S.L. 9 8 8 ( 1 2 5 ) , 9 9 1 ( 1 4 7 - 1 4 9 ) , 996, Tanabe, K. 8 9 ( 5 1 ) , 9 4 Tanaka, A . 9 1 6 ( 2 4 6 ) , 9 2 4 Tanaka, H. 4 0 8 ( 1 0 6 ) , 4 5 2 Tanaka, M . 6 6 6 , 6 6 7 ( 6 1 a ) , Tanaka, N . (53h), Tanaka, Y . Tang, R . G . Tang, Y . N .

605

997

678

5 9 7 , 5 9 8 ( 2 1 0 a , 2 1 0 b ) , 607, 6 9 1 737 673 (79), 679 36 (34), 77 841 (113a), 8 4 2 , 8 4 3 ( l l 3 a , 114,

117), 889

A u t h o r index Tanida, H. 3 8 2 ( 1 8 4 ) , 393, 7 1 2 , 7 1 7 ( 1 1 9 a ) ,

740 Taniguchi, M . 5 6 1 ( 4 5 c ) , 60J Tanko, J. 6 8 2 ( 3 a ) , 735 Tanko, J . M . 9 6 4 ( 4 ) , 9 7 2 ( 7 3 ) , 9 8 3 ( 4 ) , 9 9 1 ( 4 , 146), 9 9 2 ( 1 5 2 ) , 994, 995, 997 T a n n e n b a u m , E . 3 2 1 ( 6 5 ) , 348 Tanner, D . D . 5 8 2 ( 1 5 9 b ) , 605, 9 6 4 ( 1 0 ) , 9 6 9 ( 1 0 , 5 3 ) , 9 7 2 ( 7 4 ) , 9 8 6 ( 1 1 9 , 120), 9 8 7 ( 1 0 , 1 2 0 , 121), 9 8 8 ( 1 1 9 , 1 2 4 - 1 2 6 , 129, 131), 9 8 9 ( 1 1 9 , 137), 9 9 1 ( 1 4 5 , 1 4 7 - 1 4 9 ) , 994-997 Tanno, K. 7 6 5 ( 3 7 ) , 7 7 9 Tapie, P. 9 0 4 ( 8 4 ) , 9 2 7 Tarazona, M . P . 1 7 2 ( 1 3 0 ) , 184 Tardvita, K. 9 0 5 ( 1 1 3 ) , 9 2 7 Tashiro, T. 8 1 2 , 8 1 5 , 8 2 2 ( l a , I c , I d ) , 885 Tatevskii, V . M . 2 3 5 ( 4 3 ) , 286 Tatiochi, A . 3 6 8 ( 6 4 ) , 390 Tatsumi, K. 5 8 7 ( 1 8 1 b ) , 606 Tatsuno, T. 5 6 3 ( 5 4 a ) , 602 Tatticchi, A . 169 ( 1 2 4 ) , 184 Tavernier, D . 123 ( 1 7 2 , 1 7 3 , 1 7 7 ) , 132 Taylor, E.G. 5 7 8 ( 1 2 9 c ) , 5 8 5 ( 1 6 9 c ) , 604, 605 Taylor, G . K . 9 7 1 ( 7 0 ) , 9 9 5 Taylor, J . W . 4 7 7 ( 5 6 ) , 5 0 8 ( 1 6 1 ) , 526, 528 Taylor, R. 8 0 ( 1 9 , 2 0 ) , 8 4 ( 2 0 ) , 93

1053

T h e i l h e i m e r , W . 5 5 5 ( 6 ) , 600 Thiebault, A . 7 8 2 ( 1 8 c , 2 0 , 2 1 , 2 3 ) , 7 8 3 ( 2 3 ) , 7 8 4 ( 2 0 ) , 806 T h i e l , W . 4 7 7 ( 5 3 ) , 4 8 9 ( 1 3 6 ) , 526, 528, 9 3 0 (35), 9 5 9 T h i e l e , E . 2 2 4 ( 1 6 ) , 285 Thier, W . 5 5 8 ( 2 7 ) , 601 T h i e s , H. 4 2 6 ( 1 7 6 ) , 453 T h i j s s e , G.J.E. 9 1 5 ( 2 3 7 ) , 924 T h o m a s , A . 5 0 8 ( 1 6 1 ) , 528 T h o m a s , F. 123 ( 1 8 8 ) , 132 T h o m a s , R . R . 6 9 8 ( 6 8 ) , 738 T h o m a s , T. 3 2 1 ( 6 1 ) , 348 Thomas, T.D. 547 (153), 557 T h o m a s , W . A . 3 1 6 ( 4 6 ) , 347 T h o m p s o n , D . 5 7 0 ( 8 8 a ) , 603 Thompson, G.A. 9 0 4 (74), 927 T h o m p s o n , H . B . 103 ( 5 9 ) , 7 2 9 Thompson, M.L. 928 (13), 9 5 9 Thompson, M.S. 6 5 4 , 6 7 2 (2), 6 7 7 T h o m p s o n , T . S . 3 3 0 ( 8 7 ) , 348 T h o m s e n , J. 2 3 6 ( 4 7 ) , 286 Thomsen, M . W . 7 0 0 (75b, 7 6 ) , 7 0 2 (75b), 7 0 3 ( 7 5 b , 7 6 ) , 738 T h o m s o n , T.R. 151 ( 7 2 ) , 183 Thornber, C W . 9 3 5 ( 7 6 ) , 960 T i c h y , M . 5 3 7 , 5 3 8 ( 5 3 , 5 4 ) , 549, 6 9 2 , 6 9 5

Taylor, R . T . 4 7 8 ( 9 1 , 103), 5 2 7 Teal, J.J. 9 1 8 ( 2 8 8 ) , 9 2 5 Teather, G . G . 7 7 3 ( 5 0 a , 5 0 b , 5 1 ) , 780 Tebbe, F . N . 6 5 9 ( 3 4 ) , 677 Tecklenborg, U . 3 8 4 , 3 8 6 ( 2 0 8 ) , 393

( 6 0 ) , 738 T i c k l e , I. 81 ( 2 3 ) , 93 T i d w e l l , T . T . I l l , 1 1 2 , 1 1 6 ( 1 0 4 ) , 130 T i e m a n , T . O . 7 5 4 ( 1 5 ) , 778 Tikhomirov, M . V . 4 0 4 (42), 4 1 5 (135), 4 2 5

T e c o n , P. 4 4 4 ( 2 2 9 , 2 3 0 , 2 3 2 ) , 4 4 6 ( 2 3 5 ) , 4 4 7 ( 2 3 5 , 2 3 6 ) , 454 Tedder, J . M . 7 8 9 ( 3 9 a , 3 9 b ) , 807, 9 6 8 ( 3 2 ) , 9 6 9 ( 3 7 , 3 8 , 4 8 , 4 9 ) , 9 7 0 ( 6 1 ) , 994, 995 Teeter, R . M . 3 2 2 ( 6 6 ) , 3 3 3 ( 9 6 ) , 348 Teller, E. 4 8 7 ( 1 3 1 ) , 528 Telnaes, N . 3 7 7 ( 1 4 5 ) , 392 T e m p a s , C.J. 1 0 9 , 1 1 0 ( 9 7 , 9 8 ) , 130 Tenschert, G. 3 9 9 , 4 0 0 ( 2 7 ) , 450 T e o , K G . 3 6 1 , 3 6 2 ( 3 9 ) , 390 Teranishi, Y . 9 1 6 ( 2 4 6 ) , 924 Terao, T. 3 6 9 , 3 7 0 ( 9 0 ) , 391 Terashima, K. 6 9 2 , 6 9 4 , 6 9 5 ( 5 9 b ) , 738 Terashima, P. 8 9 9 ( 2 9 ) , 920 Teratake, S. 7 1 2 , 7 1 7 ( 1 1 9 a ) , 740 Ter-Kazarova, M . A . 6 7 0 ( 6 4 b ) , 6 7 9 T e r l o u w , J.K. 4 1 2 ( 1 2 4 ) , 452

( 1 7 2 ) , 450, 452,453 T i l m a n , P. 7 7 3 , 7 7 5 ( 5 6 ) , 780 Tilquin, B . 7 7 3 , 7 7 5 ( 5 6 ) , 780 T i m m i n s , G. 8 2 6 ( 7 0 b , 7 1 ) , 887 Timmons, R.B. 988 (127), 996 T i m o n e n , R . S . 2 5 9 ( 7 2 ) , 287 Timoshenko, M.M. 4 7 7 (81), 5 2 6 T i n n e m a n s , A . H . A . 7 0 5 ( 8 3 a ) , 739 Tipker, J. 2 0 2 ( 3 7 ) , 2 7 i Tipper, C . F . H . 5 4 0 ( 7 6 ) , 549, 6 7 1 ( 6 8 ) , 6 7 9 T i s h c h e n k o , N . A . 8 8 2 ( 2 7 1 ) , 8 8 3 ( 2 7 3 ) , 893 Tissot, B . P . 3 2 5 ( 7 5 ) , 348, 9 0 8 ( 1 7 1 ) , 9 0 9 ( 1 8 8 ) , 923

Ternansky, R.J. 3 8 2 ( 1 8 6 ) , 393, 5 9 2 ( 1 9 6 b ) ,

606 Teschner, M . 9 0 9 ( 1 9 5 ) , 923 T e t e n y i , P. 8 6 0 ( 1 9 3 - 1 9 5 ) , 8 6 1 ( 1 9 4 , 1 9 5 , 2 0 0 ) , 891 Tezuka, T. 7 7 3 ( 4 8 ) , 7 7 9 Thaler, W . A . 9 6 9 ( 5 0 ) , 9 9 5 Theard, L . M . 7 5 6 ( 1 7 ) , 7 7 9

Tjabin, M . B . 8 6 8 ( 2 1 9 ) , 8 6 9 ( 2 2 0 ) , 8 7 0 ( 2 1 9 ) , 8 7 1 ( 2 2 4 ) , 892 T o b e , Y . 6 9 2 , 6 9 4 , 6 9 5 ( 5 9 b ) , 738 Tobias, D.J. 9 8 , 9 9 ( 2 0 ) , 128 Tobias, I. 166 ( 1 2 1 ) , 184 Tobias, S. 3 6 8 ( 6 3 ) , 390 Tobler, H, 5 7 4 , 5 7 5 ( 1 1 3 g ) , 603 Toda, M . 5 7 4 ( 1 1 1 a , 1 1 1 b ) , 603 Todd, D . 5 7 4 ( 1 1 2 ) , 603 Todd, P.J. 4 1 2 ( 1 2 5 ) , 452 Todd, S . S . 2 2 7 ( 1 9 ) , 2 6 4 ( 8 0 ) , 285, 287 T o g a s h i , A . 5 9 7 , 5 9 8 ( 2 1 0 a ) , 607

1054

A u t h o r index

T o g a s h i , M . 8 4 ( 3 4 ) , 93 T o h , H . T . 6 4 3 ( 1 0 4 ) , 652 Toi, H. 5 7 2 ( 1 0 4 ) , 603 Toi, K. 8 1 2 , 8 1 5 , 8 2 2 ( l a , I c , Id), 885 T o k a c h , S . K . 6 8 7 , 6 8 8 ( 3 8 b , 3 8 c ) , 736 T o k u d a , M . 7 9 9 ( 6 1 ) , 807 T o k u m a r u , K. 7 0 5 ( 8 3 c , 8 3 d ) , 739 T o k u n a g a , Y . 6 6 6 , 6 6 7 ( 6 1 a ) , 678 Tolbert, M . A . 5 4 1 ( 9 4 ) , 550 T o l m a n , C . A . 6 5 9 ( 3 1 ) , 677 T o m a t , R. 8 0 2 ( 6 9 ) , 8 0 4 ( 7 7 ) , 807, 808 T o m e s z k o , E . S . 7 8 2 ( 1 5 b ) , 806 T o m e z s k o , E . 9 1 5 ( 2 3 0 ) , 924 T o m i n a g a , T. 8 4 2 ( 1 1 5 ) , 889 T o m i o k a , K. 5 8 2 ( 1 5 0 ) , 605 T o n e l l i , A . E . 3 7 3 ( 1 0 7 ) , 3 7 7 ( 1 5 2 ) , 39J, 392 T o n g , H . Y . 3 3 0 ( 8 7 ) , 348 Tong, S.-B. 9 6 9 , 9 7 4 , 9 7 5 , 9 9 2 , 9 9 4 (60),

995 T o n g i o r g i , E . 8 5 9 ( 1 8 3 ) , 891 T o n g p e n y a i , N . 5 5 7 ( 1 7 ) , 600 T o o m , J . M . v a n der 3 6 1 ( 4 8 ) , 390 T o p p , A . 9 5 0 ( 1 1 7 ) , 961 Torek, B . 5 3 2 ( 2 1 , 2 6 ) , 548, 6 1 3 ( 1 7 ) , 6 1 7 ( 1 7 , 3 2 a , 3 2 b ) , 649, 650 Tori, K. 3 8 2 ( 1 8 4 ) , 393 Torii, S. 8 0 1 ( 6 5 b , 6 6 a ) , 807 Toriumi, H . 3 6 9 ( 8 6 , 8 7 ) , 391 T o r i y a m a , K. 3 7 6 ( 1 4 2 ) , 392, 4 1 7 ( 1 4 2 ) , 4 2 5 (167), 452,453 T o m a b e n e , T . G . 2 9 5 ( 1 1 ) , 346 Torti, E . 1 2 0 ( 1 3 6 ) , 131 Torupka, E.J. 5 8 3 , 5 8 4 ( 1 6 5 e ) , 605, 9 5 0 ( 1 1 5 ) ,

961 T o s c h , W . C . 3 1 6 ( 4 7 ) , 347 Totten, C E . 9 0 4 ( 7 7 ) , 921 Tour, J . M . 5 5 7 ( 1 4 ) , 600 T o u r o u d e , R. 8 6 4 ( 2 0 6 ) , 891 T o y n e , K.J. 5 6 1 ( 4 5 b ) , 601 Toyota, A. 4 7 8 (104), 5 2 7 T r a c e y , B . M . 1 6 3 , 1 6 4 ( 1 1 2 ) , 184 Traeger, J . C . 4 1 4 ( 1 3 0 ) , 452 Tranham, J.G. 9 7 6 , 9 8 2 , 9 8 3 ( 7 8 ) , 995 T r a t e y a k o v , V . P . 6 5 8 ( 2 4 ) , 677 T r a y n h a m , J.G. 141 ( 3 4 ) , 182, 4 3 2 ( 1 8 7 ) , 453 Trecker, D.J. 5 9 7 , 5 9 8 (21 Of), 607 T r e m i l l o n , B . 5 3 8 ( 6 2 ) , 549, 6 1 5 ( 2 4 ; 2 5 ) , 6 1 6 ( 2 5 ) , 649, 650, 7 8 5 ( 2 9 , 3 0 ) , 806 Tremper, H . S . 5 6 2 ( 4 7 ) , 601 Trendel, J . M . 3 4 5 , 3 4 6 ( 1 1 5 ) , 349 Trenen-y, V . G . 9 4 8 ( 1 0 7 ) , 961 Trevor, D.J. 6 7 3 ( 8 1 ) , 679 Trifunac, A . D . 6 8 3 ( 2 2 a ) , 736 Trimmer, M . S . 6 7 2 (74b), 6 7 9 Trinajstic, N . 1 8 6 , 1 8 8 - 1 9 0 , 2 0 6 ( 7 ) , 2 7 2 , 3 5 6 ( 2 5 ) , 389 Tripodi, M . K . 4 0 6 ( 8 4 ) , 451

Trivedi, N . 6 1 2 , 6 1 3 ( 1 4 b ) , 649 Trivedi, N.J. 6 4 3 - 6 4 5 ( 1 0 7 a ) , 6 5 2 Trka, A . 6 9 0 ( 5 1 c ) , 737 T r o m b i n i , C . 5 8 2 ( 1 5 4 ) , 605 Troni, W . 9 1 7 , 9 1 8 ( 2 6 4 ) , 9 2 5 T r o t m a n - D i c k e n s o n , A . F . 8 8 1 ( 2 6 4 , 2 6 5 ) , 893, 966 (16), 9 6 7 (28), 9 6 9 (35, 36, 51), 9 7 0 ( 5 1 ) , 9 8 3 ( 1 1 0 ) , 994-996 Trucks, G . W . 8 5 , 8 7 ( 4 1 ) , 94 True, N . S . 1 1 8 , 121 ( 1 2 2 ) , 131 Truhlar, D . G . 8 8 5 ( 2 7 5 ) , 893 T r y d i n g , N . 8 5 5 ( 1 5 8 ) , 890 T r y g o w s k i , T . M . 8 9 ( 5 2 ) , 94 Tsai, E.G. 9 7 2 ( 7 4 ) , 9 8 8 ( 1 2 6 ) , 995, 996 Tsanaktsidis, J. 5 7 8 ( 1 3 1 b , 1 3 1 c ) , 604, 7 1 1 ( 1 0 6 b ) , 740 T s a n g , C h . W . 4 3 5 ( 2 0 6 ) , 454 T s a n g , W . 9 6 6 ( 2 2 ) , 994 T s c h u i k o w - R o u x , E . 2 5 9 ( 6 8 ) , 287, 9 6 6 ( 1 8 ) ,

994 Tse, C . - W . 6 8 2 ( 3 a ) , 735 T s o n o p o u l o s , C . 2 0 7 ( 5 4 ) , 213 T s u b o y a m a , A . 1 1 9 ( 1 2 8 ) , 131 T s u c h i h a s h i , K. 5 9 3 , 5 9 5 ( 2 0 3 a ) , 607, 6 9 1 ( 5 3 f ) , 737 T s u c h i y a , M . 7 0 5 ( 8 3 c ) , 739 T s u c h i y a , T. 5 8 0 ( 1 4 3 ) , 604 Tsuji, J. 5 9 5 ( 2 0 5 ) , 607 Tsuji, T . 4 7 9 ( 1 1 8 ) , 5 2 7 T s u k i y a m a , K. 5 5 7 ( 1 9 ) , 6 0 7 T s u n o d a , T. 9 3 8 ( 8 2 ) , 960 T s u s h i m a , T. 3 8 2 ( 1 8 4 ) , 393 T s u z u k i , S. 8 9 ( 5 1 ) , 94 Tucker, A . O . 9 0 3 ( 7 0 ) , 9 2 7 Tufariello, J.J. 5 7 2 ( 1 0 3 ) , 603 T u i l l i e z , J.E. 9 1 7 ( 2 7 3 ) , 9 2 5 Tuladhar, S . M . 7 1 1 ( 1 0 8 c ) , 740 Tuleen, D.L. 991 (142), 9 9 7 T u l l i e z , J.E. 8 5 5 ( 1 6 3 ) , 890, 9 0 6 ( 1 4 2 ) , 922 T u l l o c h , A . P . 9 1 6 ( 2 5 0 ) , 924 Tumas, W . 5 4 4 , 5 4 6 , 5 4 7 ( 1 4 7 , 148), 5 5 7 Tunitskii, N . M . 4 2 5 ( 1 7 2 ) , 453 Tunitskii, N . N . 4 1 5 ( 1 3 5 ) , 452 Turecek, F. 4 2 4 , 4 3 4 , 4 4 4 ( 1 6 3 ) , 453 Turkenburg, L . A . M . 7 0 3 , 7 0 4 , 7 1 2 , 7 1 9 ( 8 0 ) ,

739 Turner, D . W . 4 7 1 , 4 7 6 ( 1 9 ) , 4 7 7 ( 1 9 , 5 1 , 5 4 ) , 4 8 7 ( 1 3 2 ) , 5 0 8 , 5 0 9 ( 5 1 ) , 525, 526,

528 Turner, M.J. 9 1 7 ( 2 7 0 ) , 9 2 5 Turner, T . F . 3 7 7 ( 1 4 8 ) , 392 Tun-o, N . J . 7 0 3 ( 8 1 a , 8 1 b ) , 7 0 7 ( 9 2 a ) , 7 0 8 (92a, 9 2 b , 9 9 , 101b, 102a, 102b), 7 0 9 (92a, 99), 7 1 0 (92a, 92b, 101b, 102a, 102b), 739, 740, 9 7 2 ( 7 2 ) , 9 9 5 T w i d d y , N . D . 5 3 7 , 5 3 8 ( 5 3 , 5 4 ) , 549

A u t h o r index Tyabin, M . B . 5 4 0 ( 8 8 ) , 549, 6 5 7 ( 1 8 ) , 6 5 9 ( 3 6 ) , 6 7 7 , 678 T y m i n s k i , I.J. 123 ( 1 8 7 a ) , 132 U c h i d a , A . 6 9 6 , 6 9 8 ( 6 7 a , 6 7 b ) , 738 U c h i d a , T. 8 0 1 ( 6 8 ) , 807 U e d a , Y . 6 8 3 ( 2 1 a ) , 736 U e m i y a , S. 6 8 6 ( 3 5 ) , 736 U e n o , N . 4 7 6 ( 4 9 ) , 5 2 6 , 801 ( 6 5 b ) , 807 U e n o , Y . 5 6 8 ( 7 7 ) , 602 U h l i c k , S . C . 8 6 0 ( 1 9 6 ) , 891 U m a n i - R o c h i , A . 5 8 2 ( 1 5 4 ) , 605 Ungar, G. 7 7 7 ( 6 7 ) , 780 U n w a l l a , R . U . 1 2 2 ( 1 6 2 ) , 131 U p t o n , C.J. 9 8 4 ( 1 1 4 ) , 996 Urbanek, T h . 5 1 9 ( 1 7 8 ) , 5 2 9 U r c h , D . 8 2 8 ( 8 1 b ) , 888 U r e y , H . C . 8 5 8 , 881 ( 1 6 9 ) , 890 Url, N . 9 0 5 ( 1 0 3 ) , 9 2 7 U s h a , R. 5 9 7 ( 2 1 3 ) , 607 U s h i d a , K. 7 1 2 , 7 1 3 ( 1 1 5 e ) , 740 U t i m o t o , K. 5 6 6 ( 6 7 ) , 602 U t l e y , J.H.P. 7 8 2 ( 1 8 d ) , 806

1055

Vegter, G . C . 9 8 2 ( 1 0 0 , 1 0 2 ) , 9 9 6 Veillard, A . 2 2 2 ( 5 ) , 285 Veksli, Z. 9 5 2 ( 1 2 3 ) , 9 6 7 Velluz, L. 1 4 0 ( 2 2 ) , 182 Ven, L.J.M. v a n de 3 5 2 ( 1 3 ) , 3 6 9 ( 8 1 ) ,

389,

391 V e n e p a l h , B.R. 9 2 9 , 9 3 0 , 9 3 3 , 9 4 4 ( 1 9 ) , 9 4 5 (19, 100), 959, 967 V e n k a t a c h a l a m , M . 5 5 6 ( 1 3 f ) , 600, 9 4 0 ( 8 8 ) ,

960 Venter, H.J. 5 7 4 , 5 7 5 ( 1 1 3 i ) , V e n z m e r , J. 85 ( 3 6 ) , 93 Verbh, L. 143 ( 5 0 ) , 182 Verhuis, J. 6 2 1 ( 4 6 ) ,

604

650

Verkeke, G. 9 6 6 ( 1 7 ) , 994 Verloop, A . 2 0 2 ( 3 7 ) , 213 Verma, A . L . 158 ( 1 0 0 ) , 183, 2 2 8 , 2 4 1 , 2 4 4 , 2 4 8 , 2 7 5 ( 2 4 ) , 285 Verma, K.K. 2 3 5 ( 4 4 ) , 286 Verma, L . A . 1 1 0 ( 1 0 1 ) , 130 Vernet, C. 9 1 6 ( 2 5 4 ) , 924 V e s e l y , M . 7 0 6 ( 8 8 d ) , 739 Vestal, M . L . 4 0 5 , 4 0 7 , 4 0 8 , 4 1 0 , 4 1 4 ( 5 8 ) , 457

V a i d y a n a t h a s w a m i , R. 5 9 3 , 5 9 5 ( 2 0 3 c ) , 607 Valle, G. 5 6 2 , 5 6 3 ( 5 1 b ) , 601 Van, A . A . 6 7 2 ( 7 4 b ) , 6 7 9 Van A l l a n , J.A. 9 3 5 ( 7 4 ) , 960 Van A l s e n o y , C. 8 8 ( 4 6 - 4 8 ) , 8 9 ( 4 6 ) , 94 Van B o s t e l e n , P . B . 9 6 9 ( 5 3 ) , 9 9 5 v a n C a t l e d g e , F . A . 122 ( 1 6 2 ) , 131 Vanderbih, J.J. 5 7 1 ( 1 0 0 ) , 603, 6 9 1 , 6 9 2 ( 5 5 d ) ,

737 Vanderesse, R. 5 6 7 ( 7 2 ) , 602 Vanderhart, D . L . 3 7 6 ( 1 3 8 ) , 392 Van der M e e r , W.J. 4 7 9 ( 1 1 2 ) , 5 2 7 VanDerveer, D . 9 4 5 ( 1 0 2 ) , 9 6 7 Van E n d e , D . 5 7 7 ( 1 2 4 ) , 604 Van E n g e n , D . 81 ( 3 0 ) , 93 Vanerin, R . E . 9 8 8 ( 1 2 7 ) , 9 9 6 Vanhee, P. 123 ( 1 7 3 , 177), 132 Van H o e r e n , W . 9 0 7 ( 1 6 5 ) , 923 Van H o o k , W . A . 8 2 5 ( 6 9 b - d ) , 887 Van Klavern, J.A. 8 2 6 ( 7 4 ) , 888 Van M e e r s s c h e , M . 9 4 7 ( 1 0 5 ) , 9 4 9 ( 1 0 9 , 111), 9 5 1 ( 1 0 5 , 121), 9 6 7 Van V l e e t , E . S . 8 5 8 ( 1 7 7 ) , 890 Varkevisser, F . A . 165 ( 1 1 6 ) , 184 Varmuza, K. 4 1 8 ( 1 4 6 ) , 452 V a m e , Z. 9 0 5 ( 1 0 9 ) , 9 2 7 Vaughan, W . E . 9 9 2 ( 1 5 3 - 1 5 7 ) , 9 9 7 Vaziri, C. 1 2 0 - 1 2 2 ( 1 4 3 ) , 131 Vebel, E.G. 9 0 6 ( 1 3 1 ) , 9 2 2 Veda, E. 5 8 5 ( 1 7 0 ) , 605 Veda, M . 9 1 6 ( 2 4 6 ) , 924 Vedejs, E. 5 7 4 ( 1 1 0 a ) , 603 Veen, A . van 1 2 2 ( 1 5 8 , 160), 131

Vetter, W . 5 5 6 ( 1 3 c ) , 600 V i c e n t e , M . 6 8 2 ( 1 5 b ) , 735 Vidal, Y . 6 4 0 ( 9 9 a ) , 6 5 7 V i e u , C. 9 1 9 ( 3 0 3 ) , 9 2 6 V i l e s o v , F.I. 4 7 7 ( 6 3 ) , 5 2 6 V i l l e m , J. 4 7 7 ( 6 2 , 6 2 ) , 5 2 6 Villem, N. 4 7 7 (62, 62), 5 2 6 Villemin, D . 578 (135),

604

V i n k o v i c , V . 5 9 3 , 5 9 4 ( 2 0 2 f ) , 607,

691, 692,

6 9 5 ( 5 5 h ) , 737, 9 5 2 ( 1 2 4 ) , 9 6 7 Viret, J. 9 1 9 ( 2 9 5 ) , 9 2 5 Visser, R.J.J. 81 ( 2 3 ) , 93 Vitek, J. 6 9 0 ( 5 1 c ) , 737 Viviani, D . 5 3 5 ( 4 4 ) , 548 V l a d u c h i c k , S . A . 5 9 3 ( 1 9 9 ) , 606 Vodicka, L. 3 2 0 , 3 2 4 ( 5 7 b ) , 347, 9 1 7 ( 2 7 2 ) , 925 V o g e l , P. 4 0 6 ( 6 0 ) , 4 0 8 , 4 3 2 , 4 3 3 ( 9 9 ) , 4 5 7 , 5 3 5 ( 4 6 , 4 8 ) , 548, 549, 7 3 1 , 7 3 2 ( 1 3 7 a ) , 747 Vogt, J. 3 9 9 ( 1 6 ) , 450 Vogt, S. 5 9 3 ( 2 0 0 a ) , 606 V o g t l e , F. 9 3 6 ( 7 8 ) , 960 Voigt, A . F . 8 2 1 ( 4 7 a , 4 7 b ) , 8 5 3 ( 1 4 0 ) , 887,

889 Void, R . L . 3 6 9 ( 8 9 ) ,

391

Volger, H . C . 6 7 2 ( 6 9 ) , 6 7 9 , 6 9 2 ( 6 2 a ) , V o l k o v a , L.K. 8 8 3 ( 2 7 3 , 2 7 4 ) , 893 V o l k o v a , V . S . 8 1 9 ( 3 2 ) , 886 Volnina, E . A . 7 0 3 ( 7 8 ) ,

738

739

Volpi, G.G. 4 0 6 ( 6 4 ) , 4 5 7 , 5 3 5 ( 4 1 ) , 548, ( 9 5 ) , 888 V o l ' p i n , M . 6 2 0 ( 4 5 a ) , 650

833

1056

A u t h o r index

Volpin, M . E . 5 5 7 ( 1 6 ) , 5 6 0 ( 4 2 ) , 5 6 9 ( 8 5 ) ,

600, 601, 603 V o l t e r , J. 861 ( 2 0 2 ) , 891 Volz, W . 4 7 7 (75), 5 2 6 Vorpagel, E.R. 5 4 0 ( 7 5 ) , 549 V o s , A . 81 ( 2 3 , 2 4 ) , 93 V o s t r o w s k y , O. 6 9 2 , 6 9 4 ( 5 9 c ) , 738 Vyshinskaja, L.I. 6 7 0 ( 6 4 a ) , 678 V y s o t s k i i , A . V . 8 1 6 , 8 7 3 ( 2 4 ) , 886

Walter, J.E. 136 ( 6 ) , 181 Walter, L. 7 2 4 , 7 2 7 ( 1 3 2 f ) , 741, 779

763 (29b),

Walter, S.R. 3 8 0 ( 1 7 5 ) , 392 W a l t m a n , R.J. 3 0 8 , 3 1 1 ( 3 2 ) , 347 W a l t o n , J.C. 7 1 2 , 7 1 3 ( 1 1 5 e ) , 740, 7 8 9 ( 3 9 b ) , 807, 9 6 9 ( 3 8 , 4 8 ) , 9 7 0 ( 6 1 ) , 9 7 6 ( 7 9 , 8 0 ) , 977 (80, 83), 978 (88), 979 (92), 9 8 0 ( 8 8 , 9 2 ) , 9 8 2 ( 8 3 , 104), 9 8 3 ( 7 9 , 8 3 ) , 9 8 8 ( 8 8 ) , 995, 996

W a a c k , R. 5 4 2 ( 1 2 1 , 1 2 4 ) , 5 5 0

Wampler, D.L. 928 (14), 9 5 9

W a c k h e r , R . C . 6 2 1 ( 4 7 ) , 650 Wada, K. 6 6 6 , 6 6 7 ( 6 1 a ) , 678

W a n g , H . - Y . 4 0 7 ( 9 2 ) , 451 W a n g , J.-Q. 5 0 9 ( 1 6 6 , 1 6 8 ) , 5 1 1 , 5 1 3 ( 1 6 8 ) , 529

Wada, N . 989 Wada, T. Waddell,

9 8 6 ( 1 1 9 ) , 9 8 8 ( 1 1 9 , 124, 131), ( 1 1 9 ) , 996 765 (34a), 779 S.T. 9 3 4 ( 6 7 , 7 2 ) , 9 5 4 ( 6 7 , 135a,

1 3 5 b ) , 9 5 6 - 9 5 8 ( 1 3 5 a , 135b), 960, 962 W a d d i n g t o n , G. 2 2 7 ( 1 9 ) , 285 W a d e l l , S.T. 41 ( 3 8 ) , 7 7 W a d s w o r t h , E.T. 9 9 2 , 9 9 3 ( 1 6 3 ) , 9 9 7 W a e g e l l , B . 122 ( 1 6 5 ) , 132 W a g n e r , C D . 4 1 1 ( 1 1 8 ) , 452, 5 3 8 ( 6 6 , 6 7 ) , 549, 6 1 2 ( 1 5 ) , 649, 8 3 8 ( 1 0 2 ) , 888 W a g n e r , F. 8 5 4 ( 1 5 2 g ) , 890 W a g n e r , H . - U . 5 6 8 ( 7 6 ) , 602, 9 5 6 ( 1 3 8 ) , 962 W a g n e r , J.J. 3 7 5 ( 1 3 1 , 132), 391, 392 Wahrhaftig, A . L . 4 1 1 ( 1 2 0 ) , 452 Wainright, M . S . 3 2 3 ( 6 8 ) , 348 W a k a b a y a s h i , T. 7 0 5 ( 8 3 c , 8 3 d ) , 739 Wakefield, B.J. 5 4 2 ( 1 2 0 ) , 550 W a l b o r s k y , H . M . 1 6 3 , 164 ( 1 1 1 ) , 165 ( 1 1 7 ) , 184, 5 8 1 ( 1 4 8 ) , 605 Waldron, R.F. 3 7 6 ( 1 4 0 ) , 392 Walia, J.S. 152 ( 8 2 ) , 183 Walker, D . M . 5 7 4 , 5 7 5 ( 1 1 3 j ) , 604 Walker, F.H. 41 ( 3 8 ) , 7 7 , 3 6 8 ( 6 0 ) , 390, 5 8 3 , 5 8 4 ( 1 6 5 b , 1 6 5 d ) , 605, 9 3 3 ( 6 3 - 6 5 ) , 9 3 4 (67), 9 5 2 ( 6 3 - 6 5 ) , 953 (63), 954 (63, 67),

960 Walker, E . M . 9 6 4 ( 7 ) , 994 Walker, G. 4 2 6 ( 1 7 6 ) , 453 Walker, J . D . 8 5 3 ( 1 4 5 ) , 889 Walker, R.F. 9 6 5 ( 1 5 ) , 994 Walker, R . W . 2 5 9 ( 6 6 ) , 287,

969 (41), 995

W a l l i n g , C. 9 6 4 ( 3 ) , 9 6 9 ( 4 3 ) , 9 7 5 , 9 8 3 ( 3 ) , 988 (128), 989 (138), 9 9 0 (139), 991

( 1 4 5 , 149, 150), 994-997 Wallner, A . 5 8 9 ( 1 8 7 c ) , 606 Walsh, A . D . 5 2 (46), 77, 508 (158), W a l s h , R. 3 ( 1 0 ) , 7 7 , 2 3 7 , 2 4 1 ( 4 8 ) ,

528 286,

682, 6 9 1 , 711 (7), 7 1 2 , 7 1 9 (123),

735,

741 Walter, H. 7 1 2 , 7 1 4 , 7 1 6 , 7 2 3 , 7 2 4 ( 1 1 6 c ) ,

740 Walter, J.A. 9 1 4 ( 2 2 4 ) ,

924

W a n g , J.-X. 8 1 2 ( l e ) , 8 1 5 , 8 2 2 ( l e , I h - k ) ,

885, 886 W a n g , Q. 6 4 1 ( 9 9 c ) , 6 5 7 W a n g , W . 5 8 9 ( 1 8 9 ) , 606 Wang, X. 6 4 3 , 6 4 4 (107c), 6 5 2 Warburton, G . A . 3 3 8 , 3 3 9 ( 1 0 2 ) , 348 Ward, D . M . 8 9 7 (1 1), 9 7 9 Ward, J.S. 5 7 0 ( 8 9 b ) , 603 Ward, J.W. 6 3 7 ( 9 4 ) , 6 5 7 Wardeiner, J. 3 8 4 ( 1 9 8 ) , 393 W a r d e n , J.L. 5 8 9 ( 1 8 8 ) , 606 W a r m a n , J.M. 7 5 9 , 7 6 2 ( 2 1 ) , 7 7 9 W a m e , R.J. 8 1 4 ( 1 3 ) , 886 Warner, J.M. 8 7 7 ( 2 5 6 ) , 893 Warner, P. 9 3 6 ( 8 0 ) , 9 4 7 ( 1 0 6 ) , 960, 961 Warner, S . A . 9 0 7 ( 1 6 3 ) , 923 W a s s e r m a n , E.P. 6 6 2 ( 4 5 ) , 678 Wassif, M . K . 9 0 7 ( 1 6 2 ) , 923 W a s y l i s h e n , R . E . 3 8 2 , 3 8 4 ( 1 8 9 , 1 9 3 ) , 393 Watanabe, K. 4 0 8 ( 1 0 0 ) , 4 5 7 Watanabe, M . 7 1 2 , 7 1 7 ( 1 1 9 a ) , 740 Watanabe, T. 8 1 2 , 8 1 5 , 8 2 2 ( l a , I c ) , 885 Watanabe, Y . 5 6 8 ( 7 7 ) , 602 W a t s o n , C.R., Jr. 5 3 9 ( 7 2 ) , 5 4 9 W a t s o n , D . G . 8 0 , 8 4 ( 2 0 ) , 93, 9 0 4 ( 8 7 ) , 927 W a t s o n , H.R. 6 5 9 , 6 7 4 ( 3 2 ) , 6 7 7 W a t s o n , P.L. 6 7 2 ( 7 4 a ) , 6 7 9 Watson, R.T. 9 6 5 , 9 6 6 , 9 7 0 (13), 9 9 4 Watts, C D . 8 9 6 ( 1 0 ) , 9 7 9 Watts, L. 5 7 8 , 5 7 9 ( 1 3 4 c ) , 604 W a y l a n d , B . B . 6 6 3 ( 5 8 ) , 678 W a y n e S i e c k , L. 4 2 5 ( 1 7 3 ) , 453 W e a v e r , W . 2 0 5 ( 4 4 ) , 213 W e a v e r s , R.T. 5 6 5 ( 6 1 ) , 602 W e b b , J.K. 9 0 4 ( 8 7 ) , 927 Weber, W . 4 7 9 , 4 8 0 , 5 1 4 ( 1 1 5 ) , 5 2 7 Weber, W.P. 6 1 4 , 635 (22), 6 4 9 Webster, D . E . 8 7 0 ( 2 2 2 ) , 892 W e d a , T. 123 ( 1 8 1 ) , 7 i 2 W e e d o n , B . C . L . 2 9 4 ( 6 , 7 ) , 346 W e e s e , G . M . 4 3 5 ( 2 0 0 ) , 453 W e g n e r , G. 3 7 6 ( 1 4 1 ) , 392

A u t h o r index W e h l e , D . 120, 121 ( 1 4 7 , 151a, 151b), 131, 5 5 6 , 557 (13j), 5 6 0 , 561 (44a, 44b), 5 7 4 ( 1 1 3 d ) , 5 8 9 ( 1 8 7 e ) , 600, 601, 603, 606 Wehner, H. 9 0 9 ( 1 9 5 ) , 923 Wehrli, S. 9 4 0 ( 8 8 ) , 960 W e i d m a n n , K. 4 8 0 ( 1 3 0 ) , 528 W e i g a n d , E.F. 361 ( 4 1 ) , 390 Weigert, F.J. 3 8 5 ( 2 1 3 ) , 393 Weiller, B . H . 6 6 2 ( 4 4 , 4 5 ) , 678 Weiner, B . 3 2 4 , 3 2 6 ( 7 3 ) , 348 Weiner, S. 112 ( 1 0 5 ) , 130, 314 ( 1 2 7 ) , 391 W e i n h o l d , F. 4 6 4 ( 1 7 ) , 525 W e i n m a n , E . O . 8 6 0 ( 1 9 7 ) , 891 Weinstein, H. 3 6 ( 3 4 ) , 7 7 W e i s a n g , F. 6 8 4 ( 2 9 ) , 736 Weisberger, G. 6 3 2 ( 6 9 ) , 651 W e i s m a n , G.R. 361 (41), 390 W e i s s , J. 7 7 5 ( 5 9 ) , 780 W e i s s , U. 5 5 6 ( 1 3 0 , 600, 9 3 9 ( 8 6 ) , 9 4 0 ( 8 7 , 8 8 ) , 960 W e i s s e r m e l , K. 6 4 4 ( 1 0 9 a ) , 652 W e i t e m e y e r , C. 3 6 8 ( 6 2 ) , 390 W e i z m a n n , C. 8 5 4 ( 1 5 0 ) , 890 W e l c h , D.I. 8 9 6 ( 1 0 ) , 919 W e l c h , J.A. 7 0 5 , 7 0 6 ( 8 5 b ) , 739 W e l c h , M.J. 8 2 0 ( 4 4 ) , 887 W e l l s , P . B . 8 7 0 ( 2 2 2 ) , 892 Welte, D . H . 3 2 0 ( 5 3 ) , 3 2 5 ( 7 5 ) , 347,

348,

908

( 1 7 1 , 180), 923 W e l t s t e i n - K n o w l e s , P . v o n 9 1 6 ( 2 7 5 ) , 925 W e l z e l , P. 7 8 2 ( 7 a ) , 806 Wenck, H. 5 9 3 ( 2 0 I d ) , 607 W e n d e l b o e , J.F. 4 0 8 ( 1 0 4 , 105), 4 1 1 , 4 1 2 , 4 1 5 , 4 4 4 ( 1 0 4 ) , 452 Wender, P.A. 9 3 8 ( 8 4 ) , 9 3 9 , 9 4 2 ( 8 5 ) , 960 Wenderoth, B . 5 8 6 ( 1 7 8 ) , 606 Wendisch, D. 507 (156), 5 2 8 W e n d o l o s k i , J.J. 9 3 0 ( 3 4 ) , 9 3 3 ( 4 8 ) , 959 Wenkert, E. 3 6 8 ( 6 4 ) , 390, 5 9 7 , 5 9 8 ( 2 1 0 c ) , 607, 6 9 1 , 6 9 2 , 6 9 5 ( 5 5 e ) , 737 W e n n b e r g , L. 4 0 7 ( 8 8 ) , 451 Wentrup, C. 711 ( 1 1 4 0 , 740 W e n z e l , T.T. 6 6 3 ( 5 2 ) , 678 Wepster, B . M . 119, 120 ( 1 3 0 ) , 122 ( 1 5 7 - 1 6 0 ) ,

131 Werme, L.G. 4 7 4 ( 2 6 ) , 4 7 6 ( 3 7 ) , 4 8 7 , 4 8 9 (134), 525,528 W e m e r , H. 120, 121 ( 1 4 6 ) , 122 ( 1 6 4 ) , 132, 361 ( 2 9 , 3 2 ) , 3 7 4 ( 1 2 4 ) , 390, 391 Werp, J. 4 7 9 ( 1 1 1 ) , 5 2 7 Werst, D . W . 6 8 3 ( 2 2 a ) , 736 Wershuk, N . H . 8 2 6 ( 7 0 b , 7 1 , 7 2 ) , 887, 888 Wertz, P.W. 9 0 6 ( 1 4 5 ) , 9 0 7 ( 1 5 3 ) , 9 2 2 W e s d e m i o t i s , C. 4 3 0 ( 1 8 0 ) , 4 4 7 ( 2 4 0 ) , 453,

454 Wesener, J.R. 3 7 7 ( 1 5 7 , 159), 392 W e s s e l s , P.L. 5 7 4 , 5 7 5 ( 1 1 3 i ) , 604

1057

West, C.T. 5 6 9 ( 8 3 a , 8 3 b ) , 602, 603 West, J.P. 9 8 6 ( 1 1 7 ) , 996 West, P. 5 4 2 ( 1 2 1 ) , 550 W e s t b r o o k , J.D. 9 7 2 ( 7 2 ) , 9 9 5 W e s t e r m a n , P . W . 3 6 9 ( 8 4 ) , 391 W e s t e n n a n n , J. 5 7 7 ( 1 2 5 b ) , 5 8 6 ( 1 7 8 ) ,

604,

606 W e s t o n , R.E. 6 8 7 ( 3 9 c ) , 736, 8 7 3 ( 2 4 5 , 2 4 7 ) , 8 7 4 , 8 7 7 , 8 7 9 , 8 8 0 ( 2 4 7 ) , 892 W e s t o o , G. 8 5 5 ( 1 5 8 ) , 890 Westrum, E.F., Jr. 2 2 7 ( 2 0 , 2 2 ) , 2 2 8 , 2 3 0 , 2 3 5 , 244, 247, 250, 255, 257, 264, 276 (22),

283, 285 W e x l e r , S. 4 0 6 ( 6 7 ) , 451,

5 3 2 ( 3 ) , 548,

830

(82c, 84), 831 (87), 838 (105), 8 5 0 (133, 135), 888, 889 W h a l e n , D . L . 5 7 0 ( 8 9 a ) , 603 W h a l e n , R. 7 8 2 , 7 9 7 , 7 9 9 ( 8 a ) , 806 W h a l o n , M . R . 108, 117 ( 8 2 ) , 130 W h e a t l e y , D . E . 9 0 0 ( 3 7 ) , 920 W h e e l e r , J.W. 9 5 3 ( 1 2 5 ) , 961 W h e e l e r , W . D . 8 5 8 ( 1 6 7 ) , 890 W h e l a n d , G . W . 4 5 6 ( 1 ) , 4 9 6 ( 1 4 2 ) , 524, 528 W h e t t o n , R.L. 6 7 3 ( 8 1 ) , 679 W h i f f e n , D . H . 145 ( 6 9 ) , 183 W h i t c o m b e , M.J. 5 7 5 ( 1 1 9 ) , 604 W h i t e , A.J. 9 6 9 , 9 7 0 ( 5 1 ) , 9 9 5 W h i t e , A . M . 4 3 6 ( 2 1 2 ) , 454, 6 2 6 ( 5 5 ) , 650 W h i t e , E . H . 5 8 1 ( 1 4 4 ) , 604 W h i t e , H . B . , Jr. 8 5 5 ( 1 6 0 ) , 890 W h i t e , J.F. 5 8 3 , 5 8 4 ( 1 6 5 g ) , 5 9 5 , 5 9 6 ( 2 0 4 d ) ,

605, 607 W h i t e , J.R. 881 ( 2 6 6 ) , 893 W h i t e , L . S . 7 0 2 ( 7 7 c ) , 738 W h i t e , S.H. 3 6 9 , 3 7 0 ( 8 5 ) , 391 W h i t e h e a d , E . V . 3 1 8 , 3 1 9 ( 5 1 ) , 347, 8 9 8 ( 1 8 , 2 0 , 2 5 ) , 9 0 8 ( 1 8 2 ) , 9 7 9 , 920, 923 W h i t e l e y , T . A . 4 7 7 ( 5 6 ) , 526 W h i t e s e l l , J.K. 361 ( 4 3 ) , 390 W h i t e s i d e , R . A . 5 3 2 - 5 3 4 ( 3 2 ) , 548 W h i t e s i d e s , G . M . 109, 110 ( 9 6 ) , 130, 5 6 0 ( 4 0 , 4 1 ) , 601, 6 6 3 ( 5 3 , 5 7 ) , 678, 8 2 0 ( 3 9 ) ,

887 W h i t i n g , D . A . 163, 164 ( 1 1 2 ) , 184 W h i t i n g , M . C . 5 5 6 ( 1 3 a ) , 600, 6 3 9 ( 9 7 ) , 6 5 7 W h i t i n g , P.R. 7 2 4 , 7 2 6 ( 1 3 2 e ) , 741 W h i t l e y , T . A . 5 0 8 ( 1 6 1 ) , 528 W h i t l o c k , H . W . , Jr. 6 9 1 , 6 9 2 , 6 9 5 ( 5 6 a ) , 738 Whitney, F.A. 9 1 6 (258), 9 2 5 Whittaker, D . 166 ( 1 2 2 ) , 178 ( 1 3 7 ) , 184 Whittaker, R.H. 8 2 0 , 8 2 1 ( 4 6 ) , 887 Whittle, E. 2 6 2 , 2 6 4 ( 7 9 ) , 287, 9 7 6 , 9 8 3 ( 8 2 ) , 995 W h i t w e l l , I. 5 4 1 ( 9 3 ) , 5 4 9 Whitworth, S.M. 6 9 1 , 6 9 2 (55a), W h y m a n , B . H . F . 3 2 3 ( 6 9 ) , 348 Whytock, D.A. 969 (47), 995

737

Author index

1058

W i b a u h , J.P. 6 3 7 ( 9 0 , 9 1 ) , 651 W i b e r g , K . B . 13 ( 1 4 ) , 17 ( 1 8 , 2 0 ) , 2 6 , 3 4 ( 1 4 ) , 39 (35), 41 (14, 38, 39), 4 8 (18), 5 4 (20), 59 (50), 61 (18), 70, 7 4 (20), 77, 7 9 (5), 8 1 , 8 4 ( 2 8 ) , 8 9 ( 2 8 , 5 3 ) , 9 2 ( 6 2 ) , 93, 94, 9 6 ( 1 ) , 9 8 ( 1 6 ) , 101 ( 5 0 ) , 1 1 0 , 111 ( 1 6 ) , 128, 129, 3 6 8 ( 6 0 ) , 390, 4 7 8 , 5 1 9 ( 8 2 ) , 526, 5 4 0 ( 8 4 ) , 549, 5 5 8 ( 2 8 a ) , 5 6 4 ( 5 7 a ) , 578 (I33a), 5 8 3 , 5 8 4 (165a, 165b, 165d, 165f), 601, 602, 604, 605, 6 9 6 ( 6 6 b ) , 7 1 1 ( 1 0 4 ) , 7 1 2 ( 6 6 b , 116a), 7 1 3 ( 6 6 b ) , 7 1 4 , 7 1 5 ( 6 6 b , 116a), 7 1 6 ( 1 1 6 a ) , 7 1 9 (66b), 7 2 4 , 7 2 8 (134), 7 3 3 ( 1 0 4 , 138a), 738, 740, 741, 7 8 2 ( 1 0 ) , 806, 8 8 2 ( 2 7 1 ) , 893, 9 2 8 ( 5 , 7, 10, 11), 9 2 9 ( 1 5 , 2 1 ) , 9 3 0 (5, 7, 2 5 , 2 6 , 2 8 , 3 4 , 37), 931 (10, 3 7 , 44), 933 (10, 48, 54, 57, 6 1 , 63-66), 934 (21, 6 7 , 72), 9 3 6 (79), 945 (44), 9 5 0 (7, 15, 1 1 6 ) , 9 5 1 ( 1 1 ) , 9 5 2 ( 5 7 , 6 3 - 6 5 ) , 9 5 3 (63), 9 5 4 ( 6 1 , 6 3 , 6 7 , 135b), 9 5 6 ( 2 8 , 1 3 5 b ) , 9 5 7 , 9 5 8 ( 1 3 5 b ) , 958-962, 9 6 4 (7), 9 6 5 ( 1 4 ) , 9 7 8 ( 8 5 ) , 9 8 2 (103), 9 8 3 ( 8 5 ) , 9 8 8 ( 1 2 3 ) , 994-996 Wickramaratchi, M . A . 6 8 7 ( 3 9 c ) , 736 W i d g e r y , M.J. 1 2 0 ( 1 3 9 ) , 131 W i e d e r , M.J. 145 ( 6 0 ) , 182 W i e m e r , D . F . 9 0 6 ( 1 2 8 ) , 922 W i e n e r , H. 1 8 6 , 1 9 0 ( 1 , 2 ) , 2 7 2 W i e s e r , J . D . 1 2 8 ( 2 1 7 ) , 133 W i g h t m a n , R . H . 5 7 3 ( 1 0 6 ) , 603 Wijk, A . M . v a n 1 2 2 ( 1 5 8 ) , 131 W i l b y , A . H . 5 5 5 - 5 5 8 ( l l g ) , 600 W i l c o x , C . F . , Jr. 9 3 0 , 9 3 1 ( 3 0 ) , 959 W i l c o x , J . B . 4 0 7 ( 8 8 ) , 451 W i l e n , S . H . 145 ( 6 0 ) , 182 W i l h e l m , K. 3 8 4 ( 2 0 7 , 2 0 8 ) , 3 8 5 ( 2 0 7 ) , 3 8 6 ( 2 0 7 , 2 0 8 ) , 393 Wilhelm, R.S. 585 (I72b), 5 8 6 (172b, 173),

605 W i l h o i t , R . C . 2 2 3 ( 7 , 8 ) , 283-285 W i l k e , R . N . 9 5 7 , 9 5 8 ( 1 4 3 ) , 962 W i l k i n s , B . 4 7 8 ( 9 8 ) , 527 W i l k i n s , B . T . 4 7 6 ( 4 6 ) , 525 Wilkins, C L . 189, 2 0 4 (21), 2 7 2 W i l k i n s o n , G. 5 5 5 ( 2 ) , 600 Willard, J.E. 4 0 7 ( 9 2 ) , 451, 7 7 2 ( 4 4 ) , 7 7 3 ( 4 4 , 4 6 , 4 7 , 5 3 ) , 779, 780 Willett, G . D . 5 0 7 ( 1 5 4 ) , 528 W i l l i a m s , A . E . 4 0 0 ( 2 9 ) , 450 W i l l i a m s , D . H . 3 0 3 , 3 0 7 ( 2 0 ) , 346, 4 0 8 (102-104), 4 1 1 , 4 1 2 , 4 1 5 (104), 4 1 9 , 4 3 2 (150), 4 3 4 (198), 4 4 2 (225a, 225b), 4 4 4 (104), 4 4 7 (239),

451^54 W h h a m s , D . L . 8 1 5 , 8 2 2 ( I r ) , 886 W i l l i a m s , F. 7 1 2 , 7 1 3 ( 1 1 5 f ) , 7 4 0 W i l l i a m s , H . D . 9 8 3 ( 1 0 7 ) , 996

Williams, Williams, Williams, Wilhams,

I.H. 3 7 9 ( 1 6 7 ) , 392 J.A. 9 0 9 ( 1 9 3 ) , 923 J.L. 8 4 1 , 8 4 2 ( 1 1 3 a ) , 889 J.M. 6 7 2 (75), 6 7 9

W i l l i a m s , K . C 5 4 2 ( 1 2 3 ) , 550 Williams, M.L. 9 1 9 (291), 9 2 5 Williams, Williams, 496 Williams,

P . G . 1 2 0 ( 1 4 0 b ) , 131 T.A. 4 7 4 - ^ 7 6 (25), 4 7 7 (50), 4 9 3 , ( 2 5 ) , 525, 526 V . Z . , Jr. 5 9 7 , 5 9 8 (21 Of), 607, 9 8 2

( 1 0 3 ) , 996 Williamson, D . O . 6 3 9 (98), 657 W i l l i a m s o n , M . 128 ( 2 2 0 ) , 133 Williamson, M . M . 6 7 2 (78a), 6 7 9 W i l l i s , C R . 5 6 6 ( 6 8 ) , 5 6 9 ( 8 4 ) , 602, 603 W i l l i s , J . N . , Jr. 1 2 3 ( 1 8 4 ) , 132 W i l l s c h , H. 3 2 0 ( 5 3 ) , 347 Willstatter, R. 2 9 3 ( 2 ) , 346 Wilner, D . 1 5 2 ( 8 2 ) , 183 W i l s o n , A . R . N . 3 5 2 ( 1 3 ) , 389 W i l s o n , C V . 5 7 8 ( 1 2 8 a ) , 604 W i l s o n , E . B . 1 1 3 ( 1 1 1 ) , 130, 4 5 6 ( 1 ) , 524 W i l s o n , J.S. 5 6 5 , 5 6 6 ( 6 6 f ) , 602 W i l s o n , L. 9 0 4 ( 8 6 ) , 9 2 7 W i l s o n , R.J. 1 8 8 ( 1 1 ) , 2 7 2 Wilson, S.E. 7 2 4 ( 1 2 9 a - c ) , 7 2 6 , 7 3 2 (129c), 747 Wilson, W . W . 635 (83), 657 W i m a l a s e n a , J.H. 2 5 9 ( 5 8 ) , 287 W i n i k e r , R. 101 ( 4 6 ) , 1 1 2 ( 1 0 5 ) , 7 2 9 , 130 Winkler, H . U . 4 4 7 (240), 4 5 4 W i n k l e r , J . D . 5 8 9 ( 1 8 7 a , 1 8 7 b ) , 606 W i n k l e r , T. 3 6 8 ( 7 0 ) , 390 W i n n i k , M . A . 3 6 9 ( 7 9 , 8 0 ) , 390, 391 W i n s t e i n , S. 1 1 8 , 1 1 9 ( 1 2 5 ) , 131, 5 7 0 ( 8 8 a ) ,

603 Winter, M . 4 7 6 ( 4 8 ) , 5 2 6 Winter, W . 8 1 ( 2 9 ) , 93 Winters, J . C . 9 0 9 ( 1 9 3 ) , 923 W i p k e , W . T . 5 9 7 ( 2 0 9 ) , 607, 6 9 1 ( 5 7 ) , 738 Wirth, T. 5 8 1 ( 1 4 7 ) , 605 Wirz, B . 3 9 7 ( 6 ) , 4 3 7 ( 2 1 4 ) , 4 3 8 ( 6 , 2 1 4 ) , 4 3 9 ( 2 1 4 ) , 450, 454 W i s e , M . B . 5 4 1 ( 9 7 ) , 550 W i s e m a n , J.R. 3 6 1 ( 4 5 ) , 390, 5 7 1 ( 1 0 0 ) , 603, 6 9 1 , 6 9 2 (55d), 7 3 7 Wiskott, E. 5 9 0 , 591 (194h), 5 9 7 , 5 9 8 (210b), 606, 607, 6 9 1 ( 5 3 h ) , 737 Witholt, B . 9 1 6 ( 2 4 5 ) , 9 2 4 W i t h , F. 6 8 7 ( 4 1 ) , 736 W o h r l e , D . 7 0 5 ( 8 4 b ) , 739 Wojnarovits, L . 6 8 7 ( 3 7 a , 3 8 a , 3 9 b , 4 0 a , 4 3 ) , 6 8 8 ( 3 7 a , 3 8 a , 4 3 ) , 6 9 0 ( 4 9 ) , 736, 737, 756, 763, 765 (19), 7 6 6 (40), 769, 7 7 0 (42), 7 7 4 (19), 7 7 9 Wolczanski, P.T. 6 7 2 (76), 6 7 9 W o l d , S. 3 3 3 ( 9 4 ) , 348

A u t h o r index W o h , A.P. 816 (26), 818 (27), 819 (29, 30), 8 2 0 ( 4 1 , 4 3 ) , 8 2 2 (48b), 831 (88),

886-888 Wolf, H. 3 6 1 ( 4 9 ) , 390 Wolf, W . H . de 7 0 3 , 7 0 4 , 7 1 2 , 7 1 9 ( 8 0 ) , 739 W o l f e , J.R., Jr. 143 ( 4 8 ) , J82 Wolff, S. 5 6 2 , 5 6 3 ( 5 1 a ) , 601, 9 4 4 ( 9 7 , 9 9 ) , 9 4 5 ( 1 0 0 , 1 0 3 ) , 961 Wolff, T. 6 8 2 ( 2 0 a ) , 736 W o l f g a n g , R. 4 0 6 ( 8 2 ) , 451,

821 (48a, 49a),

828 (81b), 832 (94a), 833 (94b), 838 ( 1 0 3 ) , 8 3 9 ( 1 0 9 ) , 887-889 W o l f g a n g , R . L . 8 5 2 ( 1 3 7 ) , 889 W o l f s b e r g , M . 8 5 2 ( 1 3 8 ) , 889 W o l f s c h u t z , R. 4 3 0 ( 1 8 0 ) , 453 W o l i n s k i , K. 8 8 ( 4 7 ) , 94 Wolkoff, P. 4 0 9 ( 1 0 8 ) , 4 1 0 ( 1 1 6 ) , 4 1 1 ( 1 0 8 , 116), 4 1 2 (116), 4 1 3 (108, 116), 4 1 4 (116), 415 (134), 418 (147), 422 (134, 152), 4 4 4 ( 1 1 6 , 134), 452 Wollrab, V . 8 9 8 ( 2 4 ) , 9 0 1 ( 5 2 ) , 920 W o n g , A . 8 4 ( 3 5 ) , 93 W o n g , C.K. 5 6 8 , 5 7 7 ( 7 8 ) , 602 W o n g , C.S. 9 1 6 ( 2 5 8 ) , 925 W o n g , H . N . C . 6 8 2 ( 3 a ) , 735 W o n g , M . W . 4 0 6 ( 6 2 ) , 4 0 7 ( 8 9 ) , 451 W o n g , W . H . 8 3 9 ( 1 0 7 ) , 888 W o o , S . M . 9 0 5 ( 1 0 5 ) , 921 W o o d , K . A . 3 6 9 ( 9 2 ) , 391 W o o d , W . W . 1 4 5 , 164 ( 6 7 ) , 183 W o o d c o c k , D.J. 5 8 1 ( 1 4 4 ) , 604 W o o d c o c k , G.J. 9 0 4 ( 8 6 ) , 9 2 7 W o o d g a t e , P . D . 5 7 4 ( 1 1 0 b ) , 603 Woodward, R.B. 945 (101), 967 W o o l f s o n , A . D . 2 0 8 ( 5 8 ) , 213 Worley, S . D . 4 7 6 ( 3 0 ) , 4 7 8 ( 8 9 , 9 7 , 9 9 , 102), 5 1 4 ( 8 9 ) , 525, 527 Worth, J. 6 2 0 ( 4 5 c ) , 650 Worth, J. 7 9 ( 7 ) , 93, 592 ( 1 9 7 ) , 606 W o z i a k , K. 8 9 ( 5 2 ) , 94 Wray, V . 3 8 7 ( 2 1 7 ) , 393 Wright, J.G. 3 7 9 ( 1 6 5 ) , 392 Wright, J.L.C. 9 1 4 ( 2 2 4 ) , 924 W r i x o n , A . D . 1 5 2 ( 7 9 , 8 0 ) , 183 W r o c z y n s k i , R.J. 103 ( 5 6 ) , 1 0 4 ( 6 5 ) , 105 ( 5 6 , 6 5 ) , 109 ( 6 5 ) , 114 ( 5 6 ) , 115 ( 6 5 ) , 7 2 9 W u , A . 5 9 6 ( 2 0 8 a ) , 607 W u , A . - H . 6 2 0 ( 4 4 b ) , 650 W u , J. 9 1 6 ( 2 5 8 ) , 9 2 5 W u , Y . - D . 1 0 0 , 124, 128 ( 3 5 ) , 7 2 9 W u r m i n g h a u s e n , T. 7 8 6 ( 3 4 - 3 6 ) , 7 9 5 ( 3 4 , 3 5 ) ,

807 Wurthwein, E.-U. 9 3 0 (33, 36), 931 (39), 9 5 9 Wuthrich, K. 3 6 1 , 3 8 1 , 3 8 2 , 3 8 4 ( 3 7 ) , 390 Wyatt, J.M. 9 1 5 ( 2 3 3 ) , 924 Wyckoff, J. 7 8 2 , 7 9 7 , 7 9 9 ( 8 a ) , 806 Wyckoff, R . W . C . 9 0 0 ( 4 0 ) , 920

1059

W y n b e r g , H. 1 2 0 ( 1 4 9 ) , 131, 151 ( 7 3 , 7 4 ) , 183, 9 3 5 ( 7 7 ) , 960 W y s s , H.R. 1 4 0 ( 2 1 ) , 182 Wyvratt, M.J. 5 9 9 ( 2 1 6 ) , 608 X i e x i a n , G. 6 8 3 , 6 8 4 ( 2 5 ) , 736 X i o n g , Y . 7 1 1 ( 1 0 8 a ) , 740 Y a a c o b , K. 9 0 3 ( 6 8 ) , 920 Yabe, A . 6 8 7 ( 4 6 a ) , 6 8 9 ( 4 6 b ) , 737 Y a b l o k o v , V . A . 8 1 5 , 8 2 2 ( I q ) , 886 Yager, B.J. 2 0 2 ( 3 4 ) , 213 Yakushkina, N . I . 4 7 7 ( 6 2 ) , 526 Y a m a b e , S. 5 3 2 , 5 3 4 , 5 3 8 , 5 4 0 ( 3 8 ) , Yamada, N . 5 8 5 ( 1 7 0 ) , 605 Yamada, S. 5 8 2 ( 1 5 0 ) , 605 Y a m a g u c h i , M . 5 7 0 ( 9 2 ) , 603

548

Y a m a g u c h i , R. 6 9 6 ( 6 6 a , 6 6 c , 6 6 d ) , 6 9 8 ( 7 0 ) , 706, 707 (87d), 7 1 2 , 7 1 9 (66a, 66c, 66d), 7 2 4 , 7 2 7 ( 1 3 2 f ) , 738, 739, 741, 8 0 1 ( 6 7 a , 6 7 b ) , 807 Y a m a g u c h i , Y . 3 8 8 ( 2 2 7 ) , 393,

4 9 9 , 501 (144),

528 Y a m a m o t o , M . 4 0 8 ( 1 0 6 , 1 0 7 ) , 452 Y a m a m o t o , S. 123 ( 1 8 1 ) , 132, 6 8 9 , 6 9 0 ( 4 8 c ) , 737, 8 5 3 ( 1 4 7 b ) , 889 Y a m a m o t o , Y . 5 7 2 ( 1 0 4 ) , 603 Yamamura, S. 5 7 4 (11 l a , 11 l b ) , 603 Yamamura, S.H. 3 5 2 ( 8 ) , 389 Yamanaka, I. 8 0 4 ( 8 0 ) , 8 0 5 ( 9 0 ) , 808 Y a m a n o b e , T. 128 ( 2 2 4 ) , 133, 3 7 6 ( 1 3 5 , 136, 1 3 9 ) , 392 Yamashita, T. 7 9 9 ( 6 1 ) , 807 Y a m a z a k i , T. 4 7 6 , 4 7 7 , 4 8 9 , 5 0 2 , 5 0 3 , 5 0 7 , 509 (32), 5 2 5 Yan, D . Y . 3 6 ( 3 4 ) , 7 7 Yang, C . - X . 7 1 1 ( 1 0 8 a ) , 740 Yang, D . 9 7 2 ( 7 4 ) , 9 9 5 Yang, G.K. 6 6 2 ( 4 3 ) , 678 Yang, J.Y. 6 8 7 - 6 8 9 ( 4 4 ) , 737 Yang, K. 5 6 7 ( 7 5 ) , 602, 8 3 2 ( 9 3 ) , 8 3 5 ( 9 7 , 9 8 ) , 888 Yang, Q . Y . 6 8 6 ( 3 4 a , 3 4 b ) , 736 Yang, Z . - Z . 4 6 4 , 4 6 6 , 4 6 7 , 4 7 1 , 4 7 5 , 4 7 6 , 4 9 0 , 497, 5 0 3 - 5 0 5 (14), 5 2 5 Y a n k w i c h , P.E. 8 7 7 , 8 8 1 , 8 8 2 ( 2 6 1 ) , 893 Yannoni, C . S . 8 4 ( 3 3 ) , 93 Yannoni, N . 81 ( 3 1 ) , 93 Yarovoi, S . S . 2 3 5 ( 4 3 ) , 286 Yashu, Y . 6 8 3 , 6 8 4 ( 2 5 ) , 736 Yates, B . F . 1 0 1 , 1 1 0 ( 4 2 ) , 7 2 9 Y e h , L.L 5 3 2 , 5 3 4 ( 1 5 ) , 548 Y e o , A . N . H . 4 3 4 ( 1 9 8 ) , 453 Yemiakov, Y.I. 6 7 2 (72), 6 7 9 Y i p , Y . - C . 6 8 2 ( 3 a ) , 735 Y o k o y a m a , S. 8 7 1 ( 2 2 9 ) , 892 Yokoyama, Y. 476, 477 (44), 5 2 5

1060

Author index

Yoneda, N . 6 3 3 ( 7 0 , 7 1 , 7 2 a ) , 6 3 5 ( 8 2 , 8 5 ) , 636 (85, 86), 6 3 7 - 6 3 9 (87a), 6 4 0 (82, 8 7 a ) , 651 Y o n e m h s u , O. 7 9 ( 1 0 ) , 93, 5 6 1 ( 4 5 c ) , 5 9 3 (202g, 203f), 5 9 4 (202g), 595 (203f),

601, 607 Yonetani, H. 8 9 9 ( 2 9 ) , 920 Y o n e z a w a , T. 155 ( 9 2 ) , 183, 9 8 3 ( 1 0 5 , 1 0 6 ) ,

996

( 1 9 ) , 7 3 0 ( 1 9 , 7 9 a ) , 7 3 1 ( 1 9 ) , 736, 739,

741 Z a n t e n , B . v a n 8 2 0 ( 4 2 ) , 887 Zapf, L. 5 8 2 ( 1 5 6 ) , 605 Zard, S.Z. 5 6 5 , 5 6 6 ( 6 6 b ) , 602 Z d a n o v i c h , V . I . 5 5 9 ( 3 0 ) , 601 Zeini-Isfahani, A . 8 6 5 ( 2 1 1 ) , 891 Z e i s s , H . H . 8 2 3 ( 5 7 ) , 887 Zeller, K . - P . 6 9 1 ( 5 3 i , 5 3 j ) , 737 Zerner, M . C . 8 4 ( 3 5 ) , 93 Z h a n g , H. 8 1 2 , 8 1 3 , 8 1 5 , 8 2 2 ( I f ) , 885 Z h i y i n , L . 6 8 3 , 6 8 4 ( 2 5 ) , 736

Y o s h i d a , M . 8 7 1 ( 2 3 1 ) , 892 Y o s h i d a , T. 5 6 0 ( 4 3 ) , 601 Y o s h i d a , Z.-I. 7 0 5 ( 8 4 a ) , 739 Yoshihara, K. 4 7 6 , 4 7 7 ( 4 4 ) , 5 2 5 Y o s h i m i n e , M . 2 6 1 ( 7 8 ) , 287 Yotsui, Y . 3 4 1 ( 1 1 2 ) , 349 Y o u n g , J.R. 5 9 0 ( 1 9 1 ) , 606 Young, L.B. 5 4 3 (144), 557 Yu, K . O . 9 1 7 ( 2 6 7 - 2 6 9 , 2 7 1 ) , 9 1 8 ( 2 6 9 ) , 925 Yuh, Y . H . 8 0 , 9 2 ( 1 7 ) , 93, 9 9 , 1 0 0 , 1 1 0 , 1 1 8 , 1 2 3 , 127 ( 2 9 ) , 7 2 9 , 9 3 4 ( 7 0 ) , 960 Y u r c h e n k o , A . G . 6 9 2 , 6 9 4 ( 5 8 ) , 738

Z h u k , S.Ya. 6 7 0 ( 6 4 a ) , 678 Zielinski, M. 8 1 2 (4, 5), 8 1 3 (4), 8 1 5 (5), 825 (69a), 8 2 9 (82a), 8 5 9 (185b), 866 (212), 8 7 3 , 879 (248a), 8 8 2 (267, 268), 883 (185b), 886-888,

891-893 Z i e s e l , J.P. 3 9 9 ( 1 9 ) , 450 Zijl, P . C . M . v a n 3 7 1 ( 9 8 ) , 391 Z i m m e r , H. 6 8 4 , 6 8 6 ( 2 7 ) , 736 Z i m m e r m a n n , G. 3 6 1 ( 4 0 ) , 390, 7 8 6 , 7 9 4 , 7 9 5 ( 3 7 ) , 807 Zimtseva, C P . 6 5 8 (24), 6 7 7 Zinov'ev, Y.M. 9 9 2 (161), 9 9 3 (167), 9 9 7 Z i o l k o w s k i , J.J. 6 6 3 ( 5 4 ) , 678

Z a c h a r o v , I.I. 9 3 0 ( 3 3 ) , 9 5 9 Zadro, S. 3 3 3 ( 9 7 ) , 348 Z a h l s e n , K. 9 1 8 ( 2 8 9 ) , 9 2 5 Z a h n , W . 8 5 4 ( 1 5 2 g ) , 890 Zakharov, V. 6 7 2 ( 7 2 ) , 6 7 9 Z a k r z e w s k i , J. 6 6 3 , 6 6 4 , 6 6 6 , 6 6 8 , 6 7 0 ( 5 5 a , 5 5 b ) , 678 Z a l a n , E . 1 4 2 ( 4 0 ) , 182 Z a l k o w , V . 1 0 9 ( 9 4 ) , 130 Zambach, W. 4 7 7 - 4 7 9 (80), 5 2 6 Z a m e c n i k , J. 5 7 4 , 5 7 5 ( 1 1 3 k ) , 604 Z a n g , G. 6 8 2 , 7 0 0 ( 1 9 ) , 7 0 3 ( 7 9 a ) , 7 0 8 ( 9 6 a ) , 7 1 2 ( 1 9 , 96a, 121b), 7 1 5 ( 1 9 ) , 7 1 6 ( 1 9 , 9 6 a ) , 7 1 8 ( 1 2 1 b ) , 7 2 2 ( 1 9 , 121b), 7 2 3 (19), 7 2 4 ( 1 9 , 79a), 7 2 5 (79a), 7 2 6 , 7 2 7

Zirnet, U . A . 2 2 3 ( 1 0 ) , 285 Zoch, H.-G. 951 (120), 967 Z o e b e l e i n , H. 7 8 2 ( 3 b ) , 806 Z o n , G. 5 4 0 ( 8 7 ) , 549 Z u a n i c , M . 3 7 9 ( 1 6 0 ) , 392, 5 9 3 , 5 9 4 ( 2 0 2 h ) ,

607 Z u m b e r g , J.E. 3 3 8 , 3 3 9 ( 1 0 2 ) , 348 Zuniac, M. 9 4 9 , 9 5 0 (114), 967 Zvereva, T.E. 9 0 6 (141), 9 2 2 Z w o l i n s k i , B.J. 2 0 7 ( 5 0 ) , 2 7 i , 2 2 3 ( 7 , 8 ) , 2 3 5

(38),

Index compiled hy K. Raven

283-286

Subject index Abies species, cuticular waxes of 902, 904 Abietane, chiroptical properties of 173 mass spectrum of 309, 312, 314 Ah initio calculations, for alkylbutanes 110, 111 for fenestranes 931, 933 for propellanes 933, 934 in conformational analysis 101, 110, 111 in mass spectrometry 406, 408, 448 in structural determinations 87-91 Acetamidoalkanes, as electrochemical products 792 Acidities, gas-phase 543-548 in solution 542, 543 Acinetobacter species, occurrence of alkanes in 907 Action principle 11 Acyclic alkanes—see also n-Alkanes, Branched alkanes alkylation of 624-626, 629-631 analysis of 291-297 carbonylation by metal complexes 664, 667, 668 carboxylation of 632, 633 chemical shift values for 352-355 chiroptical properties of 141-162 cleavage reactions of 621-624 dehydrogenation by metal complexes 664-666 deuterated, radiation decomposition of 867, 868 electrochemical oxidation in superacids 614, 615 enumeration of 188, 189 formylation of 633 halogenation of 642-648 IR spectra of 314-316 isomerization of 615-619 mass spectra of 302-306

metabolism of, by animals and plants 916-918 by micro-organisms 914-916 nitration of 641, 642 oligocondensation of 624, 631, 632 oxyfunctionalization of 635-640 PE spectra of 476, 487-505 pharmacology of 918, 919 photochemistry of 687, 688 protolytic ionization of 610-614 rearrangement on transition-metal surfaces 683, 684 separation of, from crude oils 322-329 from mixtures 318-322 stereochemical determination of 294 sulphuration of 641 synthesis of, by coupling reactions 583, 585-588 from alcohols 562, 563, 565, 566 from alkenes 555-560 from alkyl halides 568-572 from amines 581 from carbonyl compounds 577, 578, 595 from carboxylic acids 580 from isonitriles 581 from nitriles 582 from nitroalkanes 582, 583 from selenides 568 from thiols and thioethers 567, 568 toxicology of 918, 919 Adamantanecarboxaldehydes, synthesis of 633-635 Adamantanecarboxylic acids 634 Adamantane rearrangement 691, 692, 694, 695 Adamantanes, alkylation of 627-629 analysis of 301 chemical shift values for 365 electrolysis of 792-794 electrophilic oxygenation of 637


1062

Subject index

A d a m a n t a n e s (cont.) formylation o f 6 3 3 - 6 3 5 halogenation of 6 4 3 i s o t o p i c a l l y labelled 8 1 6 - 8 1 9 m a s s spectra o f 3 0 8 , 3 1 1 nitration o f 6 4 1 s y n t h e s i s of, b y c o u p l i n g reactions 5 8 5 b y p h o t o d e c a r b o x y l a t i o n reactions 5 8 0 , 581 from a l c o h o l s 5 6 2 from alkyl halides 5 7 1 from carbonyl c o m p o u n d s 5 7 3 from C i o precursors 6 1 9 from nitriles 5 8 2 from p h o s p h o r o d i a m i d a t e s 5 6 7 Adamantanols 6 3 4 A d a m a n t a n o y l cations 6 3 4 A d a m a n t y l b u t a n e s , b o n d lengths in 101 A d a m a n t y l cations 6 3 4 A d a m s catalyst 5 5 6 Additivity laws 2 3 3 - 2 3 8 Agostic systems 6 5 5 Alcohols, acidities o f 5 4 6 reduction of, direct 5 6 2 indirect 5 6 2 - 5 6 7 unsaturated—see Unsaturated a l c o h o l s A l d i t o l s , structural c h e m i s t r y o f 8 7 Algae, b i o g e n e s i s o f alkanes in 9 1 3 , 9 1 4 intracellular w a x e s in 9 0 2 o c c u r r e n c e o f alkanes in 8 9 6 , 9 0 7 , 9 0 8 A l k a n e activation, b o n d strengths in 6 5 7 catalytic c h e m i s t r y o f 6 6 4 - 6 7 0 stoichiometric chemistry o f 6 6 0 - 6 6 4 theoretical a s p e c t s o f 6 5 5 , 6 5 6 t h e r m o d y n a m i c aspects o f 6 5 6 , 6 5 7 Alkane conversion, surface-bound o r g a n o m e t a l l i c s p e c i e s in 6 7 2 A l k a n e fragments, l o s s o f in m a s s spectrometry 4 1 5 , 4 1 6 , 4 2 1 , 4 4 8 Alkane ions 3 9 6 , 3 9 7 , 4 0 0 , 4 2 1 Alkanes, a c y c l i c — s e e A c y c l i c alkanes bicyclic—see Bicycloalkanes b r a n c h e d — s e e B r a n c h e d alkanes cyclic—see Cycloalkanes deuterated—see D e u t e r o a l k a n e s pentacyclic—see Pentacycloalkanes polycyclic—see Polycycloalkanes straight-chain—see n - A l k a n e s tetracyclic—see Tetracycloalkanes tricyclic—see Tricycloalkanes n - A l k a n e s — s e e also A c y c l i c alkanes

biogenesis of 9 1 1 - 9 1 3 b o i l i n g points o f 2 9 2 , 2 9 3 , 2 9 6 , 2 9 7 deuterated, structural c h e m i s t r y o f 8 5 , 86 m e l t i n g points o f 2 9 3 , 2 9 6 , 2 9 7 specific gravities o f 2 9 2 , 2 9 3 , 2 9 6 , 2 9 7 Alkenes, catalytic h y d r o g e n a t i o n o f 5 5 5 - 5 5 8 c h e m i c a l reduction o f 5 6 0 cyclopropanation o f 5 9 3 , 5 9 4 hydroboration/protonolysis o f 5 5 9 ionic h y d r o g e n a t i o n o f 5 5 9 i s o t o p i c a l l y labelled 8 6 1 - 8 6 4 m a s s spectra o f 4 4 3 ^ 4 7 photocycloaddition of 5 9 0 - 5 9 2 radical c y c l i z a t i o n o f 5 8 8 , 5 8 9 reactions with a l u m i n i u m and boron hydrides 5 5 9 rearrangement o f 5 9 7 - 5 9 9 transfer h y d r o g e n a t i o n o f 5 5 8 A l k o n i u m i o n s , structure o f 5 3 2 - 5 3 5 Alkoxide ions, photolysis of 5 4 4 A l k y l a t i o n reactions 6 2 4 - 6 3 2 A l k y l b u t a n e s — s e e also A d a m a n t y l b u t a n e s , D i a l k y l b u t a n e s , Trialkylbutanes conformation of 110 Alkylcarbonium ions 3 0 3 A l k y l cations, as alkylating a g e n t s 625-627 A l k y l c y c l o a l k a n e s — s e e also Alkylcyclobutanes, Alkylcyclohexanes, Alkylcyclooctanes, Alkylcyclo p e n t a n e s , A l k y l c y c l o p r o p a n e s , tertButylcycloalkanes, Dialkylcycloalkanes c h e m i c a l shift v a l u e s for 3 5 8 - 3 6 1 A l k y l c y c l o b u t a n e s , c o n f o r m a t i o n o f 123 A l k y l c y c l o h e x a n e s — s e e also Dialkylcyclohexanes, Hexaalkylcyclohexanes, Neopentylcyclohexanes, Tetraalkylcyclohexanes conformation of 1 1 8 - 1 2 3 fragmentation o f 4 2 3 ^ 3 2 geometry of 8 2 , 8 9 isotopically labelled, u s e in g a s chromatography 8 2 5 N M R spectra o f 3 7 1 , 3 7 2 , 3 7 4 o c c u r r e n c e in p e t r o l e u m 8 9 7 s p i n - s p i n c o u p l i n g in 3 8 6 A l k y l c y c l o o c t a n e s , N M R spectra o f 3 7 3 A l k y l c y c l o p e n t a n e s — s e e also Dialkylcyclopentanes fragmentation o f 4 2 5 in strawberry aroma c o m p o n e n t s 9 0 3 o c c u r r e n c e in p e t r o l e u m 8 9 7 rearrangement o f 6 8 5 s p i n - s p i n c o u p l i n g in 3 8 6

Subject index

1063

A l k y l c y c l o p r o p a n e s — s e e also Dialkylcyclopropanes, Tetraalkylcyclopropanes chiroptical properties o f 1 6 3 hydrogenolysis of 560, 561 photochemistry of 7 0 0 - 7 0 4 radical attack o n 9 6 4 , 9 8 3 - 9 8 6 rearrangement o f 6 9 2 , 6 9 3 , 6 9 6 - 6 9 9 s p i n - s p i n c o u p l i n g in 3 8 4 A l k y l d e c a l i n s , c h e m i c a l shift v a l u e s for 3 6 7

A l k y l p r o p a n e s — s e e also D i a l k y l p r o p a n e s conformation of 109 isotopically labelled, s y n t h e s i s o f 8 1 3 , 8 1 4 A l k y l radical g r o u p s , enthalpies for 2 5 8 - 2 6 0 entropies for 2 6 0 , 2 6 1 heat capacities for 2 6 0 , 2 6 1 A l k y n e s , c h e m i c a l reduction o f 5 6 0 Amblyomma s p e c i e s , o c c u r r e n c e o f alkanes in 906

increment s y s t e m for 3 6 2 , 3 6 3 A l k y l e t h a n e s — s e e r^-zt-Butylethanes, Dialkylethanes, Hexaalkylethanes, Pentaalkylethanes, Tetraalkylethanes, Trialkylethanes A l k y l f l u o r i d e - a n t i m o n y pentafluoride

A m i n e s , reductive d e a m i n a t i o n o f 5 8 1 A M I method 91 Androstanes, c h e m i c a l shift v a l u e s for 3 6 7 chiroptical properties o f 1 3 8 , 1 7 5 , 177 electrolysis of 7 9 0 N M R spectra o f 3 1 6 A n i m a l s , alkanes in,

c o m p l e x e s , as alkylating agents 6 2 4 , 6 2 5 A l k y l fragments, loss o f in m a s s spectrometry 416,419, 421,422 A l k y l halides, c o u p l i n g of, with alkali m e t a l s 5 8 3 , 5 8 4 with Grignard reagents 5 8 4 , 5 8 5 with o r g a n o - b o r a n e s a n d -alanes 5 8 7 with transition metal reagents 5 8 5 - 5 8 7 dehalogenation of 569, 5 7 0 hydrogenolysis of 5 6 9 reduction of, electrochemical 5 7 1 , 5 7 2 with metal hydrides 5 7 0 , 5 7 1 with o r g a n o m e t a l l i c s 5 7 2 Alkylheptanes, chiroptical properties o f 1 3 6 isotopically labelled, u s e in g a s chromatography 8 2 5 A l k y l h e x a d e c a n e s , isotopically labelled, metabolism of 855, 8 5 6 A l k y l h e x a n e s — s e e also D i a l k y l h e x a n e s , Tetraalkylhexanes chiroptical properties o f 1 3 6 , 1 3 8 , 157-160 fragmentation o f 4 2 0 , 4 2 2 , 4 3 5 in orange aroma c o m p o n e n t s 9 0 3 isotopically labelled, u s e in g a s chromatography 8 2 5 Alkyl ions 3 9 7 , 4 0 0 , 4 3 2 - 4 4 3 A l k y l n o r b o m a n e s — s e e also Dialkylnorbomanes steric effects in 3 6 1 , 3 6 2 A l k y l p e n t a n e s — s e e also D i a l k y l p e n t a n e s , Tetraalkylpentanes, Trialkylpentanes degradation o n a super-acid catalyst, tracer study o f 8 6 2 , 8 6 3 in strawberry aroma c o m p o n e n t s 9 0 3 radical reactions o f 9 7 5 rearrangement o f 6 8 4 Alkylphosphorodichloridation mechanism 9 9 3

biogenesis of 9 1 4 occurrence of 8 9 6 , 9 0 6 , 9 0 7 , 9 1 8 , 9 1 9 A n t s , o c c u r r e n c e o f alkanes in 9 0 6 Apis s p e c i e s , cuticular w a x e s o f 9 0 5 Appearance energies 3 9 8 , 4 1 4 A p p e a r a n c e potentials 3 0 2 , 3 0 3 Aralkyl h y d r o c a r b o n s , h a l o g e n a t i o n o f 9 9 0 Arbutus s p e c i e s , cuticular w a x e s o f 9 0 4 Aromatization 6 8 4 Artemisia s p e c i e s , cell s u s p e n s i o n s o f 9 0 4 Arthropoda s p e c i e s , b i o g e n e s i s o f alkanes in 9 1 3 A r y l b u t a n e s , i s o t o p i c a l l y labelled, s y n t h e s i s o f 823 A r y l e t h a n e s — s e e also H e x a a r y l e t h a n e s i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 2 4 A r y l e t h a n o l s , chiroptical properties o f 1 4 0 A s y m m e t r i c carbon a t o m s , relative stereochemistry o f 87 Atomic asymmetry 143 A t o m i c charges 4 4 , 4 8 - 5 2 hybridization m o d e l a n d 5 1 , 5 2 Atomic energies 4 4 , 5 3 , 5 4 A t o m i c first m o m e n t s 4 4 A t o m i c interaction line 12 A t o m i c interactions 3 7 ^ 0 closed-shell 39 shared 3 7 Atomic populations 4 4 , 5 3 , 5 4 A t o m i c properties 4 1 - 6 1 definition a n d c a l c u l a t i o n o f 4 3 A t o m i c quadrupole m o m e n t s 4 4 A t o m i c surfaces 11 Atomic volumes 4 5 , 5 2 - 5 9 hybridization m o d e l a n d 5 6 Atoms, definition o f 4 , 11 in a m o l e c u l e , definition o f properties o f 4 3 electronic e n e r g y o f 4 3

1064

Subject index

Attagenus s p e c i e s , cuticular w a x e s o f 9 0 5 A u t o x i d a t i o n reactions 9 6 4 , 9 6 5 , 9 7 4 , 9 9 3 Azoalkanes, photochemistry of 7 0 7 - 7 1 0 Bacteria, alkanes in, biogenesis of 9 1 4 occun-ence of 8 9 6 , 9 0 7 , 9 0 8 Bacterial e n z y m e s y s t e m s , o x i d a t i o n o f alkanes by 8 5 3 , 8 5 4 Baeyer-Villiger oxidadon 6 3 5 , 6 3 6 B a r t o n - M c C o m b i e reaction 5 6 5 - 5 6 7 B a s i s sets 8 8 , 8 9 B e e t l e s , occurrence o f alkanes in 9 0 5 , 9 0 6 B e n z e n e s , i s o t o p i c a l l y labelled, s y n t h e s i s o f 820 Benzvalene 693 B e n z y l radicals 9 9 1 B i c y c l o a l k a n e s — s e e also B i c y c l o b u t a n e s , Bicycloheptanes, Bicyclohexanes, Bicyclononanes, Bicyclooctanes, Bicyclopentanes, Bicyclotetradecanes c h e m i c a l shift v a l u e s for 3 6 1 , 3 6 2 m a s s spectra o f 3 0 7 P E spectra o f 4 7 7 , 5 2 0 , 5 2 3 , 5 2 4 radical reactions o f 9 7 8 - 9 8 3 reactions with h e l i u m tritide ions 8 4 0 , 8 4 1 s y n t h e s i s of, b y c y c l i z a t i o n reactions 5 9 0 by p h o t o d e c a r b o x y l a t i o n reactions 5 8 1 from a l k e n e s 5 5 9 from tricyclic t h i o p h e n e s 5 6 7 Bicyclobutanes, Laplacian o f p in 4 1 photochemistry of 731 reactions with transition-metal i o n s 5 4 0 reactivity o f 9 5 6 - 9 5 8 rearrangement o f 7 2 4 - 7 3 3 strain e n e r g y in 6 4 theoretical studies o f 9 3 4 B i c y c l o h e p t a n e s , reactions with transidonmetal i o n s 5 4 0 B i c y c l o h e x a n e s , reactions with transition-metal ions 5 4 0 B i c y c l o n o n a n e s , structural c h e m i s t r y o f 8 2 Bicyclooctanes, electrolysis of 7 8 8 electronic charge density in, relief m a p s o f 16 strain e n e r g y in 6 4 , 6 5 Bicyclopentanes, P E spectra o f 5 2 0 , 5 2 3 , 5 2 4 reactions with transition-metal i o n s 5 4 0 rearrangement o f 7 1 1 - 7 2 4 strain e n e r g y in 6 5 Bicyclopentyl anions 5 4 7 Bicyclopropyl, gas-phase chlorinadon of 9 8 4 B i c y c l o t e t r a d e c a n e s , reactions with acids 5 3 9

Biogenesis, in higher plants 9 0 9 - 9 1 4 in p e t r o l e u m 9 0 8 , 9 0 9 Biomarkers 3 3 0 , 3 4 5 , 3 4 6 Birds, alkanes in, biogenesis of 9 1 4 occurrence of 9 0 6 , 9 0 7 Bitumens, G C profile o f 3 3 0 , 3 3 1 o c c u r r e n c e o f alkanes in 8 9 9 , 9 0 0 Blattella s p e c i e s , alkanes in, biogenesis of 9 1 4 occun-ence of 9 0 5 , 9 0 6 B o a t c o n f o r m a t i o n s 121 B o i l i n g points, as indicators o f intermolecular f o r c e s 2 0 7 o f n-alkanes 2 9 2 , 2 9 3 , 2 9 6 , 2 9 7 B o m b calorimetry 2 2 7 , 2 2 8 Bombyx s p e c i e s , cuticular w a x e s o f 9 0 5 Bond angles, distortion o f 1 0 2 in dialkylbutanes 111 in h e x a a l k y l e t h a n e s 111 in propanes 1 0 8 , 1 0 9 in tetraalkylmethanes 1 0 9 o p e n i n g o f 1 0 8 , 1 0 9 , 111 Bond dipoles 9 6 B o n d dissociadon energies 2 6 1 , 2 6 2 , 9 6 6 , 9 6 7 B o n d d i s s o c i a t i o n enthalpies 2 6 1 B o n d ellipticity 3 1 - 3 4 B o n d lengths, d e p e n d e n c e o n basis set 8 9 distortion o f 101 B o n d orders 2 1 - 2 7 B o n d path a n g l e s 2 7 - 3 1 B o n d paths 13 B o m a n e s , c h e m i c a l shift v a l u e s for 3 6 7 Branched alkanes, alkylation o f 6 2 4 - 6 2 6 analysis o f 2 9 2 - 2 9 7 biogenesis of 9 1 3 c h e m i c a l shift v a l u e s for 3 5 3 - 3 5 5 chiroptical properties o f 1 3 6 , 1 3 8 , 1 5 7 - 1 6 0 chlorinadon of 9 7 3 , 9 7 4 conformadon of 97, 9 8 , 101-118 degradation o f 8 6 2 , 8 6 3 fragmentation o f 4 2 0 , 4 2 2 , 4 2 3 , 4 3 5 , 4 4 2 in aroma c o m p o n e n t s 9 0 3 i s o t o p i c a l l y labelled, metabolism of 855, 9 5 6 synthesis of 8 1 3 - 8 1 5 use in g a s c h r o m a t o g r a p h y 8 2 5 N M R spectra o f 3 7 1 , 3 7 3 , 3 7 4 optical i s o m e r i s m in 2 2 5 oxyfunctionalization of 635, 6 3 6 , 6 3 8 , 6 3 9 radical reactions o f 9 7 5 rearrangement o f 6 8 4

Subject index s y n t h e s i s of, by c o u p h n g reactions 5 8 7 , 5 8 8 from a l c o h o l s 5 6 2 , 5 6 6 from a l k e n e s 5 5 9 from alkyl halides 5 7 2 from nitro c o m p o u n d s 5 8 2 , 5 8 3 t h e r m o c h e m i c a l c a l c u l a t i o n s for 2 7 3 - 2 7 5 Branching index 1 9 0 - 1 9 3 , 195 Brassica s p e c i e s , cuticular w a x e s o f 9 0 4 in alkane m e t a b o l i s m 9 1 6 B r i d g e h e a d radicals 9 8 2 , 9 8 3 n-Butane, conformation o f 9 8 , 9 9 , 103, 105, 110 free radical o x i d a t i o n o f 8 8 3 , 8 8 4 geometry of 8 2 , 9 0 reactions with h e l i u m tritide ions 8 3 7 structure o f the m o l e c u l a r i o n 4 0 7 ^ 1 4 t h e r m o c h e m i c a l c a l c u l a t i o n s for 2 7 5 Butane/butene mixtures, d e h y d r o g e n a t i o n of, ^^C study o f 8 5 9 , 8 6 0 Butanes, alkyl-substituted—see A l k y l b u t a n e s aryl-substituted—see A r y l b u t a n e s Buttressing, o f m e t h y l e n e group 117 Butyl anions 5 4 7 Butyl cations 4 3 3 ^ 3 6 carbon scrambling in 6 1 0 , 6 1 1 re/t-Butylcycloalkanes, conformation o f 1 2 2 N M R spectra o f 3 7 3 r^rr-Butylethanes, N M R spectra o f 3 7 3 C A D M S - M S 336, 337 C a g e m o l e c u l e s , structural c h e m i s t r y o f 7 9 C a g e return 9 8 8 C a g e s , as e l e m e n t s o f m o l e c u l a r structure 16, 17 Caglioti reduction 5 7 4 - 5 7 6 C a h n - I n g o l d - P r e l o g notation 1 4 4 C a m b r i d g e Structural Database 8 0 Camphane, analysis of 3 0 0 Candida s p e c i e s , in alkane m e t a b o l i s m 9 1 5 , 916 Caprostanes, c h e m i c a l shift v a l u e s for 3 6 7 Caranes, chiroptical properties o f 1 6 8 , 169 Carbene insertion reactions 5 9 3 - 5 9 5 Carbenium i o n s , /3-cleavage o f 6 2 1 , 6 2 4 Carbon, flattened 9 2 8 inverted 9 2 8 C a r b o n - 1 3 kinetic i s o t o p e effects 8 7 9 - 8 8 2 Carbonyl c o m p o u n d s , reduction of, direct 5 7 3 , 5 7 4 indirect 5 7 4 - 5 7 7 reductive alkylation o f 5 7 7 , 5 7 8

1065

Carboxylate a n i o n s , c o l l i s i o n - i n d u c e d decarboxylation of 5 4 6 C a r b o x y l a t i o n reactions 6 3 2 , 6 3 3 C a r b o x y l i c a c i d s — s e e also A d a m a n t a n e c a r b o x y l i c acids anodic o x i d a t i o n o f 7 9 7 indirect d e c a r b o x y l a t i o n o f 5 7 8 photodecarboxylation of 580, 581 thermal d e c a r b o x y l a t i o n o f 5 7 8 - 5 8 0 C a r b o x y l i c esters, anodic o x i d a t i o n o f 7 9 8 , 7 9 9 reduction o f 5 6 4 , 5 6 5 Camauba wax 901 Carotenes, C 4 o - p e r h y d r o g e n a t e d 3 3 2 Catalysts, bifunctional 6 4 6 olefin m e t a t h e s i s 6 9 6 zeolite 6 4 6 , 6 4 7 Catenane, structural c h e m i s t r y o f 7 9 Cavity surface areas 1 9 3 - 1 9 5 C — C bond cleavage 6 7 0 - 6 7 2 in c y c l o p r o p a n e s 7 9 9 - 8 0 1 in p o l y c y c l o a l k a n e s 8 0 1 C — C b o n d protolysis 6 1 0 - 6 1 4 versus /3-cleavage 6 2 1 - 6 2 4 Chair-chair interconversions 1 2 0 - 1 2 2 Charged particles, f a s t - m o v i n g , e n e r g y l o s s e s of 7 4 5 - 7 5 0 Charge r e c o m b i n a t i o n 7 4 4 Charge s c a v e n g e r s 7 6 0 - 7 6 2 C — H b o n d l e n g t h s , variations in 8 7 , 9 0 C — H bond protolysis 6 1 0 - 6 1 4 C — H bonds, remote, oxidation o f 7 9 5 - 7 9 9 C H / D 2 e x c h a n g e studies 8 7 2 C h e m i c a l graphs 1 8 7 , 188 e n u m e r a t i o n o f subgraphs from 1 8 9 C h e m i c a l shift theory 3 5 2 C h e m i c a l shift v a l u e s , aromatic s o l v e n t - i n d u c e d shift effect o n 3 6 8 , 369 deuterium i s o t o p e effects o n 3 7 7 - 3 7 9 for a c y c l i c alkanes 3 5 2 - 3 5 5 for c y c l o a l k a n e s 3 5 7 - 3 6 2 , 3 6 4 - 3 6 8 m e d i u m effects o n 3 6 9 - 3 7 1 Chi i n d i c e s 1 9 5 - 2 0 2 Chiral centres 2 2 5 , 3 1 0 Chiral c h r o m o p h o r e s 155 Chlorella, o c c u r r e n c e o f alkanes in 9 0 7 , 908 Chlorine a t o m s , c o m p l e x e d 9 7 0 - 9 7 3 Chloronium ions 6 4 2 , 6 4 3 Cholestanes, c h e m i c a l shift v a l u e s for 3 6 7 chiroptical properties o f 138 electrolysis of 7 9 0 natural o c c u r r e n c e o f 8 9 8 , 9 0 0 Chromatographic retention index 2 0 8

1066

Subject index

Chrysopa s p e c i e s , o c c u n e n c e o f alkanes in 906 Citrus fruits, cuticular w a x e s o f 9 0 1 w a x lining in j u i c e s a c s o f 9 0 2 Clathration 3 2 1 /3-Cleavage reactions 6 3 3 v e r s u s C — C b o n d protolysis 6 2 1 - 6 2 4 C l e m m e n s e n reduction 5 7 4 C2p manifold 5 0 2 - 5 0 7 C2s manifold 4 9 0 - 5 0 2 C N D O / 2 a t o m i c partial charge 2 0 8 C o c k r o a c h e s , alkanes in, biogenesis of 9 1 4 occurrence of 9 0 5 , 9 0 6 C o l l i s i o n activated d i s s o c i a t i o n 4 0 5 , 4 0 6 , 4 1 2 , 417, 439, 4 4 1 , 4 4 7 C o l l i s i o n a l deactivation 7 4 4 , 7 5 6 C o m p o n e n t additivity 2 5 3 - 2 5 8 C o m p t o n effect 7 4 5 C o m p u t a t i o n a l structures 8 7 C o n c e r t e d m o t i o n s 115 Conformation, N M R studies o f 3 7 1 - 3 7 6 non-alternating 1 0 6 Conformational analysis 9 6 - 1 2 8 e x p e r i m e n t a l m e t h o d s for 9 7 , 9 8 m e d i u m effects o n 9 8 , 9 9 Conformational dissymmetry model 1 4 5 - 1 6 2 C o n f o r m a t i o n a l equilibria, i s o t o p e effects o n 120 Conformational minima 9 7 Corynebacterium species, biogenesis of alkanes in 9 1 4 C O S M I C method 91 C o t t o n effect 1 3 9 C o u l o m b attraction 7 4 4 C o u p l e d oscillator c o n c e p t 145 C o u p l i n g constants, m e a s u r e m e n t of, in conformational a n a l y s i s 105, 1 0 6 , 1 0 9 , 1 1 2 , 117 vicinal 8 5 , 8 6 Critical points 8, 9 b o n d 13 Cruciferae, cuticular w a x e s o f 9 0 1 Crystals, d e f o r m a t i o n o f 81 C S E A R C H data bank s y s t e m 3 5 5 Cubane, anodic oxidation o f 801 c h e m i c a l shift v a l u e s for 3 6 5 P E spectrum o f 5 1 5 , 5 1 7 , 5 1 8 proton affinity o f 5 3 8 reactions w i t h transidon-metal i o n s 5 4 0 structural c h e m i s t r y o f 7 9 synthesis o f 578, 5 7 9 Cuticular w a x e s 9 0 0 - 9 0 2 in control o f insect infestation 9 0 2

o f insects 9 0 4 - 9 0 6 Cycloalkane ions 4 1 7 , 4 2 3 , 4 2 4 , 4 2 9 , 4 3 0 C y c l o a l k a n e s — s e e also A l k y l c y c l o a l k a n e s , Bicycloalkanes, Pentacycloalkanes, Polycycloalkanes, Tetracycloalkanes, Tricycloalkanes biogenesis of 9 1 3 , 9 1 4 c h e m i c a l shift v a l u e s for 3 5 7 - 3 6 1 chiroptical properties o f 1 6 3 - 1 8 0 c l e a v a g e reactions o f 6 2 3 , 6 7 0 - 6 7 2 conformation of 225, 2 2 6 d e h y d r o g e n a t i o n b y metal catalysts 6 6 0 , 661, 666, 667 IR spectra o f 3 1 5 isomerization o f 6 1 8 - 6 2 1 m a s s spectra o f 3 0 6 - 3 1 4 m e t a b o l i s m of, b y a n i m a l s a n d plants 9 1 6 , 917 nitration o f 6 4 2 N M R spectra o f 3 1 6 - 3 1 8 , 3 7 4 - 3 7 6 oxyfunctionalization of 6 3 7 , 6 4 0 P E spectra o f 4 7 7 - 4 8 0 , 4 9 1 - 4 9 9 , 5 0 7 - 5 1 5 photochemistry of 6 8 7 - 6 9 1 radical attack o n 9 6 4 , 9 7 5 , 9 7 6 , 9 8 3 - 9 8 6 rearrangement o f 6 8 4 - 6 8 6 , 6 9 2 , 6 9 3 , 696-699 s p i n - l a u i c e relaxation in 3 8 8 s t e r e o c h e m i c a l determination o f 2 9 4 - 2 9 6 s y n t h e s i s of, by c o u p l i n g reactions 5 8 3 - 5 8 8 b y c y c l i z a t i o n reactions 5 8 8 - 5 9 2 b y m o l e c u l a r extrusion reactions 5 9 4 - 5 9 7 b y rearrangements 5 9 7 - 5 9 9 from a l c o h o l s 5 6 2 - 5 6 7 from a l k e n e s 5 5 5 - 5 6 2 from alkyl h a l i d e s 5 6 9 - 5 7 2 from a m i n e s 5 8 1 from c a r b o x y l i c acid derivatives 578-581 from nitriles 5 8 2 from t h i o p h e n e s 5 6 7 thermochemistry of 2 4 9 - 2 5 3 Cycloalkyl ions 4 2 5 , 4 3 0 Cyclobutane, chiroptical properties o f 138 conformation of 123 P E spectrum o f 5 1 4 , 5 1 5 reactions with h e l i u m tritide i o n s 8 3 7 , 838 strain e n e r g y in 6 3 structural c h e m i s t r y o f 7 9 Cyclobutanes, alkyl-substituted—see Alkylcyclobutanes Cyclobutyl anions 5 4 7 Cyclodecane, conformation of 128 geometry of 83

Subject index Cyclododecane, c o n f o n n a d o n o f 125, 127 geometry of 83 C y c l o h e p t a d e c a n e , c o n f o r m a t i o n o f 128 C y c l o h e p t a n e , c o n f o r m a t i o n o f 127 C y c l o h e x a d e c a n e , c o n f o r m a t i o n o f 128 Cyclohexane, c o n f o r m a t i o n o f 118, 2 2 5 electrolysis of 7 8 8 geometry of 82 in aroma c o m p o n e n t s 9 0 3 i s o t o p i c a l l y labelled 1 2 0 , 8 2 5 N M R spectrum o f 3 7 4 o x i d a d o n of, liquid-phase 8 8 4 photochemistry of 6 8 9 - 6 9 1 proton affinity o f 5 3 8 radiolysis o f 7 5 6 - 7 5 8 liquid-phase 7 6 5 , 7 6 6 solid-phase 7 7 4 , 775 reactions w i t h h e l i u m tritide i o n s 8 3 9 , 840 Cyclohexanes, alkyl-substituted—see A l k y l c y c l o h e x a n e s halo-substituted—see H a l o c y c l o h e x a n e s polyhydroxy-substituted—see Polyhydroxycyclohexanes C y c l o n o n a n e , c o n f o r m a t i o n o f 127 C y c l o n o n a n e s , tetraalkyl-substituted—see Tetraalkylcyclononanes C y c l o o c t a d e c a n e , c o n f o r m a t i o n o f 128 Cyclooctane, c o n f o r m a t i o n o f 126 geometry of 83 C y c l o o c t a n e s , alkyl-substituted—see Alkylcyclooctanes Z / f - C y c l o o c t e n e actinometer 7 0 8 C y c l o p e n t a d e c a n e , c o n f o r m a t i o n o f 128 Cyclopentane, c o n f o r m a t i o n o f 123 geometry of 82, 9 2 reactions with h e l i u m tritide i o n s 8 3 9 tritium-labelled 8 5 1 , 8 5 2 C y c l o p e n t a n e s , alkyl-substituted—see Alkylcyclopentanes Cyclopentyl anions 547 Cyclopropane, as m a s s spectrometric intermediate/product 414, 424, 425, 438 chiroptical properties o f 138 deprotonation o f 5 4 6 electronic charge d e n s i t y in 9, 10 P E spectrum o f 5 0 7 - 5 1 4 proton affinity o f 5 3 7 , 5 3 8 protonated 6 1 1 structure o f 5 3 5 - 5 3 7 reactions w i t h h e l i u m tritide i o n s 8 3 5 s p i n - s p i n c o u p l i n g in 3 7 9 , 3 8 2 , 3 8 4

1067

strain e n e r g y in 6 2 structural c h e m i s t r y o f 7 9 C y c l o p r o p a n e - p r o p a n e rearrangement, h y d r o g e n kinetic i s o t o p e effects in 873-879 Cyclopropanes, alkyl-substituted—see Alkylcyclopropanes halo-substituted—see Halocyclopropanes C y c l o p r o p a n o d e c a l i n s , chiroptical properties o f 169 Cyclopropenes, oligomerizadon of 562 Cyclopropyl anions 547 C y c l o p r o p y l c a r b i n y l radical 9 7 7 ring o p e n i n g o f 9 6 4 , 9 6 5 C y c l o t e t r a d e c a n e , c o n f o r m a t i o n o f 128 C y c l o t e t r a e i c o s a n e , N M R spectrum o f 3 7 6 C y c l o t r i d e c a n e , c o n f o r m a t i o n o f 128 C y c l o u n d e c a n e , c o n f o r m a t i o n o f 128 Cyclovoltammetry 783, 794 Decahydronaphthalenes, oxidation of 978 Decalin, analysis of 3 0 0 c o n f o r m a t i o n o f 123 m a s s spectra o f 3 0 7 , 3 0 8 N M R spectra o f 3 1 6 Decalins, alkyl-substituted—see Alkyldecalins Decalols 979 chiroptical properties o f 171 n-Decane, isotopically labelled, microsomal hydroxylation of 8 5 4 synthesis of 823 /3-Decay 8 3 0 , 831 in tritium-labelled a l k a n e s 8 4 9 - 8 5 2 in ^"^C-labelled a l k a n e s 8 5 2 D e f o r m a t i o n d e n s i t y 15, 16, 3 9 Degeneracy 220 Dehydroadamantanes, bromination of 9 8 4 Dehydrocubanes, synthesis of 711 D e h y d r o c y c l i z a t i o n reactions 5 9 2 , 6 8 4 tracer studies o f m e c h a n i s m o f 8 6 0 , 8 6 1 D e h y d r o d i m e r i z a t i o n reactions 6 8 9 , 8 0 5 D e h y d r o g e n a t i o n reactions 6 6 4 - 6 6 6 , 8 0 5 D e l t a v a l u e s 1 9 0 - 1 9 3 , 195 D e n s i t y difference m a p s 15, 16 Depolymerization, of coal 6 2 4 D e u t e r i u m i s o t o p e e f f e c t s , in g a s - p h a s e chlorination 9 6 5 Deuteroalkanes, chiroptical properties o f 1 6 0 , 1 6 2 radiation d e c o m p o s i d o n o f 8 6 7 , 8 6 8 structural c h e m i s t r y o f 8 5 , 8 6 D e w a r ' s s e m i e m p i r i c a l S C F - M O m e t h o d 91 D i a d a m a n t a n e s , c h e m i c a l shift v a l u e s for 3 6 6 Dialkylbutanes, c o n f o m i a t i o n o f 9 7 , 9 8 , 1 0 2 , 108, 1 1 0 - 1 1 2 N M R spectra o f 3 7 1 , 3 7 3

1068

Subject index

D i a l k y l c y c l o a l k a n e s — s e e also Dialkylcyclohexanes, Dialkylcyclo pentanes, Dialkylcyclopropanes c h e m i c a l shift v a l u e s for 3 5 8 , 3 5 9 c o n f o r m a t i o n o f 1 2 6 , 127 Dialkylcyclohexanes, chiroptical properties o f 1 6 5 , 1 7 1 , 173 conformation of 120, 122 deuterium i s o t o p e effects o n 3 7 9 geometry of 8 2 , 89 i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 1 6 N M R spectra o f 3 7 4 , 3 7 5 Dialkylcyclopentanes, chiroptical properties o f 165 t h e r m o c h e m i c a l c a l c u l a t i o n s for 2 8 2 Dialkylcyclopropanes, chiroptical properties o f 1 3 8 , 1 3 9 , 1 6 3 , 165 reactions with h e l i u m tritide ions 8 3 5 - 8 3 7 Dialkylethanes, conformation of 110 Dialkylhexanes, N M R spectra o f 3 7 1 optical i s o m e r i s m in 2 2 5 t h e r m o c h e m i c a l c a l c u l a t i o n s for 2 7 3 - 2 7 5 D i a l k y l m e t h a n e s , c o n f o r m a t i o n o f 108 D i a l k y l n o r b o m a n e s , c h e m i c a l shift v a l u e s for 367 Dialkylpentanes, chlorination o f 9 7 4 conformation of 106 N M R spectra o f 3 7 1 Dialkylpropanes, conformation of 109 Diamantane, m a s s spectrum o f 3 0 8 , 3 1 1 synthesis of 6 1 9 D i - b i c y c l o [ l . l . l ] p e n t y l , P E spectrum o f 5 2 0 , 523, 524 D i b o m y l s , chiroptical properties o f 137 Dications 4 0 6 Dihedral a n g l e s 9 6 c h a n g e s in 1 1 4 distortion in 1 0 2 - 1 0 5 , 111 in a l k y l p r o p a n e s 1 0 9 in m e d i u m - r i n g a l k a n e s 1 2 4 , 125 in tetraalkylethanes 1 1 2 D i m e n t h y l s , chiroptical properties o f 137 D i m e r s , formation of, in radiation c h e m i s t r y 764 Dipolar coupling 8 4 Dipole moments 6 7 - 7 0 a t o m i c contributions to 6 7 c h a r g e transfer contributions to 6 8 g r o u p contributions to 6 9 polarization contributions to 6 8 vibrationally i n d u c e d 7 4 - 7 6 D i s p e r s i o n c u r v e s 1 3 7 , 138 D i s s o c i a t i o n p r o c e s s e s , o f neutral e x c i t e d states 751, 752

Dissociative chemisorption, collision-induced 686 Ditriacontanes, isotopically labelled, synthesis of 827 D o c o s a n e s , i s o t o p i c a l l y labelled, s y n t h e s i s o f 826, 827 Dodecahedranes, c h e m i c a l shift v a l u e s for 3 6 6 proton affinities o f 5 3 8 structural c h e m i s t r y o f 7 9 , 9 2 synthesis of 5 9 2 , 6 2 0 , 621 D o d e c a n e , isotopically labelled, synthesis of 8 2 2 use in g a s c h r o m a t o g r a p h y 8 2 5 D R E I D I N G method 91 Drosicha s p e c i e s , cuticular w a x e s o f 9 0 5 Drosophilia s p e c i e s , cuticular w a x e s o f 9 0 5 D r u d e e x p r e s s i o n 137 Dmsilla s p e c i e s , o c c u r r e n c e o f a l k a n e s in 9 0 6 D u f o u r s g l a n d s , o c c u r r e n c e o f a l k a n e s in 9 0 6 D y n a m i c stereochemistry 1 1 3 - 1 1 8 Eclipsed conformations 106, 110, 113, 114 Edessa s p e c i e s , o c c u r r e n c e o f a l k a n e s in 9 0 6 Electrochemical conversion 7 8 1 - 8 0 5 Electron affinities 5 4 3 , 5 4 4 Electron correlation 8 9 Electron diffraction t e c h n i q u e s , in structural determinations 8 0 , 8 2 , 8 3 Electron h o l e s 7 6 2 Electronic charge d e n s i t y 5 , 6 c a l c u l a t i o n o f 17 gradient v e c t o r field o f 9 - 1 2 L a p l a c i a n o f 8, 3 5 ^ 1 reactivity and 4 0 , 4 1 local m a x i m a in 6, 7 topology of 6 - 1 7 Electronic e x c i t a t i o n 7 4 4 Electronic optical activity 1 3 7 Electrons, mobility of 759, 7 6 0 thermalization o f 7 5 3 , 7 5 4 , 7 5 9 trapped 7 7 2 , 7 7 3 E l e c t r o t o p o l o g i c a l states 2 0 9 - 2 1 2 Empirical m e t h o d s , in structural d e t e r m i n a t i o n s 91, 92 E n e - o r g a n o m e t a l l i c reagents, c y c l i z a t i o n o f 589, 5 9 0 E n e r g y additivity 5 9 - 6 1 Energy m a x i m a 87 Enthalpy, bond dissociation 261 relationship to heat c a p a c i t y 2 1 8 Enthalpy o f a t o m i z a t i o n 2 0 6 Enthalpy o f formation 1 0 0 , 2 0 6 , 3 0 2 , 3 0 3 comparison of experimental and calculated values 2 4 2 , 2 4 3 , 2 5 2 , 2 5 7

Subject index for alkyl radical g r o u p s 2 5 8 - 2 6 0 for liquid alkanes 2 6 2 - 2 6 4 for liquid c y c l o a l k a n e s 2 6 2 , 2 6 4 , 2 6 5 measurement of 2 2 7 - 2 2 9 Enthalpy o f vaporization 2 0 6 Entropy, c o m p a r i s o n o f tabulated a n d calculated values 2 4 4 - 2 4 8 , 2 5 3 for alkyl radical g r o u p s 2 6 0 , 2 6 1 for liquid a l k a n e s 2 6 4 , 2 6 6 for liquid c y c l o a l k a n e s 2 6 4 , 2 6 7 in c o n f o r m a t i o n a l a n a l y s i s 9 9 , 1 1 9 , 1 2 0 , 127 intrinsic 2 2 2 measurement of 2 2 9 , 2 3 0 of m i x i n g 2 2 4 relationship to heat capacity 2 1 8 Equilibrium constants 2 1 7 - 2 1 9 intrinsic 2 7 0 measurement of 2 2 9 Equivalent b o n d orbital m o d e l s 4 6 0 - 4 6 3 Ergostane, natural o c c u r r e n c e o f 8 9 8 E s c a p e probabilities 7 6 0 Essential o i l s , o c c u r r e n c e o f alkanes in 9 0 3 Estranes, chiroptical properties o f 1 7 5 , 176 Ethane, '^C-labelled 821 ^"^C-labelled 8 5 2 geometry of 8 2 in apple aroma c o m p o n e n t s 9 0 3 P E spectrum o f 4 8 9 , 4 9 0 proton affinity o f 5 3 8 reactions with h e l i u m tridde i o n s 8 3 3 t h e r m o c h e m i c a l c a l c u l a t i o n s for 2 7 9 , 2 8 0 tritium-labelled 8 4 9 , 8 5 0 Ethanes, alkyl-substituted—see A l k y l e t h a n e s aryl-substituted—see A r y l e t h a n e s Ethanols, aryl-substituted—see A r y l e t h a n o l s E t h o n i u m i o n , structure o f 5 3 3 - 5 3 5 Ethyl a n i o n s 5 4 7 E t h y l e n e octant rule 1 5 2 Ethylenes, catalytic h y d r o p o l y m e r i z a t i o n o f 8 6 4 , 8 6 5 deuterated, high-temperature p y r o l y s i s o f 866, 867 Euphorbia s p e c i e s , cell s u s p e n s i o n s o f 9 0 4 Eurychora s p e c i e s , cuticular w a x e s o f 9 0 5 Eutectic c o l u m n s 3 2 7 E v a n s - P o l a n y i equation 9 6 7 E x c i t e d states, fluorescent 763 triplet 7 4 4 E y r i n g ' s equation o f state 2 6 6 , 2 6 8 Fatty acids, decarboxylation of 9 1 0

1069

oxidadon of 9 1 2 anodic 7 9 6 Fatty a l d e h y d e s , d e c a r b o n y l a t i o n o f 9 1 0 Fenestranes, nomenclature of 9 2 9 photolysis of 9 4 5 , 9 4 6 structure o f 9 3 1 - 9 3 3 synthesis of 9 3 7 - 9 4 6 thermolysis of 9 4 5 X-ray studies o f 9 3 9 , 9 4 3 , 9 4 4 Fenestratetraenes 9 4 0 , 9 4 2 , 9 4 3 Ferns, cuticular w a x e s o f 9 0 2 Fichtelite, a n a l y s i s o f 3 0 0 , 3 0 8 , 3 1 2 , 3 1 4 Field ionization 3 9 9 , 4 1 4 , 4 2 2 , 4 4 4 , 4 4 7 F i s c h e r ' s c o n v e n t i o n 141 F i s h , o c c u r r e n c e o f a l k a n e s in 9 0 7 F l a m e calorimetry 2 2 8 , 2 2 9 F l a m e ionization detector 3 2 9 Fluorination, e l e c t r o c h e m i c a l 7 8 5 F o c k operator 4 5 8 F o l d e d c o n f o r m a t i o n s 107 Formica s p e c i e s , o c c u r r e n c e o f alkanes in 9 0 6 F o r m y l a t i o n reactions 6 3 3 - 6 3 5 Formyl cations 6 3 5 Fossil fuels, G C / M S / C of 3 3 0 , 3 3 2 - 3 4 0 Fragmentation p r o c e s s e s 3 9 9 , 4 0 0 , 4 0 6 , 4 1 9 , 420, 4 2 8 ^ 3 2 internal 4 1 1 - 4 1 3 , 4 1 5 , 4 1 8 , 4 2 1 , 4 2 9 terminal 4 1 2 , 4 1 3 , 4 1 5 , 4 1 8 , 4 2 2 , 4 2 3 , 4 2 9 Free i o n y i e l d 7 5 9 Fuel c e l l s 8 0 4 , 8 0 5 F u n g i , o c c u r r e n c e o f a l k a n e s in 9 0 7 , 9 0 8 G a m m a c e r a n e s , natural o c c u r r e n c e o f 9 0 0 Gas chromatography 3 1 9 as an analytical t e c h n i q u e 3 2 2 - 3 2 9 use o f i s o t o p i c a l l y labelled a l k a n e s in 8 2 5 G a s o l i n e upgrading 6 1 8 Gauche interactions 1 1 0 , 111 GC/MS/C system 3 3 0 - 3 4 0 Gel permeation chromatography 3 2 0 , 321 G m - d i m e t h y l effect 1 0 9 , 1 2 6 Geminate recombination 7 6 3 Geonium s p e c i e s , cuticular w a x e s o f 9 0 1 G i b b s free e n e r g i e s 2 1 7 - 2 1 9 G i f - O r s a y II s y s t e m 8 0 2 - 8 0 4 Gif system 8 0 2 , 8 0 3 G o n a n e s , chiroptical properties o f 1 7 4 Gottiferae s p e c i e s , h e a r t w o o d w a x e s in 9 0 2 Gradient m e t h o d s 8 8 , 8 9 , 9 1 G r a s s h o p p e r s , o c c u r r e n c e o f a l k a n e s in 9 0 5 Grignard reagents, reactions with alkyl h a l i d e s 584, 585 Ground states, e c l i p s e d 1 0 5 , 1 0 6 G r o u p additivity 2 - 5 , 2 3 3 - 2 3 8 application o f 2 7 3 - 2 8 2 reliability o f m e t h o d s 2 7 0 - 2 7 3

1070

Subject index

G r o u p type a n a l y s i s 3 2 0 - 3 2 2 Group values, summary of 270, 271 Group volumes 5 2 - 5 9 Halocyclohexanes, electrolysis of 7 8 9 Halocyclopropanes 9 8 3 - 9 8 5 H a l o f o r m y l a t i o n reactions 9 8 0 H a l o g e n a t i o n reactions 6 4 2 - 6 4 8 i n v o l v i n g m i x e d radical c h a i n s 9 8 9 - 9 9 4 H a l o h e x a n e s , i s o t o p i c a l l y labelled, u s e in g a s chromatography 8 2 5 N - H a l o i m i d e s , as h a l o g e n a t i n g a g e n t s 9 9 1 Halophosphines 9 9 3 H a l o p h o s p h o n a t i o n reactions 9 9 2 , 9 9 3 V - H a l o s u c c i n i m i d e s , as h a l o g e n a t i n g a g e n t s 991 H a l o v i n y l a t i o n reactions 9 8 6 Hartree-Fock equations 4 5 8 Heat c a p a c i t y , for alkyl radical g r o u p s 2 6 0 , 2 6 1 measurement of 229, 2 3 0 p o l y n o m i a l e x p r e s s i o n s for 2 5 7 , 2 6 7 , 2 7 2 relationship to enthalpy and entropy 2 1 8 Helical conductor model 1 5 2 - 1 5 5 H e l i c a l c o n f o r m a t i o n s 107 Helix model 164 H e n e i c o s a n e s , i s o t o p i c a l l y labelled, s y n t h e s i s of 824 n - H e p t a d e c a n e , i s o t o p i c a l l y labelled, metabolism of 855 n-Heptane, fragmentation o f 4 1 4 - 4 2 3 i s o t o p i c a l l y labelled, synthesis of 8 1 5 , 8 1 6 use in g a s c h r o m a t o g r a p h y 8 2 5 Heptanes, alkyl-substituted—see Alkylheptanes H e p t e n e , fragmentation o f 4 4 3 ^ 4 5 Heptyl ions A36-4A2 H e s s i a n matrices 8 H e t e r o p o l y a n i o n s , in alkane reactions 6 7 2 , 6 7 3 Hexaalkylcyclohexanes, conformation of 120, 122 N M R spectra o f 3 7 4 Hexaalkylethanes, conformation of 103, 105, 113, 116 N M R spectra o f 3 7 3 H e x a a r y l e t h a n e s , N M R spectra o f 81 Hexacosanes, i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 2 6 , 8 2 7 t h e r m o c h e m i c a l c a l c u l a t i o n s for 2 7 9 n - H e x a d e c a n e , i s o t o p i c a l l y labelled, metabolism of 8 5 4 , 855 synthesis of 8 1 9 , 8 2 6 Hexadecanes, alkyl-substituted—see Alkylhexadecanes n-Hexane, fragmentation o f 3 9 8 , 4 0 0 , 4 0 1 , 4 1 8 , 4 3 5 , 4 3 7

in a r o m a c o m p o n e n t s 9 0 3 i s o t o p i c a l l y labelled, N M R spectra in z e o l i t e s 3 6 9 use in g a s c h r o m a t o g r a p h y 8 2 5 structural c h e m i s t r y o f 81 Hexanes, alkyl-substituted—see Alkylhexanes halo-substituted—see Halohexanes Himatismus s p e c i e s , cuticular w a x e s o f 9 0 5 H o m o a d a m a n t a n e s , c h e m i c a l shift v a l u e s for 365 H o m o c u b a n e s , c h e m i c a l shift v a l u e s for 3 6 5 Hopanes, G C / M S / C analysis o f 3 3 6 , 3 3 8 natural o c c u r r e n c e o f 8 9 8 , 9 0 0 separation from crude o i l s 3 2 8 structure o f 3 3 3 Hot atoms 8 2 9 , 8 3 1 , 8 3 2 ^^C 8 5 2 tritium 8 4 2 , 8 4 3 Hot molecules 7 0 2 H u g g i n s formula 2 3 8 H u n s d i e c k e r reaction 5 7 8 Hybridization model 5 2 , 5 6 , 6 2 H y d r a z o n e s , reduction o f 5 7 4 - 5 7 6 Hydrindanes, chiroptical properties o f 1 6 9 , 1 7 0 , 1 7 4 m a s s spectra o f 3 0 7 H y d r i n d a n o l s , chiroptical properties o f 1 6 9 H y d r i n d a n o n e s , chiroptical properties o f 1 6 9 H y d r o g e n abstraction reactions, reversibility o f 986-989 H y d r o g e n a t o m s , relative reactivities of, t o w a r d s radical attack 9 6 7 - 9 8 3 H y d r o g e n - d e u t e r i u m e x c h a n g e reactions 610-614, 659, 868-871 H y d r o g e n kinetic i s o t o p e effect studies 873-879 H y d r o g e n o l y s i s reactions 6 8 3 H y d r o g e n - s u p p r e s s e d graph 1 9 0 Hydroliquefaction processes 6 2 4 Hyperconjugation, negative 5 4 7 Hypervirial t h e o r e m 4 2 Icanthoscelides s p e c i e s , cuticular w a x e s o f 906 Ideality, d e v i a t i o n s f r o m , in g a s e s 2 2 6 , 2 2 7 IGLO method 3 5 2 , 377 INADEQUATE 387 Increment s y s t e m s 3 5 5 - 3 5 7 , 3 6 2 , 3 6 3 Infrared s p e c t r o s c o p y 3 1 4 - 3 1 6 o f c y c l o h e x a n e s 121 of cyclopropanes 301 of menthanes 2 9 9 , 3 1 5 Insects, a l k a n e s in, biogenesis of 9 1 4 occurrence of 9 0 4 - 9 0 6

Subject index Interactions, gauche 2 3 8 - 2 4 1 , 2 4 4 1,3 1 0 3 , 1 0 8 - 1 1 0 , 1 1 3 , 1 1 6 , 1 1 9 , 1 2 0 1,5 2 4 1 - 2 4 9 Interatomic surfaces 11 Intrinsic state 2 0 9 , 2 1 0 Ionizadon cross-secdon 7 4 7 Ionization e n e r g i e s 3 9 6 , 3 9 7 , 3 9 9 , 4 1 4 , 4 1 7 , 4 7 1 ^ 7 3 , 493 Ionizadon excitation 7 4 4 Ionization potentials 3 0 2 , 3 0 3 I o n - m o l e c u l e reactions 4 0 6 , 4 3 7 , 4 4 1 in radiolysis o f m e t h a n e 7 5 4 Ion pairs 3 9 6 , 4 0 4 Iridium c o m p l e x e s , p h o t o l y s i s o f 5 4 0 Iridomyrex s p e c i e s , o c c u r r e n c e o f a l k a n e s in 906 Iron centres, o x o - b r i d g e d binuclear 8 5 8 Isobutane 4 0 7 , 4 0 8 chiroptical properties o f 1 3 8 fragmentation o f 4 1 4 geometry of 8 2 proton affinity o f 5 3 8 radical attack o n 9 6 6 reactions with h e l i u m tritide i o n s 8 3 8 Isobutyl a n i o n s 5 4 7 I s o c a m p h a n e s , chiroptical properties o f 1 3 7 Isocyanides, reducdon of 581 Isomerization, o f a c y c l i c alkanes 6 1 5 - 6 1 9 , 6 8 4 o f alkane m o l e c u l a r ions 4 0 7 , 4 0 8 , 4 1 2 , 414, 417, 418, 448, 449 o f alkyl i o n s 4 3 3 of cycloalkanes 6 1 8 - 6 2 1 of cyclopentadienes 6 1 9 of 1 -heptene 4 4 4 I s o o c t a n e , t h e r m o c h e m i c a l c a l c u l a d o n s for 275-281 Isopentane, in strawberry a r o m a c o m p o n e n t s 903 I s o p r e n o i d h y d r o c a r b o n s , natural o c c u r r e n c e o f 898 Isopropyl a n i o n s 5 4 7 Isotope analysis 3 4 0 - 3 4 6 I s o t o p e effects 8 7 3 - 8 8 5 — 5 ^ ^ also C a r b o n - 1 3 kinetic i s o t o p e effects. D e u t e r i u m i s o t o p e effects in alkane fragmentations 4 0 1 - 4 0 7 , 4 1 1 , 4 1 4 , 415 o n c h e m i c a l shift v a l u e s 3 7 7 - 3 7 9 o n c o n f o r m a t i o n a l equilibria 1 2 0 , 3 7 9 Isotope rate ratios 9 6 5 Isotopic e n v i r o n m e n t a l b i o - g e o l o g i c a l studies 858, 859 Isotopic labelling, in m a s s spectrometry 4 0 2 , 405, 411, 413, 414, 424, 426, 431, 435, 441, 4 4 3 ^ 4 5 , 447

1071

I s o t o p i c o x i d a t i o n studies 8 8 2 , 8 8 3 I s o t o p i c tracer studies, u s i n g a l k a n e s 8 5 9 - 8 6 8 Jasminum s p e c i e s , c e l l s u s p e n s i o n s o f 9 0 4 Kappa indices 2 0 2 - 2 0 6 Karplus c u r v e 8 6 , 8 7 , 3 8 2 , 3 8 6 , 3 8 7 K e r o g e n s , o c c u r r e n c e o f a l k a n e s in 8 9 9 , 9 0 0 K E S S O H O program 8 4 Ketones, remote oxidation o f 7 9 5 , 7 9 6 a ,/3-unsaturated—see a ,/3-Unsaturated ketones Ketosteroids, electrolysis of 7 9 1 Kinetic isotopic method 8 8 4 K i r k w o o d theory 1 6 2 , 1 6 4 K o c h - H a a f reaction 6 3 2 K o c h reaction 7 8 4 Kolbe electrolysis 5 8 7 , 5 8 8 Koopmans' theorem 4 7 3 Lamellae 7 7 7 Laser flash p h o t o l y s i s 9 7 1 Lattice f o r c e s 8 1 Laurenane, s y n t h e s i s o f 5 6 5 Lavandula s p e c i e s , c e l l s u s p e n s i o n s o f 9 0 4 Libration 1 0 2 - 1 0 5 , 1 1 4 barriers to 115 L i m o n e n e s , chiroptical properties o f 1 6 9 Linear e n e r g y transfer 7 4 7 - 7 5 1 , 7 7 0 - 7 7 2 Liquid chromatography 3 1 9 , 3 2 0 Liquid density 2 0 7 Liver microsomes 8 5 7 L i v e r w o r t s , cuticular w a x e s o f 9 0 2 Locusta s p e c i e s , cuticular w a x e s o f 9 0 5 L o r e n z correction 1 5 3 M a i z e , a l k a n e s as t a x o n o m i c markers for 9 0 4 M a m m a l s , a l k a n e s in, biogenesis of 9 1 4 occurrence o f 9 0 6 , 9 0 7 , 9 1 8 , 9 1 9 Manduca s p e c i e s , o c c u r r e n c e o f a l k a n e s in 905, 9 0 6 M a n g a n e s e - p o r p h y r i n , as catalyst 8 0 4 Marker rules 1 4 4 M a s s spectral f r a g m e n t s , l o s s of, p o s i d o n a l probability o f 4 1 6 , 4 2 1 , 4 2 7 , 4 3 8 - 4 4 1 , 445 M a s s s p e c t r o m e t e r detector 3 2 9 - 3 4 6 M a s s spectrometry 3 9 5 ^ 4 9 Fourier transform i o n c y c l o t r o n r e s o n a n c e 396, 422, 424, 428, 430, 444, 448 h i g h resolution 3 9 6 , 4 3 0 m e t a s t a b l e i o n s in 3 9 9 , 4 0 1 , 4 0 5 , 4 1 4 , 4 2 2 , 432, 435, 436, 439, 441, 444, 447 of acyclic alkanes 3 0 2 - 3 0 6 of cycloalkanes 3 0 6 - 3 1 4

1072

Subject index

M a s s spectrometry (cont.) of menthanes 2 9 9

M o l e c u l a r charge d e n s i t y , gradient v e c t o r o f 92

temperature d e p e n d e n c e o f 3 9 6 - 3 9 8 , 4 0 4 , 407 time dependence o f 4 1 2 , 4 1 4 , 4 2 2 , 4 3 6 , 4 4 4 Menthanes,

Molecular Molecular Molecular Molecular

c h e m i c a l shift v a l u e s for 3 6 7 chiroptical properties o f 165 IR spectra o f 2 9 9 , 3 1 5 m a s s spectra o f 2 9 9

Meso digauche conformations 147 M e t a l a t o m s , in alkane reactions, neutral 6 7 3 photoexcited 6 7 4 - 6 7 6 Metal vapour synthesis 6 7 6 Metastable ion monitoring 3 3 9 Methane, alkylation o f 6 2 9 b y olefins 6 3 0 , 6 3 1 electrophilic oxygenation o f 6 3 7 fragmentation o f 3 9 8 i s o t o p e effects o n 4 0 1 - 4 0 7 geometry of 82 halogenation of 6 4 4 - 6 4 6 i s o t o p i c a l l y labelled, interaction with d i m e t h y l c a d m i u m 8 7 1 , 872 synthesis of 8 1 2 , 8 1 3 , 821 natural o c c u r r e n c e o f 8 9 7 P E spectrum o f 4 8 7 ^ 8 9 planar, structure o f 9 3 0 proton affinity o f 5 3 8 pulse radiolysis o f 8 6 7 radiation c h e m i s t r y o f 7 5 1 - 7 5 6 reactions w i t h h e l i u m tritide i o n s 8 3 2 , 8 3 3 s p i n - s p i n c o u p l i n g in 3 7 9 s t e a m reforming o f 8 6 5 , 8 6 6 Methanes, dialkyl-substituted—see Dialkylmethanes tetraalkyl-substituted—see Tetraalkylmethanes trialkyl-substituted—see T r i a l k y l m e t h a n e s Methenium ion 5 3 2 Methonium ion 5 3 2 , 5 3 3 Methyl anions 5 4 7 Micrococcus 907

s p e c i e s , o c c u r r e n c e o f a l k a n e s in

M i c r o - o r g a n i s m s , o c c u r r e n c e o f alkanes in 896, 907, 9 0 8 M i l l s rules 151 M M 2 programs 8 7 , 9 1 , 9 2 , 9 9 M M 3 programs 8 0 , 9 2 , 9 9 M N D O studies 9 1 for fenestranes 9 3 3 Mobil process 6 4 6 M o l a r refraction 2 0 7 M o l c o n n X program 1 8 9

connectivity method 1 8 9 - 2 0 2 extrusion reactions 5 9 4 - 5 9 7 graphs 1 2 - 1 6 mechanics calculations 9 7

in c o n f o r m a t i o n a l a n a l y s i s 9 8 - 1 0 1 , 104-109, 111, 112, 115, 118, 119, 124, 1 2 7 , 1 2 8 in structural d e t e r m i n a t i o n s 9 1 , 9 2 M o l e c u l a r m e c h a n i c s principle 8 9 M o l e c u l a r orbital m o d e l s 4 5 7 - ^ 7 1 M o l e c u l a r orbitals, canonical 4 5 9 localized 4 6 3 ^ 7 1 M o l e c u l a r rotation 1 3 6 M o l e c u l a r shape 2 0 2 - 2 0 6 M o l e c u l a r s k e l e t o n 1 8 7 , 188 M o l e c u l a r structure, c o n c e p t o f 17, 18 definition o f 2 1 , 1 8 6 description o f 1 8 9 , 1 9 0 e l e m e n t s o f 16, 17 h y p o t h e s e s for 2 , 2 0 , 21 Mollusca s p e c i e s , b i o g e n e s i s o f a l k a n e s in 913 M o m e n t s o f inertia 2 2 2 M O P A C program 9 1 M o s s e s , cuticular w a x e s o f 9 0 2 M o t i o n a l anisotropy 3 8 8 M o z i n g o reaction 5 7 6 , 5 7 7 MP2/6-31G method 9 2 Multi-ion-pair g r o u p s 7 6 0 Musca s p e c i e s , a l k a n e s in, biogenesis of 9 1 4 occurrence of 9 0 6 M y e l i n , o c c u r r e n c e o f a l k a n e s in 9 1 9 Myohacterium s p e c i e s , in alkane m e t a b o l i s m 915 Myristicaceae 902

s p e c i e s , h e a r t w o o d w a x e s in

Naphthalenes, isotopically labelled, synthesis of 8 2 0 Naphthene hydrocarbons, physical constants of 298 Natural g a s , o c c u r r e n c e o f 8 9 7 Neopentane, chiroptical properties o f 1 3 8 conformation of 109 deprotonation o f 5 4 6 radical attack o n 9 6 8 structural c h e m i s t r y o f 8 2 Neopentyl anions 5 4 7 Neopentylcyclohexanes, conformation of 106 N e o p e n t y l h a l i d e s , chiropUcal properties o f 140

Subject index

Neutral m o l e c u l e s , e x c i t e d 3 9 6 , 4 0 3 N e u t r o n diffraction studies 8 0 o f propellanes 9 5 4 N e w m a n diagrams 102, 2 3 8 , 2 3 9 Nicotiana s p e c i e s , b i o g e n e s i s o f alkanes in 9 1 1 , 9 1 3 cuticular w a x e s o f 9 0 1 Nitration reactions 6 4 1 , 6 4 2 Nitriles, reductive d e c y a n a t i o n o f 5 8 2 N i t r o a l k a n e s , reduction o f 5 8 2 , 5 8 3 Nitrosation reactions 6 4 1 , 6 4 2 Nitrosonium ions 6 4 2

1073

N o m e n c l a t u r e , o f n- and branched alkanes 8 9 6 N o n a d e c a n e s , s p i n - l a t t i c e relaxation in 3 8 8 Nonane,

Olefins, in alkylation o f a l k a n e s 6 2 4 O n s a g e r length 7 5 9 Optical i s o m e r i s m 2 2 4 - 2 2 6 Optical rotatory d i s p e r s i o n 1 3 7 Optical transitions 7 4 6 Orgyia s p e c i e s , o c c u r r e n c e o f a l k a n e s in 9 0 6 Oscillator strength 7 4 6 O x a l y l c h l o r i d e , as radical trap 9 8 0 Oxidation, anodic 7 8 2 - 8 0 2 destructive 8 8 3 O x i r a n e s , chiroptical properties o f 163 O x o n i u m ions 6 4 6 Oxonium ylides 6 4 6 - 6 4 8 Oxyfunctionalization 6 3 5 - 6 4 0

fragmentation o f 4 1 5 , 4 1 6 i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 2 0 , 8 2 1 N o n a n o n e s , in essential o i l s 9 0 3 N o n e n e , fragmentation o f 4 4 4 ^ 4 6 N o n y l acetates, in essential o i l s 9 0 3 N o r a b i e t a n e s , chiroptical properties o f 173 Norboradiene, cage dimer of 88 Norbornane,

P a c k i n g forces 81 Paddlanediones 9 3 6 , 9 3 7 Paddlanes, nomenclature of 9 2 9 structure o f 9 3 0 , 9 3 1 synthesis of 9 3 5 - 9 3 7 Pagodanes,

C 2 s band s y s t e m o f 4 9 7 structural c h e m i s t r y o f 8 0 , 8 2 N o r b o r n a n e s , alkyl-substituted—see Alkylnorbomanes Norcaranyl radicals 9 8 0 N o r c h o l e s t a n e s , natural o c c u r r e n c e o f 9 0 0 N o r h o p a n e s , natural o c c u r r e n c e o f 9 0 0 N o r p i n a n e s , c h e m i c a l shift v a l u e s for 3 6 7 N o r s n o u t a n e s , c h e m i c a l shift v a l u e s for 3 6 6 N o r t r i c y c l a n e s , c h e m i c a l shift v a l u e s for 3 6 5 N o r t r i c y c l e n e , photochlorination o f 9 8 4 , 9 8 5 N o y o r i ' s catalyst 5 5 8 Nuclear magnetic resonance spectroscopy 316-318, 351-389 analytical applications o f 3 7 7 in c o n f o r m a t i o n a l a n a l y s i s 9 8 , 1 0 4 , 1 0 8 , 1 1 1 , 1 2 4 , 1 2 5 , 128 in structural determinations 81 solid-state 3 7 6 , 3 7 7 N u c l e a r O v e r h a u s e r effect 8 5 O c t a d e c a n e , i s o t o p i c a l l y labelled, metabolism of 8 5 4 - 8 5 6 synthesis of 8 1 9 O c t a n e , i s o t o p i c a l l y labelled, o x i d a t i o n b y P s e u d o n o m a d bacterium strain 853 use in g a s c h r o m a t o g r a p h y 8 2 5 O c t a n e s , tetraalkyl-substituted—see Tetraalkyloctanes Octant rule 171 Olefin fragment, l o s s o f in m a s s spectrometry 419, 4 2 1 , 4 3 8 , 439, 4 4 9 Olefinic ions 4 0 0 , 4 2 4 , 4 4 3 ^ 4 7

dehydrocyclization of 5 9 2 isomerization o f 6 2 0 , 6 2 1 structural c h e m i s t r y o f 7 9 Panthenium argentatum, inheritance studies o f 904 Partition c o e f f i c i e n t s 2 0 7 , 2 0 8 Partition functions 2 1 9 , 2 2 0 P — C b o n d c l e a v a g e , in alkane reactions 6 6 1 , 666, 667 Pentaalkylethanes, conformation of 112, 113 Pentacycloalkanes, G C / M S / C analysis of 3 3 6 m a s s spectra o f 3 1 0 structure o f 3 3 3 n-Pentane, fragmentation o f 4 1 5 , 4 3 7 i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 2 0 photodimers of 6 8 9 radiolysis of, liquid-phase 7 6 7 solid-phase 7 7 4 , 7 7 5 Pentanes, alkyl-substituted—see Alkylpentanes P e n t a p r i s m a n e s , P E spectra o f 5 1 5 , 5 1 7 - 5 1 9 P e r b e n z o i c acid, as radical trap 9 7 9 Perdeuteropropene, u s e s o f 8 6 3 , 8 6 4 Peresters, in d e c a r b o x y l a t i o n reactions 5 7 8 , 579 Perhydroanthracenes, conformation of 122, 123 increment s y s t e m for c h e m i c a l shifts in 3 6 2 , 363 Perhydroindanes, conformation o f 123 P e r h y d r o n a p h t h a c e n e s , i n c r e m e n t s y s t e m for c h e m i c a l shifts in 3 6 2 , 3 6 3

1074

Subject index

Perhydrophenalenes, confomiation of 122 Perhydrophenanthrenes, conformation o f 122, 123 i n c r e m e n t s y s t e m for c h e m i c a l shifts in 3 6 2 , 363 Perhydrophenanthrols, chiroptical properties o f 171 P e r h y d r o p y r e n e s , i n c r e m e n t s y s t e m for c h e m i c a l shifts in 3 6 2 , 3 6 3 P e r h y d r o t r i p h e n y l e n e s , chiroptical properties o f 171 Periplanata s p e c i e s , b i o g e n e s i s o f alkanes in 9 1 4 cuticular w a x e s o f 9 0 5 , 9 0 6 Peristylanes, synthesis o f 5 9 5 Peroxonium ions 6 3 5 Petroleum, b i o g e n i c / a b i o g e n i c origin o f 9 0 8 , 9 0 9 components of 897 Pharmacology 9 1 8 , 9 1 9 Phenyl anions 5 4 7 Pheromonal secretions, occurrence of alkanes in 9 0 5 , 9 0 6 P h o s p h o r a n y l radicals 9 9 3 Phosphorodichloridates 9 9 3 Photochemical smogs 9 1 8 P h o t o c y a n a t i o n reactions 9 8 6 , 9 8 7 Photocycloaddidon reacdons 5 9 0 - 5 9 2 P h o t o d e c a r b o n y l a t i o n reactions 5 9 5 - 5 9 7 P h o t o d e n i t r o g e n a t i o n reactions 7 0 8 Photoelectric effect 7 4 5 Photoelectron spectroscopy,

Pisum s p e c i e s , cuticular w a x e s o f 9 0 4 Pitzer acentric factor 2 0 8 Plankton, decomposidon of 897 intracellular w a x e s in 9 0 2 Plants, alkanes in, biogenesis of 9 0 9 - 9 1 4 occurrence of 8 9 6 , 9 0 0 - 9 0 4 Plant w a x e s 9 0 0 P M 3 method 91 P o d o c a r p a n e s , c h e m i c a l shift v a l u e s for 3 5 6 Polarizability 7 0 - 7 4 a t o m i c contributions to 7 0 charge transfer contributions to 7 1 g r o u p contributions to 7 3 polarization contributions t o 7 1 P o l l u t i o n , d u e to p e t r o l e u m 8 9 6 Polya counting polynomial 189 Polycycloalkanes, c h e m i c a l shift v a l u e s for 3 6 2 , 3 6 4 - 3 6 8 P E spectra o f 4 7 9 , 4 8 0 , 5 1 5 - 5 2 4 rearrangement o f 5 9 7 - 5 9 9 ribbon orbitals in 5 0 5 - 5 0 7 s y n t h e s i s of,

interpretation o f 4 7 3 ^ 7 5 i o n i z a t i o n e n e r g i e s and 4 7 1 ^ 7 3 m o l e c u l a r orbital m o d e l s a n d 4 5 7 ^ 7 1 of acyclic alkanes 4 7 6 , 4 8 7 - 5 0 5 of cycloalkanes 4 7 7 ^ 8 0 , 4 9 1 ^ 9 9 , 5 0 7 - 5 2 4 of ethane 4 8 9 , 4 9 0 of methane 4 8 7 - 4 8 9 of propellanes 9 5 2 , 9 5 4 P h o t o f r a g m e n t a t i o n reactions 4 0 4 , 4 0 8 , 4 0 9 ,

b y carbene insertion r e a c d o n s 5 9 3 - 5 9 5 b y c o u p l i n g reactions 5 8 4 by cyclizadon reacdons 5 8 8 - 5 9 2 by M o z i n g o reacdon 5 7 6 b y rearrangements 5 9 7 - 5 9 9 by Wolff-Kishner reduction 5 7 4 , 5 7 5 from a l k e n e s 5 5 6 - 5 5 8 from alkyl h a l i d e s 5 7 0 - 5 7 2 from c a r b o x y l i c esters 5 6 4 , 5 6 5 from c y c l o p r o p a n e s 5 6 0 , 5 6 1 from peresters 5 7 9 from p - t o l u e n e s u l p h o n a t e esters 5 6 3 Polyethylene 7 7 6 , 7 7 7 cross-linking of 7 7 6 m a i n - c h a i n s c i s s i o n in 7 7 6 N M R spectmm of 376 P o l y h y d r o x y c y c l o h e x a n e s , chiroptical

437, 442, 446, 447 P h o t o h a l o g e n a t i o n reactions 9 6 4 - 9 6 6 , 976-978, 984, 985, 988

properties o f 1 4 5 P o l y m e r s , radiation c h e m i s t r y o f 7 7 6 - 7 7 8 Pregnanes,

s o l v e n t effects in 9 7 0 - 9 7 3 P h o t o i n d u c e d e l e c t r o n transfer 7 0 5 P h o t o i o n i z a t i o n reactions 3 0 3 , 4 0 4 , 4 0 7 , 4 2 5 Phytane 2 9 3

chiroptical properties o f 1 3 8 , 1 7 6 natural o c c u r r e n c e o f 9 0 0 Prismanes,

in m i c r o - o r g a n i s m s 9 0 8 natural o c c u r r e n c e o f 8 9 8 , 9 0 0 Phytol 2 9 3 Pinanes, c h e m i c a l shift v a l u e s for 3 6 7 chiroptical properties o f 1 7 8 Pinus s p e c i e s , cell suspensions of 9 0 4 e s s e n t i a l o i l s in 9 0 3

c h e m i c a l shift v a l u e s for 3 6 5 synthesis of 5 9 5 Pristanes 2 9 3 G C quantitative separation f r o m p e t r o l e u m 323-325 in m i c r o - o r g a n i s m s 9 0 8 natural o c c u n - e n c e o f 8 9 8 , 9 0 0 stereochemical determination o f 2 9 4 n-Propane, b o n d a n g l e s in 1 0 2 , 1 0 8

Subject index I N D O - P F T c a l c u l a t i o n s for 3 8 4 ionization e n e r g i e s o f 4 9 3 isotopically labelled 8 5 0 , 851 synthesis of 8 1 3 , 8 1 4 , 821 P E spectrum o f 5 0 2 , 5 0 3 proton affinity o f 5 3 8 reactions w i t h h e l i u m tritide i o n s 8 3 3 - 8 3 5 structural c h e m i s t r y o f 8 2 , 8 8 , 9 0 Propanes, alkyl-substituted—see A l k y l p r o p a n e s Propellanes, c h e m i c a l shift v a l u e s for 3 6 6 electronic charge density in, relief m a p s o f 13, 16 free radical additions to 9 5 6 Laplacian o f p in 4 0 , 4 1 neutron diffraction studies o f 9 5 4 P E spectra o f 5 1 9 , 5 2 1 , 5 2 2 , 9 5 2 , 9 5 4 radical attack o n 9 6 4 rearrangement o f 7 3 3 - 7 3 5 strain e n e r g y in 6 4 structure o f 9 3 3 , 9 3 4 synthesis o f 9 4 7 - 9 5 6 thermolysis of 9 5 4 vibrational spectra o f 9 5 4 X-ray studies o f 9 4 9 , 9 5 1 , 9 5 4 Propellenes, nomenclature of 9 2 9 synthesis o f 5 9 3 P r o p e n e l l - ^ ' ^ C ] , catalytic reactions o f 8 6 1 , 862 Propyl a n i o n s 5 4 7 Proton affinities 5 3 7 , 5 3 8 Pseudoasymmetric atoms 2 4 7 Pseudomonas s p e c i e s , in alkane m e t a b o l i s m 915, 9 1 6 Pseudorotation 1 2 1 , 1 2 3 - 1 2 7 P u l a y ' s gradient m e t h o d 8 7 P u l s e radiolysis 7 6 2 Q S A R 186, 188, 195, 2 0 0 , 2 0 6 , 2 0 7 Quadricyclane, anodic o x i d a t i o n o f 8 0 1 c h e m i c a l shift v a l u e s for 3 6 5 reactions w i t h transition-metal i o n s 5 4 0 synthesis o f 5 9 0 , 5 9 2 Quadricyclane/norbomadiene interconversion 705-710 Q u a d r i c y c l e n e , C 2 s band s y s t e m o f 4 9 7 Q u a n t u m action principle 4 2 Quantum yields 7 6 4 Q u a s i - e q u i l i b r i u m theory 4 0 4 , 4 0 5 , 4 4 8 Radiation, h i g h - e n e r g y , t y p e s o f 7 4 5 Radiation c h e m i c a l y i e l d 7 5 0 , 7 5 1 Radiation c h e m i s t r y , gas-phase 7 5 1 - 7 5 8 kinetics o f 7 5 3 , 7 5 4

1075

liquid-phase 7 5 8 - 7 7 2 kinetics o f 7 7 0 - 7 7 2 product y i e l d s in 7 6 5 - 7 7 0 solid-phase, product y i e l d s in 7 7 3 - 7 7 6 trapping o f intermediates in 7 7 2 , 7 7 3 Radiation d a m a g e , N M R study o f 3 7 6 Radical attack, o n a l k a n e s 9 6 3 - 9 7 5 steric effects in 9 7 3 - 9 7 5 Radical c a t i o n s 7 8 3 e l e c t r o n i c state o f 4 7 3 fragmentation o f 7 9 3 Radical c h a i n reactions 9 6 6 , 9 8 6 - 9 9 4 Radical c h a i n s , m i x e d 9 8 8 , 9 8 9 Radicals, disproportionation o f 7 6 4 trapped 7 7 3 Radiochemical studies, hot atom 8 2 9 - 8 5 3 Radiochemical synthesis 8 2 1 , 8 2 2 R a m a n optical a c h v i t y 1 4 0 Randomization 4 1 0 - 4 1 2 , 4 3 4 , 4 4 0 Random phase approximation 164 R a n e y nickel 5 5 6 , 5 6 2 , 5 6 7 , 5 6 9 , 5 7 6 Reciprocal-square-root algorithm 193, 197 Recoil energy 8 2 8 - 8 3 1 R e s o n a n c e giants 1 3 9 Ring inversion 1 2 5 - 1 2 7 barrier t o 1 2 7 R i n g s , a s e l e m e n t s o f m o l e c u l a r structure 16, 17 R o s a c e a e , cuticular w a x e s o f 9 0 1 Rosa s p e c i e s , cell suspensions o f 9 0 4 essential o i l s in 9 0 3 Rotamers 2 3 8 - 2 4 1 Rotation, external 2 2 1 internal 2 2 1 - 2 2 3 R o t a h o n a l barriers 1 0 3 - 1 0 5 , 2 2 2 , 2 2 3 in a l k y l p r o p a n e s 1 0 9 in butanes 1 1 0 in / m - b u t y l g r o u p s 1 0 8 , 1 1 6 , 1 1 7 in p e n t a a l k y l e t h a n e s 1 1 3 , 1 1 7 in p r o p a n e s 1 0 8 in tetraalkylethanes 1 1 2 in trialkylethanes 1 1 5 Rotational potentials 1 0 0 onefold 115 sixfold 1 1 2 - 1 1 5 threefold 1 1 6 twofold 1 1 4 - 1 1 6 Rotational s p e c t r o s c o p y , i n c o n f o r m a t i o n a l analysis 9 7 Rotivity 136, 154 Ruta s p e c i e s , cell suspensions o f 9 0 4 essential o i l s in 9 0 3

1076

Subject index

Rydberg bands 152 Rydberg excitation 7 0 0 R y d b e r g transitions 7 0 8 S a d d l e points 8 7 Salvia s p e c i e s , c e l l s u s p e n s i o n s o f 9 0 4 Sarcina s p e c i e s , a l k a n e s in, biogenesis of 9 1 4 occurrence of 9 0 7 Saturation current 7 6 2 S c a n n i n g tunnelling m i c r o s c o p y 8 5 S c h w i n g e r ' s principle 4 2 , 4 3 S C O T capillary G C c o l u m n 3 2 3 - 3 2 6 , 3 2 8 , 3 2 9 S e d i m e n t s , o c c u r r e n c e o f a l k a n e s in 8 9 9 , 9 0 0 S e e d s , intracellular w a x e s in 9 0 2 S e l e c t e d i o n recording 3 3 4 , 3 3 6 S e l e n i d e s , reduction o f 5 6 8 S e l f - c o n s i s t e n t - f i e l d treatments 4 5 8 SELINQUATE 387 Semiempirical calculadons, for fenestranes 9 3 1 for t h e r m o d y n a m i c functions 2 3 0 S e s q u i t e r p a n e s , m a s s spectra o f 3 0 7 , 3 0 9 , 3 1 0 S h a l e o i l s , o c c u r r e n c e o f alkanes in 8 9 9 , 9 0 0 S h a n n o n equation 2 0 5 S h i e l d i n g constants 3 5 2 Shilov systems 6 5 4 , 6 5 7 - 6 5 9 S i d e - c h a i n s , g e m i n a l and v i c i n a l 2 4 3 S i g m a bond metathesis 6 5 4 , 6 7 2 Silicon anions, decomposition of 5 4 4 Simmons-Smith reacdon 5 9 3 Sinapsis s p e c i e s , cuticular w a x e s o f 9 0 4 Sitophilus s p e c i e s , cuticular w a x e s o f 9 0 5 S k e w i n g 1 0 2 , 1 0 3 , 117 c o h e r e n t 1 0 4 , 1 0 5 , 115 in alkylbutanes 1 1 0 , 111 incoherent 1 0 4 , 1 0 5 , 115 in h e x a a l k y l e t h a n e s 111 in propanes 108 in tetraalkylethanes 1 1 2 in tetraalkylmethanes 1 0 9 S o i l w a x e s , o c c u r r e n c e o f alkanes in 8 9 9 , 9 0 0 Solandra s p e c i e s , cuticular w a x e s o f 9 0 2 Solutions, thermochemistry of 2 6 9 , 2 7 0 S P E C I N F O data bank s y s t e m 3 5 5 S p i n - l a t t i c e relaxation 3 8 7 - 3 8 9 S p i n m u l t i p l i c i t y effect 7 0 8 S p i n - s p i n coupling constants 3 7 9 - 3 8 7 Spiroalkanes, radical r e a c d o n s o f 9 7 6 - 9 7 8 strain e n e r g y in 6 6 Stabilomers 691 Staffanes 9 5 6 synthesis of 5 6 8 Staphylemid s p e c i e s , o c c u r r e n c e o f a l k a n e s in 906 Star graphs 2 0 4

Steranes, G C / M S analysis o f 3 3 6 , 3 3 8 , 3 3 9 , 8 9 6 m a s s spectra o f 3 1 3 separation from crude o i l s 3 2 8 stereostructure o f 3 3 2 Steric c r o w d i n g 9 1 Steric e n e r g i e s 9 9 , 1 0 0 Steric interactions, attractive 1 0 6 , 1 0 7 Steric repulsion 1 0 2 - 1 0 5 S t i g m a s t a n e , natural o c c u r r e n c e o f 8 9 8 Stilbenes, isotopically labelled, synthesis o f 8 2 4 Stomoxys s p e c i e s , o c c u r r e n c e o f a l k a n e s in 9 0 6 Strain e n e r g i e s , definition o f 6 1 , 6 2 hybridization m o d e l a n d 6 2 in c y c l i c m o l e c u l e s 6 2 - 6 6 Stress tensors 4 4 Stretching f r e q u e n c i e s , d e u t e r i u m - i s o l a t e d C H 89 Structural c h a n g e , bifurcation m e c h a n i s m o f 19, 2 0 , 3 2 conflict m e c h a n i s m o f 18, 19 Structural c o m p l e x i t y , representation o f 1 8 6 Suberin-associated w a x e s 9 0 2 Substitution, a n o d i c , in acetic acid 7 9 0 in acetonitrile 7 9 2 - 7 9 4 in fluorosulphonic acid 7 8 2 - 7 8 5 in h y d r o g e n fluoride 7 8 5 in m e t h a n o l 7 9 0 , 7 9 1 in sulphur d i o x i d e 7 9 4 , 7 9 5 in trifluoroacetic a c i d 7 8 6 - 7 9 0 in trifluoroethanol 7 9 5 S u l p h o n a t e esters, deuterated 8 2 4 reducdon of 562, 5 6 3 S u l p h o x i d a t i o n reactions 9 9 2 Sulphuration reactions 6 4 1 S u p e r e x c i t e d states 7 5 1 S y m m e t r y , tetrahedral 2 3 8 Symmetry numbers 2 2 4 - 2 2 6 S y n c h r o t r o n irradiation 8 2 1 , 8 2 2 Taft steric parameter 2 0 8 , 2 0 9 Tanacetum s p e c i e s , c e l l s u s p e n s i o n s o f 9 0 4 Tartaric a c i d s , c o n f i g u r a d o n o f 141 T a x o n o m i c markers, a l k a n e s as 9 0 3 , 9 0 4 Termites, o c c u r r e n c e o f a l k a n e s in 9 0 6 Terpanes, m a s s spectra o f 3 0 7 - 3 1 0 s t e r e o c h e m i c a l determination o f 2 9 4 , 3 0 0 Tetraalkylcyclohexanes, conformation of 122, 3 7 9 N M R spectra o f 3 7 4 Tetraalkylcyclononanes, conformation o f 127 T e t r a a l k y l c y c l o p r o p a n e s , chiroptical properties of 163, 164

Subject index

Tetraalkylethanes, conformation of 1 1 0 - 1 1 2 N M R spectra o f 3 7 3 Tetraalkylhexanes, N M R spectra o f 3 7 3 Tetraalkylmethanes, c o n f o r m a t i o n o f 1 0 9 , 1 1 0 Tetraalkyloctanes, fragmentation o f 4 2 3 , 4 4 2 Tetraalkylpentanes, chlorination o f 9 7 4 N M R spectra o f 3 7 3 7,7,8,8-Tetracyanoquinodimethane 4 3 3 Tetracycloalkanes, G C / M S / C analysis of 336, 3 3 8 , 3 3 9 m a s s spectra o f 3 1 0 P E spectra o f 4 7 9 rearrangement o f 6 9 9 stereostmcture o f 3 3 2 synthesis o f 5 7 3 Tetrahedrane, electronic charge density in 6 , 7 P E spectrum o f 5 1 5 - 5 1 7 strain e n e r g y in 6 5 , 6 6 Tetrahydrodicyclopentadiene, i s o m e r i z a d o n o f 619

1077

Triblattanes, chiroptical properties o f 1 7 9 , 1 8 0 Trichoplusia s p e c i e s , cuticular w a x e s o f 9 0 5 Tricycloalkanes, c h e m i c a l shift v a l u e s for 3 6 5 G C / M S / C analysis o f 3 3 6 , 3 3 8 m a s s spectra o f 3 0 8 - 3 1 4 P E spectra o f 4 7 8 photochemistry of 7 3 0 - 7 3 3 radical reactions o f 9 8 3 rearrangement o f 6 9 9 s y n t h e s i s of, by c o u p l i n g r e a c d o n s 5 8 5 by M o z i n g o reaction 5 7 7 by p h o t o d e c a r b o x y l a t i o n reactions 5 8 1 from a l c o h o l s 5 6 2 from alkyl h a l i d e s 5 7 1 from c a r b o n y l c o m p o u n d s 5 7 3 from c a r b o x y l i c esters 5 6 4 from nitriles 5 8 2 from p h o s p h o r o d i a m i d a t e s 5 6 7 Trifluoroacetates, a s e l e c t r o c h e m i c a l products

T E X A S program 8 8 Thermal c o n d u c t i v i t y detector 3 2 9 Thermal e n e r g i e s 9 7

786-789 TRIPOS method 91 Triterpanes, a n a l y s i s o f 8 9 6 Tritium a t o m s , reactions o f 8 4 1 - 8 4 6 Tritium d e c a y , in tritium-multilabelled a l k a n e s

Thermodynamic calculations, stadsdcal 2 1 9 , 220, 230 Thermodynamic functions,

846-852 T r o u t o n ' s rule 2 6 8 Twistane,

p o l y n o m i a l e x p r e s s i o n s for 2 3 0 - 2 3 3 s e m i e m p i r i c a l m e t h o d s for 2 3 0 Thin layer c h r o m a t o g r a p h y 3 1 9 Thioethers, r e d u c d o n o f 5 6 7 , 5 6 8 T h i o l s , reduction o f 5 6 7 Thujanes, chiroptical properties o f 1 6 6 - 1 6 8 T o p o g r a p h y , definition o f 1 8 6 T o p o l o g i c a l state 2 0 9 - 2 1 2 T o p o l o g y , definition o f 1 8 6 Toxicology 918, 9 1 9 Trachylobane, synthesis o f 5 9 0 Transition-metal i o n s , basicities towards 540-542 Translational functions 2 2 1 Triacontane 3 9 6 , 3 9 8 i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 2 6 , 8 2 7 Trialkylbutanes, c o n f o r m a t i o n o f 1 1 2 Trialkylethanes, conformation o f 105, 106, 110

c h e m i c a l shift v a l u e s for 3 6 5 chiroptical properties o f 1 8 0 T w i s t - b o a t c o n f o r m a t i o n s 1 1 8 , 121 Twist c o n f o r m a t i o n s 1 2 0 , 1 2 2 Undecane, i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 2 0 , 821 s p i n - s p i n c o u p l i n g in 3 8 7 U n d e c a n o n e s , in e s s e n t i a l o i l s 9 0 3 Unsaturated a l c o h o l s , reductive s o l v o l y s i s o f 590 Q,/3-Unsaturated k e t o n e s , as e l e c t r o c h e m i c a l products 7 8 3 , 7 8 4 U r e a i n c l u s i o n c o m p o u n d s , N M R spectra o f 369, 370

c o n f o r m a t i o n o f 1 0 4 , 1 0 5 , 1 0 9 , 117 N M R spectra o f 3 7 3 Trialkylpentanes,

Van der W a a l s ' interactions 1 0 0 Van't H o f f ' s relation 2 2 9 Vaporization p r o c e s s e s 2 6 6 , 2 6 8 , 2 6 9 Vibration 2 2 3 , 2 2 4 Vibrational circular d i c h r o i s m 1 4 0 Vibrational o p d c a l activity 1 4 0 Vibrational s p e c t r o s c o p y ,

chlorinadon of 9 7 3 , 9 7 4 i s o t o p i c a l l y labelled, s y n t h e s i s o f 8 1 5 Trialkylsilanes, c o n f o r m a t i o n o f 115 Triamantane, s y n t h e s i s o f 5 9 7 , 6 1 9

in c o n f o r m a t i o n a l a n a l y s i s 9 7 o f propellanes 9 5 4 Vicia fahia, cuticular w a x e s o f 9 0 2 Virial e q u a t i o n s o f state 2 2 6 , 2 2 7

N M R spectra o f 3 7 3 , 3 7 4 Trialkylmethanes,

1078

Subject index

Virial t h e o r e m 3 7 , 4 3 VSEPR model 35, 4 0

o f fenestranes 9 3 9 , 9 4 3 , 9 4 4 o f propellanes 9 4 9 , 9 5 1 , 9 5 4

W a g n e r - M e e r w e i n rearrangement 3 0 0 , 7 2 2 , 730, 732, 733 Water solubility 2 0 7 W i l k i n s o n ' s catalyst 5 9 5 W M I N program 81 W o l f f - K i s h n e r reduction 5 7 4 - 5 7 6 Wurtz c o u p l i n g 5 8 3 , 5 8 4 X - r a y studies 8 0 , 8 1 , 8 4 in c o n f o r m a t i o n a l a n a l y s i s 9 7

Yeast, o c c u r r e n c e o f a l k a n e s in 9 0 7 , 908 Zeise's dimer 6 9 9 Zero-dose yields 7 6 5 Z e r o flux boundary c o n d i t i o n s 4 3 Z e r o flux surface 12 Zero-point energies 9 7 Z i g z a g effects 175 Zwitterions 7 3 0

Index compiled hy P. Raven

The Chemistry of alkanes and cycloalkanes

Mechanisms of atmospheric oxidation of the alkanes

The Chemistry of Death

The Chemistry Of Evil

The theories of chemistry

The Basics of Chemistry

The Chemistry of Tears

The Basics of Chemistry

The Theories of Chemistry

The Chemistry of Tears

The Theories of Chemistry

The Chemistry of Soils

The Story of Chemistry

The Chemistry of Anilines

The chemistry of fragrances

The chemistry of fullerenes

The Chemistry of Death

The chemistry of phenols

The Chemistry of Death

The Chemistry of Photography

The Chemistry of Polymers

The Chemistry of Phenols

The Chemistry of Death

The Theories of Chemistry

The Chemistry of Life

The Basics of Chemistry

The Chemistry of Polymers

Chemistry of the elements

The Chemistry of Death

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