Structure and Function

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Structure and Function

Peter Comba Editor

Structure and Function

123

Editor Peter Comba Universität Heidelberg Anorganisch-Chemisches Institut Im Neuenheimer Feld 270 69120 Heidelberg Germany [email protected]

ISBN 978-90-481-2887-7 e-ISBN 978-90-481-2888-4 DOI 10.1007/978-90-481-2888-4 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009934511 c Springer Science+Business Media B.V. 2010 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Jan C.A. Boeyens – A Holistic Scientist

Jan Christoffel Antonie Boeyens was born 75 years ago on October 2, 1934 in a farming community in the small rural town of Wesselsbron in the Free State Province of South Africa. Growing up in such a region, it is natural to develop a love of Nature in all her manifestations, and especially a love of the open veldt, and Jan was no exception in this regard. Today he still loves to walk alone in the veldt, contemplating and observing. In rural communities every boy then had to learn some of the practical manual skills required to make life comfortable. Today, he still likes to work with his hands building things and doing woodwork of outstanding quality. He lives with his wife Martha on a farm on the banks of the Crocodile River outside Pretoria. He named his home “Blandings” after the fictional location in the stories of British writer P.G. Wodehouse. This is an ideal location for him, where the open veldt allows him to take long walks, giving him an opportunity to contemplate, to think and to dream up new, unexpected, simple and elegant solutions for old scientific problems, with the emphasis on the concepts “simple” and “direct”, always emerging as ingenious models describing aspects of Nature. As a young boy he had no aspirations to study science, and had no idea that one day he would become one of the foremost scientists in the country whose work would gain worldwide recognition. After his schooling he completed a B.Sc. degree at the then University of the Orange Free State. Jan graduated with a degree in Chemistry, Physics and Mathematics and then completed his M.Sc. degree at the same university and a D.Sc. degree at the University of Pretoria, while employed at the National Physical Laboratory of the Council for Scientific and Industrial Research, CSIR. v

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Jan Boeyens is an avid reader. Having a rather catholic taste, with an emphasis on non-fiction, his interests range from religious historiography and philosophy to the history of science, and especially the history of quantum mechanics. His investigations always entail an in depth study of the literature, and he makes a point of tracking down many obscure papers and insists on reading the originals of the 1920s and even eighteenth and nineteenth century papers, in the process discovering that many famous scientists have been misquoted in textbooks and even misinterpreted. As a scientist, Jan Boeyens is perhaps best characterized by simply calling him a “universal chemist”. His rampant and persistent curiosity has taken him into most branches of chemistry and physics and also into some branches of mathematics and biology, with special emphasis on the ordered structure of matter, such as that revealed by X-ray and neutron diffraction. He has also made notable contributions to the fields of chemical reactions, industrial chemical processes and applied chemistry. Jan is never content with only reading current publications on any subject, but always insists on obtaining and studying the original papers, no matter how obscure the journal or the publication is, or when it was published. Part of his ability to attack an old problem from a new and fresh angle stems from his insistence on precisely understanding what the original papers said, or which approximations and/or models were used by the original authors. More often than not, he finds that the original work is not accurately represented in modern approaches and interpretations. There is a lesson to learn in this for all of us, and especially for the sometimes uncritical writers of textbooks who depend only on other textbooks. An illustration of this is the uncritical description of the concept of “hybridization” in many textbooks, for instance, tetrahedral or sp 3 -hybridization, as introduced by Pauling, to which Jan has recently drawn attention to.1 Jan’s passion and focus has always centred on the theories which provide the framework for the physical sciences. He has taken a critical stance of the current paradigm that dominates science, and developed a rather unique approach in his own theories, conjectures and speculations which have been largely captured in two of his recent books: “New theories for Chemistry” and “Chemistry from First Principles”. A reviewer of his book “Chemistry from First Principles” said: “According to the author Boeyens, quantum ideas have often been inappropriately or even incorrectly applied, and the current situation is so bad that quantum chemistry is seriously at risk of becoming the new alchemy. . . . because the quantum world is so bizarre and counterintuitive, it tends to exert an almost hypnotic influence on us and hold us in its thrall. All of which means that we are now in serious danger of being dominated by a quasi-alchemical theory that is widely deemed to be untouchable but one that is in fact unable to deal with many of the real issues in chemistry.”2

1 C. Schutte and J.C.A. Boeyens, Linus Pauling, Chemistry World, December 2006, p. 24 (Your Views). 2 D. Rouvray, “Is quantum chemistry the new alchemy?” book review, Chemistry World, March 2009, 62.


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Jan’s ability to approach well-known and new scientific problems from an unconventional and sometimes rather astonishing direction, using very simple models, has yielded exceptional results. However, this approach sometimes flies in the face of modern scientific dogma, which makes reviewers and journal editors hesitate to publish an article that rejects or questions “established” ideas. He is not alone in experiencing this, for the same happened to other scientists, such as David Bohm,3 who developed a new way of looking at quantum mechanics. In his review of Bohm and Hiley’s book The Undivided Universe, Chris Clarke said: This book disturbs the reader, because the profound originality of its thinking differs so much from mainstream physics and what the new age has made of physics. It could be that it will, in the course of time, also disturb the course of physics.3

It also happened to João Magueijo, when he proposed (against all scientific dogma) that the speed of light might vary (Varying Speed of Light Theory: VSL) – the fascinating story can be read in his book,4 in which he says towards the end: I am often asked . . . ..whether it will be humiliating for me if VSL is disproved. My answer is invariably that there is no humiliation in seeing your theory ruled out. That is part of science. The important thing is to try new ideas, and regardless of what has happened to VSL that’s what I have done. I have struggled to expand the frontiers of knowledge by jumping into that grey area where ideas are not yet right or wrong, but are mere shadows of “possibilities”. I have thrown myself into the darkness of speculations, and thus participated in the big Detective Story so vividly described in the Evolution of Physics. . . .5

Both these quotes mutatis mutandis apply to some of the papers and books of Jan Boeyens. Jan has never shied away from controversy – he would call himself a dissident scientist. He sometimes had to struggle for the right to be heard and read, but, thankfully, he can be rather persistent. In his search for explanations for the observed periodicity in matter he uncovered new relations and new phenomena, new applications of number theory in Nature and new interpretations of Nature. It is an intellectual adventure to read the book Number Theory and the Periodicity of Matter.6 Every page brings more surprises, with examples ranging from the golden number to nuclear structure and cosmology. In this brief foreword we can only give some indication of the scope of the work of Jan Boeyens by highlighting a selection of his published contributions to science [1–41]. To date Jan Boeyens has published over 250 peer-reviewed articles that have been cited more than 4,000 times, and he has authored four books [36–40]. Besides the careful analysis of hundreds of single-crystal structures, Jan developed a method for structure solution using a centric projection in direct methods [1] 3 (a) D. Bohm, Quantum Theory, Dover, New York, 1951. (b) D. Bohm and B.J. Hiley, The Undivided Universe, Routledge, London, 1993, (c) C. Clarke in Network, and on the back flap of the soft-cover edition of the book. 4 J. Magueijo, Faster Than the Speed of Light, Arrow Books, London, 2003. 5 A. Einstein and L. Infeld, The Evolution of Physics, Cambridge University Press, Cambridge, 1947. 6 J.C.A. Boeyens and D.C. Levendis, Number Theory and the Periodicity of Matter, Springer, Berlin, 2008.

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(a method that was coded into the early versions of the much used crystallographic programs SHELX and PLATON written by Sheldrick and Spek, respectively). He also derived theoretical models for the analysis of molecular geometry, such as the puckering of 5, 6 and n-member rings [2–4] (his three papers on the analysis of ring puckering in these compounds alone have been cited over 400 times). Jan has, in his own distinctive and novel way, made a wealth of contributions to the understanding of fundamental concepts in chemistry and science in general, which include studies on the valence-bond and electron-pair bonds [5–11], single-crystal neutron diffraction studies [8], molecular modelling and the modelling of multiple metal–metal bonds [12–20], the nature of the electron and electron spin [23, 24, 29], ionic radii [22], electronegativity [27,37], angular momentum [35], periodicity [32,37] and the link between number patterns and nature [33]. Jan Boeyens only realized later in his career that several common themes permeate his research, and in recent years he has succeeded in weaving these threads together in the books and chapters in books to integrate his ideas on the nature of matter and molecules, the origins and theoretical description of matter, the nature of space, cosmology and general relativity [38–41]. Jan’s creativity has no end, and one can expect new books and publications of his to emerge in the near future, for example around the theme of emergent properties, which seeks to address an issue captured in a quote from the physics Nobel prize winner Philip Anderson: “the ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. . . Instead, at each level of complexity, entirely new properties appear.”7 However, a selection of publications and bibliometric indices alone cannot give an insight to the mind of Jan Boeyens, let alone give any measure of his impact on the field, which may take decades to appreciate. It is noteworthy that a theoretician of Jan’s standing gets deeply involved in practical applications. There are many examples of this, but the most recent is his contribution as the expert scientific adviser in helping to get the international patent for a new and possibly revolutionary multipole hybrid battery8 that has just been licensed to a company based in the USA. His integrity as a scientist is the one quality of Jan Boeyens that stands out. His unbiased criticism and appraisal of his peers’ research in reviewing processes is well-known. He never deviates from what he sees as the truth, despite the fact that this sometimes lands him in hot water. However, those same people criticising him will be quick to ask Jan for his expert opinion or to sit on assessment panels because of just those qualities. This integrity and his ability to lead in the true sense of the Latin word educare, made him an inspiration to young scientists over the years, and reflects in the 40 or more M.Sc.’s and Ph.D.’s that he supervised. Jan Boeyens is recognized as the founder of the Indaba series of workshops that had its first meeting in 1995 in the Kruger National Park in South Africa. The meaning of the Zulu word ‘Indaba’ embodies the nature of Jan’s approach to science. . . “an African term used to describe a meeting to analyze a difficult problem from

7 8

P.W. Anderson, Science, 1972, 177, 393–396. J.P. Human, Electrical Storage Device, patent WO/2008/075317.


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all angles”. Jan has also made significant contributions to professional societies, both local (the South African Chemical Institute, the Royal Society of South Africa (of which he is a fellow), the South African Crystallographic Society (founding member), and international (member of the American Chemical Society, the NY Academy of Sciences and of the executive committee of the International Union of Crystallography from 1996 to 2002). While on the IUCr executive, he successfully proposed the IUCr Africa initiative, which set up grants for African students studying towards a PhD in a crystallographic field, and the support by the Cambridge Crystallographic Structural Database of African universities. Jan has always had his roots in Africa, and has been invited to give workshops in several African countries. He has received many prestigious awards, including AECI and SACI Gold Medals, the Ernst Oppenheimer Fellowship, the Claude Harris Leon Award, the Alexander von Humboldt Research Prize, the Distinguished Research Award (Wits) and the Centennial Leading Mind (University of Pretoria). We are truly honoured and privileged to have one of the world’s leading creative minds amongst us! Pretoria Johannesburg

Casper J.H. Schutte Demetrius C. Levendis

Selected Publications of J.C.A. Boeyens 1. JCA Boeyens, Use of centric projections in direct methods. Acta Cryst., 1977 (A33) 863–864. 2. IK Boessenkool and JCA Boeyens, Identification of the conformational type of sevenmembered rings. J. Cryst. Mol. Struct., 1980 (10) 11–18. 3. JCA Boeyens and DG Evans, Group theory of ring pucker. Acta Cryst. B, 1989 (45) 577–581. 4. DG Evans and JCA Boeyens, Conformational analysis of ring pucker. Acta Cryst. B, 1989 (45) 581–590. 5. JCA Boeyens and RH Lemmer, A valence-bond study of dialkalis and alkali hydrides. J. S. Afr. Chem. Inst., 1976 (29) 120–131. 6. JCA Boeyens and RH Lemmer, Valence bond studies. Part 2. Diatomic compounds of copper, silver and gold. J.C.S. Faraday Trans.II, 1977 (73) 321–326. 7. JCA Boeyens, Valence-bond studies. Part 3. Calculation of atomic radii. S Afr. J. Chem., 1978 (31) 121–123. 8. JCA Boeyens and JA Pretorius, X-ray and neutron diffraction studies of the hydroquinone clathrate of hydrogen chloride. Acta Cryst., 1977 (33) 2120–2124. 9. JCA Boeyens, Valence-bond studies. Part 4. Electron pair bonds. S. Afr. J. Chem., 1980 (33) 14–20. 10. JCA Boeyens, Valence-bond studies. Part 5. Analytical wave functions and Heitler-London integrals for electron-pair bonds. S. Afr. J. Chem., 1980 (33) 63–65. 11. JCA Boeyens, Valence-bond studies. Part 6. Calculation of bond angles. S. Afr. J. Chem., 1980 (33) 66–70. 12. JCA Boeyens, Multiple bonding as a screening phenomenon. J. Cryst. Spectr. Res., 1982 (12) 245–254. 13. JCA Boeyens, Fundamentals of molecular modelling. In W Gans A Amann and JCA Boeyens (eds), Fundamental Principles of Molecular Modeling, 1996, 1–9, Plenum, New York. 14. JCA Boeyens, Environmental factors in molecular modelling. In W Gans A Amann and JCA Boeyens (eds), Fundamental Principles of Molecular Modeling, 1996, 99–103, Plenum, New York.

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15. JCA Boeyens and P Comba, Molecular mechanics: the theoretical basis, rules, scope and limits. Coord. Chem. Rev., 2001 (212) 3–10. 16. JCA Boeyens, FA Cotton and S Han, Molecular mechanics of low bond order interactions in tetrakis (carboxylato) dimetal systems. Inorg. Chem., 1985 (24) 1750–1753. 17. JCA Boeyens and FMM O’Neill, Molecular modelling of dimetal systems. Dimolybdenum quadruple bonds. Inorg. Chem., 1995 (34) 1988–1995. 18. JCA Boeyens and FMM O’Neill, Molecular modelling of dimetal systems. Part 2. Low-order dimolybdenum. Inorg. Chem., 1998 (37) 5346–5351. 19. JCA Boeyens and FMM O’Neill, Molecular modelling of dimetal systems. Part 3. Dichromium bonds. Inorg. Chem., 1998 (37) 5352–5357. 20. J Bacsa and JCA Boeyens, Molecular modelling of dimetal systems. Part 4. Dirhenium bonds. J. Organomet. Chem., 2000 (596) 159–164. 21. JCA Boeyens, The geometry of quantum events. Specul. Sci. Technol., 1992 (15) 192–210. 22. JCA Boeyens, Ionization radii of compressed atoms. J. C. S. Faraday Trans., 1994 (90) 3377– 3381. 23. JCA Boeyens, Understanding electron spin. J. Chem. Ed., 1995 (72) 412–415. 24. JCA Boeyens and RB Kassman, The Schrödinger equation and spin. S. Afr. J. Chem., 1996 (49) 1–7. 25. JCA Boeyens, Red shifts in a curved space. S. Afr. J. Sci., 1995 (91) 220. 26. SD Travlos and JCA Boeyens, A modified Morse function to describe pairwise atomic interactions. S. Afr. J. Chem., 1997 (50) 17–21. 27. JCA Boeyens and J du Toit, The theoretical basis of electronegativity. Electr. J. Theor. Chem., 1997 (2) 296–301. 28. JCA Boeyens, Intermolecular bonding. In W Gans and JCA Boeyens (eds), Intermolecular Interactions, Plenum, New York, 1998, 3–7. 29. JCA Boeyens, Structure of the Electron. Trans. Roy. Soc. S. Afr., 1999 (54) 323–358. 30. JCA Boeyens, Quantum Potential Chemistry. S. Afr. J. Chem., 2000 (53) 49–72. 31. JCA Boeyens, Symmetry and Structure: An Overview. Cryst. Eng., 2001 (4) 61–100. 32. JCA Boeyens, Periodicity of the stable isotopes. J. Radioanal. Nucl. Chem., 2003 (257) 33–43. 33. JCA Boeyens, Number Patterns in Nature. Cryst. Eng., 2003 (6) 167–185. 34. JCA Boeyens, Quantum theory of molecular conformation. C.R. Chimie, 2005 (8) 1527–1534. 35. JCA Boeyens, Angular Momentum in Chemistry. Z. Naturforsch., 2007 (62b) 373–385. 36. JCA Boeyens, The holistic molecule. In: JCA Boeyens and JF Ogilvie (eds), Models, Mysteries and Magic of Molecules, 2007, Springer, 447–475. 37. JCA Boeyens, The Periodic Electronegativity Table, Z. Naturforsch., 2008 (63b) 199–209. 38. JCA Boeyens, The Theories of Chemistry, Elsevier, Amsterdam, 2003. 570 pp., ISBN: 0444514910 39. JCA Boeyens, New Theories for Chemistry, Elsevier, Amsterdam, 2005. 279 pp., ISBN: 0 444 51867 3 40. JCA Boeyens and DC Levendis, Number Theory and the Periodicity of Matter, Springer, The Netherlands, 2008. 350 pp., ISBN 10: 1402066597 41. JCA Boeyens, Chemistry from First Principles, Springer.com, 2008. ISBN: 978-1-4020-85451 e-ISBN: 978-1-4020-8546-8 321 pp.

Preface

The art of chemistry is to thoroughly understand the properties of molecular compounds and materials and to be able to prepare novel compounds with predicted and desirable properties. The basis for progress is to fully appreciate and fundamentally understand the intimate relation between structure and function. The thermodynamic properties (stability, selectivity, redox potential), reactivities (bond breaking and formation, catalysis, electron transfer) and electronic properties (spectroscopy, magnetism) depend on the structure of a compound. Nevertheless, the discovery of novel molecular compounds and materials with exciting properties is often and to a large extent based on serendipity. For compounds with novel and exciting properties, a thorough analysis of experimental data – state-of-the-art spectroscopy, magnetism, thermodynamic properties and/or detailed mechanistic information – combined with sophisticated electronic structure calculations is performed to interpret the results and fully understand the structure, properties and their interrelation. From these analyses, new models and theories may emerge, and this has led to the development of efficient models for the design and interpretation of new materials and important new experiments. The chapters in this book therefore describe various fundamental aspects of structures, dynamics and physics of molecules and materials. The approaches, data and models discussed include new theoretical developments, computational studies and experimental work from molecular chemistry to biology and materials science. Chapters 1 (Naidoo), 2 (Deeth), 3 (Atanasov and Comba) and 4 (Marques, Egan and de Villiers) describe fundamental theory- and computational modeling-based approaches related both to molecular and materials chemistry, and including applications in biological and medicinal chemistry. The remaining papers are primarily based on experimental approaches but, in some cases heavily rely on theory and modeling. In Chapters 5 (Fukuzumi), 6 (Hanson) and 7 (Egli), the focus is on molecular science and biological systems, while Chapters 8 (Lidin), 9 (Bourne, Báthori and Moitsheki) and 10 (Bacchi and Carcelli) relate to materials sciences. Despite the widely different approaches, ranging from molecular dynamics, novel molecular mechanics and quantum-chemical models, experimental X-ray and spectroscopybased structural studies, biophysics and applications from host–guest chemistry, intermetallic phases and medicinal chemistry, there is considerable overlap in terms

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of the underlying fundamental principles, and the common ground is the discussion of structure (design, preparation, characterization and interpretation) and structure– property correlations. The chapters of this book are based on some of the keynote lectures presented at the Indaba 6 Meeting “Structure and Function”, held in September 2009 in the Krüger National Park in South Africa. Indaba is an African term to describe a meeting setup to analyze a difficult problem from all angles. The Indaba series of workshops therefore is highly interdisciplinary and the problem of structure and structure–property correlation is typical in that it is fundamental and of importance to various disciplines in science and beyond. The Indaba series has been initiated by Jan C.A. Boeyens in 1995 and Indaba 6 is the first in the series not organized by Jan. To honor his numerous and important contributions to many areas of science (described in a short communication by Levendis and Schutte) and to celebrate his 75th birthday, all authors have decided to dedicate this book to Jan C.A. Boeyens. I wish to thank all authors for their time and energy spent to write exciting and accurate chapters, to Karin Stelzer for assembling the book and to the publisher – specifically to Dr. Sonia Ojo and Ms. Claudia Thieroff, for the good collaboration. Heidelberg, June 2009

Peter Comba

Contents

Jan C.A. Boeyens – A Holistic Scientist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .

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Preface .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . xi Contributors . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . xv 1

Molecular Associations Determined from Free Energy Calculations . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . Kevin J. Naidoo

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Molecular Modelling for Systems Containing Transition Metal Centres . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 21 Robert J. Deeth

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Magnetic Anisotropy in Cyanide Complexes of First Row Transition Metal Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 53 Mihail Atanasov and Peter Comba

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Structure and Function: Insights into Bioinorganic Systems from Molecular Mechanics Calculations . . . . . . . . . . . . .. . . . . . . . . . . 87 Helder M. Marques, Timothy J. Egan, and Katherine A. de Villiers

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Artificial Photosynthetic Reaction Center . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .111 Shunichi Fukuzumi

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Multifrequency EPR Spectroscopy: A Toolkit for the Characterization of Mono- and Di-nuclear Metal Ion Centers in Complex Biological Systems . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .133 Graeme R. Hanson

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On Stacking . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .177 Martin Egli

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Contents

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Structurally Complex Intermetallic Thermoelectrics – Examples from Modulated Rock-Salt structures and the System Zn-Sb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .197 Sven Lidin

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Solid State Transformations in Crystalline Salts . . . . . . . . . . . . . . .. . . . . . . . . . .219 Susan A. Bourne, Nikoletta B. Báthori, and Lesego J. Moitsheki

10 Influence of Size and Shape on Inclusion Properties of Transition Metal-Based Wheel-and-Axle Diols . . . . . . . . . . . . .. . . . . . . . . . .235 Alessia Bacchi and Mauro Carcelli Index . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . .255

Contributors

Mihail Atanasov Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Acad.Georgi Bontchev Str. Bl.11, 1113 Sofia, Bulgaria, [email protected] Alessia Bacchi Dipartimento di Chimica Generale ed Inorganica, Chimica Analitica, Chimica Fisica, Università di Parma, V.le G.P.Usberti – Campus Universitario, 43124 Parma, Italy, [email protected] Nikoletta B. Báthori Centre for Supramolecular Chemistry Research, Department of Chemistry, University of Cape Town, Rondebosch 7700, South Africa, [email protected] Susan A. Bourne Centre for Supramolecular Chemistry Research, Department of Chemistry, University of Cape Town, Rondebosch 7700, South Africa, [email protected] Mauro Carcelli Dipartimento di Chimica Generale ed Inorganica, Chimica Analitica, Chimica Fisica, Università di Parma, V.le G.P.Usberti – Campus Universitario, 43124 Parma, Italy, [email protected] Peter Comba University of Heidelberg, Heidelberg, Anorganisch-Chemisches Institut, Im Neuenheimer Feld 270, 69120 Heidelberg, Germany, [email protected] Robert J. Deeth Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK, [email protected] Katherine A. de Villiers Department of Chemistry and Polymer Science, University of Stellenbosch, Private Bag X1, Matieland, 7602 South Africa, [email protected] Timothy J. Egan Department of Chemistry, University of Cape Town, Private Bag, Rondebosch, 7700 South Africa, [email protected] Martin Egli Department of Biochemistry, Vanderbilt University, Department of Biochemistry, Robinson Research Bldg., Nashville, Tennessee 37212, USA, [email protected]

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Contributors

Shunichi Fukuzumi Department of Material and Life Science, Division of Advanced Science and Biotechnology, Graduate School of Engineering, Osaka University, SORST, JST, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan, [email protected] Graeme Hanson Centre for Magnetic Resonance, Level 2, Gehrmann Laboratories, Research Road, The University of Queensland, Brisbane. QLD. 4072, Australia, [email protected] Sven Lidin Department of Physical, Inorganic and Structural Chemistry, Arrhenius Laboratory, Stockholm University, 106 91 Stockholm, Sweden, [email protected] Helder M. Marques Molecular Sciences Institute, School of Chemistry, University of the Witwatersrand, P.O. Wits, Johannesburg, 2050 South Africa, [email protected] Lesego J. Moitsheki Centre for Supramolecular Chemistry Research, Department of Chemistry, University of Cape Town, Rondebosch 7700, South Africa, [email protected] Kevin J. Naidoo Department of Chemistry, University of Cape Town, Private Bag, Rondebosch 7701, South Africa, [email protected]

Chapter 1

Molecular Associations Determined from Free Energy Calculations Kevin J. Naidoo

Abstract In this chapter we describe the development and implementation of a computational method able to produce free energies in multiple dimensions, descriptively named the free energies from adaptive reaction coordinate forces method (FEARCF). We use this method to investigate the structure of associative liquids such as water. Important chemical phenomena such as the free energy of ion pairing in methanol have been studied using the FEARCF method as have the reaction surfaces of chemical reactions in solution. More recently, a multidimensional intermolecular orientational free energy was developed from FEARCF. This multidimensional intermolecular free energy W .r; 1 ; 2 ; / provides means to measure the orientationally dependent molecular interactions, that are necessary for applications in complex systems such as proteins, where molecular anisotropic features govern the structure. It is a highly informative free energy volume and is shown to probe the thermodynamic nature of water’s tetrahedral local structure.

1.1 Introduction By 1912, X-ray diffraction from crystals had been discovered by Friedrich et al. [1]. The major result that followed was that, because crystal atoms are arranged in a regular pattern, X-rays of wavelength incident on the crystal are selectively diffracted at certain angles. The intensities of the diffraction peaks are related to the scattering power of the atoms and the way they are arranged in the crystal. Due to the regularity of the atomic arrangements, crystals have short and long range order in the atomic patterns in the crystal. The long range ordering results in enhanced diffraction intensities and so the peaks are sharp. The study of the arrangement of atoms in solids using measurements of X-ray scattering subsequently formed the basis of X-ray crystallography.

K.J. Naidoo () Department of Chemistry, University of Cape Town, South Africa 7701 e-mail: [email protected]

P. Comba (ed.), Structure and Function, DOI 10.1007/978-90-481-2888-4 1, c Springer Science+Business Media B.V. 2010

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Kevin J. Naidoo

Fig. 1.1 A cartoon of the differences between neutron and x-ray diffraction of liquids

The diffraction experiment can be done with either an X-ray or a neutron source. The results gained from these two experimental types differ in two important ways because of the way these species are scattered by the atoms in the material. Here, we are interested principally in molecular interactions in solution and so mention the differences in these experiments that affect the study of liquid structure and intermolecular interactions in solvents. Firstly, in the X-ray experiment the scattering amplitude for an atom is significantly affected by the reciprocal distance or wave number Q. As Q increases the scattering amplitude f 0 .Q/ for that atom decreases monotonically (see Fig. 1.1). This makes the deconvolution of the individually contributing structure factors from atoms in a molecule strongly dependent on a knowledge of their individual f 0 .Q/s. In the neutron diffraction experiment f 0 .Q/ is independent of Q and depends only on the nature of the atom and its nuclear components. Secondly, the scattering amplitude of X-rays increases with atomic number since the scattering is due to the electrons around each atom. In the case of water the total structure factor is composed principally of the partial structure factor arising from the oxygen. For neutron diffraction the neutrons are scattered by both the oxygen and the proton atoms. In a liquid the atoms are not regularly arranged and they are in a constant state of flux. Therefore, there is no long range order and the diffraction peaks are broad and not as intense as in the solid state case. However, there is short range order in a liquid and one is able to calculate the probability distribution of liquid molecules over short distances. This can be expressed in relation to the correlation that pairs of molecules will associate with each other as a function of the distance between them. The structure of the liquid is therefore conveniently described in terms of a pair correlation function g(r). The pair correlation function is related to the structure

1

Molecular Associations Determined from Free Energy Calculations

3

factor S.Q/ of the liquid. Central to our discussion here, the pair correlation function is strongly dependent on the interatomic potential, u.r/. Contributions to this potential u.r/ originate mostly from two-body potentials uij .r/ and to a lesser extent, to three-body uijk .r/ and higher potentials. The discussion in this chapter will refer to the interatomic potential as being synonymous with the two-body potential uij .r/; ignoring the minor contributions from higher order potentials. The intermolecular potential is then the sum of all the interatomic potentials U.r/ D †u.r/. Using the tools of statistical mechanics, theoretical models can be developed to describe the solid and liquid states. In the case of liquids a theory is considered successful if bulk properties can be explained from the intermolecular potential. In the bulk solvent we commonly deal with a large number of molecules .1025 =l/. Statistical thermodynamics provides the analytical connection between the intermolecular potential and thermodynamic observables such as pressure and free energy. Nonequilibrium statistical mechanics provides a similar connection for time-dependent properties such as viscosity and thermal conductivity. Two of the four distinct forces in nature (i.e., the strong nuclear force, and the weak nuclear force) are short range . 0/ while bonding in the two mutually perpendicular directions to the M–L vector (the local z axis) is shown for a donor .e > 0/

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terms are atom-like – i.e. spherical. Only the ligand field potential, as modelled by the AOM, contains any information about the molecular symmetry. Within this approximation, therefore, it is possible to carry out ‘exact’ ligand field calculations. However, since only the d functions are explicit, only a subset of the molecular energy levels is accessible and hence exact LFT is, at best, only a semi-quantitative model of chemical bonding. In contrast, full MO theory offers, in principle, a complete treatment. The problem here is that it is impossible to carry out an exact MO calculation on a TM complex or indeed on any system with more than one electron. However, recent advances in quantum chemistry, lead in particular by Density Functional Theory (DFT) have allowed us to get fairly close. DFT is relatively quick and accurate and has established an impressive reputation for TM species [2]. Especially in its hybrid B3LYP form, DFT has become the de facto standard for quantum chemical modelling of coordination complexes including those of biological relevance [3]. Of course, no current functional is perfect, including B3LYP, and the quest for better functionals continues [4]. However, while we can argue the merits of different pure and hybrid functionals, all quantum methods are relatively compute intensive which ultimately limits the size of system and/or the type and number of calculations which can be achieved in a reasonable time. Therefore, our approach has been to dispense with quantum schemes and develop a classical molecular mechanics (MM) approach.

2.2 Molecular Mechanics Molecular mechanics treats the system as a collection of atoms connected by (possibly anharmonic) ‘springs’. Electrons are not considered explicitly (although electrostatic interactions can be included by assigning to each atom a partial atomic charge) and, in its simplest form (2.1), the total potential energy, Etot , is expressed as a simple sum of terms describing respectively bond stretching, Estr , angle bending, Ebend , torsional twisting, Etor , and non-bonding interactions, Enb . The latter can include both van der Waals (vdW) and electrostatic terms. Etot D

X

Estr C

X

Ebend C

X

Etor C

X

Enb

(2.1)

Each term in (2.1) is represented by a relatively simple mathematical expression. For example, the harmonic oscillator approximation is often used for Estr (2.2) where, for each unique type of bond in the system with an actual length of r, we need to define the reference bond length, r0 , and the associated force constant, kstr , which describes the energy penalty for deviations of the actual bond length from its ‘target’ reference value. (2.2) Estr D kstr .r r0 /2

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Molecular Modelling for Systems Containing Transition Metal Centres

25

Other simple expressions can be defined for the remaining terms in (2.1) such as those given in (2.1) where the k are appropriate force constants, are bond angles, are torsion angles, n is the torsional periodicity parameter, the torsion offset, are partial atomic charge, " is the dielectric constant, A and B are Lennard-Jones vdW parameters and the summations run over bonded atom pairs (ij), angle triples (ijk) and torsional quadruples (ijkl). The non-bonded terms are summed over the distances, dij , between unique atom pairs excluding bonded pairs and the atoms at either end of an angle triple. For the atoms at the ends of a torsion quadruple, the non-bonded term may be omitted or scaled. Etot D

X

kij .rij r0;ij /2 C

i;j

X

kijk .ijk 0;ijk /2

i;j;k

2 !3 X i j X Aij B ij C kijkl Œ1 C cos.nijkl ijkl /C 4 C 6 5 12 "dij d dij ij i;j;k;l i <j i <j X

(2.3) These potential energy terms and their attendant empirical parameters together define the force field (FF). More complicated FFs which use different and/or more complex functional forms are also possible. For example, the simple harmonic oscillator expression for bond stretching can be replaced by a Morse function, EMorse (2.4) or additional FF terms may be added such as the stretch-bend cross terms, Estb , (2.5) used in the Merck molecular force field (MMFF) [5–8] which may be useful for better describing vibrations and conformational energies. EMorse D Df1 e a.rr0 / g2 D X Estb D fkijk .rij r0;ij / C kkji .rjk r0;jk /g0;ijk

(2.4) (2.5)

i;j;k

MM is a very successful model but it is clear from expressions such as (2.3) that the FF may comprise a very large number of parameters and since the quality of the FF will depend crucially on these parameters, developing a truly ‘universal’ FF is an enormous (perhaps impossible) challenge [9]. Consequently, most FFs were originally designed for a specific class of molecular system such as small organic molecules (e.g. MMFF [5–8]), or large biomolecules like proteins and DNA (e.g. AMBER [10] or CHARMM [11]). Fortunately, these specific classes encompass an enormous amount of chemistry and biology plus the FFs are continually being developed to increase their applicability. The computational efficiency of a FF approach also enable simulations of dynamical behaviour – molecular dynamics (MD). In MD, the classical equations of motion for a system of N atoms are solved to generate a search in phase space, or trajectory, under specified thermodynamic conditions (e.g. constant temperature or constant pressure). Such a trajectory is important for two reasons. Firstly, it provides configurational and momentum information for each atom from which

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thermodynamic properties of the system can be calculated. Secondly, the trajectory represents an exploration of the conformation space accessible to a particular system under ‘realistic’ conditions of temperature and pressure. MM and MD have become extremely powerful and useful computational tools for studying a wide variety of chemical and biological problems. However, a significant proportion of real systems also rely on TM centres for their structure and/or function. The presence of TM coordination soon exposes fundamental shortcomings in simple FF equations like (2.3).

2.2.1 Shortcomings of MM for TM Systems Perhaps the first hurdle encountered in MM for TM complexes is how to describe the angular geometry at the metal centre when using a FF expression like (2.3). The situation for carbon chemistry is straightforward since the three common geometries – tetrahedral, trigonal planar and linear – are each associated with a single valence angle – 109:5ı , 120ı, and 180ı, respectively. Hence, the reference value, 0 , for the bond angle term is clear. In contrast, for common coordination symmetries like octahedral and trigonal bipyramidal, there are multiple reference angles for the same A-M-A triad (Fig. 2.4). Landis refers to this as the ‘unique labelling problem’ [12] and while the MM programs of the day could be persuaded to circumvent the problem, this required the definition of “multiple equilibrium positions and redundant atom labelling schemes” resulting in a “tedious over-definition of the molecular topology”.

Fig. 2.4 Valence angles at central atom for various regular geometries

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Many more elegant solutions to this problem have been suggested. A conceptually simple one is based on the Gillespie–Nyholm or valence shell electron pair repulsion (VSEPR) idea that the groups around a central atom will arrange themselves so as to maximise their separation or, equivalently, to minimise their mutual repulsions. Kepert put this essentially ‘points on a sphere’ (POS) approach onto a more quantitative footing by minimising the ligand-ligand repulsion assuming an inverse dependence on the ligand–ligand distance, with powers ranging from 4 to 8, and successfully rationalised the structures of some 5,000 main group compounds [13]. Within MM, a POS or ligand–ligand repulsion scheme removes the angle bend term at the metal and thus 0 values are not required. This approach has been adopted by Hambley and Comba in their MOMEC program [14]. However, a POS scheme generates the ‘Platonic’ solids – i.e. regular coordination polyhedra – and cannot on its own generate square planar or square pyramidal geometries unless these are enforced by the ligand structure. The alternative to circumventing the angle bending potential at the metal centre is to replace the harmonic expression in (2.3) with something more sophisticated. For example, the SHAPES FF [12] uses a Fourier expression for the angular potential which can be designed to produce multiple minima say 90ı and 180ı as illustrated in the original application to square planar low-spin d8 RhI complexes. Carlsson and Zapata [15] went even further and derived, from the AOM, analytical expressions for the angular potential around metal centres. The functional forms are simple trigonometric functions and depend on the or natures of the ligands which facilitate a calculation of the LFSE. This method is thus a simplification of our ligand field molecular mechanics (LFMM) approach, described in the next section, which calculates the LFSE from a full AOM treatment which requires construction and diagonalisation of the ligand field potential, VLF . However, despite its promise, the analytical approach outlined by Carlsson and Zapata does not appear to have been developed further and has, to our knowledge, not been incorporated into any molecular modelling software.

2.2.2 Ligand Field Molecular Mechanics Ligand field molecular mechanics (LFMM) was first introduced by Burton et al. [16] in 1995. The central idea of LFMM is to merge conventional MM for the ‘organic’ parts of a TM complex with an AOM treatment of the LFSE for the metal centre. The LFSE only accounts for the effects of the d electrons and is infinitely negative at zero M–L distances so the FF must include the ‘usual’ terms for M–L stretching (a Morse function is used) and L–M–L angle bending (a ligand–ligand term is used). The LFSE contribution is thus fully integrated into the MM calculations and the electronic effects feed directly into determining the structure and energy. The LFMM method is therefore distinct from Comba’s MM/AOM method [17] which uses a ‘pure’ MM approach to generate the structure followed by a subsequent AOM calculation to compute various ligand field properties such as d–d spectra and EPR g-values. Both approaches initially ignored electrostatic interactions.

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The LFMM model was significantly overhauled in 2005 [18] and a number of new or upgraded features were implemented: 1. A more general functional form was implemented for the distance dependence of the AOM parameters (2.6); e D a0 C a1 r C a2 r 2 C a3 r 3 C a4 r 4 C a5 r 5 C a6 r 6

2.

3.

4. 5. 6.

(2.6)

the 6–9 van der Waals ligand–ligand repulsion term was replaced by a purely repulsive term, ALL =r n where usually n D 6 for first-row donors or n D 4 for second row donors. M–L bonding was fully implemented including the contributions from forces acting on the ‘subsidiary’ atoms – i.e. the non-metal atoms connected to the donor atom. An explicit AOM d-s mixing term, eds , was included to treat the configuration interaction between the valence metal s orbital and the d functions (in D4h ŒCuCl4 2 , for example, the Cu 4s mixes with 3dz2 depressing the latter by about 6;000 cm1 ). The LFSE contributions to the potential energy gradients were computed analytically. Electrostatic interactions were added. The whole model was incorporated into a fully-functional molecular modelling package, the Molecular Operating Environment (MOE).

The final point is probably the most significant since it provides a much improved application and development platform. The new program – d orbital molecular mechanics in MOE (DommiMOE [18])– was designed to take advantage of existing force fields – e.g. MMFF, AMBER and CHARMM – to describe the ligand. Most of these force fields do not have explicit metal–ligand parameters and those that do are not compatible with LFMM since they do not separate the LFSE and bond stretch contributions (vide infra). Hence, the metal is explicitly decoupled from the rest of the molecule. Each molecule is divided into two overlapping regions as illustrated in Fig. 2.5 for a ŒM.ethylenediamine/2 nC complex. The coordination region contains the metal and its immediately bonded donor atoms (e.g. the MN4 unit) and the ligand region comprises everything except the metal atom (e.g. the ethylenediamine ligands). The LFMM routines focus on the coordination region and handle the LFSE, M–L bond stretching and L–M–L angle bending although, for the latter, there is no explicit L–M–L angle bending potential, rather the angular geometry is affected by a direct repulsive term between the ligand donor atoms. The MOE FF file treats all the interactions in the ligand region and, using Fig. 2.5 as an example, is augmented with M–N–C angle, N–M–N–C torsion and M–N–C–C torsion terms which span the coordination and ligand regions. MOE also handles all non-bonding interactions – van der Waals and electrostatic – for the entire molecule. The construction in Fig. 2.5 may at first sight seem like that used in QM/MM approaches. However, there are significant differences. Firstly, to the extent that

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Fig. 2.5 Schematic representation of division into coordination and ligand regions and force field terms which span the two

LFMM can be considered a QM/MM method at all, the metal is the only ‘QM’ atom. Hence, the ‘QM’ region is not the same as the coordination region. Secondly, the ‘link’ atoms typical of many QM/MM implementations would correspond to the ligand donor atoms. In a ‘real’ QM/MM calculation, the link atoms are different in the QM and MM regions, typically being H and C respectively. This construction is not required in the LFMM and there is no ‘join’. The LFMM thus provides a uniform, seamless theoretical treatment of the entire molecule. However, compared to a conventional MM scheme, LFMM has more parameters. In particular, there are up to four AOM parameters – e , ex , ey and eds – which have no ‘conventional’ counterparts. The first three are normally fixed with respect to experimental or computed d-orbital energy data for homoleptic systems while eds acts like a ‘switch’ and once it exceeds a threshold value, its precise magnitude is less important (see later). Hence, in terms of the actual number of parameters which are free to vary, LFMM and conventional MM are comparable, especially for FFs like MMFF which use a quartic expansion for bond stretching and thus require three parameters just like the Morse function employed in LFMM.

2.3 Applications of LFMM The magnitude of the LFSE can be significant. In octahedral complexes, values for oct are typically of the order of 10,000 to 20;000 cm1 and so the stabilisation energy for, say, a low-spin d6 Co(III) complex .12=5oct/ is substantial .120–240 kJ mol1 /. Conversely, the LFSE for high-spin d5 Mn(II) or Fe(III) is, by construction, zero.

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Although the LFMM represents a completely general method for coordination complexes, species at either end of the LFSE extreme can often be well treated by conventional MM – i.e. where the electronic effects of the LFSE are treated implicitly. Indeed, conventional MM may be easier to implement since there are fewer parameters. For example, the Comba group has applied MM to a range of lowspin d6 Co(III) complexes [19–22] and since the Co–L interactions are modelled via a simple quadratic function, essentially only two parameters are required per Co–L combination. In contrast, in LFMM, the Morse function, ligand–ligand repulsion, and LFSE all contribute strongly to the Co–L bond length which may require up to six parameters. Thus, the bulk of the applications of LFMM, and related methods, has been directed at complexes with an intermediate LFSE and especially to strongly Jahn– Teller active species like d9 Cu(II) centres for which conventional MM does not provide a general approach. While other groups have normally restricted themselves to simplified -bonding-only implementations of the LFMM, work from this laboratory includes bonding and d-s mixing contributions as appropriate. As for the ‘organic’ part of the FF, well-established parameter sets such as MMFF or MM3 are typically used although we do not consider this aspect in any detail here. The interested reader should consult the primary references for specific information.

2.3.1 Simple Coordination Complexes: Cu(II) Amines The first application of the LFMM model was to simple four- and six-coordinate copper(II) amine complexes [23]. These species are invariably planar and tetragonally-elongated respectively – suggestions based on single crystal X-ray diffraction that certain hexacoordinate complexes have regular, undistorted structures turn out to be artefacts of averaging. The structures of the CuN4 systems result from a competition between ligand– ligand repulsion, which favours tetrahedral coordination, and the LFSE, which favours planar coordination. Clearly, the latter is more important for amine ligation since the experimental and LFMM structures are exclusively planar (Fig. 2.6 and Table 2.1). In addition to predicting a planar coordination for these ŒCuL2 2C complexes (L D bidentate amine), the LFMM also describes the steric effects such as the general elongation of the Cu–N bonds for the tetramethyl derivative (7) and the asymmetry between the unsubstituted and substituted nitrogens in the N,N-diethyl complex (10). The magnitudes of the AOM parameters are estimated from previous ligand field ˚ e .N/ is analyses of d–d spectra [24–26]. Hence, for a Cu–N distance of 2.0 A, 1 around 6;000 cm .

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Fig. 2.6 Structural diagrams for Cu(II) amine complexes

Table 2.1 Comparison of calculated and experimental Cu–N bond lengths and chelate bite angles for complexes shown in Fig. 2.6. Data from Ref. [23] ˚ Cu–N/A Bite angle/ı Complex Calc./Exp. Calc./Exp. 5 2.02/2.02 85.4/84.1 6 2.00/2.04 84.8/86.7 7 2.04/2.06 86.7/85.3 8 2.01/2.01 86.3/85.9 2.04/2.06 9 2.03/2.02 86.2/85.0 2.02/2.01 10 2.10/2.08 85.2/87.6

2.3.2 ŒMC l4 2 Complexes Compared to amines, chloride donors have both smaller e values and non-zero e parameters resulting in an overall weaker ligand field. In addition, ligand–ligand repulsions are relatively more significant for chloride donors than nitrogens. For most complexes containing the ŒCuCl4 2 ion, the geometry balances partway between the extremes of planar and tetrahedral. The LFMM automatically generates this ‘flattened’ structure [18] (Fig. 2.7). The flattening of ŒCuCl4 2 can also be viewed as a Jahn–Teller distortion of the parent tetrahedral 2 T2 system. In contrast, the ground state for ŒCoCl4 2 is 4 A2 and is therefore not Jahn–Teller active. The LFMM predicts a perfectly tetrahedral structure. Tetrahedral ŒNiCl4 2 is also formally Jahn–Teller unstable with a 3 T1 ground state but now the LFMM predicts a tetragonally elongated structure (Fig. 2.7, top right). The sense of the Jahn–Teller distortions in ŒNiCl4 2 and ŒCuCl4 2 can be interpreted in terms of a simple d-orbital splitting diagram (Fig. 2.8). A ‘tetragonal’

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Fig. 2.7 LFMM structures for ŒMCl4 2 complexes

Fig. 2.8 d-orbital splitting diagram for tetragonal distortions of a tetrahedral complex

distortion – i.e. one that maintains D2d symmetry and hence an S4 axis – splits the t2 orbitals into a degenerate e set and a non-degenerate b2 function. Compression raises the b2 orbital which, in the limit of planar coordination, corresponds to the dxy orbital since the global X and Y axes are rotated 45ı relative to the conventional D4h assignment. Elongation lowers b2 relative to the e set. Thus, in order to avoid generating an orbitally degenerate ground state upon distortion, the d9 configuration favours compression while the high-spin d8 configuration favours elongation. For illustrative purposes, and as a prelude to spin-state effects discussed later, Fig. 2.7 also includes the optimised structure for the (hypothetical) low-spin ŒNiCl4 2 complex. The much increased LFSE for a low-spin d8 configuration now overcomes the ligand–ligand repulsion which results in a planar geometry. Thus we see that the spectrum of four-coordinate geometries from regular tetrahedral through to square planar is related to the disposition of the d electrons.

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2.3.3 Cu(II) Bis-oxazoline Complexes The subtle balance between planar and tetrahedral coordination is also seen in Cu(II) bis-oxazoline (box) complexes (Fig. 2.9) [27]. For example, the diaqua and dichloro complexes of box with R D t Bu (tb-box) are neither planar nor ‘tetrahedral’. For the former, the twist angles, ¦, between the plane of the C2 -symmetric oxazoline ligand and the CuL2 plane (Fig. 2.10) would be zero while for a ‘tetrahedral’ arrangement, they would be 90ı . These complexes catalyse the asymmetric Diels–Alder coupling reaction shown in Fig. 2.9 with the asymmetric induction controlled by the R groups on the oxazoline moieties. Clearly, the predicted asymmetry is reversed for ¦ D 0 versus ¦ D 90ı . An LFMM FF for box and pybox ligands was developed based on a set of X-ray crystal structures [27]. The calculated twist angles for ŒCuftb-boxgL2 nC , .L D Cl; n D 0I L D OH2 ; n D 2/ agree well with experiment (Table 2.2).

Fig. 2.9 Generic structural diagrams for copper complexes of box (top left) and pybox (top right) ligands plus the two-point asymmetric Diels–Alder reaction that they catalyse (bottom)

Fig. 2.10 Definition of the twist angle ¦, and overlay of X-ray (yellow) and LFMM structure for ŒCuftb-boxg.OH2 /2 2C

34 Table 2.2 Calculated and experimental twist angles for Cu(II) oxazoline complexes

R.J. Deeth

Complex ŒCuftb-boxgCl2 ŒCuftb-boxg.OH2 /2 .O3 SCF3 /2 ŒCuftb-boxg.OH2 /2 .SF6 /2

Calc./Exp. 53/52 30/45 30/33

Fig. 2.11 Schematic representation of the d orbital energy changes accompanying a tetragonal Jahn–Teller elongation of an octahedral Cu(II) complex

2.3.4 Jahn–Teller Effects in Six-Coordinate Cu(II) Complexes Six-coordinate d9 copper(II) complexes invariably display large tetragonal distortions from octahedral symmetry with the vast majority being tetragonally elongated. This observation can be rationalised on the basis of the d electron stabilisation energy (Fig. 2.11). The geometric distortion raises the original 2 Eg degeneracy of the parent octahedral system such that there are two stabilising electrons in dz2 versus a single destabilising electron in dx2y2 . The net lowering of the electronic energy by EJT drives the distortion but is resisted by the vibrational potential which is a minimum at the octahedral geometry. When these two forces are in balance, a stable structure results. Figure 2.11 shows an elongation along the Z axis but this is clearly only part of the complete picture.

2.3.4.1 The Mexican Hat Potential Energy Surface In the absence of external perturbations, an octahedral CuL6 species could equally well elongate along the X or the Y axes. These possibilities are accommodated in the more complex diagram shown in Fig. 2.12 [28]. In Oh symmetry, the Jahn–Teller-active vibration, Q, is doubly degenerate with modes Q™ and Q" (Fig. 2.12, bottom). In order to display the energy as a function of two vibrational modes, a three-dimensional figure is necessary. The so-called ‘Mexican hat potential surface’ is commonly used (Fig. 2.12, top), with the proportions of the two modes determined by the mixing parameter, . The Q™ mode generates

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Fig. 2.12 First-order Jahn–Teller potential energy surface – the Mexican hat

the ‘normal’ elongation along Z but suitable combinations of both modes generate the other elongated structures, plus compressed geometries plus all the intervening rhombic structures. To first order – i.e. a harmonic vibrational potential and a linear relationship between the Jahn–Teller energy and the vibrational displacement (linear vibronic coupling) – all these structures are equienergetic. However, this feature is lost to second order since the vibrational mode is anharmonic, the vibronic coupling is non-linear and as soon as the symmetry becomes less than Oh there is the possibility of d–s mixing which preferentially stabilises one of the d orbitals. The effect of d–s mixing can be illustrated in tetragonal D4h symmetry where the metal dz2 and valence s orbital both transform as a1g and may therefore mix. In planar ŒCuCl4 2 , detailed low temperature single crystal electronic absorption experiments have established that the dz2 orbital is about 6;000 cm1 lower than predicted based on simple AOM calculations, which include just the chloride e and e parameters [29].

2.3.4.2 The Warped Mexican Hat In the context of the Jahn–Teller effect, the second order terms differentiate between elongated and compressed structures. They have about the same magnitudes with both anharmonicity and d–s mixing favouring elongation while second-order electronic effects favour compression [28]. On balance, therefore, tetragonal elongation is lower in energy which leads to a ‘warping’ of the Mexican hat surface.

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Fig. 2.13 Warping of the Mexican hat PE surface. The plotted curves represent the minimum energy pathways around the base of the Mexican hat

The warping is quite a subtle effect. Figure 2.13 displays representations of the path along the bottom of the PE surface as a function of the Q™ =Q" mixing parameter, , for three possible scenarios. In an isotropic environment (Fig. 2.13, top), all three elongation axes are equally likely and hence each local minimum is equally occupied. Significantly, although each individual molecule is elongated, any timeaveraged structural technique, in particular single-crystal X-ray diffraction, would appear to report a regular octahedron. In contrast, spectroscopy – e.g. EXAFS or d-d electronic absorption – would detect the underlying distorted structure. Thus, while the room temperature X-ray structure of ŒCu.tach/2 .NO3 /2 (tach D 1; 3; 5triaminocyclohexane) shows essentially six equal Cu–N distances, the perchlorate salt has a ‘normal’ elongated structure [30]. The d–d spectra of both complexes are the same and show two absorption maxima consistent with the underlying tetragonal structure. The second scenario is when two wells are occupied while the third is essentially unoccupied (Fig. 2.13, middle). Here, the averaged structure would appear to be tetragonally compressed as was originally reported for K2 CuF4 [31] with four ˚ and two shorter contacts at 1.95 A. ˚ However, these data longer Cu–F bonds of 2.08 A were based on an incorrect space group, presumably due to the relatively crude instrumentation available in 1959. Subsequent investigation by Reinen and Krause [32] established the true structure as comprising interchanging elongated structures oriented at 90ı as shown in Fig. 2.14. The final, and most common, scenario (Fig. 2.13, bottom) is where the environment and/or the ligand result in one well being significantly more stable than the other two (or possibly, there being only one minimum). This results in the ‘conventional’ elongated structure. Where more than one elongation is possible, there is an intervening transition state with a compressed geometry. The barrier, 2ˇ, between successive wells

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Fig. 2.14 Diagram of the arrangement of the CuF6 polyhedra in the (001) plane of K2 CuF4 (After Figure 4 of Ref. [32])

(Fig. 2.13) determines the dynamics of the system. If the barrier is significantly lower than kT then the complex is free to ‘hop’ from one well to the next – the dynamic Jahn–Teller effect. If the barrier is significantly larger than kT, then the complexes are ‘frozen’ in their respective wells – the static Jahn–Teller effect. The dynamic behaviour is thus temperature dependent. Indeed, the earlier example of apparently octahedral ŒCu.tach/2 .NO3 /2 oscillates between two minima just above the phase transition temperature of 120 K and below this, reverts to a classic ‘static’ elongated system.

2.3.4.3 Theoretical Treatment of the Jahn–Teller Effect in Cu(II) Species Capturing all this complexity is a challenge for theory. On the one hand, there is the thorny issue about whether it is theoretically justifiable to use ‘normal’ computational approaches at all. The models tend to assume the Born–Oppenheimer approximation which does not apply where there is significant vibronic coupling [33]. However, in practice, it appears that providing we move away from the octahedral singularity, ‘normal’ QM and MM methods appear to work quite well. On the other hand, the energetics are significant but subtle. To first order (i.e. the harmonic approximation), the first d–d transition corresponds to 4EJT which, for Cu(II) complexes with typical band energies of 6,000 to 9;000 cm1 , corresponds to EJT 17 to 27 kJ mol1 . Thus, the distorted structure is significantly more stable than the octahedral precursor. A second order treatment further distinguishes elongated from compressed geometries but the energy differences are only a fraction of EJT . For example, variable temperature EPR experiments place the barrier height, 2ˇ, in ŒCu.tach/2 2C at around 300 cm1 (4 kJ mol1 ).

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Fig. 2.15 Training set of Cu(II) complexes for the LFMM treatment of Jahn–Teller distortions. Cambridge Structural Database refcodes are included

The very first application of the LFMM included the Jahn–Teller distortions of some simple hexacoordinate Cu(II) complexes [23]. This study has recently been significantly extended and enhanced [34]. Seventeen six-coordinate Cu(II) complexes of nitrogen donor ligands were selected as a training set (Fig. 2.15) based on the criterion that the species with the largest possible Jahn–Teller distortion will suffer the smallest crystallographic ‘averaging’ errors.

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˚ Fig. 2.16 Comparison of LFMM (white bars) and experimental (black bars) structural data (A) for complexes sketched in Fig. 2.15

The comparison between the crystallographic and LFMM structures is shown in Fig. 2.16 which displays the average Cu–N distance at the top and the difference between the averaged Cu–N (axial) and averaged Cu–N (equatorial) distances. The agreement is generally excellent. A significant feature of LFMM for these complexes is d–s mixing. Since the vibrations are anharmonic and the electronic term non-linear, d–s mixing plays the deciding role in stabilising elongated over compressed geometries. The eds parameters acts like a switch in that it needs to exceed a certain threshold before the elongated structure becomes lower in energy.

2.3.4.4 Barriers Between Successive Elongations As mentioned in the previous section, the barrier, 2ˇ, between successive elongated geometries can be of the order of kT and can therefore be measured experimentally via, for example, variable temperature EPR. However, since the intrinsic barrier

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is relatively small, the behaviour of a given complex can dramatically depend on the crystal environment. For example, the perchlorate salt of ŒCu.tach/2 2C has a ‘normal’ elongated structure at room temperature while the nitrate salt displays six almost equal Cu–N bond lengths at 300 K. However, variable temperature EPR measurements on the latter down to 4 K show dynamic Jahn–Teller behaviour at room temperature with a phase transition to static behaviour at 120 K [30]. The EPR measurements establish 2ˇ at around 300 cm1 . Standard MM codes are designed to locate local minima efficiently. The compressed tetragonal structures for (most) Cu(II) complexes are first-order saddle points, or transition states (TSs), and will not be automatically located unless special modifications are made such as in Warshel’s empirical valence bond (EVB), Truhlar’s multiconfiguration MM (MCMM), or Goddard’s ReaxFF methods [35–37]. However, for simple homoleptic complexes like ŒCu.tach/2 2C it is relatively straightforward to locate the TS manually. A series of constrained LFMM calculations, where the axial bond is fixed at progressively shorter distances, eventually leads to a structure with two short and four long Cu–N contacts. Significantly, the energy difference between the compressed TS and the elongated structure is 270 cm1 , in excellent agreement with experiment, plus the application of a uniaxial strain does not force the structure through an ‘octahedral’ geometry but instead a series of rhombic structures. The LFMM thus correctly follows the ‘valley floor’ of the warped Mexican hat PE surface (Fig. 2.17). Further suitable experimental data are sparse since most of the temperature dependent studies have been carried out on doped systems where the structures of the Cu(II) centres are heavily influenced by the host lattice and are unknown in detail anyway. However, by way of illustration, 2ˇ barriers were also computed for ŒCu.NH3 /6 2C and ŒCu.terpy/2 2C (terpy D terpyridyl). These complexes were chosen since the former has no ligand constraints to Jahn–Teller elongation, while the latter comprises meridonally coordinated tridentate donors, which are more constrained than tach. This is consistent with the computed barriers of 1,100 and 215 cm1 , respectively [34].

Fig. 2.17 Schematic representation of the effect of applying uniaxial strain to ŒCu.tach/2 2C . The initial effect is a rhombic distortion (middle) leading to the compressed geometry (right)

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Fig. 2.18 Tridentate ligands designed by Halcrow to explore preferential stabilisation of truly compressed Cu(II) complexes

2.3.4.5 Truly Compressed Complexes Compressed six-coordinate Cu(II) species doped into diamagnetic host lattices, typically of Zn(II), have been observed spectroscopically. However, pure Cu(II) complexes with compressed geometries are much rarer. Nevertheless, the relatively low barriers between successive elongated geometries in ‘normal’ complexes of only a few kJ mol1 prompted Halcrow [38] to look for ligand systems which might be able to stabilise a compressed structure preferentially. The tridentate, meridonally-coordinating ligands shown in Fig. 2.18 and Table 2.3 can generate elongated and compressed structures, depending on the steric demands of the R substituents. A combination of crystallography and spectroscopy was used to assign the structure as either compressed or elongated and the LFMM-optimised structures (Table 2.3) are in excellent qualitative agreement. Significantly, the LFMM parameterisation was based exclusively on elongated structures.

2.3.5 Spin-State Effects Many TM configurations can support multiple spin states. A potential advantage of LFMM over other MM methods is that the addition of a term to describe d–d interelectron repulsion results in a single parameter set for all spin states, and their energies can thus be directly compared. A ‘proof of concept’ study was undertaken for Co(III) fluoride and cyanide complexes [39]. To our knowledge, ŒCoF6 3 is the only homoleptic high-spin complex of d6 Co(III) while ŒCo.CN/6 3 is certainly

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˚ for comTable 2.3 Experimentally-assigned ground state and LFMM-optimised bond lengths (A) plexes based on the ligands shown in Fig. 2.2. The non-standard d orbital designation dy2z2 is adopted to retain a single axis frame definition for both ground states where the z direction coincides with the Cu-N vector to the central donor atoms of the tridentate ligands LFMM M-L(av) LFMM Geometry rx ; ry ; rz Complex Exp ground state ŒCu.L2 H/2 ŒBF4 2 fdy2z2 g 2.29, 2.11, 1.90 Elongated ŒCu.L2 Ph/2 ŒBF4 2 dz2 2.24, 2.19, 1.90 Rhombic (compressed) ŒCu.L2 Mes/2 ŒClO4 2 dz2 2.22, 2.21, 1.88 Compressed ŒCu.L2 iPr/2 2C – 2.25, 2.19, 1.90 Rhombic (compressed) ŒCu.L2 tBu/2 2C – 2.38, 2.38, 1.90 Compressed ŒCu.L2 CF3 /2 2C – 2.25, 2.19, 1.90 Rhombic (compressed) ’-ŒCu.L3 /ŒClO4 2 fdy2z2 g 2.28, 2.14, 1.90 Rhombic (elongated) ŒCu.L1 Cy/2 ŒBF4 2 fdy2z2 g 2.38, 2.06, 1.91 Elongated ŒCu.L1 tBu/2 ŒBF4 2 dz2 2.34, 2.34, 1.92 Compressed ŒCu.L1 NH2 /2 ŒClO4 2

dz2 (RT) fdy2z2 g (5 K)

2.30, 2.03, 1.93

Elongated

ŒCu.L1 OH/2 ŒClO4 2

dz2 (RT) fdy2z2 g (low temp)

2.29, 2.02, 1.93

Elongated

dz2

2.37, 2.15, 1.82

Rhombic (compressed)

4

ŒCu.L /2 ŒClO4 2

low-spin. LFMM parameters for both high- and low-spin forms of each complex were developed with the aid of DFT calculations. For example, DFT-optimised Co–L bond lengths for the ground state complexes plus the hypothetical low-spin ŒCoF6 3 and high-spin ŒCo.CN/6 3 species were part of the target data for the FF parameters. In addition for these complexes, a comparison of LFT predictions with DFT indicated that the latter gives a reasonable spin-state energy difference (see Ref. [39] for details) and was subsequently used to map out the spin-state energy difference, Espin , for each complex as a function of the Co–L distance. The structures of all the mixed-ligand systems ŒCoFn .CN/6n 3 , n D 1 to 5, were then computed by both LFMM and DFT and the energies of the former empirically corrected for spin state effects using the spin-state energy differences, Espin , expressed on a per-ligand basis derived from the homoleptic complexes. As shown in Fig. 2.19, the agreement between DFT and LFMM is satisfactory.

2.3.6 Type 1 Copper Enzymes The Type 1 (T1) ‘blue’ copper enzymes are responsible for a range of redox processes in biological systems [40]. For example, plastocyanin (Pc) is involved in plant photosynthesis while azurin (Az) participates in bacterial photosynthesis. Compared to ‘normal’ copper complexes, the T1 active site possesses a number of unusual structural and spectroscopic features [41]:

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Fig. 2.19 Comparison of calculated spin-state energy differences for ŒCoFn .CN/6-n 3 complexes

A distorted tetrahedral (or trigonal bipyramidal) structure with a strong Cu-

thiolate bond even in the oxidised form plus a long thioether or carbonyl oxygen contact. A very intense charge transfer transition around 600 nm. Relatively high redox potentials and fast electron self-exchange. In the EPR spectra of the oxidised Cu(II) form, there is an unusually low copper hyperfine coupling in the gjj region. The T1 active site appears to have features of both ‘normal’ Cu(II) and Cu(I) complexes. For example, oxidised copper is often planar four-coordinate with an N4 donor set while d10 Cu(I) is often tetrahedral and, as a softer metal, prefers second row donors like sulphur. Given its role in electron transfer (ET) and the expectation from Marcus theory that efficient ET is associated with a small reorganisation energy, œ, the idea that the protein somehow enforces the structure around the metal centre to minimise œ became very popular. This ‘entatic state’ [42] (or rack [43]) model is certainly appealing and prompted Ryde to try and calculate its magnitude using DFT [44]. However, B3LYP optimisation of a model for the T1 active site in Pc gave basically the same coordination geometry at the metal centre as that reported in the full protein structure. Ryde et al. [44] were forced to the unexpected and somewhat controversial conclusion that the geometry in oxidised T1 centres is not under any protein strain. Instead, the structure is dominated by the strong Cu–thiolate bond. The combined electronic effects of the d9 configuration and Cu–thiolate binding present some significant challenges for LFMM [45,46]. We begin with the presumption that although protein molecules may be large and complex, they form simple

44

R.J. Deeth ˚ for species shown in Fig. 2.21. First entry is Table 2.4 Cu–L bond lengths (A) LFMM, second is DFT Compound Cu–N Cu–S(thioether) Cu–S(thiolate) ŒCu.imidazole/4 2C 1.99/2.00 ŒCu.DMS/4 2C 2.37/2.35 ŒCu.SMe/4 2 2.32/2.33 ŒCu.SMe/.imidazole/2 .DMS/C 2.02/2.04 2.90/2.70 2.14/2.16

M-L coordinate bonds – i.e. a Cu–N(imidazole) bond can be handled in exactly the same way irrespective of whether it corresponds to an isolated imidazole or to a histidine (Table 2.4). However, in order to parameterise the enzyme system, we require information on the specific types of bonds involved which is straightforward for imidazole coordination, where significant experimental data are available, but difficult for thiolate and thioether bonds where experimental data on small-molecule systems are sparse or absent. We resort, therefore, to using DFT calculations on model homoleptic species as a basis for developing LFMM parameters. Hence, as shown in the box in Fig. 2.21, LFMM parameters are developed for the homoleptic complexes which reproduce the DFT-optimised Cu–L distances and L–Cu–L angles. The parameters are then applied unaltered to the same active-site model used by Ryde et al. [44] in their DFT study. The good agreement between LFMM and DFT once again confirms that the LFMM behaves just like DFT in its ability to capture M–L bonding electronic effects. Furthermore, just as in six-coordinate complexes (Section 2.3.4.3), d–s mixing plays a pivotal role. There are two stable forms of the T1 active site model – the lower energy trigonal one shown in Fig. 2.21 and a higher energy, essentially planar form. DFT calculations [47] suggest a delicate energy balance with the trigonal model being more stable. Interestingly, a comparable LFMM result is only obtained once the eds value for the Cu-S(thiolate) bond exceeds a threshold value. Once again, d–s mixing acts like an electronic ‘switch’. LFMM was applied to 24 crystallographically-characterised proteins [46] and ˚ and 8ı in L–Cu–L bond angles an rmsd in the Cu–L bond lengths of 0.11 A achieved – i.e. the LFMM and PDB results are basically the same within experimental uncertainty. A comparison of structures representative of the three active site types shown in Fig. 2.20 is given in Fig. 2.22, Tables 2.5 and 2.6. The quality of the LFMM results can also be assessed with respect to comparable QM/MM calculations [48] (Fig. 2.23). In both instances, explicit solvent is included and again, the agreement is good. The fact that the LFMM data were obtained several orders of magnitude faster than the QM/MM results bodes well for using the LFMM for molecular dynamics simulations.

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Fig. 2.20 Schematic representations of T1 active site structures of plastocyanin (Pc), stellacyanin (STC) and azurin (Az)

Fig. 2.21 Species used to develop LFMM parameters for T1 centres

2.3.7 Dinuclear Copper Centres Another common copper enzyme active site is the dinuclear Type 3 centre (Fig. 2.24) which is implicated in O2 transport and activation [40]. The fully oxidised T3 site is an attractive target for LFMM since it combines the electronic activity of d9 centres with the first attempt at modelling both multi-nuclear species and complexes with bridging ligands [49].

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Fig. 2.22 Rmsd overlays of experimental (blue) and computed (yellow or CPK) backbone carbons (top) and active sites (bottom) for Amicyanin (left), Stellacyanin (middle) and Azurin (right) (PDB codes 1AAC, 1JER, 1DYZ). The solvent layer is omitted for clarity

˚ for complete proteins shown Table 2.5 Comparison of PDB and LFMM Cu–L bond lengths (A) in Fig. 2.22 1AAC PDB LFMM 1JER PDB LFMM 1DYZ PDB LFMM HIS53 1.954 2.029 HIS46 1.960 2.045 GLY45 2.720 2.666 CYS92 2.108 2.148 CYS89 2.178 2.176 HIS46 2.040 2.014 HIS95 2.033 2.023 HIS94 2.043 2.028 CYS112 2.135 2.184 MET98 2.904 2.859 GLN99 2.209 2.253 HIS117 1.988 2.062 MET121 3.260 2.924

Table 2.6 Comparison of PDB and LFMM bond angles .ı / at the metal centre for the shown in Fig. 2.22 1AAC PDB LFMM 1JER PDB LFMM 1DYZ PDB HIS53-CYS92 136 141 HIS46-CYS89 133 139 GLY45-HIS46 78 HIS53-HIS95 104 97 HIS46-HIS94 101 98 GLY45-CYS112 104 HIS53-MET98 84 86 HIS46-GLN99 94 87 GLY45-HIS117 86 CYS92-HIS95 112 108 CYS89-HIS94 117 113 GLY45-MET121 148 CYS92-MET98 110 112 CYS89-GLN99 101 112 HIS46-CYS112 132 HIS95-MET98 100 104 HIS94-GLN99 101 95 HIS46-HIS117 106 HIS46-MET121 73 CYS112-HIS117 121 CYS112-MET121 105 HIS117-MET121 88

proteins LFMM 82 98 83 156 140 103 75 116 105 92

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Fig. 2.23 Comparison of LFMM (lighter bars) and QM/MM (darker bars) metrics for selected T1 sites. PLC D plastocyanin; CBP D cucumber basic protein; AZU D azurin. ¥ is the angle between the CuN2 and CuS2 planes Fig. 2.24 Schematic representation of the fully oxidised T3 active site with a bound peroxido ligand

In contrast to the T1 centre, several crystallographically-characterised structural models for the T3 site are available (Fig. 2.25) from which an LFMM treatment was developed. The AOM calculation underpinning the LFSE presumes independent metal centres. Thus, the extension of the LFMM to multi-metal centres could be problematic if the metals were strongly coupled. However, for the model test system ŒfCu.NH3 /3 g2 O22C , and the dinuclear species shown in Fig. 2.25, the particular combination of electronic configuration and geometry ensures that the gradient of the LFSE is dominated by the highest energy combination of d functions which

48

R.J. Deeth

Fig. 2.25 Dinuclear Cu complexes as structural models for the T3 active site [49]

Fig. 2.26 Definition of folding angle, ˛, about the O-O vector in dinuclear complexes

mirrors the situation in the mono-nuclear model species ŒCu.NH3 /3 .O2 / and thus the ‘isolated metal’ approach remains satisfactory in the dinuclear systems [49]. An important feature of the dinuclear complexes is that the ŒCu2 O2 2C subunit prefers to be planar – i.e. the folding angle shown in Fig. 2.26 is 180ı . This is implicitly accounted for in the LFMM by defining the Cu–O -bonding directions relative to the second copper centre rather than the other oxygen atom. One of the originally perceived advantages of the LFMM was the explicit treatment of separate and bonding effects via the AOM e and e parameters [16] and here, we see a powerful demonstration of this feature. The LFMM is in generally good agreement both with experimental and DFT data (Fig. 2.27) [49]. The agreement extends to the energies (relative to DFT) of other conformations of each system which lie within about 12 kJ mol1 of the respective

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Fig. 2.27 Observed X-ray structure (left), LFMM-computed structure (centre) and DFT-optimized geometry (right) for 11 showing Cu-N distances. All comparable structural data for the X-ray and LFMM versions of 12 are virtually the same. H atoms omitted for clarity

global minimum. The exception is 14 where the LFMM and DFT energies disagree substantially but this is traced to a generic shortcoming in the ‘organic’ force field treatment of the macrocyclic ligand. In common with previous LFMM applications to five-coordinate Cu(II) species [16], we see strong apical elongations. Significantly, the demands of a particular ligand can make the two copper centres different, a feature which also figures in enzymes like tyrosinase.

2.4 Conclusions The structural, spectroscopic and magnetic properties of Werner-type coordination complexes are profoundly affected by the d electrons. They also result in complicated electronic states which, from a theoretical perspective, appear to demand a full quantum-mechanical treatment. Yet, despite the ever-increasing speed and power of modern digital computers, QM treatments of TM systems are relatively computeintensive. Long simulation periods or screening of large numbers of small molecules are, and will remain, intractable. In contrast, ligand field theory, which is specifically designed for d states, is computationally efficient. Over the last half century or so it has also been shown to provide a reasonable, if semi-quantitative, description of the nature of metal ligand bonding. The addition of an explicit LF-based d-electron-energy term to the conventional MM potential energy expression captures most of the essential physics around the metal centre. Coupling this with a term to treat d–d interelectron repulsion further improves the method such that MM is able to provide a treatment comparable to full QM but at a much reduced computational cost. The all-important LFSE can be based on the angular overlap model which, being bond centred, is ideally suited for incorporation into MM. Aside from providing a general framework within which to treat TM centres, LFMM accurately describes a number of significant electronic effects which are omitted in conventional MM: The full Mexican hat potential energy surface describing the Jahn–Teller effect

in six-coordinate d9 Cu(II) complexes.

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The ability to treat multiple spin states of complexes with a single set of param-

eters and thus be able to use LFMM to predict the lowest energy spin state. The effects of explicit d-s mixing in tetragonal Cu(II) complexes plus the trigonal

geometry of the Type I active site in blue copper proteins. The explicit M-L effects necessary to keep the ŒCu2 O2 2C core of Type 3

copper model complexes planar. All of these examples have been tested against comparable DFT treatments and shown to produce at least as good a result and sometimes an even better one. An empirical approach offers some distinct advantages over QM in that experimental data can also be used to inform the parameterisation. The outlook for the future is encouraging.

References 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.

Johnson, D. A.; Nelson, P. G., Inorg. Chem. 1995, 34, 5666–5671. Ziegler, T.; Autschbach, J., Chem. Rev. 2005, 105, 2695–2722. Siegbahn, P. E. M.; Blomberg, M. R. A., Chem. Rev. 2000, 100, 421–437. Schultz, N. E.; Zhao, Y.; Truhlar, D. G., J. Phys. Chem. A 2005, 109, 11127–11143. Halgren, T. A., J. Comput. Chem. 1996, 17, 490–519. Halgren, T. A., J. Comput. Chem. 1996, 17, 520–552. Halgren, T. A., J. Comput. Chem. 1996, 17, 553–586. Halgren, T. A.; Nachbar, R. B., J. Comput. Chem. 1996, 17, 587–615. Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M., J. Am. Chem. Soc. 1992, 114, 10024–10035. Pearlman, D. A.; Case, D. A.; Caldwell, J. W.; Ross, W. S.; Cheatham, T. E.; Debolt, S.; Ferguson, D.; Seibel, G.; Kollman, P., Comput. Phys. Commun. 1995, 91, 1–41. Brooks, B. R.; Bruccoleri, R. E.; Olafson, B. D.; States, D. J.; Swaminathan, S.; Karplus, M., J. Comput. Chem. 1983, 4, 187–217. Allured, V. S.; Kelly, C. M.; Landis, C. R., J. Am. Chem. Soc. 1991, 113, 1–12. Kepert, D. L., Inorganic Stereochemistry. Springer, Berlin/Heidelberg/New York, 1982. Comba, P.; Hambley, T. W., Molecular Modeling of Inorganic Compounds. VCH, Weinheim, 1995. Carlsson, A. E.; Zapata, S., Biophys. J. 2001, 81, 1–10. Burton, V. J.; Deeth, R. J.; Kemp, C. M.; Gilbert, P. J., J. Am. Chem. Soc. 1995, 117, 8407–8415. Comba, P.; Hambley, T. W.; Hitchman, M. A.; Stratemeier, H., Inorg. Chem. 1995, 34, 3903–3911. Deeth, R. J.; Fey, N.; Williams-Hubbard, B. J., J. Comp. Chem. 2005, 26, 123–130. Bartol, J.; Comba, P.; Melter, M.; Zimmer, M., J. Comput. Chem. 1999, 20, 1549–1558. Comba, P.; Sickmuller, A. F., Inorg. Chem. 1997, 36, 4500–4507. Comba, P.; Sickmuller, A. F., Angew. Chem.-Int. Ed. Eng. 1997, 36, 2006–2008. Comba, P.; Jakob, H.; Nuber, B.; Keppler, B. K., Inorg. Chem. 1994, 33, 3396–3400. Burton, V. J.; Deeth, R. J., J. Chem. Soc., Chem. Commun. 1995, 573–574. Deeth, R. J.; Gerloch, M., Inorg. Chem. 1984, 23, 3846–3853. Deeth, R. J.; Gerloch, M., Inorg. Chem. 1985, 24, 1754–1758. Deeth, R. J.; Gerloch, M., J. Chem. Soc., Dalton Trans. 1986, 1531–1534. Davies, I. W.; Deeth, R. J.; Larsen, R. D.; Reider, P. J., Tett. Lett. 1999, 40, 1233–1236. Deeth, R. J.; Hitchman, M. A., Inorg. Chem. 1986, 25, 1225–1233. Hitchman, M. A.; Cassidy, P. J., Inorg. Chem. 1979, 18, 1745.

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30. Ammeter, J. H.; Burgi, H. B.; Gamp, E.; Meyer-Sandrin, V.; Jensen, W. P., Inorg. Chem. 1979, 18, 733–750. 31. Knox, K., J. Chem. Phys. 1959, 30, 991–993. 32. Reinen, D.; Krause, S., Inorg. Chem. 1981, 20, 2750–2759. 33. Bersuker, I. B., Chem. Rev. 2001, 101, 1067–1114. 34. Deeth, R. J.; Hearnshaw, L. J. A., Dalton Trans. 2006, 1092–1100. 35. Villa, J.; Bentzien, J.; Gonzalez-Lafont, A.; Lluch, J. M.; Bertran, J.; Warshel, A., J. Comput. Chem. 2000, 21, 607–625. 36. Albu, T. V.; Corchado, J. C.; Truhlar, D. G., J. Phys. Chem. A 2001, 105, 8465–8487. 37. Nielson, K. D.; van Duin, A. C. T.; Oxgaard, J.; Deng, W. Q.; Goddard, W. A., J. Phys. Chem. A 2005, 109, 493–499. 38. Halcrow, M. A., Dalton Trans. 2003, 4375–4384. 39. Deeth, R. J.; Foulis, D. L.; Williams-Hubbard, B. J., Dalton Trans. 2003, 3949–3955. 40. Kaim, W.; Schwederski, B., Bioinorganic Chemistry: Inorganic Elements in the Chemistry of Life. Wiley, Chichester, 1994. 41. Solomon, E. I.; Szilagyi, R. K.; George, S. D.; Basumallick, L., Chem. Rev. 2004, 104, 419–458. 42. Vallee, B. L.; Williams, R. J. P., Proc. Natl. Acad. Sci. USA 1968, 59, 498–505. 43. Malmstrom, B. G., Eur. J. Biochem. 1994, 223, 711–718. 44. Ryde, U.; Olsson, M. H. M.; Pierloot, K.; Roos, B. O., J. Mol. Biol. 1996, 261, 586–596. 45. Deeth, R. J., Chem. Commun. 2006, 2551–2553. 46. Deeth, R. J., Inorg. Chem. 2007, 46, 4492–4503. 47. Olsson, M. H. M.; Ryde, U.; Roos, B. O.; Pierloot, K., J. Biol. Inorg. Chem. 1998, 3, 109–125. 48. Ryde, U.; Olsson, M. H. M., Int. J. Quant. Chem. 2001, 81, 335–347. 49. Diedrich, C.; Deeth, R. J., Inorg. Chem. 2008, 47, 2494–2506.

Chapter 3

Magnetic Anisotropy in Cyanide Complexes of First Row Transition Metal Ions Mihail Atanasov and Peter Comba

Abstract The relationship between structure and magnetic anisotropy in monoand oligonuclear paramagnetic complexes, based on low-spin ŒFe.CN/6 3 and hexacoordinate NiII complexes with bridging CN groups, are analyzed with special emphasis on the contributions of spin-orbit coupling and Jahn–Teller distortions as well as strain-induced distortions at the ŒFe.CN/6 3 subunit. The basic theoretical principles are described, which allow to treat the lowest multiplets of FeIII and NiII , due to the t2g5 and t2g6 eg2 electronic configurations, respectively, and their anisotropic exchange coupling. Examples are then presented, to show how small angular distortions of ŒFe.CN/6 3 lead to dramatic changes of the magnetic anisotropy of the corresponding oligonuclear complexes. The nature of the lowest spin multiplet and the spin-anisotropy gap are analyzed with a combination of density functional theory and ligand field theory (LFDFT). A general ab-initio approach is also proposed, which allows to calculate the magnetic anisotropy of oligonuclear complexes with transition metals in orbitally degenerate or nearly-degenerate electronic ground states.

3.1 Introduction In the early 1990s ŒMn12 O12 .OOCCH3 /16 .OH2 /4 [1], known as Mn12 , was discovered to exhibit magnetic bistability [2–4]. The magnetic anisotropy due to the negative axial zero-field splitting D leads to removal of the degeneracy of the M. Atanasov () University of Heidelberg, Anorganisch-Chemisches Institut, Im Neuenheimer Feld 270, D-69120 Heidelberg, Germany and Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Acad. Georgi Bontchev Str. Bl.11, 1113 Sofia, Bulgaria e-mail: [email protected] P. Comba () University of Heidelberg, Anorganisch-Chemisches Institut, Im Neuenheimer Feld 270, D-69120 Heidelberg, Germany e-mail: [email protected]


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sublevels of the S D 10 ground state, such that the state with the largest multiplicity, Ms D ˙10, is lowest in energy. The magnetization induced by an applied magnetic field is blocked below a given temperature (the blocking temperature; for Mn12 TB D 3:8 K) such that the molecule remains magnetic with a relaxation time of 2 months at 2 K, when switching-off the field. The bistability of such single molecule magnets (SMM), together with their size of 2 to 5 nm are expected to open the way to magnetic information storage materials of unprecedented density. SMMs are also of interest in fundamental science as excellent examples to study quantum effects, and have attracted attention in the fields of quantum computing, magnetic refrigeration and spin-based molecular electronics. The field has flourished in the last decade and the physics of SMM behavior as well as experimental approaches for their characterization are well developed [5]. However, while a large number of new oligonuclear paramagnetic molecules with oxide and cyanide as bridging ligands were described in the literature, so far there is only one compound with a slightly larger anisotropy and blocking temperature than Mn12 .TB D 4:5 vs: 3:8 K/ [6]. The slow progress has two main reasons. (i) Although the crucial parameters for a significant increase of the magnetic anisotropy are known – ferromagnetic coupling with a large exchange coupling constant J , leading to a high-spin ground state, well separated from the lowest excited state with a lower spin, and a large and negative zero-field splitting parameter D (referring to the magnetic anisotropy of the whole spin cluster) – there are no generally applicable methods for their reliable prediction. Due to size limitation, electronic structure methods based on ab-initio theory still are largely confined to mono- and dinuclear complexes [7–9]. Density functional theory (DFT) can be applied to larger transition metal complexes but breaks down for excited states because of the single reference character of its many electron wave function [10]. (ii) The synthesis of oligonuclear complexes with specific structures has been difficult to achieve, especially for oxo-bridged complexes, to which Mn12 belongs. This is due to the multifarious geometries of the oxo bridges, their flexibility and their redox instability [11]. We have developed and successfully used a combination of ligand field theory and DFT (ligand field density functional theory, LFDFT) to model the electronic properties of transition metal complexes. Since its formulation [12–14] the method has been applied to and validated with optical [12, 15, 16] and EPR spectra [17] of 3d-metal complexes (NiII [12, 18], CuII [19], CrIII [15], CoII [19] and MnIII [20]) with monodentate .L D H2 O; F ; Cl ; Br ; I ; CN / and more complex ligands, such as porphyrine [19]. Optical and magnetic properties as well as g- and hyperfine coupling tensors 3d and 4f complexes have been described [17, 21, 22]. The method has been extended to magnetic exchange in dinuclear transition metal complexes [23, 24], and its ability to also describe anisotropic exchange in cyanide complexes with an orbitally degenerate ground state has been demonstrated [25–28]. Qualitative rules toward a systematic search of novel SMM materials have also been formulated [25, 27]. Here, we focus on the structure–function relationship (magnetic anisotropy) of paramagnetic complexes with low-spin ŒFe.CN/6 3 and octahedral NiII -amine building blocks. Special emphasis is given to the interplay between spin-orbit coupling and distortions of the ŒFe.CN/6 3 subunit due to Jahn–Teller effects or steric

3

Magnetic Anisotropy in Cyanide Complexes of First Row Transition Metal Ions

55

strain. Examples show how small angular distortions of ŒFe.CN/6 3 can lead to dramatic changes in the magnetic anisotropy. The nature of the lowest spin multiplet and the spin-anisotropy gap are analyzed with LFDFT. Finally, a general and user-oriented ab-initio approach is described, which allows the parameter-free calculation of the magnetic anisotropy of oligonuclear transition metal complexes in orbitally degenerate or nearly-degenerate electronic ground states.

3.2 Jahn–Teller Coupling Versus Spin-Orbit Coupling in the Ground State of ŒFe.CN/6 3 FeIII in low-spin complexes with a 2 T2g ground state is subject to Jahn–Teller distortions which split it into sublevels and lead to an orbitally non-degenerate ground state. Such distortions follow the normal modes in an octahedral complex, with a doubly degenerate "g mode leading to tetragonal distortions (D4h ), and a triply degenerate £2g mode leading to trigonal distortions (D3d , Fig. 3.1). In addition, the combination of these modes can induce orthorhombic geometries on the ground state potential surface. These distorted configurations and the geometric parameters used in their description are shown in Fig. 3.2, along with the corresponding energy changes of the 2 T2g sublevels. A cross section of the ground state potential surface for the tetragonal .Q™ / and trigonal (Q£ D QŸ D Q˜ D Q— ) distortion modes is depicted in Fig. 3.3. For such distortions, the 2 T2g state splits into 2 B2g and 2 Eg .Q™ ; D4h / or 2 A1g and 2 Eg .Q£ ; D3d /, and the non-degenerate ground states are stabilized by the Jahn–Teller stabilization

Fig. 3.1 Components and shapes of the "g and £2g octahedral vibrations (Adapted from Ref. [20])

56


Fig. 3.2 Geometric parameters describing Jahn–Teller distortions of the type Tg ˝ "g .D4h /, Tg ˝ £2g .D3d / and Tg ˝ ."g C £2g / deduced from DFT geometry optimizations for ŒFe.CN/6 3 with electronic configurations with correct spin and space symmetries in D4h .2 B2g /, D3d .2 A1g / and D2h .2 B2g /. (Top), and induced 2 T2g energy splitting due to these distortions (shown schematically, bottom) (Adapted with modifications from Ref. [20])

Fig. 3.3 Energy profile for the components split from the 2 T2g ground states for ŒFe.CN/6 3 , d5 , due to Tg ˝"g .Tg ˝£2g / Jahn–Teller coupling, along a distortion pathway which preserves the highest possible symmetry D4h .D3d / and lifts the orbital degeneracy. The basic model parameters – the Jahn–Teller stabilization energy, EJTm , the energy of the vertical (Franck-Condon) transition at the D4h .D3d / minimum EFCm , and the distortions of the active mode Qvibm , Qvibs .vib D "g ; £2g / for the minima (m) and saddle points (s) are illustrated; values of V" , V£ , K" , K£ , EJTm .D4h /, EJTm .D3d /, ˚ 70,000, 5,770 (cm1 =A ˚ 2 ); 5,142,14 EFCm .D4h /, EFCm .D3d / from DFT are 808, 1;110.cm1 =A/, 1 and 427 cm , respectively (Adapted from Ref. [20])

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57

energy with respect to the non-distorted octahedral complex (EJT , Fig. 3.3). The energy of the vertical excitation from 2 B2g .2 Ag / to 2 Eg at the geometry of the energy minimum of the distorted configuration D4h .D3d / is the Franck-Condon energy EFC m , i.e. an observable quantity, and the two parameters, EJT and EFC m yield important information about the stability of the geometry. A procedure to deduce EJT and EFC m as well as the distortion coordinates Q™m .D4h / and Q£m .D3d /, corresponding to the minima (m) of the ground state potential energy surface, from DFT geometry optimization have been described [20]. The matrix of the 2 T2g ˝ ."g C £2g / vibronic coupling problem in the linear approximation is described by Eq. 3.1 with V" and V£ – the linear JT coupling constants for the Tg ˝ "g and Tg ˝ £2g problems – and K" and K£ – the harmonic force constants for the "g and £2g vibrational modes (I is the 3 3 identity matrix).

2 6 H1 D 6 4

V":

1 2 Q™

p 3 2 Q"

V£ Q—

V":

V£ Q— 1 Q 2 ™

C

p

3 Q" 2

V£ Q˜

3

7 7 V£ QŸ 5

(3.1)

V£ Q˜ V£ QŸ V" Q™ 1 1 C K" Q2™ C Q2" C K£ Q2Ÿ C Q2˜ C Q2— I 2 2

From the analysis of this matrix, explicit connections between the model parameters V" , V£ , K" and K£ , with the DFT values of EJT and EFC m as well as Q™m .D4h / and Q£m .D3d / are obtained (Eqs. 3.2 and 3.3). From such calculations we have found that 2 B2g and 2 A1g ground states are stabilized by tetragonal and trigonal compressions of the ŒFe.CN/6 3 complex. The same procedure [20] allows to deduce all energetic and distortion parameters of the ground state potential surface from DFT calculations and to explore its topology. 2 EFmC .D4h / I 3 Qm 1 EFmC .D3d / V D I 3 Qm V" D

2 EFmC .D4h / 3 .Qm /2 2 EFmC .D3d / K D 9 .Qm /2

K" D

(3.2) (3.3)

Absolute minima for a trigonally compressed geometry with a deviation of the angle ™ by only 1:4ı from its value corresponding to a regular octahedron (™ D 54:735ı) have been deduced. So far we have neglected spin-orbit coupling within the 2 T2g ground state of the ŒFe.CN/6 3 complex. For an octahedral complex, it leads to a splitting of the 2 T2g ground state into lower and higher lying Kramers doublet and quartet states, 7 (or E00 ) and 8 (or U0 ), respectively, separated in energy by .3=2/—, where — is the effective spin-orbit coupling constant of ŒFe.CN/6 3 . A comparison of the effects from trigonal distortions and spin-orbit coupling (Fig. 3.4) shows that they are comparable in magnitude and should be accounted for on the same footing. An energy level diagram in dependence of the extent of the trigonal distortion (in units

58


Fig. 3.4 Splitting of the 2 T2g ground state due to Jahn–Teller coupling with the trigonal distortion mode (Q£ , left) and due to spin-orbit coupling (right). The values used for the plot are derived from a trigonally compressed geometry, corresponding to the absolute minimum of the ground state potential surface (left) and for the spin-orbit coupling constant of Fe3C , reduced by covalence (right). g-value expressions for an octahedral geometry are also included (k D 0:79; note the negative g-tensor value for the octahedral ground state)

Fig. 3.5 Competition between Jahn–Teller coupling along the trigonal mode and spin-orbit coupling in the 2 T2g ground state of ŒFe.CN/6 3

of —, Fig. 3.5) illustrates the interplay of these two opposing forces – geometric distortion due to Jahn–Teller activity and spin-orbit coupling. Irrespective of their relative magnitude, one always obtains an orbitally non-generate ground state, well separated from the two other states at higher energy. Let us now focus on the anisotropy of the g-tensor in dependence of trigonal distortions. A plot of the g-tensor versus the angle of trigonal distortions (Fig. 3.6) shows that there is a dramatic effect of such distortions on the g-tensor anisotropy; trigonal compressions (i.e. those leading to a Jahn–Teller non-degenerate ground state 2 A1g ) lead to a strong decrease of the axial (z, i.e. this becomes a hard axis) and an increase of the in-plane components of the g-tensor (x,y, i.e. this becomes an easy plane) (Fig. 3.6).

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59

Fig. 3.6 g-tensor values of ŒFe.CN/6 3 in dependence of the sign and magnitude of the deviations of the polar angle ™ from its octahedral value (™ D 54:735ı ); •™ > 0ı , trigonal compression, •™ < 0ı , trigonal elongation

Fig. 3.7 Molecular structure of Œf.talent-Bu2 /.Mn.MeOH//3 g2 ŒFe.CN/6 g3C .Mn6 Fe/ in crystals of (Mn6 Fe/:18MeOH:2H2 O, perpendicular to the approximate molecular pC3 axis; the CFeC angles (’) along the pseudo C3 axis are 91:28ı , 90:89ı , 90:92ı Œsin D .2= 3/ sin.˛=2/; in average •™ D 0:73ı , and with this value gz D 0:91, gx;y D 2:33; for ligand field parameters see Ref. 20) (Adapted from Ref. [29])

A cyanide bridged Mn6 Fe complex with a nearly threefold symmetry and a tiny trigonal compression of ŒFe.CN/6 3 (•™ D 0:73ı ) has recently been reported [29]. The compound is not a SMM and possible reasons have been discussed. However, effects due to the degeneracy of ŒFe.CN/6 3 have not been analyzed. Using the experimental geometry, we calculate g-tensor values (gz D 0:91, gx;y D 2:33)

60

M. Atanasov and P. Comba Table 3.1a Geometric and g-tensor values for ŒFe.CN/6 3 in its monoclinic form, given by experiment and simulated with a vibronic JT coupling model Monoclinic b Geometry from a X-ray struct. fit to g-tensor gexp [30] [38] (exp) values (I) (II) (III) † CFeC: ’Ÿ ’˜ ’— QŸ Q˜ Q— Q.’1g / Q."g Wx/ Q."g Wy/ g-tensor: g1 g2 g3 SDa a1 e e(xy) e(yz) e(xz)

0.915 2.100 2.350 –

90:9c (89.1) 90:8c (89.2) 90:5c (89.5) 0:061.0:061/ 0:054.0:054/ 0:034.0:034/ 0:086.0:086/ 0:019.0:019/ 0:005.0:005/

91.1 91.0 90.6 0.077 0.069 0.041 0.105 0:025 0.005

1.186(1.462) 2.139(1.702) 2.332(2.512) 0.137(0.348) 103 .108/ 33, 70 (38, 70)

0.994 2.180 2.429 0.069 129 39, 90

25 99 65

a

SD-standard deviation between calculated and experimental g-values; k D 0:79; D 345 cm1 ; B D 720; C D 3;290 cm1 . b ˚ Pseudo orthorhombic, crystallographic axes: a D 13:422 A; ˚ c D 8:381 A, ˚ Pnca-space group. b D 10:399 A; c Adapted from the reported bond angles ’ just changing the sign of (’ 90ı ) from negative to positive values (see text).

close to those reported for ŒFe.CN/6 3 in K3 ŒFe.CN/6 (g1 D 0:915; g2 D 2:100, g3 D 2:35 [30], see below and Table 3.1). We note that the anisotropy of the gtensor of FeIII has a sign opposite to that resulting from the zero-field splitting of the six elongated MnIII octahedra, with an angle of 36:5ı between their long (Jahn– Teller) axes, and the pseudo threefold .S6 / axis of the Mn6 Fe complex. Therefore, a reduction of the overall anisotropy of the complex, resulting from the ŒFe.CN/6 3 subunit, is deduced. However, dominated by the large spin moments of the six MnIII ions .S D 2/, the magnetic properties of this compound are not sensitive to the local anisotropy of FeIII . As we shell see, complexes of lower nuclearity are better suited for these purposes, and we will return to this point in Sections 3.3 and 3.4. Based on early work on the paramagnetic resonance of ŒFe.CN/6 3 , the electronic structure of ŒFe.CN/6 3 has been studied extensively [30, 31]. Magnetic susceptibility studies, including crystal anisotropies and crystal structures have also been reported [32–34]. Efforts to fully interpret these data were based on the

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61

assumption of an orthorhombic symmetry with orthorhombic axes parallel to the three Fe-CN bonds [31]. A reasonable fit with three parameters (two crystal field energies, which define the splitting of the xy, yz, and xz orbitals A(xy), B(yz) and C(xz), respectively; A C B C C D 0 and the spin-orbit coupling constant) have been shown to reproduce the g-tensors and the anisotropic susceptibility data. However, the Mössbauer data of ŒFe.CN/6 3 [35–37] could not be explained. The room temperature (295 K) crystal structures of K3 ŒFe.CN/6 in its monoclinic and orthorhombic forms have been accurately determined [38]. From the observed C–Fe–C angles (Table 3.1a – ’Ÿ ; ’˜ and ’— ), it emerges that ŒFe.CN/6 3 has a trigonally elongated geometry with the C3 axis approximately parallel to the crystallographic axis (a), perturbed by an orthorhombic distortion. We have used these structural parameters to estimate the geometric strain, described by QŸ s ; Q˜ s and Q—s (see Table 3.1a) and the vibronic coupling constants of ŒFe.CN/6 3 , to deduce the strain matrix (Eq. 3.4), in order to calculate the g- and susceptibility tensors of ŒFe.CN/6 3 from a full CI ligand field calculation. However, with this matrix, we have not 3 2 0 V£ Qs V£ Qs Ÿ.yz/ 7 6 0 V£ Qs 5 (3.4) ˜.xz/ 4V£ Qs —.xy/ V£ Qs V£ Qs 0 been able to reproduce the sign of the magnetic anisotropy. Apparently, the geometry of ŒFe.CN/6 3 , doped in K3 ŒCo.CN/6 ] is not the same as that of the room temperature structure of K3 ŒFe.CN/6 , which may change at lower temperatures. The reason probably is a distortion, dominated by a trigonal compression. This is compatible with the stabilization of a non-degenerate 2 A1g ground state, in accordance with the Jahn–Teller theorem. If we adopt the values of QŸ s ; Q˜ s and, Q— s deduced from X-ray data of the two modifications, but change their sign (i.e. from a trigonal elongation to a trigonal compression), accurate computed anisotropic g-tensor components (Table 3.1a) and low temperature magnetic susceptibility (Fig. 3.8) are obtained. Structural data together with experimental and computed g-tensor values are listed in Table 3.1a; experimental and simulated single crystal magnetic susceptibilities data are plotted in Fig. 3.8 with the following set of parameters [20]: < xy jVLF j xy >D 5; < xy jVLF j yz >D 67; < yz jVLF j yz >D 2; < xz jVLF j xy >D 77; < yz jVLF j xz >D 108; < xz jVLF j xz >D 3 < x 2 y 2 jVLF j x 2 y 2 >D< z2 jVLF j z2 >D 34950 B D 720; C D 3290I — D 345 cm1 I k D 0:79: Readjustment of the values of QŸ s ; Q˜ s and Q— s did not modify the agreement with experiment. The data in Table 3.1b also yield the orientation of the principal axes of the g-tensor with respect to the two sets of axes, the octahedral Fe-C bond directions and the crystallographic a, b and c axes. From the orientations, the (1,1,1), (0; 1; 1) and (2; 1; 1) trigonal directions for g1 ; g2 and g3 emerge. These orientations show that g1 , g2 and g3 are (within angles of 11ı ; 8ı and 17ı ) parallel to

62


Fig. 3.8 Experimental (black squares) [34] and theoretical anisotropic magnetic susceptibilities for ŒFe.CN/6 3 (Adapted from Ref. [20]); notations ¦a , ¦b and ¦c are defined as ¦a D ¦1 ¦3 ; ¦b D ¦2 ¦1 ; ¦c D ¦2 ¦3 ; ¦1 , ¦2 , ¦3 are the principle crystal susceptibilities with orientations along the a, b and c-crystallographic axes, respectively; these coincide (within an angle of ˙5ı ) with the (1,1,1), .2; 1; 1/ and .0; 1; 1/ D3d directions of the ŒFe.CN/6 3 complex (in a coordinate system x,y,z defined by the Fe-C bond vectors) and with principal axes of the molecular g-tensor 0.915, 2.100 and 2.350 (T D 12 K, [30]), respectively; the following set of ligand field parameters, describing the effect due to the geometrical strain (in cm1 ) have been used (geometric data: set III, Table 3.1, in combination with Eq. 3.4) Table 3.1b Directional cosines of the principal axes of the g-tensor with respect to the octahedral Fe-C bond directions (x,y,z) and the crystallographic a,b,c (orthorhombic setting) as deduced from experiment (I) and simulated (best fit of geometric parameters) for ŒFe.CN/6 3 in its monoclinic (III) forms (I) (III) g1 g2 g3 g1 g2 g3 x y z a b c

0.915 0.002 0.710 0:694 0.000 0.866 1.000

2 100 0.573 0.567 0.581 0.500 0.866 0.000

2.350 0:819 0.418 0.423 0.000 0.500 0.000

x y z a b c

0.991 0.535 0.563 0.630 0.988 0.142 0.058

2.181 0.759 0:648 0:066 0:147 0.896 0.404

2.430 0:371 0:514 0.774 0.005 0:404 0.906

the (a), (c) and (b) crystal axes in the orthorhombic lattice. In the monoclinic form, the axis of g1 is parallel to (a) but the directions of g2 and g3 interchange and become aligned along (b) and (c), respectively. This phenomenon has been described before [36]. There is a misfit between the directions of g1 and ¦1 (both jja, see the entry for (III) in Table 3.1b) and the orientation of g1 reported in Ref. [30] (crystal

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63

structure of K3 ŒFe.CN/6 not known at that time). In agreement with the susceptibility data, the magnetic anisotropy of ŒFe.CN/6 3 in the two crystallographic forms of K3 ŒFe.CN/6 is very similar and only compatible with a trigonally compressed geometry, as indicated by the JT coupling model. It is striking that a change of the angle ™ from an ideal octahedral geometry (™ D 54:735ı) by only 1ı is large enough to account for the observed anisotropy in the g- and the susceptibility (¦) tensors. As we shall see in Sections 3.3 and 3.4 this is of importance in oligonuclear complexes with ŒFe.CN/6 3 building blocks.

3.3 Modeling of the Magnetic Anisotropy in Ni-NC-FeIII Pairs 3.3.1 Theory To deduce the tensors g and D in the simplest case of an exchange coupled transition metal complex pair, one starts with the Born-Oppenheimer Hamiltonian, H BO consisting of a one-electron part H BO (1), the kinetic energy and electronnuclear attraction, and a two electron part H BO (1,2) of interelectronic repulsion. In a non-relativistic approximation, H BO commutes with the operators of the square of the total spin, S 2 and its z projection, S Z , and the eigenfunctions of H BO are characterized by the quantum numbers S, Ms (spin-part) and ” (i.e. a compound orbital quantum number). One can split H BO into two parts, one which does not depend on the spin and is discarded here and one which depends on it. The spin-dependent Hamiltonian H EXC (the exchange Hamiltonian) interchanges independently spins and orbitals occupied by a single electron between two centers. It then becomes clear, that a spin-only Hamiltonian description is ill-defined if symmetry is high and the electronic state is orbitally degenerate. However, there are usually small perturbations to lead to a lift of the orbital degenarcy (JT coupling, structural distortions, spin-orbit coupling H SO ) as shown, e.g., for ŒFe.CN/6 3 (Fig. 3.5) with an energy separation between the ground state E00 and the excited states E00 or U0 , and this is fulfilled for the entire range of the energy ratio V£ Q£ =— (i.e., energies of the trigonal distortion V£ Q£ and spin-orbit coupling —). Therefore, if exchange coupling is much weaker than these splittings (weak exchange coupling limit as is the case here) one can define the ground state spin Hamiltonian and calculate its parameters, either variationally or with perturbation theory to various orders, using the effective Hamiltonian approach. Even in this case, calculations of g and D, are a challenge for electronic structure ab-initio methods, and the DFT approach, is in-adequate. Therefore, we use LFDFT to approximate the values of g and D of the FeIII -CN-NiII exchange pair. We take the 2 T2g ground state with a single hole on the t2g orbitals Ÿ.dyz /; ˜.dxz / and —.dxy / and neglect configuration mixing of this state with excited states of the same symmetry via Coulomb repulsion and mixing of the Ÿ; ˜ and — orbitals with ™.dz2 / and ".dx2y2 /, which takes place when lowering the symmetry. Because of the large value of 10Dq of ŒFe.CN/6 3v (34; 950 cm1 /,

64


this is acceptable for small angular distortions. When combined with the spins (’ and “), this gives rise to six degenerate micro-states, which are split by spin-orbit and Jahn–Teller coupling. There is a weak exchange coupling of these micro-states with the 3 A2g .dx2y2 1 dz2 1 / ground state of the hexacoordinate NiII complex in a FeIII -NiII pair. We consider the ground states of NiII as well defined and include all orbital effects on its spin ground state in the effective g-tensor values .g2 /, with positive deviations from the spin only value (go D 2) and in case of distortions from Oh symmetry in the zero-field splitting tensor D2 for NiII . Under these conditions, the electronic states of the FeIII -NiII exchange pair are described by the Hamiltonian in Eq. 3.5, where HO SO D 1 lO1 sO1 and HO LF are the spin-orbit coupling and ligand field operators of ŒFe.CN/6 3 (1 is the spin-orbit HO D HO SO C HO LF C HO exc C HO Z1 C HO Z2 C HO SFS2

(3.5)

coupling constant of FeIII ), and HO Z1 D B .s1 C kl1 /B and HO z2 D B s2 g2 B are the Zeeman operators for ŒFe.CN/6 3 and Ni, respectively (k is the covalency reduction factor, s1 and l1 are the spin and orbital moment operators of FeIII ); HO SFS2 D DNi .Osz2 2=3/ is the operator which takes account of the possible single center anisotropy in the s2 D 1 ground state of NiII . The exchange coupling term HO exc in Eq. 3.5 takes account of the spins of FeIII .s1 / and NiII .s2 /, and also of the orbital degrees of freedom due to the degeneracy of the 2 T2g ground state of ŒFe.CN/6 3 (see Eq. 3.6). HO exc D

X

J

sO1 sO2

(3.6)

D ;;

J

. D Ÿ; ˜; —/ are the orbital exchange coupling constants between the spins .s1 / on the singly occupied magnetic orbitals dyz .Ÿ/, dxz .˜/ and dxy .—/ of FeIII and the unpaired spins .s2 / of NiII . In Eq. 3.6 we assume a C4v -pseudo symmetry of the FeIII -NiII pair with the local z axis along the FeIII -CN-NiII bridge. This defines two exchange coupling parameters JŸŸ D J˜˜ JE and J—— JB2 for the FeIII -NiII pair, when off-diagonal terms J . ¤ / are neglected. We approximate these parameters with their values obtained from broken symmetry DFT calculations on a FeIII -CN-NiII pair (JE D 12:9; JB D 0 cm1 ) [25]. The well-aligned magnetic orbitals Ÿ; ˜; — and the matrices, which represent all operators in Eq. 3.5 are then transformed, using eigenvectors of the ligand field operator HO LF on each center to ensure invariance of the results with respect to the orbital rotations. For the qualitative analysis presented here, we start with octahedral .Oh /ŒFe.CN/6 3 and restrict the treatment to a particular form of HO LF , i.e., the matrix of the Jahn– Teller effect (Eq. 3.1), which operates within the 2 T2g ground state of ŒFe.CN/6 3 . We have shown (see Section 3.2) that from the five Jahn–Teller active "g and £2g vibrations, coupling of the 2 T2g ground state of ŒFe.CN/6 3 to the trigonal modes £2g dominates [20]. This leads to the stabilization of a D3d -distorted 2 A1g ground state, derived from a trigonally compressed octahedron.

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65

We now focus on the spin levels of the electronic ground state and consider the coupling of the effective spin of FeIII .s0 1 D 1=2/ with the real spins of NiII .s2 D 1/. These are described by the spin Hamiltonian of Eq. 3.7. J is the isotropic coupling constant; D12 (with the usual notations for the axial (D) and Hsph D J s1 s2 C s1 D12 s2 C s2 D2 s2 C s1 A12 s2 C B s1 g1 B C B s2 g2 B (3.7) orthorhombic splitting parameters (E)) and A12 are the traceless tensors for the symmetric (Eq. 3.8) and antisymmetric exchange (Eq. 3.9), respectively; D2 is the zero-field splitting parameter for NiII I g1 and g2 are the effective g-tensors of 3 2 2 3 Dxz Dxy Dxz Dxx Dxy 3 D C 2E 5D4 D 4Dxy Dyy Dyz Dxy 23 D 2E Dyz 5 (3.8) 4 Dxz Dyz Dxx Dyy Dxz Dyz 3D 2

D12

2

A12

3 0 Az Ay D 4Az 0 Ax 5 Ay Ax 0

(3.9)

the ŒFe.CN/6 3 and the NiII sites. The effective Hamiltonian approach is used to reduce the 18 18.6 3/ matrix of Eq. 3.5 from an explicit ligand field calculation to the ground state spin-manifold .6 6.3 2// of the Fe-Ni pair, and to determine the parameters of the spin Hamiltonian of Eq. 3.7 by comparison between the two data sets (see Ref. [28] for more details and examples).

3.3.2 Regular .C4v / Versus Distorted .Cs / ŒFe.CN /3 and Its 6 Influence on the Magnetic Anisotropy of the Fe-Ni Pair The E00 .’00 ; “00 / ground state of FeIII couples with the S D 1 spin of NiII to give rise 00 00 and two excited spin states E.2/ to three Kramers doublets, i.e. the ground state E.1/ and E0 . Energy expressions in terms of the exchange coupling energies JE and JB as well as of the energy of the NiII zero field splitting DNi are given in Eq. 3.10. An energy level diagram is shown in Fig. 3.9, where spin eigenfunctions are also 1 1 1 00 E.1/ D JE C JB C DNi 3 6 3 2 00 E.2/ D DNi 3 1 1 1 0 E.E / D JE JB C DNi 3 6 3

(3.10)

66


Fig. 3.9 Spin energy levels and spin functions for the FeIII -CN-NiII exchange pair of C4v symmetry; ˙1; 0.’00 ; “00 / are the spins (effective spins) of NiII .FeIII /; parameters used for the C4v energy levels: J.2 E/ D 12:9 cm1 ; J.2 B2 / D 0 cm1 ; —.Fe/ D 345 cm1 ; energy levels of the pair in Oh symmetry (collapsing NiII and FeIII nuclei) the spin energy gap parameter ED and the effect of the zero-field splitting of NiII .DNi D 2:63 cm1 / are also shown (Adapted from Ref. [25])

Fig. 3.10 Zeeman splitting of the spin levels of the FeIII -CN-NiII pair in a magnetic field parallel (a) and perpendicular (b) to the bridging z axis; parameters used: k.Fe/ D 0:79; gx;y;z .Ni/ D 2:30 (other parameters as in Fig. 3.9, DNi D 0) (Adapted from Ref. [25])

included. Due to the odd number of spins, all spin states of the pair are doubly degenerate (Kramers degeneracy). There is an in-phase coupling of the local g1 (Fe) 00 ground state and an out-of-phase coupling in the and g2 (Ni) g-tensors in the E.1/ 0 E excited spin state. As shown by the dependence of the energies of these states on the magnetic field parallel and perpendicular to the z-axis of the pair (Fig. 3.10a and b, respectively), a strong anisotropy of Ising type is predicted along the z-direction. From the computed DFT values of JE and JB (12.9 and 0 cm1 , respectively) the parameters of the spin Hamiltonian (Eq. 3.7) J D 2:87 and D D 4:30 cm1 are deduced. Here, ED and EJ can be defined and used in analogy to D and J (Fig. 3.9) to quantify the anisotropic and isotropic energy gaps, respectively. Both exchange terms and the single ion zero-field splitting (DNi ) affect the value of ED (Eq. 3.11).

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67

Fig. 3.11 Effect of the trigonal (£2g ) Jahn–Teller distortions along (1,1,1) (Q£ > 0, trigonal compression) and .1; 1; 1/ (Q£ < 0, trigonal elongation) on the spin energy levels of FeIII -NiII ; the set of vibronic coupling constants of ŒFe.CN/6 3 used are those specified in Ref. [25]; other parameters are as in Fig. 3.9 (for FeIII -NiII , DNi D 0) (Adapted from Ref. [25])

1 1 JE JB DNi (3.11) 3 6 The parameter DNi is known to vary in a wide range from positive values in tetragonally elongated octahedra of NiII .9:47 cm1 [39]) to negative values in compressed octahedral structures .6:1 cm1 / [40]. Therefore, the anisotropy gap ED (calculated by DFT to be 4:3 cm1 due to exchange only contributions) can largely be tuned by ligand-enforced distortions within the NiII N6 building block. A reduction or enhancement of this energy is predicted for positive or negative values of DNi (we assume that the axes of the tetragonal tensors D Ni-Fe and D Ni are parallel). This is the case for octahedral NiII structures with tetragonal elongations (reduction of ED ) or compressions (enhancement of ED ). The spin levels of FeIII CN-NiII pairs strongly change when Jahn–Teller distortions along the trigonal axes of the octahedral ŒFe.CN/6 3 site are superimposed to the C4v symmetry (Fig. 3.11). There are four possible pathways for these distortions, which coincide with the body diagonals of the cube inscribed in the ŒFe.CN/6 3 octahedron. With the trigonal distortion along the x D y D z direction (defined by Q£ D QŸ D Q˜ D Q— ) the C4v symmetry is lowered towards Cs , with a symmetry plane that bisects the coordinate axes in the x D y.x D y/ direction and parallel 00 of the FeIII -NiII pair drops in ento z. On Q£ distortions, the excited spin state E.2/ 00 ergy and approaches the E.1/ ground state, i.e. the zero-field-split S D 3=2 ground state quartet and an S D 1=2 excited state doublet are formed. Therefore, Jahn– Teller distortions tend to restore the usual spin coupling scheme in s1 D 1=2; s2 D 1 ferromagnetically coupled pairs. The anisotropy .ED / and the isotropy gap energies .EJ /, visualized in Fig. 3.12, manifest these changes. Upon distortions ED reduces and EJ increases (Fig. 3.12). In Fig. 3.12, negative values of the zero-field splitting DNi of the S D 1 ground state of the octahedral NiII complex (tetragonal compression) or positive values of DNi (tetragonal elongation) are compared with the case with no distortions around NiII . In these calculations we have assumed, that the tetragonal axes of NiII and of the Fe-CN-Ni bridge of the FeIII -NiII pair are ED D

68


Fig. 3.12 Effect of the trigonal Jahn–Teller distortions on the spin energy gap parameters ED (a) and EJ (b) for the FeIII -NiII pair; ED and EJ at the minimum and saddle point of the ground state potential energy surface of ŒFe.CN/6 3 are indicated by arrows; parameters used are as those in Fig. 3.9. The effect of zero-field splitting of Ni (DNi ) is shown with DNi D 2:63 cm1 (as in Ref. [41]); the dotted curve for EJ refers to DNi D 0 (Adapted from Ref. [25])

parallel. Negative DNi leads to a drastic increase of the anisotropy, while positive DNi leads to a partial or complete cancellation of the contributions to ED . In an effective way, the energy EJ is also affected by DNi (Fig. 3.12).

3.3.3 Effect of Combined Spin-Orbit Coupling and Strain at the Fe III Subunit Strain effects due to an asymmetric ligand sphere or crystal packing forces can split the ŒFe.CN/6 32 T2g ground state and modify the magnetic anisotropy. Strain with the symmetry of the components of the £2g normal mode is formally described by a matrix of the form of Eq. 3.4 with a single energy parameter S£ (radial strain, replacing V£ ) and angular distortions QŸ s , Q˜ s and Q— s (angular strain, to replace QŸ , Q˜ and Q— ); the latter usually emerges from crystal structural data. We restrict ourselves here to strain with a trigonal symmetry (C3 ; Q£ s D QŸ s D Q˜ s D Q— s , see Fig. 3.11). For a CuII -NC-FeIII pair, similar to NiII -NC-FeIII , the resulting changes may be large in complexes derived from [FeIII .CN/3 L, where L is a facially coordinating tridentate ligand and where S£ >> V£ . Therefore, the strain might induce partial or complete quenching of the magnetic anisotropy (see Fig. 3.12). With angular strain alone .S£ D V£ /, the quenching of orbital momenta due to a trigonal compression is predicted to be stronger than for a trigonal elongation. The reduction of the magnetic anisotropy is due to the symmetry reduction .Cs D C4v C D3d /, and this leads to a complete loss of orbital degeneracy (however, this may change, e.g., in CuII3 FeIII 2 spin clusters with ŒFe.CN/3 L subunits, see discussion in Section 3.5.2). The orbital momentum is not necessarily quenched as a result of tetragonal .D4h / strain with a C4 molecular axis which coincides with the Fe-CN-M linear bridge.

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69

Fig. 3.13 Dependence of the spin energy gap parameters ED and EJ of a FeIII -CuII pair on the parameter D4h , which describes the tetragonal strain due to the ligand L in a transfFeIII .CN/2 .L/4 g or a trans-fFeIII L2 .CN/4 g complex. The sign of D4h is determined by the difference between the -bonding character of L and CN; for an amine ligand without orbitals for -bonding and the dominating -back bonding of CN one expects D4h to be negative [positive] for trans-fFeIII .CN/2 .L/4 g and [trans-fFe III .L/2 .CN/4 g]. Parameters used for the plot are specified in Ref. [25] (Adapted from Ref. [25])

This is described by Eq. 3.12 with D4h , the tetragonal splitting of the 2 T2g ground term. 2 Eg or 2 B2g ground terms may result, depending on the sign of D4h . As shown in Fig. 3.13, the magnetic anisotropy D (as reflected by the energy -ED ) and the isotropic exchange energy J (as reflected by EJ ) are enhanced with tetragonal strain, which leads to a 2 Eg ground state on FeIII . Based on the dominating -back bonding character of the Fe-CN bond, this is predicted to be the case in a trans f.L/2 FeIII -ŒCN-CuII .L4 /4 g complex, where L is a monodentate and L4 is a tetradentate or pentadentate amine ligand. In contrast, both parameters are strongly quenched if a non-degenerate 2 B2g ground state is separated from a 2 Eg excited state with an energy gap D4h , comparable or larger than the spin-orbit coupling energy 3—=2 [28]. Based on the dominating -back bonding character of the Fe-CN bond, this is predicted to appear in a trans-Œ.L/4 FeIII -ŒCN-CuII .L4 /2 complex. 3 0 0 D4h 2 D4 0 D4h 0 5 2 0 0 D4h 2

s HD4h

(3.12)

The effect of tetragonal strain (Fig. 3.13) is e.g. shown in the bulk magnetic susceptibility, EPR and Mössbauer data of the CN-bridged heterodinuclear FeIII -CuII complex Œ.P/Fe-CN-Cu.N4 /.ClO4 /2 :3H2 O (P D ’; ’; ’; ’-tetrakis(onicotin-amidophenyl)-porphyrin) [42]. The stabilization of a non-degenerate 2 B2g ground state on FeIII (negative D4h ) and a small positive value of J.B2 / leads to a S 0 D 1 ground state and to an excited S0 D 0 state, estimated by EPR to be only

70


0:25 cm1 higher in energy. With the DFT values of J(E) and J.B2 /, we have been able to reproduce this energy gap with a strain energy of D4h D 1; 000 cm1 . The reported small values of the anisotropic and antisymmetric exchange parameters, extracted from a simulation of the EPR spectrum, nicely show the quenching of the orbital momenta due to the relaxation of orbital degeneracy of the 2 T2g ground state of FeIII . However, subtle effects from the ligand-enforced coordination geometry on the FeIII site may lead to a wide variation of the anisotropic splitting of the sublevels of S 0 D 1 to lead to a spin-singlet ground state .Ms0 D 0/ and to absence of an EPR signal, as reported for the CN derivative of the oxidized form of the enzyme cytochrome oxidase with a pair of ferromagnetically coupled CuII and low-spin FeIII sites, and a similar S 0 D 1 ground state [43, 44]. Based on these observations, qualitative rules toward a rational design of ŒFe.CN/6 3 -based SMMs have been formulated [25, 27]: 1. A large magnetic anisotropy with an easy axis of magnetization along the cyanide bridge is predicted for FeIII -MII .M D Cu; Ni/ pairs with linear FeIII -CN-MII bridging geometry and regular ŒFe.CN/6 3 octahedra. It arises from the orbital angular momentum in the 2 T2g ground state of the ŒFe.CN/6 3 subunit, transmitted to the cluster spin ground state by an orbital dependent exchange mechanism. An enhancement of the exchange anisotropy is predicted when combined with the single ion anisotropy of NiII with a negative sign of D (leading to an Ms D ˙1 < Ms D 0 splitting of the S D 1 ground state of NiII ). This implies tetragonally compressed NiII L6 octahedra with a tetragonal axis aligned along the bridge. 2. In contrast to the MnIII -based SMMs [5, 44–46], Jahn–Teller coupling is not generally in favor for SMM behavior in spin clusters composed of FeIII -CuII and FeIII -NiII cyanide-bridged exchange-coupled pairs. Both CuII and FeIII are Jahn–Teller active (for FeIII the JT coupling is relatively small but of the same order of magnitude as the spin-orbit coupling interaction). A trigonal distortion of the ŒFe.CN/6 3 site of as little as 2ı to 3ı is able to destroy the magnetic anisotropy, i.e. to reduce the spin anisotropy gap energy (ED or U ) in both the FeIII -CuII and FeIII -NiII pairs. This also is the case in trans-Cu-Fe-Cu and trans-Ni-Fe-Ni complexes. Therefore, in the synthesis of new SMM materials it is necessary to pay attention to the angular geometry and the electronic structure of the FeIII site. The Fe-CN bond is strong, and it is expected that distortions involving the Fe-CN fragment are less important. However, for cyanide complexes with other ligands in the coordination sphere of the FeIII site, this may change (e.g., in magnetic clusters composed of the FeN3 C3 units in ŒFe.Tp/.CN/3 (Tp D hydrotris(pyrazolyl)borate), which impose a trigonal geometry [47, 48], or in fFeIII .porphyrine/.CN/-CuN4 g-type complexes with a tetragonal symmetry [42]. Based on t2g orbital splitting (reported, based on EPR, to be as large as 2; 900 cm1 [49]) one expects that ancillary ligands may significantly modify the magnetic anisotropy. In particular, for cyanide complexes of FeIII with ligands which induce a 2 Eg ground state, an increase of the magnetic anisotropy of the FeIII -CN-MII pairs is expected.

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71

3. Symmetry reduction is found to increase the magnetic anisotropy in spin clusters with high symmetry and partial or complete cancellation of the FeIII -CuII and FeIII -NiII local anisotropy tensors, as in M3 Fe2 and M4 Fe4 . 4. The use of NiII instead of CuII complex fragments in MII -NC-FeIII pairs has the advantage that it yields more regular MII polyhedra; also, these fragments may add a negative single ion anisotropy contribution to the SMM in certain cases. This can be under chemical control (i.e., well designed ligands may enforce a tetragonal compression rather than elongation in the NiII -based precursor).

3.4 Magnetic Anisotropy in Linear Trinuclear Cu-NC-Fe-CN-Cu complexes A series of trinuclear complexes with bridging hexacyanometalates .ŒM1 .CN/6 3 ; M1 D CrIII ; FeIII ; CoIII / and two ŒM2 L2C end groups (L is a pentadentate bispidine ligand with amine/pyridine donors, M2 D CuII ; NiII ; MnII / has been prepared and its structural and magnetic properties have been characterized [27]. The model discussed in Section 3.3.1 was used to interpret the magnetic data of the linear complex trans-fŒ.L/CuII -NC2 -Fe.CN/4 gC (Fig. 3.14) [27]. Two different forms of the exchange Hamiltonian were used to fit the magnetic susceptibility and magnetization data, the conventional isotropic model 1 (Eq. 3.13) and the extended Heisenberg Hamiltonian (Eqs. 3.14, 3.15, model 2). There are two exchange coupling constants, J for the Cu-Fe and J 0 for the Cu-Cu interaction in model 1, and JE and JB for the Cu-Fe and J 0 for the Cu-Cu interaction in model 2. In addition, the orbital reduction factor k and spin-orbit coupling constant — were also taken into account. Parameter values from the best fit and simulated magnetic susceptibility and magnetization data are plotted in Figs. 3.15 and 3.16.

Cu

Fe Cu

Fig. 3.14 Plot of the molecular cation of the crystallographically analyzed trinuclear complex trans-FeIII ŒCuII L1 2 ClO4 (Adapted from Ref. [27])

Fig. 3.15 ¦T vs. T diagram of trans-Fe III ŒCuII L1 2 ClO4 ; solid line: simulation using model 2 Œg.Cu/ D 2:15, black squares: experimental points, dashed line: calculation adopting a non-distorted ŒFe.CN/6 3 octahedral complex (Adapted from Ref. [26])


χT / K cm3 mol−1

72 1.6

JE= 24.0 cm−1

1.5

JB =1.9 cm−1 2

1.4 1.3 1.2

k = 1.00

1.1

ζ =50.2 cm−1

J' = 2.0 cm−1

1.0 0

20

40

60

80

100

T/K

3.5

model 1

3.0 model 2

2.5 M/NAμB

Fig. 3.16 Magnetization (in units of NA B ) vs. field plot of trans-Fe III ŒCuII L1 2 ClO4 .T D 1:8 K/: experimental data (open squares) and calculated using best fit parameters from a ¦T versus T simulations with model 1 and model 2 (solid lines) (Adapted from Ref. [26])

exp

2.0 1.5 1.0 0.5 0

10

20

30

40 H/kG

50

60

70

80

Structural data indicate that the ŒFe.CN/6 3 fragment is significantly distorted; there are deviations of the cis-C-Fe-C angles .’cis / of ˙1:3ı from 90ı [27]. The observed geometry of the ŒFe.CN/6 3 center and angular overlap model parameters for the Fe-CN bond reported previously [20] were used to approximate the ligand field matrix in model 2 (Eq. 3.16). A good fit was obtained with values of JE and JB very close to those computed by DFT (JE D 19:4; JB D 1:6 cm1 [25]). An energy level diagram of the lowest spin states is shown in Fig. 3.17. From the calculated g-tensor (g1 D 0:54; g2 D 0:56 and g3 D 5:92), the lowest spin state is found to be highly anisotropic. However, the energy gap between the ground state and the lowest excited spin state is found to be only 0:14 cm1 . From the comparison of the D values, computed with a regular octahedral geometry of the ŒFe.CN/6 3 subunit .6 cm1 / and that derived from the observed geometry .0:14 cm1 /, it follows that the zero-field splitting is reduced by more than one order of magnitude when the crystallographically determined distortion is taken into account. That is, structural changes of as little as ’cis D 90ı ˙ 1:3ı are able to account for the

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73

28 24 E (cm−1)

20 16

Eg'

12

Eg"

8 4 0

Eu" ED

ED

C1

Eu" D4h

Fig. 3.17 Spin levels for trans-FeIII ŒCuII L1 2 deduced from a calculation using model 2 and best fit parameters from Fig. 3.15, with angular distortions at ŒFe.CN/6 3 from the X-ray structure (left) and with a regular, non-distorted ŒFe.CN/6 3 complex (right); the energies (in cm1 ) are: 0.0, 0:145 , 11.31, 27.27 (left) and 0.0, 6.02, 10.18, 12 90 (right); g-tensor values (normalized to Ms D ˙1=2) of the two lowest Kramers doublets are: g1 D 0:54, g2 D 0:56, g3 D 5:92 .E D 0:0/, g1 D 1:94, g2 D 3:38, g3 D 4:72 .E D 0:145 cm1 / (left) and g1 D g2 D 0:43.x; y/, g3 D 6:68.z/ .E D 0:0/, g1 D g2 D 1:46.xy/, g3 D 2:13.z/ .E D 6:02 cm1 / (right) (Adapted from Ref. [26])

decreased anisotropy. In line with this observation, field dependent reduced magnetization data do not show any significant nesting, i.e., there is no SMM behavior. 1 D J SO 1 .SO 2 C SO 3 / J 0 SO 2 SO 3 Hexc Hexc D OO 1 SO 1 SO 2 OO 2 SO 1 SO 3 J 0 SO 2 SO 3 2 3 J.E/ 0 0 OO 1;2 D 4 0 J.E/ 0 5 0 0 J.B2 /

T2g .Ÿ/2 T2g .˜/2 T2g .—/ 2 3 95 120 34 HLF .2 T2g / D 4 120 90 118 5 34 118 5

(3.13) (3.14) (3.15)

2

(3.16)

E.cm1 / W 216 67 158 2

T2g .Ÿ/0:36 0:40 0:84

2

T2g .˜/ 0:80 0:33 0:50

2

T2g .—/0:48 0:85 0:20

(3.17)

74


3.5 Computation of the Magnetic Anisotropy in Oligonuclear Complexes with Nearly Degenerate Ground States 3.5.1 Theory In Section 3.3.1 we have assumed a C4v pseudo-symmetry for each pair with the local axis z along the FeIII -CN-MII bridge to define two exchange parameters JŸŸ D J˜˜ D JE and J−− D JB2 ; the off-diagonal terms J in HO exc (Eq. 3.6) vanish in this symmetry. This allows using DFT and the broken symmetry approach to calculate the parameters JE and JB2 from first principles. In the general case of a low-symmetry bridge with violated linearity, all six independent parameters of HO exc (Eq. 3.6, i.e. JŸŸ , J˜˜ , J—— , JŸ˜ D J˜Ÿ ; JŸ— D J—Ÿ ; J˜— D J—˜ / have to be taken into account. In such a case and in the presence of closely spaced orbitals (near degeneracy) SCF procedures in DFT calculations usually break down and do not yield estimates of the symmetry-independent exchange parameters. Here, we therefore propose a new and user oriented ab-initio-based method to allow the calculation of all symmetry-independent exchange-coupling energies for a coupled pair of transition metal ions, and to use them, after an appropriate transformation, to represent the spin-Hamiltonian of the pair, with taking full account of the multiplet structure of both ions. Let us consider an oligonuclear complex derived from such dinuclear building blocks. As long as there is a 1:1 mapping of the ground spin eigenstates of the Hamiltonians of Eqs. 3.5 and 3.7 (i.e., the energy separation between the electronic ground and excited states is much larger than the exchange coupling energy), the parameters of Eq. 3.7 can be determined unambiguously, as shown in the examples in Sections 3.3 and 3.4, and the total Hamiltonian of the oligonuclear cluster is given by Eq. 3.18, where the single and double summations run over all ions .M1 ; M2 / and over all M1 -M2 pairs; Ti , Tj and Tij are the matrices, which transform the xl , yl , zl local Cartesian axes of each magnetic center [Ti .M1 /,Tj (M2 /] and each M1 -M2 exchange-coupled pair .Tij / into the global x, y, z axes; S0i and Sj are the spin operators in the global frame; Dij .Aij / and Dj are the zero-field splitting tensors due to exchange and the single center anisotropy, respectively, the latter pertain to ions such as NiII .S D 1/ or high-spin MnIII .S D 2/ with local spins .S / larger than 1/2. X HO total D f.Jij /S0i Sj C S0i .Tij Dij Tij /Sj C S0i .Tij Aij Tij /Sj g i 2M1;j 2M 2

C

X

j 2M 2

fSj .Tj Dj Tj /Sj CB Sj .Tj gj Tj /BgC

X

B S0i .Ti gi Ti /B (3.18)

i 2Fe

Starting with the spin-Hamiltonian which characterizes each L1 M1 -CN-M2 L2 pair (L1 and L2 are terminal ligands), we perform ab-initio (or DFT) calculations of the separate L1 M1 -CN and CN-M2 L2 fragment, using methods which are well documented (DFT [50] or ab-initio [51]). We therefore avoid the ambiguity with respect

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75

Fig. 3.18 The structure of the matrix U12 of MO coefficients of an exchange coupled M1 –M2 dinuclear complex, set up from the U1 and U2 MO matrices of the constituent M1 –Lb and Lb –M2 fragments with dimensions N1 and N2 , respectively; Nb is the number of basis functions due to bridging ligands, shared between the M1 and M2 fragments (shaded area)

to the choice of the localization procedure, needed to project magnetic orbitals from the MO’s of the dinuclear subunits, delocalized over the two paramagnetic centers. The orbitals belonging to each subunit are orthogonal to each other but overlap with orbitals of the other subunits. The MO matrix of the two units combines to the MO’s of the dinuclear fragments, U12 (Eq. 3.19, see Fig. 3.18 for a detailed description of its structure) and the overlap matrix S12 (Eq. 3.20). U1 and U2 are N1 N1 and N2 N2 matrices which collect the MO coefficients (with each MO represented by a column) of the two fragments (N1 and N2 are the basis set dimensions). We use a Löwdin orthogonalization (Eq. 3.21) which yields the orthogonal molecular orbitals C12 . U1 0 (3.19) U12 D 0 U2 Q 12 :U12 S12 D U 1=2

C12 D U12 :S12

(3.20) (3.21)

The elements of S12 are given by the simple products of the MO coefficients for a given atomic orbital on the bridging ligand (CN), shared between the two M1 L1 and M2 L2 fragments. Under the assumption of a weak overlap of fragments L1 M1 -CN and CN-M2 L2 , we can consider the five MOs on each fragment, dominated by d-functions, as natural orthogonalized magnetic orbitals (termed magnetic orbitals hereafter). An average-of-configuration (AOC) procedure at the ab-initio (or DFT) step of the calculation of each unit (1 or 2) can be used to provide a set of magnetic orbitals which are common to all microstates (configuration state functions, CSF) belonging to a given configuration .dn1 or dn2 ). We can use these to calculate the spin-dependent part of the energy, due to each of the .i; j /, i 2 1I j 2 2, pair, using second-order perturbation theory. Let us denote by ai and aj the magnetic orbitals on fragments M1 and M2 , and by ¥p ; ¥0p and ¥q ; ¥0q the MO’s which are doubly occupied and empty in the electronic ground state of the two fragments. It has been shown [52] that each pair of magnetic orbitals yields a contribution of Jij .Osi sOj / to the spin-dependent part of the energy (the other term, Jij;kl .Osi sOj /.Osk sOl /, will be neglect in the following). A master formula for Jij in terms of elementary

76


excitations (Eq. 3.22) has been reported [52] and applied in ab-initio studies on the singlet-triplet separation of simple dinuclear CuII complexes [53]. In Eq. 3.22 short hand notations of two-electron integrals (Eq. 3.23) are used, and energies of oneand two-electron excitations E as well as the transfer integrals t are defined as positive. np and nq denote occupation numbers for orbitals which are not involved in the magnetic exchange (including examples with np D nq D 1/ and Œi $ j stands for the expression obtained by interchanging i and j in the preceding term; k denotes any of the magnetic orbitals on M1 and M2 which differ from i and j. We note that Eq. 3.22 can only be applied if electronic states with unpaired electrons, dominated by the 3d-functions, are well separated from charge transfer states, a prerequisite for the use of perturbation theory. This is well fulfilled in complexes of transition metal ions in “normal” oxidation states (Werner-type complexes) [14]. In Eq. 3.22 we identify the first term as the positive Heisenberg integral (potential exchange [54]) which is always positive and yields ferromagnetic exchange coupling. The term in the second line is the well known kinetic exchange energy [55] (superexchange), leading to antiferromagnetic coupling. This vanishes if, by symmetry, the magnetic orbitals are strictly orthogonal [56]. There are six more terms, which include single excitations from (to) the doubly occupied (empty) orbitals [third and fourth terms; these are also antiferromagnetic in nature and are denoted as hole (particle) polarizations] and double excitations (terms in the sixth to eighth line which are all antiferromagnetic, referred to as to as the ligand-to-metal, metal-to-ligand and kinetic exchange plus polarization energy terms, respectively). The fifth term corresponds to the double spin-polarization and yields ferromagnetic contributions to Jij . The components of the exchange coupling of Eq. 3.22 are visualized in Fig. 3.19 and have been found in computational studies on exchange coupled dinuclear CuII complexes to yield important contributions to Jij [53], [56]. X ˛ ˛2 ˝ ˝ Jij D 2 ai aj jai aj C .1=2/ aj ak jak ai =E.j

i / C Œi $ j

k¤i;j

t .aj ai /2 =E.j i / Œi $ j X ˛ ˛2 ˝ ˝ np Œ2 p ai jai aj t .aj p / C aj ai jai p =E.j p¤i;j

X

˝ ˛ .2 nq /Œ2 ai aj jaj q t .q

p/ Œi $ j

˝ ˛2 ai / C q aj jaj ai =E.q

i / Œi $ j

q¤i;j

X

˛˝ ˛ ˝ np .2 nq / q ai jai p q aj jaj p =E.q

q;p¤i;j

X

˛˝ ˛ ˝ .1=2/np np 0 Œ p 0 p jai aj ai aj jp p 0 =E.ij

p;p 0 ¤i;j

X

q;q 0 ¤i;j

X

(3.22)

p/ pp 0 /

˝ ˛˝ ˛ .1=2/.2 nq /.2 nq0 /Œ aj ai jq q0 q q0 jai aj =E.qq 0

˝ ˛2 ˝ ˛˝ ˛ np .2 nq /Œ ai q jaj p ai q jaj p ai q jp aj =E.i q

q;p¤i;j

habjcd i

Z

a.1/ b.2/ .1=r12 /c.1/d.2/d 1 d 2

ij/ jp/ Œi $ j (3.23)

3


77

Fig. 3.19 Electronic excitations which contribute to second order to the exchange coupling energy (Jij ) between the spins of the electrons on magnetic orbitals ai and aj (Adapted with modifications from Ref. [56], p. 157)

With the assumption of a weak coupling between the magnetic orbitals ai and aj of neighboring paramagnetic units, we can identify these orbitals as ligand field orbitals. However, being diagonal with respect to the one-electron ligand field operator, these orbitals and the set of Jij integrals are not of immediate use in Eq. 3.5. In a series of papers we have developed a procedure [12–15] that allows deducing the parameters of the ligand field from DFT calculations. This procedure can be applied equally well to results from ab-initio-based electronic structure methods. For a brief introduction to the method, let us denote the Kohn-Sham (KS) orbitals, dominated by 3d-functions, which result from an AOC dn KSDFT-SCF calculation, with col! umn vectors V i , and their energies with "KS i ; the latter define the diagonal matrix E. From the components of the eigenvector matrix, built-up from such columns, one takes only the components corresponding to the d-functions. Let us denote the square matrix composed of these column vectors by V and introduce the overlap matrix Sd : (3.24) Sd D VT V Since V is in general not orthogonal, we use a Löwdin’s orthogonalization to obtain an equivalent set of orthogonal eigenvectors .Cd /: 1

Cd D VSd 2

(3.25)

78


We now identify these vectors with the eigenfunctions of the effective ligand field Hamiltonian heff LF 5 X 'i D ci d .i D 1 to 5/ (3.26) D1

and "KS D h'i j heff i LF j'i i with the corresponding eigenvalues. The 5 5 LF matrix VLF D fh g is given by: ( VLF D

Cd EC1 d

D fh g D

5 X

) ci "KS i ci

(3.27)

iD1

Using the matrix Cd , calculated for each subunit, 1 and 2, we can transform the exchange coupling integrals Jij of Eq. 3.22 into quantities related to M1 and M2 basis functions of the ligand field operators, as defined in the common coordinate system (J12;¡2£1 ; as subscript numbers 1 and 2 we indicate to which fragment a given orbital belongs (Eq. 3.28); for each pair within the oligonuclear complex, there are 120 such integrals), given by the unitary transformation (Eq. 3.29). Z J 1 2;21 D J 1 2;21 D

d 1 .1/d2 .2/.1=r12/d2 .1/d1 .2/d 1 d 2

5 5 X X

c 1i c2j c2j c1i Jij

(3.28) (3.29)

i D1 j D1

In terms of J12;¡2£1 , the exchange operator (i.e. the first term of Eq. 3.5) can C C be written in a second quantized form (Eq. 3.30), with ' 1 ; 'v2 and '1 ; '2 the creation and annihilation operators. We thus arrive at a general form of the model Hamiltonian (Eq. 3.5) with all parameters deduced from first principles. 0 O s1 Os2 / D @ O exc D O.O H

5 X 5 X 5 5 X X

1 C C A J 1 2;21 ' 1 ' 2 '1 '2 .Os1 Os2 / (3.30)

D1 D1 D1 D1

With the example of the CuII -FeIII pair, the basis set consists of a total of 2,520 Slater determinants (antisymmetrized products due to the 10 microstates of CuII O in H O exc operates on the ortimes the 252 microstates of FeIII ). The first operator O 1 2 bitals, and assuming that '1 .M / and '2 .M / are singly occupied, it will convert '1 .M1 / into ' 1 .M1 / and '2 .M2 / into ' 2 .M2 /. According to Eq. 3.30, the second term acts only on spins and creates diagonal and off-diagonal exchange matrix elements. Therefore, we obtain the spin levels of each M1 -M2 pair and its exchange tensors (Eq. 3.5) from first principles, free from any approximation as to the form of the exchange parameters within the subspace of the microstates of M1 and M2 . From calculations on the L1 M1 -CN and CN-M2 L2 fragments obtained in a previous step, zero-field tensors (for ions with S > 1=2) are also available. Combining these

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79

tensors in Eq. 3.18 (the matrices of unitary transformations, Tij , Ti and Tj reduce to the identity matrix when working in a common coordinate frame) we get a simple and efficient method, allowing one to circumvent the so far technically unsolvable problems, when trying to get spin levels of a large oligonuclear magnetic cluster using correlated electronic structure methods.

3.5.2 Applications to Various Cyanide-Bridged Mn Fem Complexes .M D C uII , Ni III /[25] The first principles method described in the preceding section in its full version (i.e. accounting for the complete set of exchange integrals) is an ambitious task which has yet to be implemented in quantum-chemical codes. As a first illustration, sample calculations of the spin levels of complexes with FeIII and CuII or NiII , based on the vector coupling scheme given by Eq. 3.18 have been performed. The topologies and coordinate systems are specified in Fig. 3.20. The exchange coupling tensors of the FeIII -CuII and FeIII -NiII pairs with linear Fe-CN-M bridges and no angular distortion in ŒFe.CN/6 3 assume a simple form with only two exchange parameters (D and J ) to describe each pair (see Section 3.3.1). The local g and D-tensors of the dinuclear units have been coupled to yield the spin levels and magnetic properties of the entire magnetic clusters. The spin energy gaps between the ground states and the lowest excited states, the ground state spin degeneracies and magnetizations in dependence of the direction and the magnitude of the applied magnetic field [low field (B D 0:2T) and high field (B D 7T) limits] are included in Table 3.2, and

Fig. 3.20 Oligonuclear spin clusters based on FeIII -MII pairs (M D Cu,Ni) with linear FeIII -CN-MII bridges, used to calculate the data in Tables 3.2 and 3.3 (Adapted from Ref. [25])

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Table 3.2 Energies (in cm1 ) and multiplicities of the ground statea and lowest excited spin states, and field dependent ground state magnetizations (Mx , My and Mbz in Bohr magnetons) of highly symmetric oligonuclear model spin clusters built from FeIII -MII cyanide-bridged pairs (M D Cu, Ni).c;d Lowest excited Ground spin-state B D 0:2T B D 7T state Compl. mult. E Mult. Mx My Mz Mx My Mz CuFe 1 0.53 1 0.11 0.11 1.02 1.74 1.74 1.86 NiFe 2 4.30 2 0.14 0.14 3.16 2.95 2.95 3.16 trans-Cu2 Fe 2 6.22 2 0.28 0.28 2.85 2.61 2.61 2.85 trans-Ni2 Fe 2 4.30 4 0.24 0.24 5.46 5.00 5.00 5.46 cis-Cu2 Fe 2 0.64 2 1.22 2.24 2.24 2.68 2.89 2.89 cis-Ni2 Fe 4 1.78 4 0.80 4.33 4.33 5.10 5.34 5.34 Cu2 Fe2 1 1.29 1 0.67 0.67 0.17 3.70 3.70 3.24 Ni2 Fe2 4 1.93 4 4.67 4.67 0.73 6.21 6.21 5.59 Cu3 Fe2 2 1.11 2 2.78 2.78 2.32 4.67 4.67 4.47 Ni3 Fe2 1 0.35 3 3.92 3.92 1.57 8.31 8.31 8.37 Cu4 Fe4 1 2.37 2 1.08 1.08 1.08 7.23 7.23 7.23 Ni4 Fe4 4 0.21 12 9.23 9.23 9.23 12.20 12.20 12.20 a

Energies of the spin ground states are taken to be at zero. Magnetizations Mx , My and Mz with respect to the global Cartesian axes as defined for each model complex in Fig. 3.20. c Data for the constituting FeIII -MII dinuclear units are given for the sake of comparison. Calculations have been done using the pair model (Eq. 3.18) adopting a regular (non-distorted) octahedral ŒFe.CN/6 3 and assuming a fourfold (pseudo)symmetry of each M-NC-Fe bridge and coupling the local gi and Dij tensors of each pair toward the tensors of the total cluster; values of the isotropic spin-coupling energy J and the parameter D, defining the local anisotropy D-tensors for each M-Fe pair are 4:49, 5.93 .FeIII -CuII / and 2:87, 4.30 (FeIII -NiII ); other parameters are k D 0:79, — D 345 cm1 (for Fe); g-tensor values: gx D gy D gz D 2:30 (for NiII ); gx D gy D 2:18, gz D 2:00 (CuFe, Cu2 Fe); gx D gy D 2:05, gz D 2:25 and taking directions of gix;y and giz within and perpendicular of each Fe1-Cui -Fe2 (i D 1; 2; 3) plane for Cu3 Fe2 ; gx D gy D gz D 2:116 .Cu2 Fe2 and Cu4 Fe4 ). d Systems with a field independent magnetic moment and strong anisotropy are underlined. b

g-tensor values for the spin clusters with a doubly degenerate (bistable) ground state are listed in Table 3.3. Only in three of the systems, i.e. linear Fe-Ni, trans-CuFe-Cu and trans-Ni-Fe-Ni, a sizeable spin gap energy is calculated, comparable in magnitude with that reported for Cu3 Fe2 .D D 5:7 cm1 [48]). In these examples, a large and field-independent magnetization along the easy axis (z-direction) and almost zero perpendicular magnetization are obtained, and the g-tensor components are found to reflect this anisotropy (Table 3.3). A very small spin energy gap is calculated in all other systems. As follows from the field-dependent ground state magnetization values (Table 3.2), there is a strong effect of the magnetic field on the ground state via mixing of the closely lying ground and excited spin states. There is a cancellation of the large anisotropy of each of the FeIII -CuII and FeIII -NiII pairs when coupling their local D12 - and g-tensors to magnetic clusters of high symmetry, as in

3


Table 3.3 g-Tensor component valuesa of oligonuclear model spin clusters with CuII or NiII and FeIII with doubly degenerate (bistable) spin ground statesb

81

Spin Cluster

gx c

gy c

gz c

NiFe trans-Cu2 Fe trans-Ni2 Fe cis-Cu2 Fe Cu3 Fe2

0 0.379 0 2.294 4.862

0 0.379 0 3.860 4.862

6.351 5.693 10.920 3.860 4.160

a

See Fig. 3.20 for the definition of the global Cartesian axes x, y and z of each spin cluster. b See Ref. [25] for numerical values and definition of the local CuII g-tensors. c g-tensor values are given with respect to a s0 D 1=2 effective spin; to get the g-tensor component of the real spin the numbers of the table have to divided with the total number of 12 spins, i.e. with 3(NiFe), 3.trans-Cu2 Fe/, 5.trans-Ni2 Fe/, 3.cis-Cu2 Fe/ and 5 .Cu3 Fe2 /. Table 3.4 Deviations of the angle C-FeIII -C.•’/ from the value of ’ D 90ı , which defines a ŒFe.CN/6 3 complex without angular distortions, of the angles FeIII -C-N .•“/ and C-N-MII (M D Cu; Ni) .•”/, in (ı ) from the values of 180ı for undistorted linear Fe-C-N-M units, as derived from structural data on Cu3 Fe2 [48] and Ni3 Fe2 [47] spin clusters

Complex (M-Fe pair) Cu3 Fe2 : Fe4 -Cu1 Fe4 -Cu2 Fe4 -Cu3 Fe5 -Cu1 Fe5 -Cu2 Fe5 -Cu3 Ni3 Fe2 : Fe4 -Ni1;2;3 Fe5 -Ni1;2;3

•’ .C-FeIII -C/

•“ .FeIII -C-N/

•” .C-N-MII )

3:1 0:8 1:8 3:6 3:4 0.9

2:4 3:1 3:6 3:2 1:9 2:8

10:4 7:3 8:8 6:0 8:3 8:5

1:9 0.5

0:8 0:9

4:2 10:8

the M3 Fe2 and M4 Fe4 complexes (M D Cu, Ni). Magnetic anisotropies for Cu3 Fe2 , both in the magnetization and g-tensors, are found to be small. This is in contrast to the measured high anisotropy in the Cu3 Fe2 SMM [48]. Parameters for the angular distortions within the bridging Fe.CN/3 site [see the deviation of the C-Fe-C angles from 90ı .•’/] and for the distortion of the Fe-CN-M bridges from linearity [see the deviations of the Fe-C-N (•“) and C-N-M (•”) angles from 180ı] are listed in Table 3.4. With a Jahn–Teller coupling mechanism, there is a large dependence of the parameters of the exchange Hamiltonian on the distortions •’, as reflected by the energy ED . These distortions are very large for Fe2 M3 .MII D Cu and Ni, Table 3.4), and therefore expected to strongly influence the spin levels and magnetic properties. However, variations of •’ are irregular and do not allow to apply the simple symmetry-based Jahn–Teller description. Therefore, a full calculation, using the exact angular geometry in each magnetic cluster, is mandatory when modeling the magnetic data and this is planned to be done in the future studies. In addition to •’, the geometry of the Fe-CN-M bridge is expected to affect the anisotropy. As the FeIII -CN bond is stronger than the CN-MII bonds (M D Cu, Ni), variations of the C-N-M angle (•”) due to angular strain and packing forces are

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expected to be larger than those for the Fe-C-N angle (•“). This is supported by the data in Table 3.4. It has been shown experimentally [57] and by DFT calculations [58], that non-zero values of •” will decrease the overlap of magnetic orbitals and reduce the exchange coupling energy JE . In contrast, JB is expected to increase in magnitude. This needs to be taken into account in quantitative case studies using of the method described in Section 3.5.1. From the comparison between the computed results with model clusters of high symmetry and the reported magnetic data, we conclude that symmetry reduction, as revealed by the reported angular distortions, plays a differing role in trans-M2 Fe, M3 Fe2 and M4 Fe4 complexes (MII D Cu, Ni). Angular distortions reduce the magnetic anisotropy of the linear Cu-Fe-Cu and Ni-Fe-Ni structures but induce anisotropy in complexes of higher symmetry such as M3 Fe2 (D3h ) and M4 Fe4 .Td /. This is supported by experimental data on highly symmetric CuII 6 FeIII 8 cyanidebridged face-centered cubic clusters with SMM behavior [59, 60]. A large and accidental ground state degeneracy of four is predicted for the regular cis-Ni2 Fe, Ni2 Fe2 and Ni4 Fe4 spin clusters with C2v , D2h and Td symmetry, respectively, and an even larger degeneracy (12) is found in the lowest excited state of Fe4 Ni4 , which lies only 0.21 eV above the ground state. When coupled to angular distortions, these degenerate ground states can be modified by antisymmetric exchange, which can be very large already for small values of •’. This might help to explain the atypical relaxation behavior reported for the Fe4 N4 SMM [61].

3.6 Conclusions We have shown that there are appropriate theoretical methods for predicting the exchange coupling [62] and magnetic anisotropy of paramagnetic oligonuclear transition metal complexes [25, 27]. Based on these calculations it has been possible to derive qualitative rules for the design of hexacyanometalate-based SMMs [27]. An important and expected observation is that subtle structural changes lead to significant modifications of the magnetic exchange and anisotropy and therefore generally to a lower than anticipated anisotropy barrier. Interestingly, a reduction of the anisotropy is observed for deviations from linearity of the M-CN-M0 pair, and this is often found to be the result of Jahn–Teller coupling and/or structural or bonding strain. It emerges that the ligand-enforced control of the coordination geometry is an important tool for the design of novel SMM materials [63, 64]. Also, the design must be based on efficient and accurate methods for the structural modeling which then may be followed by single-point calculations of the electronic and exchange parameters. We have shown that, based on LFDFT, broken symmetry DFT and a vector coupling approach [25], there are efficient methods for the prediction of the electronic properties based on a known structure. It is our belief that molecular mechanics calculations are not only much more efficient but, with the correct method and force field, also lead to very accurate optimized geometries [65–73]. Therefore, apart from the need for viable preparative methods, a major requirement

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for developing novel and efficient SMMs seems to be in the area of efficient and accurate structure optimization. Acknowledgments Our studies have been supported by the German Science Foundation (DFG) and the University of Heidelberg. M.A. is grateful to Dr. P.L.W. Tregenna-Piggott (PSI and ETH Zürich) for generous support and encouragement during the preparation of this manuscript.

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Chapter 4

Structure and Function: Insights into Bioinorganic Systems from Molecular Mechanics Calculations Helder M. Marques, Timothy J. Egan, and Katherine A. de Villiers

Abstract The use of empirical force field methods for modeling important systems in bioinorganic chemistry, including the cobalt corrins (derivatives of vitamin B12 ) and the iron porphyrins, is described. Particular attention is given to the use of molecular dynamics and simulated annealing calculations in exploring the solution structures of corrin, and those of likely complexes between the ferriprotoporphyrinIX and the arylmethanol antimalarials.

4.1 Introduction Studies in bioinorganic chemistry have utilized a veritable armory of experimental techniques and methodologies drawn from the physical, chemical, mathematical and biological sciences. The advent of cheap computing power since the 1980s – and the development of the academic and commercial software packages that make the methodology readily accessible – has made computational chemistry methods useful adjuncts to the traditional methods of exploring molecular structure. In particular, there has been an explosion in the use of DFT methods and whilst the methodology may not provide all the answers [1], the insights gained are impressive (for example, Refs. [2–5]). Quantum mechanics/molecular mechanics (QM/MM) methods in which a quantum mechanical treatment of the active region (cofactor, substrate) and a molecular mechanics treatment of the surroundings (protein, solvent) is employed, is now a common strategy for exploring enzymatic processes

H.M. Marques () Molecular Sciences Institute, School of Chemistry, University of the Witwatersrand, P.O. Wits, Johannesburg, 2050 South Africa e-mail: [email protected] T.J. Egan () Department of Chemistry, University of Cape Town, Private Bag, Rondebosch, 7700 South Africa e-mail: [email protected] K.A. de Villiers Department of Chemistry and Polymer Science, University of Stellenbosch, Private Bag X1, Matieland, 7602 South Africa P. Comba (ed.), Structure and Function, DOI 10.1007/978-90-481-2888-4 4, c Springer Science+Business Media B.V. 2010

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[6, 7]. Given the ready applicability of these quantum-mechanical methods, is there still a place for molecular mechanics (MM) or empirical force field calculations in bioinorganic chemistry?

4.2 The MM Method The central tenet in MM, that structure can be described with a model founded on classical mechanics [8, 9] and is a “classical parameterization of non-classical effects” [9], has been in the literature for many years [10–13]. The molecule is treated as a set of interacting atoms and the energy consequences of all interactions describes a molecular potential energy hypersurface on which minima correspond to stable conformations, and the global minimum corresponds to the thermodynamically most stable molecular conformation. The inter-atomic interactions are described by structural parameters such as bond lengths (r), valence angles (), dihedral angles ( ), electrostatic and van der Waals interactions, and out-of-plane deformations (to treat, for example, carbonyls and aromatic systems). Each such component is treated by a potential energy function (cross-functions can be used) and the total strain energy, Estr , of the system is the sum of the contributions from each factor (Eq. 4.1). Associated with each structural parameter, p, is an equilibrium or ‘strain-free’ value, po . When the system is subjected to a deformation, a restoring force, often taken to be harmonic, operates (Eq. 4.2). The force constant, kp , is a measure of the resistance of p to the deformation. The contribution that components make to the strain energy, Ep , (Eq. 4.3) is the integral of Eq. 4.2. The functions Ep and the (po , kp ) values together constitute the MM force field. Estr D Er C E C E C Evd Waals C Eelec C Eoop @E D kp .p po / F D @p Ep D 1=2kp .p po /2

(4.1) (4.2) (4.3)

Critical in the MM method is the definition of an atom type because specifying an atom type implies a value for ro , o , o , and so on, and the associated k parameters. For example, the ro value for a C.sp2 /–C.sp2 / double bond is the same irrespective of where the atoms are in a molecule. The parameters for other carbon atoms (aliphatic, aromatic, carbonyl C in acids, etc.) are different. Insofar as bioinorganic chemistry is concerned, parameters for metal ions depend on the ion’s oxidation state, spin state, coordination number and coordination geometry. This highlights one of the major disadvantages of MM methods: it is difficult to have a “universal force field” that will reliably describe the structure of a wide range of compounds. Since MM is an interpolative method [9], the researcher has to ensure

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Fig. 4.1 The structure and standard numbering scheme of porphyrins and cobalt corrins

that the force field to be used has been adequately parameterized and validated for the system of interest. Failure to appreciate this has led to inappropriate applications of the methodology and has probably contributed to the skepticism with which MM calculations are not infrequently viewed. Some generalized force fields have indeed been developed; among the most successful are the MOMEC force field of Comba and colleagues [14], the Universal Force Field (UFF) of Rappé and coworkers [15], and the SHAPES force field of Allured, Kelley and Landis [16]. But the quality of the results is often poorer than a properly parameterized force field for a given system. We believe the methodology is still useful for studying systems that do not involve a change in electronic structure and that these computationally inexpensive calculations can still provide real insight into many questions in the discipline, provided a properly parameterize force field is used. We illustrate this with some examples from our work on the modeling of porphyrins and cobalt corrins (see Fig. 4.1).

4.3 Handling Metal Ions A well-established force field used for modeling organic compounds (such as MM2 or MM3 [17–19]) or proteins (such as AMBER [20]) is often sufficiently robust to reproduce the structure of the organic framework of a bioinorganic system. What is required are parameters for the coordination sphere of the metal ion: for the metal

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itself, and often for the donor atoms and their near neighbors since the polarizing effect of the metal ion may make the standard parameters unsuitable [21]. New atom types usually have to be defined and their associated parameters developed. There are different ways of treating the coordination sphere of metal ions [22–26]. Where the bonding between the metal (M) and the ligands (L) is predominantly ionic, as in complexes of the group I and II metals [27–29], it may be unnecessary to specify either a M–L bond length or any of the L–M–L valence angles. The coordination environment is then controlled by balancing the electrostatic and non-bonded interactions between the donor atoms and the metal, and between the donor atoms themselves and their neighbors. In the ‘points-on-a-sphere’ model [30,31], M–L bond distances are specified but the L–M–L valence angles are not; instead 1,3-nonbonded interactions between the ligand donor atoms are used to model the coordination sphere [32–34]. This is therefore the computational analog of the well-established VSEPR model that has been so useful in the structural chemistry of the main group and the f block. The approach runs into problems in d block chemistry, where structure is often dictated by the electronic effects of the partially filled d shell. So, the model will not reproduce a square planar structure and will converge instead to a tetrahedral one, and it will produce a trigonal bipyramid instead of a square pyramid. To overcome this, one might add restraints to the force field in the form of parabolic [35] or outof-plane functions [36], or dummy atoms [37], or use a force field which has been augmented to take into account ligand field effects [38, 39]. The most common approach, especially for small coordination complexes, is to treat the metal ion as any other atom, and develop parameters for metal–ligand bonds and valence angles involving the metal (for example, Refs. [35, 40–44]), whilst torsional barriers about the metal are usually set to zero. Force fields (such as AMBER) that have a Coulomb law expression for handling electrostatics require that partial charges be assigned to all atoms in the molecule, and this in itself is not a trivial problem [45–49]; in force fields (such as MM2) where electrostatics are handled by means of bond dipole moments, M–L dipole moments are usually set to zero [44, 50–52] and the electrostatics are subsumed into the M–L bond stretching and L–M–L angle bending terms. A separate set of parameters has to be developed for each oxidation state, spin state, coordination number and coordination geometry, and interconversion is not possible. This, together with the unique labeling problem [53], means that there are many parameters that have to be developed before reliable and meaningful results can be obtained.

4.4 Extending the Force Field A variety of schemes have been employed to extend established force fields such as MM2 and AMBER to deal with systems containing metal ions. Parameters from normal coordinate analyses can be useful as a starting point [50] but force

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field parameters from vibrational spectroscopy are not the same as those for MM calculations [9]. The parameters are usually derived to reproduce experimental data (solid state structures, vibrational frequencies, heats of formation) and are fitted to the experimental data either by a trial-and-error method [23,24,54] (which is tedious and questions of bias may arise [55]) or by some optimization routine [56–64]. We have found in the modeling of metalloporphyrins and cobalt corrins (derivatives of vitamin B12 / that the ‘points-on-a-sphere’ model produces significantly poorer results than those obtained if M–L and L–M–L parameters are specified, and we have settled on the latter. We have used trial-and-error methods to reproduce crystal structures as accurately as possible, in developing parameters for extending the MM2 force field for modeling iron porphyrins [44, 51, 65, 66] the cobalt corrins [35] and cobaloximes [67], and for the AMBER force field for modeling cobalt corrins [68]. In each case a representative set of structures was chosen from the Cambridge Structural Database (CSD) [69], and the parameters were evaluated by assessing the ability of the force field to reproduce structures that had been left out of the training set, or synthesizing a novel compound, crystallizing it, and comparing its molecular structure to that predicted by the MM modeling [70]. When developing the force field for the cobalt corrins we conducted a survey of Co(III) corrin structures in the CSD and determined the mean values of the bond lengths, bond angles and dihedral angles. We divided atoms into classes based on chemical intuition and calculated the mean and standard deviation of classequivalent bond lengths and bond angles. Differences between classes were checked for statistical significance and the number of classes was reduced as far as possible. We initially set values of ro and o to the crystallographically observed mean values and set the initial values of the force constants to those used in MM2 for analogous situations, to values we had used in modeling the iron porphyrins (see below), or to values used by others in the MM modeling of Co(III) compounds. The crystal structure of cyanocobalamin (CNCbl) was used as the test structure. After each energy minimization, a random number generator was used to change the coordinates of every atom to check conformational space in the neighborhood of the converged structure. The values of the structural parameters obtained were compared with the values from the statistical survey, and the force field parameters were adjusted on a trial-and-error basis until an acceptable fit to the average crystallographic values was obtained. The final force field parameters [35, 67] re˚ 2:4ı and produced the bond lengths, bond angles and dihedrals to within 0.01 A, ı 4:2 , of the crystallographic averages, respectively. Force fields ideally reproduce ˚ for bond lengths, 1ı for bond angles and these structural metrics to within 0.01 A a few degrees for torsions [15, 71, 72]. It needs to be emphasized that approaches such as this will reproduce an average structure. If a direct comparison is made between such a structure and the solid state structure of any specific cobalamin, differences will almost invariably be found, especially in the more flexible parts of the molecule. The force field was validated by satisfactorily predicting the structures of cobalt corrins not used in the training set [73, 74] or synthesizing and determining

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the crystal structure of a novel cobalt corrin [75]. A similar strategy was followed in deriving parameters for modeling cobalt corrins with the AMBER force field [68]. This augmented AMBER force field has been used by several groups to investigate the structure of Co(III) complexes as HIV type 1 integrase inhibitors [76], B12 binding proteins [77, 78] and aspects of B12 enzymomology [79–82]. In developing MM2 parameters for the first row metalloporphyrins [83–85] we adopted a somewhat different approach. The training set was still derived from CSD structures, with representative examples deliberately omitted and used for validating the parameters. We found that the parameters we used [51] for modeling ferrous and ferric porphyrins, in all their spin states, were, with some very minor changes, quite adequate for modeling all metalloporphyrins. Porphyrins are remarkably flexible molecules and the porphyrin core can adopt a range of deformations [86] as illustrated schematically in Fig. 4.2. The MM model of the porphyrin core adequately reproduced the flexibility of the porphyrin core; two representative examples are shown in Fig. 4.3. We used artificial neural networks (ANNs) [87,88] to develop parameters for the M–L bond lengths and L–M–L bond angles by defining the error function, err, as the mean difference between the modelled and the experimentally observed structural parameters. We then used a trained ANN (Fig. 4.4a) to discover the minimum in err (Fig. 4.4b). Where there were insufficient structures in the CSD to obtain reliable parameters, as in the case of Sc(III) porphyrins, we synthesized new porphyrins to add them to the ANN training set [89].

Fig. 4.2 The distortions of a porphyrin from planarity can be visualized as a combination of six common distortion modes, written here in terms of the irreducible representations of the D4h point group. The (C), (0) and () signs refer to atoms above, in and below the mean porphyrin plane, respectively

Fig. 4.3 The MM structure (—-) and solid state structure ( ) of (a) [Co(TPOMeP)] (CSD reference code TEFPEZ [90]) and (b) [Co(tetra-heptafluoropropyl)P] (SIRROA [91])

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Fig. 4.4 (a) Experimental design for determining the optimum Cu(II)–N bond length in Cu(II) porphyrins. Shown are the learning set ./, the initial training set ./ and the second training set .4/. (b) An example of an error response surface with the global minimum discovered by the ANN architecture ./

4.5 Applications of the Corrin Force Field: Structure and Function of B12 Derivatives We have used the cobalamin force field to investigate a number of aspects of B12 chemistry. We explored the structure of several alkylcobalamins [92]. We found an inverse relationship between the bond dissociation energy for the Co–C bond and the steric strain in the complex which suggests that steric strain, induced for example by a conformation change in the enzyme on substrate binding, could be a factor in the homolysis of the Co–C bond, the first step in the reaction of AdoCbl-dependent enzymes. The cobalamin force field has been extremely useful for our work on structural analogs of the Ado ligand. Many of these AdoCbl analogs fail to crystallize despite extensive attempts and we have relied on MM modeling to explore their structure. We have reported work on Ado-13-epiCbl [93], in which epimerization at C13 places the e propionamide side chain in an “upwardly” axial position and hence destabilizes the structure of AdoCbl seen in the solid state [94]; on an analog of AdoCbl in which the configuration of the N -glycosidic bond in the Ado ligand is inverted (’-ribo)AdoCbl [95]; on 3-isoAdoCbl, in which the N -glycosidic bond of the adenosyl ligand is to the adenine N3 nitrogen instead of the normal N9 [96]; and on Ado(Im)Cbl, the coenzyme B12 analog in which the axial 5,6-dimethylbenzimidazole ligand is replaced by imidazole [97]. These have all provided insights into the structure of the active site of the B12 -requiring enzymes. The cobalamin force field has also been used to generate structures that we have then explored by semi-empirical methods in an attempt to assess the feasibility of the mechanochemical trigger hypothesis, which envisages upward flexing of the corrin in response to a conformational change in the protein on binding of substrate, and which, through steric effects, causes labilization of the Co–C bond [98, 99].

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4.6 Applications of the Corrin Force Field: The Structure of the Cobalt Corrins in Solution One of the problems that researchers in B12 chemistry face is that many compounds of interest fail to crystallize. Moreover, there is always the perennial question of whether the solid state structure is indeed the same as the structure in solution. To address these questions we have made use of nOe-restrained molecular dynamics and simulated annealing (MD/SA) calculations to explore the structure of a variety of cobalt corrins in solution [94,100–104]. Aspects of this work have been reviewed [24, 105]. The technique relies on the observation of two-dimensional homonuclear (TOCSY and ROESY) experiments with Watergate solvent suppression and heteronuclear (HSQC and HMBC) experiments for resonance assignment [93, 106]. The distance restraints for the MD/SA were obtained from nOe cross peaks (excluding those resulting from geminal hydrogens) in the ROESY spectrum. The cross peaks were classified as strong, medium, weak, or very weak [107] depending on whether they first appeared in the ROESY spectra at mixing times of 50, 100, 150, or 200 ms, respectively in a 600 MHz spectrometer (40, 80, 120, and 160 ms on a 800 MHz spectrometer). A set of parabolic potential energy functions, where the restraining force constant is given by knOe D kB T S=2.ij˙ / [2, 108] where kB is the Boltzmann constant, T the Kelvin temperature, S a scaling factor, and ij ˙ the positive and negative error estimates of rij . We typically take S D 1, T D 300 K, ˚ and ij C D ij . Strong, medium, and weak nOe’s are expected when rij < 2:7 A, ˚ and 3:4 A ˚ < rij < 4:0 A ˚ [108]. We usually use rij D 2:5, 3.0, ˚ < rij < 3:4 A 2:7 A ˚ for strong, medium, weak, and very weak nOe’s, respectively, so that 4.0, and 4:5 A ˚ 2 at 300 K for these four classes knOe D 1:2, 0.52, 0.3, and 0:075 kcal mol1 A of nOe’s. For strong and medium nOe’s, violations of these distance restraints are ˚ respectively) but for weak and very taken when rij rijo C ij˙ (i.e., 3.0 and 3.8 A, o ˚ ˚ respectively, since nOe’s are weak nOe’s, when rij rij C 0:8 A, or 4.8 and 5.3 A, ˚ [108]. Pro-chiral protons are assigned on usually undetectable when rij > ca:5:0 A a trial- and-error basis until the minimum number of violations of distance criteria are obtained during a long simulation (100 to 500 ps) at 300 K. We usually find Ax0 x0 Ay0 y0 , and a non-coincidence angle in the range of “ D 24–39ı (Table 6.1). Multifrequency EPR, especially at S- and Q-band, was found to be particularly valuable in the unambiguous assignment of spin Hamiltonian parameters for these low symmetry sites. While Q-band measurements provided greater g-value resolution, larger state mixing and reduced g- and A-strain at low frequencies (S-band) allowed an accurate determination of the hyperfine matrix, including

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Table 6.1 Spin Hamiltonian parameters determined from computer simulation of the multifrequency EPR spectra shown in Fig. 6.11b and from DFT calculations [16, 49] Method gxx gyy gzz Axx Ayy Azz ’ “ Tp MoV O (cat) BP86 1:9867 1:9796 1:9402 9:2 9:5 40:5 10 43 44 BP86 C ASO 11:7 11:1 46:8 1 39 10 B3LYP 1:9790 1:9725 1:9276 16:1 16:4 50:2 10 42 34 B3LYP C ASO 19:7 18:6 57:4 0 37 2 Experiment 1:9680 1:9660 1:9194 27:0 26:0 64:2 0 36 0 Tp MoV S (cat) BP86 1:9796 1:9757 1:9042 13:3 12:7 42:6 0 36 10 BP86 C ASO 14:8 16:6 49:6 2 34 6 B3LYP 1:9698 1:9651 1:8874 20:5 19:6 51:8 1 36 9 B3LYP C ASO 25:0 22:6 59:9 2 34 6 Experiment 1:9646 1:9595 1:8970 30:0 29:0 67:5 0 34:5 0

its orientation with respect to the g matrix. This single set of g and A parameters (Table 6.1) were then used to simulate the S-, X- and Q-band spectra. The weaker -donor terminal sulfido ligand yields a smaller HOMO-LUMO gap and reduced g-values for the thiomolybdenyl complexes compared with molybdenyl analogues (Table 6.1) [16]. Crystal Field Description of Spin Hamiltonian Parameters [16]: Large noncoincidence angles can be explained by a model in which extensive mixing among Mo 4d orbitals takes place. Although ligand to metal charge transfer and metal to ligand charge transfer states of appropriate symmetry may also contribute, for transition metals the dominant contribution to gij is usually gij dd , which arises from transitions within the Mo 4d manifold. In Cs symmetry with a ¢ .XZ/ mirror plane, in which the X axis lies between the metal–ligand bonds, the dX 2 Y 2 ; dXZ and dZ 2 orbitals transform as A0 and the dXY and dYZ orbitals transform as A00 . The metal based anti-bonding wavefunctions are therefore: 0

XA2 Y 2 D ’Œa1 dX 2 Y 2 C b1 dXZ C c1 dZ 2 0

A XZ D “Œa2 dXZ C b2 dX 2 Y 2 C c2 dZ 2 0

ZA2 D ”Œa3 dZ 2 C b3 dX 2 Y 2 C c3 dXZ

(6.18)

A00

XY D •Œa4 dXY C b4 dY Z 00

YAZ D "Œa5 dY Z C b5 dXY where, by definition, ai > bi ; ci .i D 1; 2; : : :). Here covalency appears only implicitly through the metal-centered orbital coefficients ˛; : : : ; ". Since the molecular X and Y axes are placed between the metal–ligand bonds, the ground state wavefunction is ‰X 2 Y 2 . Density Functional Theory Calculations [49]: The electronic g matrix and 95;97 Mo hyperfine matrix were calculated as second-order response properties from the coupled-perturbed Kohn-Sham equations. The scalar relativistic zero-order regular

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approximation (ZORA) was used with an all-electron basis and an accurate meanfield spin-orbit operator which included all one- and two-electron terms. A comparison of the principal values and relative orientations of the g and A interaction matrices (Table 6.1) obtained from unrestricted Kohn-Sham calculations at the BP86 and B3LYP level with the values obtained from experimental spectra shows excellent agreement at the B3LYP level using ORCA [29] A quasi-restricted approach has been used to analyze the contributions of the various molecular orbitals to g and A. In all complexes the ground state magnetic orbital is dX 2 Y 2 -based and the orientation of the A matrix is directly related to the orientation of this orbital through admixture of the dXZ orbital (Fig. 6.11c). The largest single contribution to the orientation of the g matrix arises from the spin-orbit coupling of the dY Z -based lowest-unoccupied molecular orbital into the ground state (Fig. 6.11c). A number of smaller, cumulative charge transfer contributions augment the d–d contributions. All mononuclear molybdenum containing enzymes have a molybdenum cofactor (MoCo) which contains an organic component known as molybdopterin (MPT) which is a modified pterin providing an ene-dithiolene side chain responsible for ligating the Mo [50–55]. The xanthine oxidase family of enzymes contain an active site molybdenum ion coordinated by a single MPT moiety, oxo and sulfido groups and either an aqua or hydroxide ligand [56–58], while the sulfite oxidase/nitrate reductase family of enzymes contain a single MPT ligated to the molybdenum atom, with one or two oxo groups and a cysteinyl sulfur ligand completing the coordination sphere [59]. In contrast, the dimethylsulfoxide (DMSO) reductase family of enzymes contain two MPT ligands linked to a dinucleotide (in DMSO reductase this dinucleotide is guanidine and the MPT is referred to as MGD), a single oxo group and an amino acid side chain (serine in DMSO reductase) coordinated to the Mo ion (Fig. 6.12) [50, 61]. DMSO reductase catalyses the reduction of DMSO to dimethylsulfide (DMS). DMSO C 2HC C 2e > DMS C H2 O

(6.19)

Fig. 6.12 X-ray crystal structures of MoCo within DMSO reductase (PDB File: 1EU1.pdb) [60, 61] (a) the six coordinate catalytically active site and (b) the five coordinate catalytically inactive site. Atom colors: Mo, purple; S, yellow; O, red; C, green; N, blue; P, orange

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˚ resolution has An X-ray crystallographic study of DMSO reductase at 1.3 A revealed that while it contains a single molybdenum cofactor, MoCo is present in two forms a six-coordinate active form and a five coordinate inactive form (Fig. 6.12) [61]. The oxidation state of the molybdenum ion in the resting enzyme is C6 and during catalysis cycles between C6; C5 and C4 with MoV .d1 / being paramagnetic and consequently the MoV catalytic intermediates can be structurally (geometric and electronic) characterized with EPR spectroscopy [62]. Sodium dithionite reduction of DMSO reductase yields EPR signals attributable to the Low-g Type-I MoV species and a sulfur centered radical. Computer simulation of the naturally abundant (Fig. 6.13) and 95 Mo enriched Low-g Type-I MoV CW EPR spectra yields the g- and A-matrices .gx ; 1:9706I gy ; 1:9678I gz ; 1:9560I Ax ; 28:0I Ay ; 29:0I Az ; 66:3 104 cm1 ; ’; 29ı I “; 32ı I ”; 25ı / revealing that the MoV center has triclinic symmetry [6, 63, 64]. A comparison of these g- and A-matrices .gx ; 1:9542I gy ; 1:9655I gz ; 1:9706I Ax ; 27:1I Ay ; 26:2I Az ; 65:4 104 cm1 ; ’; 0ı I “; 33ı I ”; 0ı / with those of desulfo xanthine oxidase [25] ([MoV O (OH) (MPT)]) show that they are very similar, apart from the orientation of the principal components, indicating that they have very similar coordination spheres but different symmetries. In conjunction

a

* *

dχ"/dB

b

c

d

315 320 325 330 335 340 345 350 355 360 Field [mT]

Fig. 6.13 X-band EPR spectra of naturally abundant DMSO reductase treated anaerobically with sodium dithionite [6, 63, 64] (a) Experimental spectrum of naturally abundant DMSO reductase, T D 130 K; D 9:2898 GHz. (b) Computer simulation of the MoV resonances arising from the Low-g Type-I MoV species. (c) Computer simulation of the resonances arising from the sulfur centered radical. (d) Computer simulation of (a) obtained by adding (b) and (c) 0:938

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with the results for the MoV complexes presented above, the unpaired electron is located in a dX 2 Y 2 based molecular orbital (Eq. 6.18). Thus the coordination sphere [MoV O (MGD) (Ser) (OH)] of the Low-g Type I MoV species consists of an ene-dithiolene (P-MGD), Ser-147 and a protonated oxo group, which form the base of a distorted square pyramid. An oxo group completes the coordination sphere by capping the pyramid (reduced form of the five coordinate center, Fig. 6.12b). In addition to the Low-g Type-I MoV species the CW EPR spectrum reveals a species with an orthorhombic g matrix .gz D 2:0545; gy D 2:0182; gx D 1:999/ and small 95 Mo.A2 D 5:0 104 cm1 / hyperfine coupling on the gy resonance. Both 3-pulse ESEEM and HYSCORE spectra revealed the presence of one or more weakly coupled protons and isotropic hyperfine coupling .Aiso .14 N/ D 6:7 MHz/ to a single nitrogen nucleus [6, 63, 64]. The CW and pulsed EPR results are consistent with an unpaired electron centered on sulfur atom (S1) of Q-MGD which is delocalized onto the pyranopterin ring system. These results implicate sulfur centered radicals in the stabilization of the charge on the molybdenum ion in DMSO reductase and/or electron transfer between the native electron donor DorC and the Mo center via the Q-MGD. Room temperature EPR potentiometry has been utilized to determine the redox potentials for the MoVI =MoV and MoV =MoIV redox couples. Interestingly, the MoV EPR spectrum corresponded to the High-g Unsplit (Fig. 6.14)

a

a

c

b dχ"/dB

dχ"/dB

b

c d d e

325 335 345 355 365 Magnetic Field [mT]

315

325

335

345

355

Magnetic Field [mT]

Fig. 6.14 EPR spectra of naturally abundant (left panel) and 95 Mo enriched (right panel) High-g Unsplit Type-1 and 2 species from DMSO reductase that have been anaerobically reduced with DMS and subsequently oxidized with 2,6-dichlorophenolindophenol (DCPIP) [6, 63, 65]. Left panel: (a–c) Experimental spectra in 1 H2 O; 2 H2 O and in the presence of phenazine ethosulfate (PES) .1 H2 O/ respectively. (d, e) Computer simulation of the High-g Unsplit Type-1 and Type-2 spectra respectively. Right panel: (a, c) 95 Mo enriched DMSO reductase: High-g Unsplit Type-1 and Type-2 respectively. (b, d) Computer simulation of the High-g Unsplit Type-1 and Type-2 spectra respectively

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signal and not to either the Low-g or High-g Split EPR signals [6, 63, 65]. Reoxidation of the reduced .MoIV / enzyme produced the High-g Split MoV EPR signal. Computer simulation of the naturally abundant and 95 Mo enriched High-g Unsplit Type-1 and Type-2 species using an orthorhombic spin Hamiltonian (Eq. 6.1) and the spin Hamiltonian parameters (Type-1: gx ; 1:9945I gy ; 1:9840I gz ; 1:9621I Ax ; 38:40I Ay ; 25:61I Az ; 50:52 104 cm1 ; Type-2: gx ; 1:9917I gy ; 1:9832I gz ; 1:9628I Ax ; 41:50I Ay ; 27:88I Az ; 48:39 104 cm1 / produced spectra for the High-g Unsplit Type-1 and Type-2 species (Fig. 6.14) [6, 63, 65]. The spin Hamiltonian parameters determined for the High-g Unsplit Type-2 species show that g? > gjj which is unusual for oxo-molybdenumV complexes. Normally in tetragonally distorted oxo-MoV complexes the unpaired electron is located in a dX 2 Y 2 ground state molecular orbital (X and Y principal axes lie between the metal ligand bonds) which results in gjj being greater than g? [16,17,66]. However, for non-oxo molybdenum(V)complexes such as ŒMo.abt/3 [17] (abtH2 : o-aminobenzenethiol) and ŒMo.S2 C2 H2 /3 [67,68] which have a trigonal prismatic geometry (D3h symmetry), the unpaired electron is located in a 4a10 molecular orbital which involves the overlap of the Mo dZ2 atomic orbital with a set of ligand pZ atomic orbitals [68]. This results in g? being approximately equal to or greater than gjj which is found in a range of non-oxo MoV complexes .ŒMo.abt/3 ; ŒMo.S2 C2 H2 /3 , Mo-amavadin and ŒMo.hidpa/2 / [68–70]. g? is also greater than gjj for the ŒMo.Tp /.O/.cat/ and ŒMo.Tp /.S/.cat/ complexes [16, 49], however, these complexes exhibit monoclinic Cs symmetry producing a ground state molecular orbital that involves an admixture of the dX 2 Y 2 orbital with the dXZ orbital. This results in a rotation of the dX 2 Y 2 based orbital about the Y axis and the presence of a noncoincident angle, “, between the gZ ; AZ and gX AX principal axes [49]. Computer simulation of the High-g Unsplit Type-2 spectrum did not require the inclusion of a noncoincident angle indicating that the unpaired electron is in a dZ 2 based molecular orbital [6, 63, 65]. The magnitude of the g and A values and the observed g-anisotropy [16, 17, 62] indicate that both the P-MGD and Q-MGD dithiolenes are coordinated to the molybdenum atom and that the geometrical arrangement of the ligating atoms is trigonal prismatic [61]. In addition, the lack of strong proton hyperfine coupling indicates that the oxo group is not protonated. Consequently, the six coordinate trigonal prismatic geometry of the MoVI species (Fig. 6.12a) is retained upon reduction of the resting enzyme to MoV and the desoxo MoIV -DMSO species. Closer examination of the X-ray crystal structure [61] reveals that the indole nitrogen of Trp-116 is hydrogen bonded to the oxo group (Fig. 6.12a) which may explain the origin of the 14 N and 1 H hyperfine coupling observed in the ESEEM and HYSCORE spectra since the unpaired electron is in a dZ 2 based ground state with the ‘Z’ axis lying along the Mo D O triple bond. Retention of the trigonal prismatic geometry of the molybdenum center in the MoVI [61], MoV (unpaired electron located in dZ2 orbital) and MoIV [71] species in the reductive half of the catalytic cycle, establishes that the active site is poised for catalysis, i.e. an entatic state [72, 73].

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6.3.2 EPR Studies of Copper(II) Cyclic Peptide Complexes Numerous cyclic peptides of variable size and shape have been isolated from the Ascidiacea class of tunicates. In particular the patellamide family of cyclic octapeptides which 24-azacrown-8 macrocyclic structure and the smaller 18-azacrown-6 hexapeptides have been isolated from Lissoclinum patella and L. bistratum, respectively. Structural characterization of the cyclic peptides in both the solid and solution states [74–79], their biosynthesis [80], pharmaceutical activities [81] and CuII complexes have all been reported [28, 46, 47, 82–85]. While L. patella is known to concentrate a range of metal ions, including CuII , there is little information concerning their biological function in the ascidians metabolism, though carbon fixation has been suggested [82, 86–88]. Brief descriptions of the application of multifrequency EPR in conjunction with circular dichroism (CD) and electronic absorption spectral titrations, mass spectrometry and quantum chemistry calculations to the elucidation of the geometric and electronic structures of a number of mono- and di-nuclear copper(II) cyclic peptide complexes are given below.

6.3.2.1 Copper(II) Complexes with Marine Cyclic Peptides Ascidiacyclamide .ascH4 W R1 D R3 D D-Val; R2 D R4 D L-Ile) and patellamide D (patH4 W R1 D D-Ala; R3 D D-Phe; R2 D R4 D L-Ile) isolated from L. patella have a 24-azacrown-8 macrocyclic structure in which there are two oxazoline and thiazole rings, formed through condensation of threonine with an adjacent amino acid (Fig. 6.15a) [82,83,88]. The peptide chain of asidiacyclamide (Fig. 6.15b) takes on a saddle shaped conformation (Type II) [89, 90] with the thiazole and oxazoline rings at each corner of a rectangular cavity with the eight nitrogen atoms directed towards the interior of the macrocycle which is ideal for metal ion chelation. In contrast the X-ray structure of patellamide D (Fig. 6.15c) has a twisted figure eight conformation (Type III) [91] stabilized by two transannular N-H: : ::O D C- and two transannualr N-H: : ::O- (oxazoline ring) hydrogen bonds. The coordination chemistry of both patellamide D and ascidiacyclamide has been investigated thoroughly with electronic absorption, circular dichroism, mass spectrometry and EPR spectroscopy [82–84]. The formation of both mono- and dinuclear copper(II) complexes as a function of base have been found using these techniques. Formation of the mononuclear copper(II) complex ŒCu.PatH3 /C requires the addition of one equivalent of base (deprotonation of the amide nitrogen). EPR spectra of this mononucluear complex are shown in methanol and acetonitrile/toluene (Fig. 6.16) [82, 84]. While the X-band spectrum of ŒCu.PatH3 /C in methanol is consistent with a single species with a tetragonally distorted geometry, the Q-band spectrum clearly reveals five parallel copper hyperfine resonances attributable to two species. This is even more apparent in the X-band EPR spectra measured in acetonitrile:toluene where acetonitrile stabilizes the coordination of chloride to the copper(II) ion. Computer simulation of these spectra with the parameters in Table 6.2 yields the spectra

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Fig. 6.15 (a) Schematic of patellamides and X-ray crystal structures of (b) ascidiacyclamide, (c) patellamide D and (d) ŒCu2 .ascH2 /.CO3 /

shown in Fig. 6.16. Since patH4 is assymmetric, it is not surprising that copper(II) can form two complexes, namely ŒCu.PatH3 /C and ŒCu.Pat0 H3 /C . In contrast, EPR spectra of ŒCu.AscH3 /C revealed only a single species as ascidiacyclamide is symmetric. The formation equilibria can be described by:

C patH4 C ŒCu .Sol/2C C NEt3 ! k ŒCu .patH3 / .Sol/C C l Cu patH30 .Sol/ C NEt3 H C ##

m ŒCu .patH3 / Cl C n Cu patH30 Cl k C l C m C n D 1; Sol D Solvent

(6.20)

Computer simulation of the MI D 1=2 parallel copper hyperfine resonance measured at S-band frequencies reveals resonances attributable to three magnetically equivalent 14 N nuclei arising from a deprotonated peptide amide nitrogen and the

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Fig. 6.16 EPR spectra of ŒCu.PatH3 /C in methanol (left panel) and acetonitrile:toluene (50:50) (right panel). Left panel: (a, b) X- and Q-band EPR spectra D 9:2357 and 34.0194 GHz, respectively, (c, d) computer simulation of species 1 and 2 and (e) computer simulation of spectrum (b) by adding spectra (c) and (d). Right panel: (a) Experimental spectrum, n = 9.5028 GHz, (b) computer simulation of species 1, (c) computer simulation of species 2, (d) addition of (b) C1:4 x (c) Table 6.2 Spin Hamiltonian parameters for CuII complexes of patellamide D [82] Complex gjj g? Ajj .Cu/a A? .Cu/a ŒCu.MeOH/2C 2.4235 2.0884 ŒCu.patH3 /.MeOH/C Species 1 2.2390 2.055 Species 2 2.2601 2.053 ŒCu.patH3 /XnC in MeCN:toluene (1:1)b Species 1 2.2230 2.087 Species 2 2.2730 2.040 a b

119.5

3.3

153.7 133.0

11.3 11.3

135.0 137.0

60.0 40.0

The units for hyperfine coupling constants are 104 cm1 . X D Cl; n D 1; X D MeCN; n D 0.

nitrogens from the oxazoline and thiazole rings. The remaining coordination site is occupied by either solvent or chloride depending upon the solvent employed. Additional proton hyperfine coupling was also observed in HYSCORE and low frequency CW EPR spectra. Formation of dinuclear copper(II) complexes as a function of base concentration was also extensively studied spectroscopically in both methanol and acetonitrile. In methanol, the formation of the dinuclear complexes can be described by the equilibria [82]:

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Fig. 6.17 EPR spectra of dinuclear copper(II) patellamide D complexes in methanol showing resonances arising from allowed (left panel) and formally forbidden (right panel) transitions. Left and right panels: Experimental spectra of (a) ŒCu2 .patH2 /2C ; D 9:2926 GHz, (c, d) ŒCu2 .patH2 /.OH/C ; D 9:2983 and 9.2991 GHz, (f ) ŒCu2 .patH2 /.CO3 /; D 9:2858 GHz, (b, e, g) Computer simulation of the spectra shown in (a, d, f ) [82]

ŒC u .MeOH /2C C patH4 C NEt3 ! ŒC u .patH3 /C C NEt3 H C ŒC u .MeOH /2C C ŒC u .patH3 /C C NEt3 ! ŒC u2 .patH2 /2C C NEt3 H C ŒC u2 .patH2 /2C C H2 O C NEt3 ! ŒC u2 .patH2 / .OH /C C NEt3 H C ŒC u2 .patH2 / .OH /C C CO2 C NEt3 ! ŒC u2 .patH2 / .CO3 / C NEt3 H C

(6.21) EPR spectra showing the allowed and formally forbidden .Ms D ˙2/ transitions of the three dinuclear complexes is shown in Fig. 6.17. Interestingly the EPR spectra of the ŒCu2 .patH2 /2C complex (Fig. 6.17a, left panel) are typical of mononuclear copper(II) complexes containing a single unpaired electron rather than a dinuclear copper(II) complex with S D 1 [82]. Examination of the second rank dipole–dipole coupling tensor (S.J.S, Eq. 6.2) (Eq. 6.22) reveals

Jxx D gx2 1 3sin2 ˇ sin2 ˛ r

Jyy D gy2 1 3cos2 ˇ sin2 ˛ r

Jzz D gz2 1 3cos2 ˛ r Jxy D Jyx D 3gx gy sin˛ sinˇ cosˇ r Jxz D Jzx D 3gx gz sin˛ cosˇ sinˇ r

(6.22)

Jyz D Jzy D 3gy gz sin˛ cosˇ cosˇ r r D ˇe =r 3 that all of the matrix elements are inversely proportional to the internuclear distance cubed, thus increasing the distance minimizes the dipole–dipole interaction. ˚ was found Through computer simulation studies a distance of greater than 10 A

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Table 6.3 Spin Hamiltonian parameters for the dinuclear CuII complexes of patelamide D [82] Parameter ŒCu2 .patH2 /2C ŒCu2 .patH2 /.OH/C ŒCu2 .patH2 /.CO3 / gx 2:060 2:150 2:075 gy 2:060 2:050 2:075 gz 2:242 2:300 2:267 Ax .104 cm1 / 11:00 3:00 70:00 Ay .104 cm1 / 11:00 3:00 70:00 Az .104 cm1 / 160:00 150:00 111:00 ’ı 54:74 15:00 140:00 “ı 45:00 70:00 0:00 ”ı 0:00 40:00 0:00 ˚ r(A) 6:8 4:8 3:7

to eliminate the dipole–dipole coupling, however, this distance is too large for the ˚ Closer inspection of the internal cavity of the patellamide D macrocycle (7 A). diagonal elements (Eq. 6.22) shows that the dipole–dipole interaction can also be eliminated by setting ’ to 54:7ı and “ to 45:0ı , which correspond to angles used in ‘magic angle’ spinning in solid state NMR to remove anisotropic and dipolar affects. Computer simulation of the spectrum with these angles and a distance of ˚ (Table 6.3) satisfactorily reproduces the allowed resonances. A simulation of 6.8 A the forbidden transitions (spectral line shape, resonant field positions and intensity) predicted the presence of extremely weak forbidden resonances, which were found experimentally after substantial signal averaging. Computer simulation of the EPR spectra of ŒCu2 .patH2 /.OH/C and ŒCu2 .patH2 / .CO3 / with the spin Hamiltonian parameters listed in Table 6.3 reveals that the cyclic peptide backbone becomes increasingly saddle shaped (r decreases) as the base concentration increases. Similar results were found for the formation of dinuclear copper(II) ascidiacyclamide complexes [83]. The formation of a carbonate bridged complex, confirmed by mass spectrometry and crystallographically characterized .ŒCu2 .ascH2 /.CO3 /, Fig. 6.15d [83]) is interesting in that ŒCu2 .patH2 /.OH/C appears to fix carbon dioxide from the air, as the complex is not formed when the reaction is carried out anaerobically. The factors governing this reaction and its biological relevance are currently being explored in collaboration with Prof. Peter Comba. The internuclear distance between the two copper(II) ions ˚ and this has is shorter (Table 6.3) than that observed crystallographically (4.3 A) been rationalized as a change in the structure of the bridging carbonate [84]. When the corresponding experiments were performed in dry acetonitrile, a chlorobridged dinuclear copper complex ŒCu2 .patH2 /ClC was formed in which the copper(II) ions are ferromagnetically coupled [84]. When a small amount of water was added, species described by Eq. 6.21 were found to be present in solution. 6.3.2.2 Copper(II) Complexes with Westiellamide and Synthetic Analogues The copper(II) coordination chemistry of westiellamide .H3 Lwa /, isolated and purified from the ascidian L. bistratum and three synthetic analogues with an

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O

O

X

O

NH

NH N

N O

N

O

X

O

N

HN NH O

HN NH

N O

Westiellamide (H3Lwa)

N

O

X

H3L1, X = NCH3 H3L2, X = O H3L3, X = S

Fig. 6.18 Schematics of Westiellamide and the synthetic analogues [28]

18-azacrown-6 macrocyclic structure with three imidazole .H3 L1 /, oxazole .H3 L2 / and thiazole .H3 L3 / rings instead of oxazoline (Fig. 6.18) have been reported [28]. The Nheterocycle -Npeptide -Nheterocycle binding site has been shown to be preorganized for copper(II) coordination, in a similar manner to the larger patellamides. In contrast to earlier reports, the macrocyclic peptides form stable mono- and dinuclear copper(II) complexes [92]. Formation of mono- and dinuclear copper(II) cyclic peptide complexes was monitored by mass spectrometry, spectrophotometric titrations with base (n Bu4 NOMe or NEt3 ), EPR and IR spectroscopy [28]. 2 EPR spectra of the mononuclear copper(II) complexes with L D L1 ; L and wa L in methanol at 50 K reveal signals of the pure mononuclear copper(II) complexes (Fig. 6.19a–c). In contrast, EPR spectra of a solution of copper(II) trifluormethansulfonate, H3 L3 and base Œ.n Bu4 N/.OCH3 / in various ratios (x:2:y; x D 1; 2I y D 1; 2; 3) show resonances attributable to both mono- and di-nuclear copper(II) complexes [28]. Examination of the perpendicular region of the mononuclear complexes reveals nitrogen hyperfine coupling. Differentiation of the spectra and Fourier filtering procedures (Section 6.2.6) produce well resolved EPR spectra with nitrogen hyperfine coupling on the perpendicular resonances, and for ŒCu.H2 Lwa / .CH3 OH/n C n D 1; 2 also on the parallel MI D 3=2 resonance (Fig. 6.19). Computer simulation of both the first and second derivative EPR spectra, based on the spin Hamiltonian (Eq. 6.23) and with the spin Hamiltonian parameters (Table 6.4) yield the spectra shown in red. P .ˇBi gi Si C Si Ai .C u/ Ii .C u/ gn ˇn Bi Ii / H D i Dx;y;z

C

3;4 P j D1

.Si Ai .N / Ii .N / gn ˇn Bi Ii /

(6.23)

EPR spectra of ŒCu.H2 L1–2 /.CH3 OH/n C .n D 1; 2/ (Fig. 6.19a and b) were simulated, assuming ligand hyperfine coupling to two magnetically equivalent

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a

b

c

Fig. 6.19 EPR spectra of the mononuclear copper(II) complexes with L D L1 ; L2 and C Lwa . (a) ŒCu .H2 L1 /C ; D 9:3571 GHz, (b) ŒCu .H2 L2 / ; D 9:3597 GHz and (c) wa C ŒCu .H2 L / D 9:3588 GHz

Table 6.4 Anisotropic spin Hamiltonian parameters of the mononuclear copper(II) species ŒCuII .H2 L1 /.CH3 OH/2 C ; ŒCuII .H2 L2 /.CH3 OH/2 C and ŒCuII .H2 Lwa /.CH3 OH/Ca [28] ŒCuII .H2 L2 / ŒCuII .H2 Lwa / ŒCuII .H2 L1 / .CH3 OH/2 C .CH3 OH/2 C .CH3 OH/C Parameter gx 2:088 2:083 2:083 gy 2:051 2:034 2:051 gz 2:278 2:279 2:267 Ax .63 Cu/ 17:000 17:300 14:000 Ay .63 Cu/ 15:400 17:200 16:200 Az .63 Cu/ 153:400 123:000 17:500 Ax .14 N/–Nhetcyc 14:500 15:700 12:400 Ay .14 N/–Nhetcyc 7:100 7:100 6:200 Az .14 N/–Nhetcyc 9:000 9:000 10:400 Ax .14 N/–Npept .CNhetcyc /b 13:200 13:400 16:500 Ay .14 N/–Npept .CNhetcyc /b 15:200 14:100 12:700 Az .14 N/–Npept .CNhetcyc /b 9:500 9:500 13:400 a

C

Units for hyperfine coupling constants are 104 cm1 . b for ŒCuII .H2 Lwa / .

heterocyclic nitrogen nuclei and one peptide nitrogen nucleus. In contrast, for the simulation of the EPR spectrum of ŒCu.H2 Lwa /.CH3 OH/n C .n D 1; 2/, ligand hyperfine coupling to two magnetically equivalent heterocyclic nitrogen donors and two other nitrogen donors were required for a satisfactory fit. The spin Hamiltonian

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Fig. 6.20 DFT calculations of the mononuclear copper(II) complexes (a) ŒCu.H2 L1 /C , (b) ŒCu.H2 L2 /C and (c) ŒCu.H2 Lwa /C [28]

parameters reveal a rhombically distorted square pyramidal geometry for the copper(II) center in these cyclic peptide complexes. While the g matrices for the four copper(II) complexes are quite similar, Az for ŒCu.H2 Lwa /.CH3 OH/n C is considerably larger (174 104 vs. 150 104 cm1 / which is consistent with the coordination of an additional nitrogen donor [93]. DFT calculations were used to model the structures of the copper(II) complexes on the basis of the EPR spectroscopic data and their simulations [28, 39]. The mononuclear copper(II) complexes of H3 L.L D L1 ; L2 ; L3 / have a distorted square pyramidal coordination geometry with a peptide and two heterocyclic nitrogen atoms as well as a methanol oxygen donor in the basal plane and a methanol oxygen donor with a significantly longer bond in the apical position (Fig. 6.20). In agreement with the interpretation of the EPR spectra, structure optimization of the mononuclear copper(II) complex of H3 Lwa yields a different coordination mode, with the copper(II) center coordinated to all three oxazoline and one peptide nitrogen donor. In contrast to the macrocycles H3 L .L D L1 ; L2 ; L3 / the higher flexibility of H3 Lwa , due to the unsaturated heterocycles, leads to a conformation, where the third oxazoline nitrogen is able to coordinate to the copper(II) ion. A solvent molecule, methanol coordinates axially completing the coordination sphere. The absence of EPR signals for dinuclear copper(II) complexes with (H3 Lwa ; H3 L1 and H3 L2 ) results from antiferromagnetic coupling .H3 L1 / and/or from low concentrations of the dinuclear copper(II) complexes .H3 Lwa ; H3 L2 /, in agreement with the mass spectrometric data [28]. An EPR spectrum was observed for the dinuclear copper(II) complex of H3 L3 and computer simulation of the spectrum with a dipole–dipole coupled spin Hamiltonian (Eq. 6.2) produced the following parameters for site 1 .gj D 2:2090; g? D 2:090; Aj D 152:8; A? D 5:2 104 cm1 ; “ D 66:2ı / and site 2 .gj D 2:2090; g? D 2:090; Aj D 35:1; A? D 21:4 104 cm1 ; “ D 66:2ı / with an internuclear distance ˚ (Fig. 6.21). While this distance appears to be too large for the 18r D 5:0 A membered azacrown-6 macrocyclic cavity, it is known that an anisotropic term proportional to .g=g/2J can contribute to the zero field splitting, if the isotropic

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Fig. 6.21 EPR spectra and DFT calculated structure of ŒCuII2 .HL3 / .-OCH3 /.CH3 OH/n C . Left panel: (a) EPR spectrum, D 9:359 GHz, (b) computer simulation, see text for parameters. Right panel: DFT optimized structure showing the square pyramidal and tetrahedrally coordinated copper(II) ions

exchange coupling constant is large .J > 30 cm1 / [94]. Consequently, the internuclear distance is over estimated when the J values are large. Structures of dinuclear copper(II) complexes with H3 L1 and H3 L3 refined using DFT, and the two dinuclear copper complexes ŒCu2 .HL1 /. OCH3 /.CH3 OH/n C and ŒCuII 2 .HL3 /.OCH3 /.CH3 OH/n C .n D 0; 2/ existed as stable minima on the potential energy surface and the coordination geometries of the two copper(II) centers in ŒCuII 2 .HL3 /.OCH3 /.CH3 OH/n C were found to be square pyramidal and distorted tetrahedral geometries as predicted from EPR spectroscopy (Fig. 6.21).

6.3.3 Purple Acid Phosphatases Purple acid phosphatases (PAPs) belong to the family of dinuclear metallohydrolases that include Ser/Thr protein phosphatases, organophosphate-degrading triesterases, ureases, arginases, aminopeptidases and antibiotics-degrading metallo“-lactamases [95–100]. Virtually all dinuclear metallohydrolases have homodivalent metal centers of the ZnII ZnII ; FeII FeII or MnII MnII type [95, 100]. The only exception with a confirmed heterodivalent dinuclear center of the type FeIII MII (M D Fe, Zn, Mn) is PAP [95, 100, 101]. Despite a low degree of overall amino acid sequence homology and metal ion content between enzymes from different kingdoms [95,100] their catalytic sites display a remarkable similarity. The two metal ions are coordinated by seven invariant ligands (Fig. 6.22), with an aspartate residue bridging the two ions [102]. Animal PAPs have a redox active FeIII FeIII=II center, where only the mixed-valent form is believed to be catalytically competent [103]. Reduction of the active FeIII FeII center to FeII FeII leads to inactivation and loss of one

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Fig. 6.22 Schematic illustration of the active site of FeMn-spPAP [102]. His201, His295 and Glu365 assist in substrate binding and orientation. The substrate is shown in a possible transition state whereby the bridging oxygen acts as nucleophile

or both metal ions depending upon exposure times to the reductant [104, 105]. In fact this approach has been successfully employed to generate metalloderivatives of PAPs [106–110]. In most plant PAPs the divalent metal ion .MII / is either a ZnII or MnII [95, 100]. While the precise mechanistic details remain to be elucidated, it has been proposed that the MII is essential in substrate binding and orientation, and the FeIII activates the hydrolysis-initiating nucleophile [95,100,102]. This has been confirmed through metal ion replacement studies by substituting FeIII with manganese in sweet potato purple acid phosphatase (spPAP). In the native spPAP enzyme there is an unprecedented, strongly antiferromagnetically coupled FeIII -.-O/-MnII required for optimal catalytic activity (Fig. 6.22) [100–102]. EPR spectroscopy of the MnMn-spPAP reveals resonances arising from an extraneous mononuclear MnII .S D 5=2; I D 5=2I g D 2; A=g“ D 9:3 mT/ center . jDj/ the spin system is best characterized by a total spin operator

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Fig. 6.23 EPR spectra of MnMn-spPAP showing the experimental spectrum (purple), a cubic 55 point (low and high field sections) Savitsky-Golay filter [112] (blue) and the resultant spectral subtraction (red). The resonance at 160 mT arises from a magnetically isolated FeIII center

ST D S1 C S2 ; for two antiferromagnetically coupled high spin MnII .S D 5=2/ ions there are a total of six spin multiplets characterized by ST D 0; 1; 2; 3; 4 and 5, where ST D 0 is the ground spin state and each of the spin multiplets is .2ST C 1/-fold degenerate. The energies of these levels are given by Bencini and Gatteschi [12]: E.ST / D J ŒST .ST C 1/ S1 .S1 C 1/ S2 .S2 C 1/

(6.24)

and the energy level difference between adjacent levels is E.ST / E.ST 1/ D 2ST J

(6.25)

For a strongly antiferromagnetically exchange coupled dinuclear MnII center, only the ground spin state .ST D 0/ will be populated and the system is EPR silent. A strong exchange interaction is mediated by a -O bridge (note that in the isolelectronic FeIII --O-MnII center of FeMn spPAP j2Jj > 140 cm1 / [101]. Protonation of the -oxo bridging ligand (-OH or -OH2 ) reduces the magnitude of the exchange coupling resulting in either (i) complex EPR spectra if j 2Jj is of a similar order of magnitude as jDj or (ii) EPR spectra which only arise from transitions within the ST spin states providing j 2Jj is greater than the microwave quantum .h/, as is usually the case at X-band frequencies. A variable temperature study from 2 to 200 K showed that the resonances centered at 298.4 and 383.7 mT initially increased, then gradually decreased, consistent with an antiferromagnetically coupled dinuclear Mn center in the MnMn-spPAP enzyme. Consequently, the various spin

6


Table 6.5 Values for of the electron spin (S) and numerical coefficients .c1 ; c2 / for various dinuclear Mn centers [12]

Table 6.6 Numerical coefficients .d1 ; d2 ; d12 / of the projection operators given in Eq. 6.26 for MnII and MnIII dimers [12]

167 Center

S1

S2

c1

c2

MnII MnII MnII MnIII MnIII MnIII MnIII MnIV

5/2 5/2 2 2

5/2 2 2 3/2

1/2 7/3 1/2 2

1/2 4=3 1/2 1

d2 16=5 10=21 1=45 C1=7 C2=9 21=10 3=14 C1=10 C3=14

d12 C37=10 C41=42 C47=90 C5=14 C5=18 C13=5 C5=7 C2=5 C2=7

S1 5/2

S2 5/2

2

2

ST 1 2 3 4 5 1 2 3 4

d1 16=5 10=21 1=45 C1=7 C2=9 21=10 3=14 C1=10 C3=14

Hamiltonian interactions in Eqs. 6.1 and 6.2 can be simplified by treating them as a perturbation of the isotropic exchange interaction, enabling the overall manganese hyperfine and zero field splittings to be written as [12, 111]: HS D ˇB gs ST C ST DS ST C c1 ST A1 I1 C c2 ST A2 I2 gs D c1 g1 C c2 g2 Ds D d1 D1 C d2 D2 C d12 D12 (6.26) where the values of ci ; di and dij .i; j D 1; 2I i ¤ j/ are the numerical coefficients of the projection operators and depend upon the values of Si and the resultant ST (Tables 6.5 and 6.6). For dinuclear MnII and MnIII c1 D c2 D 0:5 and consequently the intensity ratio of the 11 equally spaced manganese hyperfine resonances .Aeff D 1 =2 .A=g“// in the EPR spectrum of MnMn-spPAP would be expected to be 1:2:3:4:5:6:5:4:3:2:1. Since resonances from the mononuclear MnII center overlap with these resonances in the spectrum (Figs. 6.23 and 6.24) and are themselves inhomogenously broadened by a distribution of D and E values, we have fitted a cubic Savitsky-Golay filter [112] based on 55 points for the low and high field regions (Figs. 6.23 and 6.24) to establish the relative intensities of the manganese hyperfine resonances and they do indeed have the expected ratio (Fig. 6.24). This intensity ratio of 1:2:3:4:5:6:5:4:3:2:1 effectively rules out a mixed valent dinuclear Mn center (Table 6.5) as the numerical coefficients .ci / of the projection operators would not yield 11 equally spaced multi-line resonances with this intensity ratio. Thus, these resonances arise from either a dinuclear MnII or MnIII center. Interestingly, the only resonances observed in the EPR spectrum of MnMn-spPAP are those centered at 275.8, 298.4, 342.5 and 383.7 mT (Fig. 6.24). This can be readily

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Fig. 6.24 EPR spectrum of MnMn-spPAP at pH 6.5. D 9:382041 GHz; T D 4:7 K [111]. The insets show an expansion of (b, c) the experimental resonances associated with the dinuclear MnII center after baseline correction with a cubic 55 point (low and high field sections) SavitskyGolay filter [112]. (d, e) Computer simulation of (b) and (c), respectively, with the parameters gS D 2:0023; A1 D A2 D 44:5 104 cm1 ; DS D 410 104 cm1 . (f, g) Fitting of the 11 line multiplets at 275.8 and 342.5 mT, respectively

explained by the presence of a large distribution of zero field splitting parameters. Replacement of Ds ; D1 ; D2 and D12 , by Ds D1 ; D2 and D12 in Eq. 6.26, and a comparison of the numerical coefficients (d1 ; d2 and d12 , Table 6.6) of the projection operators shows that only transitions from an ST D 3 spin state of a dinuclear MnII center would be observed (smallest values of d1 and d2 ) as all of the resonances from other spin states .MnII MnII W ST D 1; 2; 4; 5I MnIII MnIII W ST D 1; 2; 4/ would exhibit significant strain broadening. In addition, the magnitude of A=g“ (44.5 mT), the absence of visible absorption bands and the loss of acidic phosphatase activity (vide infra) are consistent with a dinuclear MnII center in MnMn-spPAP.

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In order to gain an insight into the origin of the resonances we employed Molecular Soph (MoSophe) [11] and Octave [113] to simulate each of the four 11 line multiplets (Fig. 6.24) with an effective Seff D 1 =2 spin Hamiltonian [111]: Heff D ˇB giso Seff C Seff A1 I1 C Seff A2 I2

(6.27)

to determine the resonant field positions for each of the multiplets and the hyperfine couplings. Once the resonant field positions were determined (Fig. 6.24) we undertook computer simulations (spectra, energy level diagrams and roadmaps) using MoSophe [18] and the spin Hamiltonian in Eq. 6.26 to fit the resonant field positions, assuming the resonances arise from an ST D 3 spin state. The following spin Hamiltonian parameters .gs D 2:0023; A1 D A2 D 44:5 104 cm1 ; DS D 410 104 cm1 / were found to reproduce the resonant field positions at 298.4 and 383.7 mT (Fig. 6.24) [111]. An inspection of Fig. 6.25 shows that the resonances arise from the MS D 1 $ 0 transition (blue) and that the low field resonances centered at 298.4 mT (Fig. 6.24) correspond to perpendicular resonances (extremum at 90ı , Fig. 6.25) and those at 383.7 mT (Fig. 6.24) to an off axis extremum at 20ı (Fig. 6.25). Introducing a distribution of zero field splittings (E-strain) results in the broadening of the resonances arising from all of the transitions shown in red in Fig. 6.25. Close examination of the experimental spectrum with the baseline subtracted (Fig. 6.24) reveals additional resonances (not readily apparent) in the experimental spectrum centered at 342.5 and 275.8 mT. The former correspond to perpendicular resonances of the MS D 0 $ 1 transition while the origin of the latter resonances is at this stage unknown, although, they may arise through state mixing (intermediate exchange regime) if J were relatively small .2 cm1 / but still larger than D1 and D2 0:1 cm1 and h. Examination of the numerical coefficients d1 ; d2 and d12 for the ST D 3 spin state (Table 6.6) reveals that the zero field splittings for each individual MnII center will contribute negligibly to DS and further that the major contribution to DS arises from the dipole–dipole interaction. D12 is therefore estimated to be 745 104 cm1 using the given value of d12 . Using the point dipole–dipole approximation and assuming an isotropic g factor yields an internuclear distance of ˚ This represents an upper limit for the internuclear distance as the values 4.05 A. of D1 and D2 will be non-zero and without additional spectroscopic information their contribution cannot be defined as their magnitude, orientation of their principal axes and sign remain unknown. A comparison of the internuclear Mn–Mn distance with the type of bridging ligand (-O; -OH; -OH2 , and -CH3 CO2 ) for some representative model complexes ŒMn2 .-O/2 .H2 O/8 , r(Mn-Mn) D 2.890 ˚ [114, 115], Mn2 ŒRu.CN/8 :8H2 O .ŒMn-.-OH2 /2 -Mn, r(Mn-Mn) D 3.7A) ˚ A ˚ [117], [116], L02 Mn2 .-OH/.-CH3 CO2 /2 .ClO4 / .r.Mn-Mn/ D 3:5 ˙ 0:2 A) 0 ˚ [117], ŒMn2 .-OH/L3C L2 Mn2 .-CH3 CO2 /3 .BPh4 / (r(Mn-Mn) D 4.034 A) ˚ r(Mn-Mn) D 3.615 A [118], and enzymes such as FeMn-spPAP .ŒFeIII -.O/-MnII , ˚ [102], catalase .ŒMn-.-OH2 /.-CH3 CO2 /1–2 -Mn, r(Mnr(Mn-Mn) D 3.26 A) ˚ ˚ Mn) D 3.59 A) [119] and the multiple forms of arginase (r(Mn-Mn) D 3.36–3.57 A)

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Fig. 6.25 Transition roadmap showing orientational dependence of the resonant field positions (red, blue) of each of the transitions within the ST D 3 spin state with respect to the external magnetic field. The blue curve corresponds to the MS D 1 $ 0 transition. The green lines correspond to the centers of the 11 line multiplets at 298.4 and 383.7 mT

[119, 120], indicates that a -O bridging ligand is not present in the active site of MnMn-spPAP and that most likely the bridging ligands consist of one or more -OH, -OH2 , and -RCO2 functional groups [111]. Kinetic studies of the MnMn-spPAP reveal that while the enzyme is as catalaytically active as the FeMn-spPAP it no longer functions as an acid phosphatase, but as a neutral phosphatase [111]. Thus PAP’s may have evolved from homo-divalent ancestors in response to its biological function in often acidic environments (e.g. bone resorptive space, soil [121]). Furthermore, the metal ion replacement studies demonstrate the importance of having a trivalent metal ion for acid phosphatase activity, thus increasing our understanding of the role of the chromophoric metal ion as an activator of the nucleophile in acid hydrolysis.

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6.4 Conclusions In this chapter, I have presented various theoretical and experimental aspects of multifrequency CW and pulsed EPR and END(T)OR spectroscopy and computer simulation of spectra from these techniques. In conjunction with quantum chemistry calculations these techniques allow the determination of the geometric and electronic structure of metal centers in biological systems. These aspects were highlighted by examples in molybdenum bioinorganic chemistry, copper cyclic peptide complexes and the manganes derivative of purple acid phosphatase. Acknowledgments I would like to thank my many collaborators and students involved in the various research areas described above, whom without their involvement would not have lead to the significant advances described herein. Specifically Dr. Christopher Noble whom has and continues to have a signifcant involvement in the development of computer simulation software and its application to the characterization of metal ions in biological systems. Assoc. Profs. Lawrence Gahan and Gerhard Schenk for their long standing collaboration on the characterization of transition metal ion complexes, copper(II) cyclic peptide complexes and purple acid phosphatase. Prof. Alastair McEwan, Dr. Simon Drew, Dr. Ian Lane and Assoc. Prof. Charles Young for their keen intersest and collaboration in molybdenum bioinorganic chemistry. Prof. Peter Comba and the many exchange students from the University of Heidelberg whom over the last decade, have been involved in the geometric and electronic structural characterization of mono- and di-nuclear copper(II) cyclic peptide complexes. Drs. Lutz Lötzbeyer, Anne Ramlow, Björn Seibold and Ms. Nina Dovalil, Marta Zajaczkowski and Lena Daumann have had extremely productive visits to the University of Quuensland and I am sure they also enjoyed visiting Australia and I wish them well in their future ventures.

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Chapter 7

On Stacking Martin Egli

Abstract The term ‘stacking’ is normally associated with – interactions between aromatic moieties. The parallel alignment between adjacent DNA bases arguably constitutes the best-known example and provides the dominating contribution to the overall stability of DNA duplexes. Beyond canonical – interactions, a preliminary inspection of crystal structures of nucleic acids and their complexes with proteins reveals a wealth of additional stacking motifs including edge-to-face, H– , cation– , lone pair– and anion– interactions. Given the ubiquity and diversity of such motifs it seems reasonable to widen the meaning of stacking beyond the standard cofacial interactions between pairs of aromatics.

7.1 Introduction Stacking interactions between aromatics are commonly dubbed – contacts, but considered separately from the underlying framework of ¢-bonds, the dominant interaction resulting from closely approaching clouds would be a repulsive one. Some 20 years ago Hunter and Sanders developed several simple rules to characterize the nature of – interactions [1], i.e. (i) – repulsion dominates a face-to-face -stacked geometry; (ii) –¢ attraction dominates an edge-on or T-shaped geometry; (iii) –¢ attraction dominates in an offset -stacked geometry; (iv) in contacts involving polarized systems, charge–charge interactions dominate. We note that the authors are differentiating between two parallel relative orientations of stacked bases: Face-to-face leading to maximum overlap and cofacial but slipped. This simple electrostatic model accounted for many of the experimental observations with stacking, for example that maximum -overlap that would be favored by solvophobic effects is rarely observed. Thus, the electrostatic contribution is dominant

M. Egli () Department of Biochemistry, Vanderbilt University, Nashville, Tennessee 37232, USA e-mail: [email protected]


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Fig. 7.1 Base stacking in DNA and RNA. (a) CpG base pair step in a B-form DNA duplex (Dickerson-Drew dodecamer, PDB ID code 436D [22]). (b) CpG base pair step in an A-form RNA duplex (dodecamer with G:A mismatches, PDB ID code 2Q1R [23]). The views are into the major groove and carbon atoms of guanine bases are highlighted in yellow to illustrate the different degrees of inter-strand stacking in the two duplex types. Thin solid lines indicate the approximate orientations of the helical axes

as far as the geometry of the stacking interaction is concerned. Van der Waals interactions make an appreciable contribution but cannot override electrostatics, as cofacial arrangements between aromatics with no offset would otherwise be prevalent. Therefore, although other contributions to the total energy of the interaction besides electrostatics, such as induction (polarization), dispersion and repulsion can play an important role, in the absence of significant stabilizing effects by polarization, cofacial-offset or edge-on geometries will be preferred over face-to-face alignments. Crystal structures of nucleic acids are highly instructive regarding the former [2–4] in that base overlap is modulated by helical twist, and the observed stacking interactions between bases in DNA [5] (Fig. 7.1a) and presumably also in RNA duplexes (Fig. 7.1b) support the above electrostatic model. Although there is no agreement as to the dominant influence on the stacking strength and the importance of the electrostatic contribution [6–11], clever PAGE assays with asymmetrically nicked and base-gapped DNAs were recently used to partition the contributions by base stacking and pairing (Watson-Crick hydrogen bonds) to the overall stability of duplex DNA [12]. These data leave no doubt that base stacking is the main stabilizing factor in the DNA duplex, triggering a major paradigm shift in the interplay of forces that hold the duplex together. This is because the higher thermodynamic stability of pairing between DNA strands with increasing GC-content is normally attributed to the influence of three hydrogen bonds in G:C compared to the two in A:T pairs. However, the research by Frank-Kamenetskii and coworkers demonstrated that base stacking is always stabilizing for both GC- and AT-containing contacts in the duplex. Conversely, base pairing between G and C does not contribute to stability and the pairing between A and T is actually destabilizing in the overall context. Further, the effects of salt concentration and temperature on stacking resemble the dependences of the total thermodynamic stability of DNA duplexes on the two parameters. In other words,

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it is the dependence of the stacking component of stability on both these parameters that determines their influence on the overall stability. This is remarkable as is the insight, that for all temperatures, heterogeneities in stacking related to GC- versus AT-involving interactions make up at least half of the heterogeneity of the total stability. The other half is the result of the different energetics of G:C and A:T pairing. The contribution of stacking to the stability of a polynucleotide in the single-stranded state has recently been measured for oligo (dA) by atomic-force spectroscopy and amounts to ca. 3:6 kcal mol1 per adenine base ([13] and cited references). More extensive stacking is most likely also the reason behind the significantly higher stability of an artificial nucleic acid pairing system (xDNA) with size-expanded base pairs compared with native DNA [14]. Clearly there are countless other examples that support the importance of stacking for stability that are not cited or discussed here in detail. With stacking thus emerging as the chief contributor to the stability of the DNA double helix, it is reasonable to review different types of stacking beyond the standard interactions between bases in nucleic acid duplexes, interactions involving aromatic moieties in crystal structures of proteins including edge-on contacts between oxygen atoms and Phe [15] and those between hydrogen bond donors and the face of -systems [16–18], or the cofacial, edge-on and coplanar pairing types of aromatics in the crystals of small organic molecules [19, 20]. The examples presented in this brief review are taken mostly from crystal structures of native DNA and RNA and chemically modified nucleic acid systems and are certainly not meant to provide an exhaustive account of this topic. Moreover, the description is mostly qualitative and experimental data for the stability of the individual interactions or estimates based on semi-empirical computations are cited wherever available but are not explicitly provided here.

7.2 Intra- and Inter-Strand Base Stacking Adjacent base pairs in DNA and RNA duplexes provide excellent examples for the cofacial-offset stacking type. Helical twist that amounts to 36ı and 33ı in the canonical B-form DNA and A-form RNA duplex forms along with shifts (see Ref. [21] for a definition of helical parameters) preclude face-to-face orientations of bases. But DNA and RNA exhibit very different types of stacking that are related to the conformational preferences of the sugar moiety in their backbones. The ribose in double-stranded RNA adopts the C30 -endo pucker and the 20 -deoxyribose in B-form DNA adopts the C0 -endo pucker [2]. This leads to the base pairs being inclined relative to the helical axis in RNA whereas DNA base pairs are orientated in a more or less perpendicular fashion relative to the helical axis. Thus, in the illustrations of DNA and RNA base-pair steps in Fig. 7.1, the helical axis for DNA coincides approximately with the vertical direction. However, the axis in RNA is inclined relative to the base pair planes. An important consequence of the chemical and conformational differences between DNA and RNA is the relative slip of stacked base pairs

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along their long dimension. As can be seen in Fig. 7.1a, DNA stacking is mostly of the intra-strand type. By comparison, the RNA duplex is virtually devoid of overlap between bases from the same strand and instead the stabilization is due to interstrand stacking. This is particularly obvious at 50 -pyrimidine-purine-30 steps, for example the 50 -CpG-30 step depicted in Fig. 7.1b. The pairing stability of RNA strands significantly exceeds that of the corresponding DNA strands and is the result of a favorable enthalpy term [24]. However, RNA duplexes exhibit a more extensive hydration compared with DNA and this difference is directly associated with the presence of 20 -hydroxyl groups in the RNA minor groove [25]. This renders the entropy term of the free energy of pairing unfavorable in the case of RNA. Unfortunately, it is not straightforward to partition the individual contributions, i.e. base stacking, base pairing and hydration, to the overall pairing stability of RNA. Assays to determine the relative importance of stacking and pairing like those reported for DNA [12] have not been carried out with RNA to my knowledge. So although we are aware of the different stacking patterns in DNA and RNA duplexes, it is initially unclear how significant this difference is with regard to the higher pairing stability of the latter. Comparison between the experimentally determined stability increases due to dangling ends (an unpaired base either at the 50 - or the 30 -end) in DNA and RNA duplexes ([26] and cited refs.) supports the notion that inter-strand stacking provides higher stability. Similar experimental data for the (20 -40 )-linked pyranosyl-RNA (pRNA) analog that exhibits even more pronounced inter-strand stacking than RNA are also in line with this conclusion [27].

7.3 Parallel and Perpendicular Intercalating Agents Planar aromatic compounds can insert themselves between DNA or RNA base pairs and thereby pry them apart. The intercalator takes on the role of a base pair and its -face overlaps extensively with the base pairs above and below, the latter now ˚ or twice the typical distance between stacked base pairs. separated by about 6.8 A Intercalation does not lead to disruption of Watson-Crick hydrogen bonds. Simple chromophores intercalate such that their long axis runs more or less parallel to the long axis of the surrounding base pairs. The dyes ethidium bromide [28] and acridine orange [29] are well-known examples of so-called parallel intercalators [30] (Fig. 7.2a). Parallel intercalation is usually accompanied by unwinding of the duplex and the sugar pucker and backbone torsion angles need to adapt in order to bridge the wider step [2]. Intercalator and flanking base pairs are typically aligned so as to maximize overlap; electrostatics and van der Waals interactions likely dominate the energetics of the parallel intercalation mode. By comparison, more extensive conformational distortions in DNA are observed upon intercalation of chromophores that feature bulky substituents. The presence of a sugar moiety, as in the anthracycline antibiotics daunorubicin and doxorubicin (anticancer agents), prevents a parallel intercalation mode [33]. Thus, the chromophore is forced to rotate and enter the base-pair stack in a perpendicular mode. This places

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Fig. 7.2 Parallel and perpendicular intercalators. (a) The bis-intercalating drug ditercalinium in complex with the duplex Œd.CGCG/2 exemplifies the parallel stacking type (PDB ID code 1D32 [31]). (b) Nogalamycin intercalates at the CpG base pair steps in the duplex Œd.CGTACG/2 and is representative of the perpendicular intercalation mode (PDB ID code 1D17 [32]). Both duplexes are viewed into the major groove and carbon atoms of drug molecules are highlighted in yellow

the substituent in the groove where it can engage in hydrogen bonds to donors and acceptors on the base edges. Nogalamycin differs from the more common daunorubicin-type anthracyclines in that it is substituted on both ends of the intercalating chromophore and thus takes on the shape of a dumbbell (Fig. 7.2b) [32]. The bicyclic amino sugar that carries a positively charged dimethylamino group is fused to one side and is located in the major groove upon intercalation where it forms hydrogen bonds to N7 of G and N4 of C. The nogalose sugar at the other end enters the minor groove but no hydrogen bonds are established. However, the carbonyl oxygen of the methylester substituent that also resides in the minor groove is hydrogen bonded to the exocyclic amino group of the terminal G (Fig. 7.2b). Unlike parallel intercalators that unwind the DNA at the site of intercalation, the unwinding caused by these so-called perpendicular intercalators occurs at the adjacent base-pair step [30]. Other consequences of parallel intercalation include concerted changes in the ˛ and backbone torsion angles [34]. Moreover, the perpendicular intercalation mode is often accompanied by severe buckling of base pairs that wrap around the chromophore. This leads to partial unstacking on one side but may allow for more optimal relative orientations of acceptors and donors on nucleobases and intercalator for hydrogen bond formation. In place of the cofacial-offset stacking type seen with parallel intercalators, exocyclic keto and hydroxyl groups of the nogalamycin aglycone are tilted relative to the -faces of bases on one side (Fig. 7.2b). Therefore, the parallel and perpendicular intercalator modes differ distinctly and perpendicular intercalators display a mixture of hydrogen bonding and cofacial and edge-on stacking to bind to DNA.

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7.3.1 Cofacial Versus Edge-On Stacking Simple aromatics such as benzene can pair via cofacial and edge-on stacking and the stabilities afforded by these interaction modes are likely very similar [20]. Unlike the -systems in benzene or in phenylalanine those in the nucleobases are polarized as a result of their heterocyclic nature and the presence of exocyclic substituents. In addition backbone constraints and regular parallel -stacking in DNA duplexes render edge-on interactions of bases very unlikely. Moreover, in crystals of oligonucleotides or protein-DNA complexes end-to-end stacking by duplexes of the cofacial-offset type constitutes the most common packing motif. The singlestranded nature of RNA permits considerably more structural variety but stems (double helical portions) make up much of the secondary structure and the parallel stacking type is prevalent. We were interested in the consequences of incorporation of simple aromatic moieties as far as the geometry of stacking interactions is concerned. In one study we analyzed the conformational properties of an RNA octamer CCCpGGGG with an incorporated phenyl-ribonucleotide (p). In the crystal structure, strands pair such that a configuration with a phenyl ring placed opposite a G is avoided [35]. Instead phenyls ‘pair’ under formation of a 30 -dangling G (Fig. 7.3). This arrangement generates a seamless -stack and repulsive contacts to nucleobases are avoided by isolating the hydrophobic phenyl moieties in the core of the duplex. Despite potentially favorable hydrophobic and van der Waals interactions resulting from the phenyl pair, incorporation of a single p residue in an RNA leads to drastically reduced stability of pairing. In the case of the octamer duplex, the melting temperature was reduced by 35ı C (Gı 37 C7:5 kcal mol1 ) relative to the native Œr .CCCCGGGG/2 duplex [35]. In comparison to the phenyl-modified RNA duplex, the crystal structure of a DNA duplex with stilbenediether (Sd, Fig. 7.4a) caps revealed multiple stacking types (Fig. 7.4) [36]. One of the two hairpin molecules per crystallographic

Fig. 7.3 ‘Pairing’ of phenyl-ribonucleotides (p) in the center of the RNA duplex Œr .CCCpGGGG/2 (PDB ID code 1G2J [35]). The dotted surfaces illustrate that phenyl rings from opposite strands are virtually in van der Waals contact

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Fig. 7.4 Conformations of a stilbene diether moiety (Sd) that caps the DNA hairpin d(GTTTG)se-d(CAAAAC) (PDB ID code 1PUY [36]). (a) Structure of Sd. (b) Canonical stacking of Sd on the adjacent C:G base pair. The trans-stilbene portion of Sd adopts a planar conformation. (c) Unstacked (phenyl ring on the left) and edge-on interaction with the cytosine below (phenyl ring on the right) of Sd in the second DNA hairpin per crystallographic asymmetric unit

asymmetric unit displayed a parallel offset orientation (Fig. 7.4b). In the second molecule, the stilbene’s planarity was lost; the dihedral angle between phenyl rings amounted to 10ı . One of the phenyls was partially unstacked from the neighboring G and the other adopted an edge-on orientation relative to C (Fig. 7.4c). Unlike the phenyl moieties in the RNA duplex discussed above, the Sd linkers are located at the end of a duplex and are free to interact with one another in the crystal lattice. For example, in the structure of an Sd-capped DNA duplex co-crystallized with Sr2C , four Sd moieties engaged in a pinwheel-like arrangement, featuring exclusively edge-on type stacking [37]. This observation reinforces the view that simple aromatics can easily switch between the parallel and edge-on stacking modes. Unlike the aforementioned phenyl-ribonucleotide the Sd linker greatly stabilizes DNA duplexes.

7.4 Base-Backbone Inclination and Sugar-Base Stacking (40 !60 )-Linked oligo-20, 30 -dideoxy-“ -D-glucopyranose nucleic acid (homoDNA) was studied as part of research directed at an etiology of nucleic acid structure [38, 39]. Homo-DNA was considered an autonomous pairing system until recently,

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i.e. homo-DNA oligonucleotides do not pair with DNA and RNA or any of the artificial nucleic acid analogs. The only exception identified to date is L-cyclohexanyl nucleic acid (L-CNA) that forms a left-handed duplex with homo-DNA [40]. The crystal structure of a homo-DNA octamer duplex showed a right-handed he˚ and 14ı , respectively, and a highly lix with average values for rise and twist of 3.8 A irregular geometry (Fig. 7.5a) [41]. Strongly inclined backbone and base-pair axes are one of the hallmarks of the homo-DNA duplex. Unlike RNA in which backbones and base-pair planes exhibit a negative inclination (ca. –30ı), the inclination angle in homo-DNA is positive (ca. 45ı on average [41–43], Fig. 7.5). Thus, stacking between adjacent base pairs is exclusively of the inter-strand type in homo-DNA. As Fig. 7.5 illustrates there is virtually no overlap between adjacent bases from the same strand.

Fig. 7.5 Structure of homo- (hexose-) DNA. (a) The crystal structure of the homo-DNA duplex 60 Œdd.CGAATTCG/2 40 viewed into the major groove (PDB ID code 2H9S [41]). Nucleotides A3 in the first strand and A11 in the second are looped out and interact with a neighboring duplex, whereby adenosines from the latter insert themselves into the gaps created. In the crystal lattice homo-DNA duplexes form tightly interacting dimers. (b) H– type sugar-base stacking: Hydrogen atoms of 20 , 30 -dideoxyglucopyranoses (highlighted in yellow) point into the adjacent nucleobase. The illustration depicts the (C1:G16)p(G2:C15) base pair step

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Owing to a favorable entropic contribution, the pairing stability of homo-DNA oligonucleotides exceeds that of DNA by far [44]. This property is consistent with the reduced conformational flexibility of the hexose sugar compared with 20 -deoxyribose. The exceptionally large slide between adjacent base pairs combined with the limited helical twist result in another unique feature of the homo-DNA duplex: sugar-nucleobase stacking (Fig. 7.5b). Instead of the standard intra-strand – stacking seen in B-DNA, the 20 , 30 -dideoxyglucopyranose of the 60 -nucleotide sits directly above the nucleobase of the 40 -nucleotide and equatorial C20 -H bonds of the former are pointing into the -face. Although the sugar-base stack may involve mainly van der Waals interactions (distances between C20 atoms from the ˚ it is unlikely to sugar and the best plane through base atoms are as short as 3.1 A), be repulsive. In any case, the extensive inter-strand base stacking characteristic of homo-DNA, will likely offset any destabilizing consequences of the close approach between sugar and nucleobase. A recent report by Leumann and colleagues appears to provide evidence that C-H stacking contacts between a saturated hydrocarbon and a phenyl moiety are not merely tolerated but may actually be stabilizing [45]. Thus they analyzed the thermodynamic stability of DNA duplexes with 1-3 phenylcyclohexyl-C-nucleoside pairs incorporated into their center and found the modification to be associated with an increase in duplex stability. The higher stability is enthalpic in nature and seems to arise from cyclohexyl phenyl interactions.

7.4.1 Amino Acid-Nucleobase Stacking Interactions between OH or NH donors and the -faces of aromatic side chains in amino acids were analyzed extensively in the crystal structures of proteins [16, 18]. Such interactions are ubiquitous and it is intuitively clear that a short contact between a donor functionality and a negatively polarized -system can be stabilizing. Another motif seen quite frequently involves C-H moieties and the -faces of aromatic acid side chains or nucleobases [46]. Two examples are depicted in Fig. 7.6. At the active site of death-associated protein kinase (DAPk), the C• methyl group of a methionine points directly into the six-membered ring of adenine from ATP (Fig. 7.6a, b) [47]. All kinases (DAPk belongs to the family of Ser/Thr kinases) bind ATP, but they catalyze the transfer of the ATP ”-phosphate to different targets. Although the ATP-binding pockets of different kinases exhibit certain similarities, they deviate from each other to various degrees to allow for the observed specificity of the kinase reaction. Thus, an apparently minor contact like the one depicted in Fig. 7.6a, b may well make a subtle contribution to specificity. At the active site of the human trans-lesion DNA polymerase-kappa (hPol ›) in complex with a DNA template-primer construct containing an 8-oxoG adduct, we observed another type of Met nucleobase stacking (Fig. 7.6c, d). The methionine side chain snakes along the base plane of 8-oxoG, whereby the relative orientations of amino acid and nucleobase differ only minimally in the two complexes per crystallographic asymmetric unit. This arrangement leads to various C-H contacts

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Fig. 7.6 H– type amino acid-nucleobase stacking motifs. Met ATP (AMPPnP) in the crystal structure of death associated protein kinase (DAPk, PDB ID code 1IG1 [47]). (a) Viewed from the side, and (b) rotated by ca. 90ı around the horizontal axis and viewed approximately along the normal to the aromatic moiety. Met 8oxoG in the crystal structure of the human Pol-kappa (hPol›) DNA complex (PDB ID code 2W7P [48]). (c) The amino acid-base stack in one of the two complexes per crystallographic asymmetric unit, and (d) the interaction in the second complex. Carbon atoms of methionine are highlighted in yellow and the sulfur atom is highlighted in magenta

between Met methylene groups and the 8-oxoG base moiety. In addition, the sulfur ˚ from the best plane through nucleobase atoms atom exhibits a distance of ca. 3.1 A ˚ in both complexes, well below the sum of van der Waals radii for carbon (1.7 A) ˚ The Met 8-oxoG stacking interaction likely stabilizes the syn and sulfur (1.8 A). conformation of the adducted nucleotide, thus leading to incorrect insertion of dATP opposite 8-oxoG.

7.5 Stacked Dipoles: The C-Rich i-Motif Cytidine-rich (C-rich) DNAs form a four-stranded arrangement, whereby two parallel-stranded duplexes intercalate (i-motif ) into each other such that their backbones run into opposite directions [49, 50] (Fig. 7.7a, b). The tetraplex is held together by interdigitated, hemiprotonated C:CC base pairs that are rotated by about 90ı between neighboring planes (Fig. 7.7c). One of the striking features of the i-motif is the absence of overlap between the six-membered rings of Cs from neighboring base pairs. Instead the main contribution to stability likely comes from

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Fig. 7.7 Crystal structure of the central portion of the four-stranded self-intercalated i-motif formed by the DNA tetramer d(CCCC) (PDB ID code 190D [50]). Carbon atoms in the parallelstranded duplex whose strands run from top to bottom are colored in gray and those in the duplex with strands running in the opposite direction are colored in yellow. (a) The tetraplex viewed into a major groove. (b) Rotated by ca. 90ı around the vertical axis and viewed into a minor groove. (c) Rotated by ca. 90ı around the horizontal axis (relative to panel a) and viewed down the stack of hemi-protonated C:CC base pairs, illustrating the lack of an overlap between cytosine six-membered rings. Pairs of C4-N4 .H2 / and C2DO2 moieties that are aligned in an antiparallel fashion (C2 and C4 carbon atoms are highlighted in green) may instead contribute significantly to the overall stability of the i-motif. Hydrogen bonds in cytosine pairs and C-H O40 interactions between 20 -deoxyribose sugars across the minor groove are shown as thin solid lines

stacks of dipoles with an antiparallel orientation (•C C2DO2 • = • O2DC2 •C ). If we further consider a tautomeric form of CC with the positive charge on the exocyclic N4 amino group, additional stability would be provided by this charge being positioned above the cloud of the cytosine underneath (Fig. 7.7c). Thus, there must be a significant electrostatic contribution to the stability of the C-rich i-motif, consistent with the presence of hemiprotonated C:CC base pairs. Additional contributions to the stability of the i-motif may stem from a network of C - H O40 hydrogen bonds between adjacent 20 -deoxyriboses from antiparallel strands (Fig. 7.7) [51]. It is noteworthy that T-rich oligonucleotides cannot form a self-intercalated four-stranded structure analogous to that adopted by C-rich strands. The pKa of N3 of C (50 -nucleotide) is ca. 4.6 and the nucleobase is therefore protonated under slightly acidic conditions (summarized in Ref. [52]). Thymine on the other hand is neutral as the pKa of N3 is ca. 10.5 (50 -nucleotide).

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7.6 Cation– Interactions It should come as no surprise that cations can interact favorably with the -face of an aromatic system [53, 54]. In their analysis of the nature of – interactions, Hunter and Sanders discussed the optimum geometry of the porphyrin–porphyrin pair [1]. Accordingly, the most stable configuration is one where the pyrrole ring of one porphyrin is located under the -cavity at the center of the other. Metallation places a positive charge in the central cavity and results in a favorable interaction with the -electrons of the adjacent pyrrole ring, thus enhancing porphyrin aggregation. Another nice example of a cation- stacking interaction is found in the structure of a DNA-protein complex (Fig. 7.8) [55]. The Ndt80 protein uses arginines to interact with the major groove edge of Gs from the same strand in the 50 -TGTG sequence motif. This sequence-specific Arg G interaction is present in virtually every protein-DNA complex. The guanidinium moiety of Arg is protonated at neutral pH and in addition to probing the major groove edge of G, the protein uses the positive charge to pull thymines out of the base-pair stack (Fig. 7.8). Thus, the guanidinium moiety engages in a cofacial contact with T and in addition the Arg C“ methylene group forms a hydrophobic contact with the 5-methyl group of the nucleobase. The Ndt80 complex attests to the never-ending repertoire that proteins rely on to establish sequence-specific interactions with DNA, in this case by using Arg to not only gauge the separation between two Gs in the major groove, but to also exploit the particular conformational plasticity of the TpG step(s).

Fig. 7.8 Cation– interactions in the crystal structure of the yeast sporulation regulator Ndt80 in complex with DNA (PDB ID code 1MNN [55]). A pair of arginines interacts with the major groove edges of guanines whereby the guanidinium moiety from Arg stacks onto the 50 -adjacent T. The protein uses the formation of these Arg-T stacks to specifically recognize the tandem 50 -TpG-30 sequence motif. The view is into the major groove, hydrogen bonds are shown as thin solid lines, and carbon atoms of arginine and thymine are highlighted in yellow

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7.7 Lone Pair– and Anion– Interactions Unlike cation– interactions those between lone electron pairs (lp) or anions and the -faces of aromatic systems may initially seem counterintuitive. Of course, an H– interaction, say, involving water and benzene or tryptophan is energetically favorable compared to a configuration with the water oxygen located above the center of the aromatic ring and directing its lone pair(s) into the -cloud. However, when the aromatic system is strongly polarized, as in hexafluorobenzene [56], or carrying a positive charge, i.e. protonated imidazole [57], the lp– interaction can result in a significant stabilization. In terms of electrostatics, the H– interaction involves the HOMO of the aromatic ring and the LUMO of water ( ! ) and the lp– interaction involves the HOMO of water and the LUMO of the aromatic ring (n! ) [58–60]. Many years ago, we described the conserved 20 -deoxyribose (cytidine) guanine stack in crystal structures of the left-handed Z-DNA duplex Œd.CGCGCG/2 [58]. Unlike with homo-DNA where the hexose is positioned above the adjacent nucleobase such that a C-H moiety points into the -system, it is the ’ lone pair of the sugar O40 atom that is directed into the six-membered ring of guanine (Fig. 7.9a). In left-handed Z-DNA the helical twist alternates between high and low values for neighboring base-pair steps and C and G exhibits different conformations of the sugar. At CpG steps there is a virtual absence of overlap between the cytosine and guanine base planes and the sugar of the former takes the place of the nucleobase instead (Fig. 7.9a). The distance between the 40 -oxygen and the best plane defined ˚ in the structures of the so-called by guanine atoms varies between 2.82 and 2.96 A magnesium, spermine and mixed magnesium/spermine crystal forms [61] of the left-handed hexamer. At the time

we interpreted the close approach of the sugar as an n.O40 /! C2DN2H2 C interaction (see inset in Fig. 7.9a). We based our assumption of a tautomeric form of G with N2 and O6 being positively and negatively charged, respectively, on the frequently observed coordination of Mg2C to the major groove edge of G in Z-DNA crystals. Distances between O40 (C) and C2(G) vary be˚ in the crystal structures and are thus similar to the distances tween 2.90 and 3.09 A between the oxygen and the G-plane. CG-repeats show a particular propensity for adopting the left-handed duplex type and insertion of TpA steps destabilizes the formation of the Z-duplex [62]. Adenine cannot mimic the particular polarization of guanine in Z-DNA and the stabilizing contribution as a result of the sugar-base stack at CpG steps [63] will be at best neutral at a TpA step. The stacking arrangement between a 20 -deoxyribose and guanine is a hallmark of Z-DNA and provided early support for the existence of lp– interactions in biological systems. Another striking example of an lp– interaction is found in the C-loop of a –1 ribosomal frameshifiting pseudoknot RNA (pk-RNA). There, a water molecule sits directly above a protonated cytosine, and our conclusion that one of the oxygen lone pairs points into the -face of the nucleobase is supported by the tight distance (2.93 ˚ Fig. 7.9b) and the particular distribution of hydrogen-bond acceptor and donor A; moieties around this water molecule [66]. We know that the cytosine is protonated from the particular pairing geometry of the base observed in the crystal structure

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Fig. 7.9 Lone pair– (lp– ) stacking. (a) The lp– stacking motif at CpG steps in the crystal structure of the left-handed Z-DNA duplex Œd.CGCGCG/2 (PDB ID code 131D [64]). The 20 deoxyribose of cytidine (carbon atoms highlighted in yellow) is lodged above the guanine base, resulting in an interaction between a 40 -oxygen (asterisk) lone pair and the positively polarized ring portion of G (the inset depicts a tautomeric form of G relevant in the case of lp– stacking). (b) The C-turn in the crystal structure of the –1 frameshifting RNA pseudoknot from beet western yellow virus (BWYV pkRNA, PDB ID code 1L2X [65]). A water molecule (highlighted in cyan) sits directly above a protonated cytidine (yellow). The particular environment of this water molecule (neighboring hydrogen bond donor and acceptor moieties) and the tight spacing between the water oxygen atom and the aromatic plane are consistent with an lp(oxygen)– (C) interaction (indicated by the arrow)

of the pk-RNA at atomic resolution [65]. Calculations performed at various levels of theory provide a consistent picture, namely that lp– interactions yield substantial stabilization when the aromatic moiety is strongly polarized or, as in the above case, positively charged [57, 63, 67]. Naturally, it would be very interesting to conduct a neutron diffraction study with crystals of the pk-RNA as this would allow visualization of the position of hydrogen (deuterium) atoms and also permit a better

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characterization of other potential lp– and several H– interactions in the crystal [66]. In addition to the Z-DNA and pk-RNA examples, we recently reviewed other types of lp– interactions involving carbonyl oxygens and aromatics [63]. Based on an analysis of protein crystal structures others have recently found numerous occurrences of close interactions between carbonyl oxygens and the side chains of aromatic amino acids with a geometry that is between those of ideal – and lp– stacking interactions [60]. Obviously many more examples of lp– type stacking interactions will emerge in the structures of small and macro molecules in the coming years as closer attention is being paid to novel types of weak interactions (for example Refs. [68, 69]). The aforementioned cases of lp– interactions involve neutral species (i.e. 20 deoxyribose O40 , water, or carbonyl oxygen), but there are others in which the moiety contributing the lone pair is negatively charged. For example in the so-called U-turn RNA tertiary structural motif [70], a phosphate group sits above a uracil base, an interaction that may contribute favorably to stability thanks to the particular polarization of U [63]. However, there are also numerous examples of anion– interactions in the structures of small molecules (for example Refs. [71–75]).

7.8 Unique Properties of the TATA-Motif Major Groove Hydrogen bonding and stacking play crucial roles in determining the stability and three-dimensional structure of the DNA double helix. Although we often treat them as separate entities – Watson-Crick hydrogen bonds linking nucleobases more or less perpendicularly to the helix axis and – interactions coupling nucleobases along the direction of the axis – it is clear that the electrostatics of hydrogen bonding affect the stacking geometry and thus the sequence-dependent shape of the double helix and its recognition by proteins. It is normally assumed that base moieties are perfectly planar, but theoretical and experimental studies have provided support for out-of-plane positions of hydrogen atoms from amino groups [76–80]. Bifurcated hydrogen bonding involving adenine and thymine across adjacent levels from the stack have also been reported in DNA crystal structures [81] and analyzed with theoretical means [82]. In addition bifurcated cross-strand hydrogen bonding between non-planar amino groups from A and C and A and A from adjacent base pairs has also invoked [83–85]. However, the resolutions of crystal structures of macromolecules typically do not allow visualization of hydrogen atoms, and the degree of a potential out-of-plane perturbation of the exocyclic adenine, guanine and cytosine amino groups therefore has not been settled based on crystallographic data. The major groove of the central TATA tetramer in the crystal structure of an A-form DNA duplex exhibits a remarkable hydration pattern [86]: All acceptor functions from bases with the exception of adenine N6H2 form hydrogen bonds to water molecules (Fig. 7.10). The absence of waters associated with these exocyclic amino groups is initially puzzling, but closer inspection of the major groove

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Fig. 7.10 Major groove hydration in the central TATA portion of the DNA duplex ŒdGCGTAtACGC2 (t D 20 -methoxy-30 -methylene-T, see arrows) visualized at atomic resolu˚ PDB ID code 1DPL [86]). All potential hydrogen bond (thin solid lines) acceptor tion (0.83 A, moieties of nucleobases near the floor of the groove (O4 of T and N7 of A) engage in contacts to water (cyan spheres), whereas exocyclic N6 amino groups (magenta) from adenines (carbon atoms colored in yellow) are not associated with water. Instead adenines engage in bifurcated hydrogen bonds to paired (Watson-Crick) and stacked thymines, thus apparently limiting the capability of N6(A) to interact with solvent molecules. Superimposed sugar moieties of the adenosine residue visible near the bottom edge of the figure indicate a rystallographic disorder

indicates that N6(A), in addition to being hydrogen bonded to O4 from the T it pairs with, also appears to establish a hydrogen bond to O4 from the 30 -adjacent T. Figure 7.10 also depicts hydrogen bonds between N6(A) and O4 from the 50 -adjacent T because the distances between N6(A) and O4 .30 T/ and N6(A) and O4 .50 T/ are similar. Without knowledge of the positions of hydrogen atoms, it is not straightforward to settle the geometry of the hydrogen-bond network. However, the potential formation of such bifurcated hydrogen bonds is facilitated by the sliding of adjacent base pairs in the A-form environment and the high propeller twist of A:T pairs. In turn, bifurcated hydrogen bonds will affect the geometry of the duplex and the particular shape of the TATA-repeat. This motif is contained in the TATA-box sequence that is usually located 25 base pairs upstream to the transcription site which is recognized by RNA polymerase II as part of a multi-protein complex [87]. Although the energetic consequences of the network of hydrogen bonds in the major groove of the TATA sequence are not understood in detail, the thought that bifurcated hydrogen bonds could influence its geometry and the recognition by the TATA-binding protein (TBP, [88] and refs. cited) is intriguing.

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7.9 Conclusion In this brief overview I have provided examples of various types of stacking, the term stacking designating the relative orientation of a chemical moiety interacting with an aromatic system whereby the former sits above the -face of the latter either in the face-to-face or cofacial-offset modes. Instead of a somewhat narrow use of ‘stacking’ as an interaction between -systems of parallel orientation and forces that are mainly dispersive in nature, stacking here simply refers to moieties, including aromatics, hydrocarbons, cations, anions, water, etc., interacting with the -cloud of an aromatic system. The resulting catalog of interactions shows a considerable range of stacking-type supramolecular building blocks. The nature of these interactions is decidedly Coulombic in some cases and thus different from parallel stacks between the side chains of aromatic amino acids or nucleobases of various polarizations. Compared to the familiar stacking of base-pairs in DNA, lone pair– , cation– , and anion– stacking and interactions between hydrocarbons such as sugars and the -faces of aromatic systems have not been analyzed in a systematic way. It is likely that many more examples of such interactions can be retrieved from the three-dimensional structures of proteins and RNAs, as those described here merely represent cases over which we and others had stumbled in a more or less fortuitous manner. A particularly interesting example of a non-standard stacking interaction, of the cation- type, has recently been demonstrated to be at the origin of the higher affinity for nicotine by acetylcholine receptors in the brain (thought to underlie nicotine addiction) relative to receptors in the muscle [89]. The last item reviewed here, the potential role of non-planar amino groups in the formation of bifurcated hydrogen bonds that affect the stacking geometry and stability of macromolecular assemblies, i.e. DNA duplexes, would undoubtedly profit from single-crystal neutron diffraction studies. The renewed interest in neutron diffraction with crystals of macromolecules in recent years and the availability of spallation sources that permit the use of smaller crystals raise the possibility that we may be able to gather experimental evidence for or against the non-planarity of amino groups in the near future. Acknowledgments Research by my laboratory on the structure and function of native and chemically modified nucleic acids is supported by the US National Institutes of Health (grant R01 GM055237).

References 1. Hunter, C. A.; Sanders, J. K.M., J. Am. Chem. Soc. 1990, 112, 5525–5534. 2. Saenger, W., Principles of nucleic acids structure. Springer, New York, 1984. 3. Berman, H. M.; Olson, W. K.; Beveridge, D. L.; Westbrook, J.; Gelbin, A.; Demeny, T.; Hsieh, S.-H.; Srinivasan, A. R.; Schneider, B., Biophys. J. 1992, 63, 751–759 (http://ndbserver.rutgers. edu). 4. Neidle, S., Principles of nucleic acids structure. Academic Press, London, 2008. 5. Hunter, C. A.; Lu, X.-J., J. Mol. Biol. 1997, 265, 603–619.

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Chapter 8

Structurally Complex Intermetallic Thermoelectrics – Examples from Modulated Rock-Salt structures and the System Zn-Sb Sven Lidin

Abstract Thermoelectric materials are semiconductors that are characterized by poor thermal transport. A large class of interesting compounds for thermoelectric applications are therefore structurally complex intermetallics. This paper deals with two groups of intermetallics, one defined from the point of view of their structures, the Rock-Salt like structures, and the other from their chemical composition, the binary system Zn-Sb.

8.1 Introduction If a thermal gradient is established across a material, mobile particles will diffuse from the hot side to the cold side, much like molecules in the gas phase. For charged particles, this directional diffusion leads to a build-up of an electric gradient, a potential. This is the Seebeck effect, and the magnitude of this effect is measured by the Seebeck coefficient. Conversely, the passing of a current through a conductor will concurrently transport heat, and so establish a thermal gradient. This effect is known as the Peltier effect. Both effects may be used practically, either for power generation from waste heat, or for refrigeration. In both cases, the process is rather inefficient, but the fact that the process interconverts heat and electric power directly without any need for moving parts, makes it attractive. While the Seebeck coefficient is important, thermoelectric efficiency depends on other factors as well. First, the material should be a good enough conductor to avoid Joule heating, secondly the material must be a thermal insulator, or the efficiency will be hampered by thermal short circuiting. A complication in optimizing the performance of a thermoelectric material is that the Seebeck coefficient and the electrical conductivity are inextricably linked. A metallic conductor has a low, while an insulator has a high Seebeck coefficient. These various (and partially conflicting) S. Lidin () Division of Inorganic Chemistry, Arrhenius laboratory, Stockholm University, 106 91 Stockholm, Sweden e-mail: [email protected]


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requirements on a good thermoelectric are often expressed in terms of the dimensionless figure of merit, ZT D ’2 ¢T=œ where ’ is the Seebeck coefficient, ¢ is the electronic conductivity, T is the absolute temperature and œ is the thermal conductivity. A good value of ZT is above unity. The optimal material is a heavily doped semiconductor. Tuning the carrier concentration is relatively straight-forward to achieve by doping. The thermal conductivity consists of two parts, electronic and phononic transport. The electronic part scales with the carrier concentration and is therefore linked to the conductivity, but conversely, the phononic thermal conduction may be manipulated independently. The most obvious way to do this is to replace a lighter element by a heavier one, since a massive object more efficiently dampens vibrations. It is therefore no surprise that one of the most commonly used materials today is bismuth telluride, Bi2 Te3 . Apart from mass, there are numerous ways to achieve low thermal conductivity. A complex or poorly ordered structure will fit the bill but such a material will often have a low electronic conductivity as well. The catch-phrase “electron crystal-phonon glass” coined by Slack [1] nicely sums up what is needed: a material where the electronic structure remains well ordered despite the complexity of some details. A common strategy is to employ a material that contains nanosized inclusions within a relatively rigid network. The inclusions are not part of the electronic network, but scatter phonons. Such materials may be engineered as composites, but there are also many examples of thermodynamically stable phases that form spontaneously. This is an obvious advantage for high temperature applications. Skutterudites and inorganic clathrates (Fig. 8.1) are materials that figure prominently among the candidates. Understanding thermal transport properties of complex compounds requires detailed structural studies, and the challenge lies in getting the details right. Many of the interesting materials have a relatively simple substructure that governs the

Fig. 8.1 The inorganic clathrate Ba8 Ga16 Ge30 [2]. Compounds such as this one that contain oversized voids, allow for encapsulated (clathrated) ions to rattle, acting as efficient scatterers for phonons

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electronic properties, and this is readily understood, but understanding the phononic properties requires knowledge of the local details, which is often a much more demanding task. In this chapter we examine the structures of some state-of-the-art thermoelectrics and some materials that are structurally or chemically closely related to these. Our focus is on the structural aspects of complexity that contribute to the poor thermal transport properties of the materials, and on the challenges this complexity brings to the structural chemist. A common phenomenon in these structures is incommensurability, and we therefore devote an introductory paragraph to the basics of incommensurate structure analysis.

8.1.1 Incommensurate Structure Analysis Once thought an oddity and a rarity, incommensurability is becoming recognized as commonplace and incommensurate behaviour has been detected in every conceivable chemical system from low temperature polymorphs of elements to protein structures. In a modulated structure, a periodic distortion is acting on an average structure to produce a superstructure. This is manifested in satellite reflections that appear at positions in reciprocal space that are not described by the reciprocal lattice or the average structure. In this paper we will deal with unidirectional modulation and, therefore, we need only consider the case when all reflections are indexable, using the normal three Miller indices together with an additional single index, referring to displacement in reciprocal space along a linearly independent modulation q-vector. The q-vector is often specified in terms of the reciprocal axes .a ; b ; c / so that a modulation vector signifying a doubling of the c-axis, is 001=2 .a ; b c / or simply 001=2 (generally ’“ ). If the period of the modulation is not a simple fraction of the reciprocal unit cell of the average structure, the structure is said to be incommensurately modulated or simply incommensurate, and the satellite reflections cannot be explained by exchanging the lattice of the average structure by another lattice that is a simple multiple of the original cell, such as a doubling or a trebling typical for a conventional super structure. Even when the satellite reflections are indexable in a simple super structure, the modulation may be incommensurate (but metrically commensurate). This is easy to understand from a concrete example. Consider a structure that displays a temperature dependent modulation q-vector expressed in terms of a reciprocal lattice vector parallel to c . Let us assume that the q-vector of this compound spans the values q D 00; 0:3 0:4 as the temperature of the measurement is changed. This means that initially the structure is describable as a 10-fold superstructure . D 3=10/, it passes through two smaller superstructures (3-fold at D 1=3, 8-fold at 3/8) and ends up at a 5-fold superstructure . D 2=5/. In reciprocal space, this means that there is a confluence between satellites of different indices at special values, but it is much like in the case of twinning; the satellites are located at the same position, but their phases are not coherent, and the total intensity at that location is given by the sum of the squares of the structure factors for the

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two satellite reflections, rather than by the square of the sum, as would be the case for a coherent structure. In real space, this is a little more difficult to understand. If the satellites indicate a threefold superstructure, what is the additional freedom that makes this an incommensurate modulation? The answer lies in the local variation of cell parameters. In any real sample the cell parameters vary not only as a function of external parameters such as temperature and pressure, but also as a function of location within the unit cell. This is part of what we call mosaicity. These random fluctuations in cell parameters are independent for all free parameters, and this applies to the q-vector as well. It means that the threefold superstructure is but an average value, and that within the single crystal, the q-vector will take other values that differ slightly from D 1=3. In a conventional superstructure the ratio between the modulation vector and the cell parameter that it modulates is fixed. An important step in the determination of an incommensurately modulated structure is the assignment of a super space group. This is done much like for a conventional 3d structure, but the zoo of 3 C 1 dimensional superspace groups is richer than that of conventional space groups. The super space group symbol can be written in many different ways, but one common formalism used is a one line symbol. This is composed of three separate parts, first the conventional 3d space group. This is followed by a parenthesis that contains additional centring conditions that occur in higher space as well as the direction of the q-vector, and finally a part that contains information on any translational operations in the dimension (often referred to as internal space or perpendicular space). The symbol below Pmam(1=2 )s00 then refers to an orthorhombic average structure, Pmam. The modulation has an irrational component along the c direction, but it also contains a rational component of 1=2 along b . This can be interpreted as a centring in 3 C 1d reciprocal space. First order satellites will have the form fha kb lc mqg D fha .k C 1=2/ b .l C / c g, but this is more easily represented in a cell that is doubled in b, where the q-vector is axial and that same satellite has the form ha .2k C 1/ b0 .l C / c . In this new, larger cell, the reflection condition hklm: k C m D 2n applies to all observed reflections. Finally, the last part of the symbol s00 signifies that the mirror plane perpendicular to a is associated with a phase shift of 1=2 period with respect to the modulation function, while the reflections perpendicular to b and c have no effect on the phase of the modulation. It is worthwhile noticing that the point group symmetry of the 3d space group must be preserved by the q-vector. This means that monoclinic modulations are either planar, perpendicular to the unique axis, or axial along the unique axis. Orthorhombic modulations must be axial (sometimes after introducing a simple centring), while tetragonal and hexagonal systems allow single dimensional modulations only along the unique axis. Modulations in the tetragonal or hexagonal planes of tetragonal and hexagonal structures are always bidimensional. Cubic structures only allow (at least) tri-dimensional modulations. In the (common) case, where a highly symmetrical structure exhibits a low symmetry modulation, this signals that the symmetry of the average structure is broken by the modulation. An otherwise perfectly hexagonal-looking structure with a single modulation vector along a is therefore not hexagonal, but probably orthorhombic and possibly monoclinic or triclinic.

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Once the symmetry in super space is determined, it is possible to proceed to solve the structure. Today, there are many ways to do this. For a structure with weak satellite reflections, the modulation is moderate, and for such cases it is often possible to start by solving the average structure and then to proceed to phase the modulation by simply seeding a small harmonic function acting on the displacement or the occupancies of some atoms in the structure. For cases, where the satellite reflections are strong, it may be difficult to find a reasonable average structure, and in such cases, charge flipping in super space is a very powerful method. The final step determining a modulated structure is to make sense of the results. What does the modulation functions mean in real space? Here, it is useful to use a dual approach. To use electron density maps in 3 C 1d space to understand how the trajectory of an atomic surface can be understood in terms of local interactions and local occupancies is enlightening, but it must be coupled to comparison with images of the structure in 3d to yield a full understanding of what happens in higher space.

8.1.2 Modulated Rock-Salt Like Compounds Bi2 Te3 is a classical material for thermoelectric applications, and at a first glance it appears to be a simple compound, consisting of rock-salt-type five-layer-stacks of TeBiTeBiTe separated by van der Waals gaps. A look at the phase diagram (Fig. 8.2), however, reveals that Bi2 Te3 is the most Bi-poor compound in a complex phase field that extends to Bi4 Te3 .

Fig. 8.2 The phase diagram for the system Bi-Te (From Massalski, Binary alloy phase diagrams, 1996 ASM international)

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We have synthesized a number of compounds in this phase field and found that they were all fully structurally ordered, but for the most part incommensurately modulated. To better be able to distinguish between the elements, we chose to study the corresponding Bi-Se phase field that shows similar behaviour [3, 4]. The principle of what first appears as solid solubility is straight-forward; double layers of Bi2 intercalate the van der Waals gap between the Bi2 Se3 rock-salt blocks. Filling all the van der Waals gaps leads to the composition Bi4 Se3 . Even more Bi-rich compositions have been reported, and these may well contain even larger blocks of pure Bi metal. In the composition interval which we have studied, there was a simple relation between the composition and the modulation q-vector, given by q D .00 /, i.e., D 3 .3n C m/ =N, where n is the number of Bi2 Se3 blocks, and m is the number of Bi2 double layers in the full block sequence and N is the total number of layers in that sequence. For the end point compounds we get Bi2 Se3 D> n D 1, m D 0, N D 5, D 9=5 D 1:8 yielding a simple fivefold superstructure, and Bi4 Se3 D> n D 1, m D 1, N D 7, D 12=7 D 1:714 for a sevenfold superstructure. Clearly, the span of the q-vector is very limited, and intermediate values such as BiSe, which is realized as BiSe D> n D 2, m D 1, N D 12, D 21=12 D 1:75 will fall within that range. The correlation between the composition and the q-vector is the most important aspect of the model, and this is why the choice of elements is important. With the marked contrast between Bi and Se this is easy to verify. In terms of a 3 C 1 dimensional model, this is really as simple as it gets. The basis is a simple cubic lattice with a positional modulation that takes up the effect of relaxations, and an occupational modulation that handles the colouring of the structure into Bi and Se. We can now easily understand the mechanisms for doping and dampening on phonons in Bi2 Te3 . A small non-stoichiometry leads to the introduction of irregularly spaced Bi2 intercalates. These enhance the metallicity of the compound, and contribute to the scattering of phonons. As the concentration of intercalated layers increases, we expect incommensurate ordering to kick in, and dominate the central part of the phase field. As we approach Bi4 Se3 we may expect again to lose full ordering as the unfilled van der Waals gaps become too distant to communicate. It should be noted that elemental Bi is a rhombohedrally distorted primitive cubic structure entirely composed of Bi2 double layers, well describable by commensurate modulation with q D .003=2/. This does fit very nicely into the scheme above, with D 3 .3n C m/ =N yielding D 3=2 for n D 0, m D 1, N D 2 (Fig. 8.3). A nice parallel is the structure of stistaite. Here the region of solid solubility extends from the Sn-rich end at Sn4 Sb3 to SnSb 2 at the Sb-rich end. Sb is isostructural to the heavier congener Bi, and is hence likewise describable as a commensurate modulation of a primitive cubic structure. The solid solubility of Sn in Sb extends to about 13% (confer Fig. 8.4). The structure of stistaite itself is composed of an ordered alternation between Sn4 Sb3 seven-layer-blocks and Sb2n intercalated at regular distances. The relation between the magnitude of the q vector and composition might therefore be a little different than for Bi-Se, but the structural behaviour is similar. As we shall see, the two relations are actually identical. The relation between the Sn content and the magnitude (i.e., the component) of the q-vector is given by D 3=2 .1- ŒSn =4/, but ŒSn D fN- .3n C 2m/g=N and

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Fig. 8.3 The phase diagram for the system Bi-Se (From Massalski, Binary alloy phase diagrams, 1996 ASM international)

Fig. 8.4 The phase diagram for the system Sn-Sb (From Massalski, Binary alloy phase diagrams, 1996 ASM international)

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N D .7n C 2m/, which simplifies to an expression identical to that used for the system Bi-Se. i.e., D 3=2 .1- ŒSn =4/ D 3 .3n C m/ =N. The difference between the two systems is more subtle. To our great surprise, the single crystal data showed a pronounced electron density contrast along the extent of the single atomic trajectory in perpendicular space. Moreover, this density contrast corresponds well to two kinds of occupants with a relative ratio that is similar to that of the analytical results for the Sn/Sb ratio. The difference in electron density should, of course, be small for the Sn/Sb couple, but it appears that the behaviour of the thermal displacement parameters for the two atoms is rather dissimilar, the Sb position showing a relatively stiff behaviour with small displacement parameters, and Sn having a much softer appearance. Another aspect of this is also displayed in the relative intensities of the satellite reflections. The satellite reflections for compounds at the Sb-rich end of the existence interval for stistaite are strong and observable up to the third order. For Sn-rich stistaite, the satellites are much weaker, and only first order reflections are systematically observable. This behaviour is caused by two factors: a decrease in the amplitude of the displacive modulation and an increasingly harmonic shape of that same modulation as the Sn content increases. This effect is clearly seen in Fig. 8.5. The corresponding real space structures are shown in Fig. 8.6 [5]. The behaviour of the modulation function is suggestive of the nature of the enigmatic compound Sn3 Sb2 that is stable in a rather narrow temperature interval (242–324ı C, see Fig. 8.4). This compound is cubic, and undergoes a nonquenchable phase transition to Sn-rich stistaite and elemental Sn on cooling. Both

Fig. 8.5 Electron density maps of the single atomic trajectory in a two-dimensional section of real and perpendicular space (x3–x4). Note, how pure Sb (a) displays a saw-toothlike modulation, corresponding to the formation of alternating long and short distances while in Sn-rich stistaite, Sn4 Sb3 (d), the modulation is harmonic and has a much smaller amplitude. Figure (b) is an Sb-rich stistaite, and (c) is an intermediate case. The atomic domain for Sb is given in blue and that of Sn in red (Reproduced from Inorganic Chemistry ASAP May 14, 2009)

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Fig. 8.6 Real space images of the structures of pure Sb (a) and stistaites with varying composition. The saw-tooth like modulation of Sb is realized as alternating long and short distances while the stistaites are composed of Sn4 Sb3 blocks alternating with slabs of pure Sb. For the Sb rich stistaite (b) the Sb slabs consist of four layers, while for the most Sn rich stistaite Sn4 Sb3 (d), there is no pure Sb at all. In the intermediate case (c), empty van der Waals gaps alternate with gaps intercalated with Bi2 double layers. The Sb atoms are shown in blue and Sn in red (Reproduced from Inorganic Chemistry ASAP May 14, 2009)

the stistaite and Sn that form are mimetically twinned to give an overall cubic diffraction pattern, i.e. tetragonal Sn is present in three different domain directions, and rhombohedral stistaite is present in four different domain directions. The diffraction pattern also contains extensive diffuse scattering indicative of strain. The crystals are shiny, metallic cubes or truncated cubes. On storing at room temperature, the crystals undergo substantial internal rearrangement. The balanced twinning is lost, giving rise to one dominant stistaite domain, the diffraction information from Sn disappears, as does the diffuse scattering. The non-quenchable nature of the transformation provides strong evidence that the high temperature structure is ordered. It appears probable that the failure of previous investigations to identify any super structure ordering (only reflections coming from the primitive cubic lattice of a disordered rock-salt-type structure have been reported) [6] is caused by two factors: the general weakening of satellite reflection intensity as a function of increasing Sn content in stistaite and the cubic structure of Sn3 Sb2 . The latter is quite important. If the structure of Sn3 Sb2 indeed is cubic, it must have a superstructure (modulated or otherwise) that displays satellites in at least three independent directions. This means that the average intensity of the satellites is decreased by a further factor, as compared to that of single crystal rhombohedral,

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room-temperature stistaite. All in all, it is conceivable that a highly ordered Sn/Sb arrangement in Sn3 Sb2 is quite invisible to an x-ray experiment, particularly a powder study.

8.1.3 The Remarkable System Sb-Zn The phase diagram of Sb-Zn shows the existence of two intermetallic phases stable at room temperature, and another four that appear at higher temperatures (see Fig. 8.7). The equimolar phase ZnSb is a classical Zintl phase that formally appears to be composed of Zn2C ions and Sb2 4 units. The existence of short Zn–Zn distances in the structure, however, modifies this first glance view to a more complex picture. The compound has a low thermal conductivity, but the electrical conductivity is too low to make it interesting from a thermoelectric perspective. The phase that has attracted most interest from the thermoelectric community is the compound known as Zn4 Sb3 , dubbed " in the phase diagram in Fig. 8.7. This not one phase but several, and in fact it is even several compounds. At room temperature, the stable compound is the “ phase. This crystallizes in a rhombohedral structure ˚ for both the a- and the c-axes in an hexagonal with cell parameters close to 12 A setting. The ideal crystallographic composition is Zn6 Sb5 but it was noted already in the initial structural studies [7,8] that the compound is richer in Zn than indicated

Fig. 8.7 The phase diagram for the system Sb-Zn (From Massalski, Binary alloy phase diagrams, 1996 ASM international)

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by this formula. Both investigations used mixed occupancies of the Sb positions to explain this aberration, but this explanation appears chemically questionable, and our own experience is that models, where the Sb occupancy is allowed to change normally, lead to an over occupancy of Sb rather than the under occupancy needed to model Zn/Sb mixed sites. A subsequent synchrotron powder study [9] indicated that the compositional variation was best explained by the presence of interstitial Zn. We were fortunate to produce single crystalline material of sufficient quality for x-ray studies, and this revealed that the compound is temperature-polymorphic. At room temperature and down to approx. 245 K, the “-phase is stable. In a relatively narrow temperature regime, the ’-phase is stable, and below 235 K, yet another polymorph is formed, ’0 . It should be noted that this sequence of transformations is quite general, although the exact transformation temperatures may depend on sample history, and the temperature dependent resistivity as measure for different samples tells this tale (see Fig. 8.8). As the single crystal sample is cooled below 245 K, we observe a fourfold super structure appearing in the diffraction pattern. The direction of this commensurate modulation is the reciprocal 111 direction, and it is accompanied by mimetic twinning that preserves the overall trigonal symmetry of the diffraction pattern. Further cooling below 235 K produces a highly complex pattern. In between the satellite reflections that signify the “ to ’ transition, new reflections appear with rather irregular distances to the ’-phase satellites. At a first glance, it appears to be a further modulation of the structure, but a closer scrutiny reveals that it is in fact a second phase that coexists with the ’-phase rather than replaces it. It constitutes a 13-fold superstructure of the original “-phase. The direction of this superstructure coincides with that of the ’-phase in reciprocal space (Fig. 8.9). The structure of the “-phase is a complex network, where all nearest neighbour ˚ The Zn atoms form pairs, each Zn distances lie in the narrow range of 2.7–2.8 A. atom tetrahedrally surrounded by Sb atoms, and these tetrahedral share edges to generate a short Zn–Zn distance. One Sb position has a tetrahedral surrounding

Fig. 8.8 Low temperature resistivity for Zn4 Sb3 . Blue line: vacuum melted sample [10]; red line: gradient freeze prepared sample [11]; top green line: solid state reaction sample [12] and bottom green line: SPS treated sample [13] (Reproduced from the thesis of Johanna Nylén, Stockholm University 2008)

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Fig. 8.9 Reconstructed reciprocal lattice images from a single crystal x-ray measurement at different temperatures. Indexing in red refers to the rhombohedral “-phase, while indices in black refer to the pseudo monoclinic unit cell of the ’-phase. Top left: room temperature, top right: 240 K, large image at bottom: 230 K (From the thesis of Johanna Nylén, Stockholm University, 2008)

from three Zn and one Sb, and the other Sb atom is surrounded by six Zn atoms (see Fig. 8.10). There are no obvious interstices in the structure where extra Zn atoms might be expected to reside. Solving the structure of the ’-phase turned out to be challenging. While this was expected for a low symmetry mimetic twin of a high symmetry parent structure, the problems where exacerbated by the fact that the undoped ’-Zn4 Sb3 contains impurities of the “-phase. The “single” crystal diffraction pattern, is hence a compound pattern composed not only of six different domain orientations of the ’-phase, but also of remnant “-phase that coexists in the same single crystal. The explanation for this unusual behaviour is that the a-phase has a slightly different composition from the “-phase, and that the phase transformation is in fact a bifurcation, where the Zn-rich ’-phase on forming depletes the “-phase of some Zn, and this leaves a remnant “-phase that is too Zn-poor to transform to the ’-phase. As mentioned above, the transformation to the ’0 -phase displays a similar behaviour. The ’0 -phase has a Zn content that is intermediate to the ’-phase and the “-phase, and when the ’0 -phase is formed, this exhausts the supply of “-phase, leaving a single crystal that

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Fig. 8.10 The idealized structure of “-Zn4 Sb3

is a composite of ’0 -phase and remnant ’-phase. In one particular sample that was studied by us in great detail we could estimate the following sequence of phases and compositions: At room temperature, the single crystal is monophasic, consisting of the pure “-phase of the composition Zn12:94 Sb10 . After the partial phase transformation at 245 K, the crystal consists of 67% of the ’-phase with the composition Zn13 Sb10 and 33% of a Zn depleted “-phase with the composition Zn12:82 Sb10 . Finally, at temperatures below 235 K, the sample consists of about 80% ’0 -phase with a composition Zn84 Sb65 and 20% ’-phase with the composition Zn13 Sb10 . We were greatly helped in the elucidation of this behaviour by doping studies. As it turns out, doping with Bi leads to a substantially larger unit cell, and presumably to a higher Zn content. In any case, in a Bi-doped single crystal, the ’ to ’0 transition is suppressed, and the ’-phase forms on cooling without leaving any measurable remnant of “-phase. The structure of the Bi-doped ’-phase was solved by using the positions of the “-phase as a starting model in the ’-phase cell and applying the appropriate twinning matrices to account for the allowable domain directions. To phase the satellite reflections, interstitial Zn positions were included as partially occupied at loci of substantial residual electron density, and any regular Zn positions with unphysical distances to the interstitial Zn were also treated as partially occupied. The model was seeded with some unbalance in the occupancies to break the inherent trigonal symmetry, and the structural refinement was run using moderate damping of the least squares procedure, periodically examining the occupancies of the partially occupied positions, and evaluating the residual electron density map for any new interstitials to be included in the model. This procedure was tried for the maximum monoclinic subgroup of R-3c under the relevant transformation, i.e. C2/c and for the three direct subgroups of that group, C2, Cc and C-1. Only the last of the three subgroups yielded a model that converged to a satisfactory agreement between model and data. Moreover, this model featured fully occupied positions only, and was judged to be the correct solution. Introducing this solution as a starting model

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for solving the undoped ’-phase yielded a solution that was acceptable, but clearly inferior to that of the Bi-doped sample. Introducing split positions for the Zn interstitials to model a mixture of the ’-phase and the “-phase resolved this problem. It is instructive to consider a slab of the electron density map from the refinements (see Fig. 8.11). A comparison of the electron density maps from the doped ’-phase and the “-phase clearly shows how a five atom arrangement in the ’-phase replaces

Fig. 8.11 Electron density map of a slab of Zn4 Sb3 viewed down [12–4] of the ’-phase triclinic unit cell. Top left: Bi-doped ’-Zn4 Sb3 as measured at 100 K. Top right: Undoped “-phase at room temperature. Bottom: Undoped ’-phase/“-phase composite at 240 K. Note the five-atom-cluster (red) in the doped ’-phase that replaces the three-atom-motif (blue) in the “-phase, and how they are both discernable in the composite crystal

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a three atom arrangement in the “-phase, to yield a structure with a larger number of well ordered Zn positions. The general role of doping is far from clear. While Bi-doping is most naturally seen as a means of expanding the lattice to allow for a higher Zn content and a resulting enhanced stability of the ’-phase, doping with Sn suppresses not only the ’-to-’0 transition, but even the “-to-’ transition. More intriguing still, doping with Pb suppresses the appearance of the ’-phase, and a Pb-doped single crystal exhibited a direct “-to-’0 transition [14]. A remaining challenge was the structure of the ’0 -phase. By considering the structure of the ’-phase in a certain projection, it was possible to make an educated guess. Looking down the triclinic b-axis in ’-Zn4 Sb3 it is clear that this structure is in fact composed of two kinds of blocks: blocks that are identical to the “-phase and contain no ordered interstitials, and blocks that contain ordered interstitials. In fact, the fourfold superstructure of the ’-phase consists of a strict alternation of slabs with and without ordered interstitials. Slabs corresponding to a single unit cell of the “-phase alternate with slabs three times as thick, containing ordered interstitials. To construct a model for the 13-fold superstructure in ’0 -Zn4 Sb3 we may consider simple variations on this theme, the most obvious being regularly inserting an extra “-phase slab after three full unit cells of the ’-phase. Alternatively, in terms of “-phase-type unit cells containing ordered interstitials .’/ or not .“/, this would be a sequence..“’’’“’’’“’’’“.. This yields a 13-fold superstructure and, employing this as a model to treat the data from the single crystal experiment, produces a refinement that shows a reasonable fit between model and data (R D 15%), and this may be acceptable for a model that contains two distinct phases, each mimetically twinned, which share all main reflections and where part of the satellites overlap as well. In order to assess the validity of the solution we undertook an attempt to solve the structure pseudo ab initio. The procedure was as follows: the multiply twinned biphasic model was used to deconvolute the data into an artificial set, containing data corresponding to a single, untwinned, ’0 -phase individual using the software package JANA [15]. This data was then used as input for charge flipping [16], as implemented in the program Superflip [17]. To our surprise and delight, Superflip did not produce the solution used as input, but a slight variation on the theme. Moreover, the solution provided by Superflip refined to a substantially better agreement (R D 11%) against the original data set. Rather than reproducing our original proposal which involved exchanging every third interstitial-free “-phase type unit cell slab for an interstitial-free slab of double thickness, the model produced by Superflip indicated that two interstitial-free slabs out of three should be 1.5 times thicker. While the improvement in agreement between model and data is convincing, it is still a little short of proof. By a second stroke of good fortune, we found that Pb-doping produces the pure ’0 -phase, and from a twinned, but single phase crystal of this sample, we were able to make a better comparison between model and data, and in this case the refinement ended up at R D 7%, which we take as final evidence that the structural proposal is very close to reality.

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Fig. 8.12 Projection of the structure of ’-Zn4 Sb3 down the triclinic b-axis. Sb atoms are shown in red, ordinary Zn in yellow and low temperature ordered interstitial Zn in blue. A unit cell of the ’-phase is indicated in black. The interstitial filled ’-type slabs are shown in red, and interstitial free “-type slabs are shown in yellow

Fig. 8.13 Structural model of ’0 -Zn4 Sb3 . Red signify ’-type and yellow “-type slabs. Note how the thickness of “-type slabs varies

Further to the Zn-rich end of the diagram, we find two more phases in the system Zn-Sb. These are the — and ˜phases of Zn3 Sb2 . To claim these as promising thermoelectrics is exaggerated. To our knowledge, no measurements have been made of any physical properties of these compounds. It may be expected that they are too metallic to have significant thermopower, but this may in such a case be resolvable by doping. Judging by their structural features, their thermal transport

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Fig. 8.14 Part of the Sb substructure of —-Sb2 Zn3 . The general scheme is simply a column of facesharing pentagonal antiprisms. The central atoms of the antiprisms form a succession of strained Sb–Sb distances

Fig. 8.15 Central atoms of the column of pentagonal antiprisms. Note how two distances occur: ˚ and normal Sb3 Sb3 ˚ These are typical distances for Sb2 4 dumbbells (2.8 A) 2.85 and 4.00 A. ˚ distances (4.0 A)

properties should be remarkable. The high temperature phase — is an interesting borderline case between a Zintl phase and a valence compound. It is slightly Zn poor and the composition is temperature dependent. The structure consists of columns of Sb-centred Sb pentagonal antiprisms. Zn resides in tetrahedral interstices. The Zn arrangement becomes complex because of the general rule that filled tetrahedra do not share faces [18]. Since the Sb network consists almost exclusively of facesharing tetrahedral, the pattern of occupancy becomes a complex colouring problem. To compound things, the Sb network is incommensurately modulated. The mechanism is simple. The distance between the centre of a pentagonal antiprism and the vertices is about 5% less than that between neighbouring vertices. In a column of pentagonal antiprisms, a strain builds up, and in our case it is released by occasional short contacts along the pseudo fivefold axis. In our description this structure crystallizes in the orthorhombic super space group Pnaa(’00)0s0 with a modulation vector of ’ D 0:385. The behaviour of the Sb in the central position of the pentagonal antiprism is simply described by a saw-tooth modulation, and this is the only sizable modulation for Sb atoms in the structure. This is a nice confluence of the geometrical factor of ratios between centre-to-vertex distances in a pentagonal antiprismatic column and the distance relation between Sb atoms in a chain containing isolated Sb3 as well as Sb2 4 . The Zn atoms are all severely modulated, and the reason is simple. All Zn reside in the tetrahedral interstices of the Sb substructure, and besides the normal constraint that no tetrahedral sharing a face may be simultaneously occupied, an additional rule for this system is that Sb tetrahedral containing a short Sb-Sb bond are unavailable for Zn occupation. This couples the modulation to the general complex rule of stuffing tetrahedrally close packed structures to yield a structure that is very complex indeed. It is interesting to note that locally, many of the features

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Fig. 8.16 Succession of local clusters of Zn (red) in —-Zn3 Sb2 . Note the similarity to the ordered interstitials in ’-Zn4 Sb3

Fig. 8.17 Sb-arrangement in —-Zn3 Sb2 . The structure is almost perfectly tetrahedrally close-packed. The exception are the yellow octahedral

from the structure of ’-Zn4 Sb3 may be found in the —-Zn3 Sb2 . In Fig. 8.16 it is particularly interesting to note the presence of the kite-like object that forms from the ordered interstitials in Zn4 Sb3 . This compound presented an unusual challenge. While the structural solution was relatively straight-forward: Direct methods yielded a mean cell content of mainly Sb positions. Successive refinement cycles revealed more and more of the Zn positions and the fit between model and data became successively better, the problem was that the structure was utterly incomprehensible from a Sb-Zn bonding perspective. After shifting focus to the Sb-substructure the principle behind the arrangement, as well as the cause of the modulation became clear. In Fig. 8.17 the full Sb-network of the structure is shown. The arrangement may be viewed as constructed from tetraederssterns and icosahedra, typical building-blocks for Frank-Kasper phases. In addition, the network contains two columns of octahedral, the exceptions to the tetrahedrally close packed arrangement of Sb. The Zn atoms may reside in any position that is the centre of a Sb-tetrahedron, but the octahedral interstices remain empty. A final phase that occurs in the Zn-Sb system is ˜ Zn3 Sb2 . This compound is globally very different from the high temperature modification —-Zn3 Sb2 , but locally the similarities are substantial. Again, we have a relatively complex structure, which is most easily described from the point-of-view of an ordered Sb-substructure with Zn interstitials. In ˜ Zn3 Sb2 the Sb substructure is largely a primitive cubic packing of Sb13 icosahedra (confer Fig. 8.18). Each icosahedron is surrounded by a complete Sb dodecahedron, but these polyhedra interpenetrate. As for the structure

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Fig. 8.18 Arrangement of Sb13 icosahedra in ˜-Zn3 Sb2 . Left: The icosahedra form a primitive cubic packing, but the orientation of the icosahedra lowers the symmetry to rhombohedral. Right: Each triangular face of the icosahedra is capped by Sb atoms, so that Sb20 dodecahedra are formed surrounding the Sb13 icosahedra

of —-Zn3 Sb2 , the structure is almost tetrahedrally close packed. In perfect agreement with the high temperature phase, octahedral interstices are empty and face sharing tetrahedra are never simultaneously filled by Zn. Although the basic struc˚ and ture is relatively simple, with a rhombohedral cell (symmetry R3) close to 12 A a rhombohedral angle close to 90ı , the Zn arrangement breaks this simple pattern and generates a fourfold super structure along the rhombohedral 111 direction (c in hexagonal setting). The resulting superstructure has a unit cell of a D b D 15:1218; c D 74:8335 at room temperature and the Zn ordering is very far from complete. There is evidence that Zn orders further at low temperatures to yield a superstructure, but here we are still waiting for better crystals to attempt a solution. Due to the large number of partially occupied positions, the structure of the compound as it stands is rather unrevealing in terms of Zn–Zn contacts. As is evident from the phase diagram, the compound is not stable at room temperature, but undergoes a slow transition to microcrystalline Zn4 Sb3 and elemental Zn. The structure is straight-forward to solve by either direct methods or charge-flipping [19].

8.2 Conclusion Complex intermetallic compounds have long been an esoteric pursuit for the few interested. The physical properties of complex intermetallics are not too promising: the transport properties are poor, the mechanical stability likewise. Most interesting

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magnetic materials are structurally relatively simple. The resurgent interest in thermoelectrics has brought new life to this area. The examples given in this paper illustrates some structural challenges that more detailed studies of complex intermetallics unearth. The frequent incommensurabilities and the disorder highlights the usefulness of non-atomistic methods for structural elucidation, in particular chargeflipping turns out to be an invaluable tool to use. The information furnished by these studies ranges from clear-cut explanations to strange phase behaviour, as for Zn4 Sb3 to less precise indications as to the mechanism for poor transport properties in the rock-salt like compounds where we believe that incommensurability may play a large role in suppressing phononic heat transport. In either case, a happy confluence between new, powerful methods for structural studies, and a renewed interest in intermetallics has brought the subject to a new level of sophistication as shown by many groups active in this area. Acknowledgements I am indebted to a large number of people who contributed to the original work that forms the basis of this compilation. My long time senior associate Ulrich Häussermann, now at ASU in Arizona, Ray Withers and Lasse Norén at the ANU in Canberra, Siegbert Schmid at Sidney University and Kjell Jansson at Stockholm University. Present and former postdocs Simeon Ponou at Stockholm University and Danny Fredrickson now at the University of Wisconsin, as well as present and former PhD students Johanna Nylén now at ASU, Jeppe Christensen now at the University of Warwick, Hanna Lind at Scania AB, Magnus Boström at Sandvik AB and Andreas Teng˚a at Stockholm University. For support and help on various aspects of the software packages JANA and Superflip, I am deeply indebted to Vaclav Petricek, Michael Dusek and Lukas Palatinus. Few commercial codes provide the customer support that comes with these freeware gems. This work was sponsored by the Swedish Research Council, the Swedich Foundation for Strategic Research, the European network for Complex Metallic Alloys. Postdoctoral support is acknowledged from the US National Science Foundation (DF) and the Wennergren Foundation (SP).

References 1. Slack, G.A., New Materials and Performance Limits of Thermoelectric Cooling 1995, CRC Press LLC 2. Bentien, A., Nishibori, E., Paschen, S. and Iversen, B.B. Physical Review 2005, B71, 14407 3. Lind, H. and Lidin, S., Solid State Sciences 2003, 5, 47–57 4. Lind, H., Lidin, S. and Häussermann, U., Physical Review 2005, B72, 184101 5. Lidin, S., Christensen, J., Jansson, K., Fredrickson, D., Withers, R., Norén, L. and Schmid, S., Inorganic Chemistry ASAP, 2009 6. Ellner, M. and Mittlmeijer, E.J., Acta Crystallographia 2002, A58, C333 7. Bokii, G.B. and Klevtsova, R.F., Zhurnal Strukturnoi Khimii 1965, 6, 830–834 8. Mayer, H.W., Mikhail, I. and Schubert, K., Journal of the Less Common Metals 1978, 59, 43–52 9. Snyder, G.J., Christensen, M., Nishibori, E., Caillat, T. and Iversen, B.B., Nature Materials 2004, 3, 458–463 10. Bhattacharaya, R.P., Hermann, V. and Keppens, T.M., Physical Review 2006, B74, 134108 11. Nakamoto, G., Takeshi, S., Masasuke, Y. and Makio, K., Journal of Alloys and Compounds 2004, 377, 59–65 12. Nylén, J., Andersson, M., Lidin, S. and Häussermann, U., Journal of the American Chemical Society 2004, 126, 16306–16307

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13. Souma, T., Nakamoto, G. and Kurisu, M., Journal of Alloys and Compounds 2002, 340, 275–280 14. Nylén, J.,Lidin, S., Andersson, M., Brummerstedt, B.B., Liu, Y., Newman, N. and Häussermann, U., Chemistry of Materials, 2007, 19, 834–838 15. Petricek, V., Dusek, M. and Palatinus, L., JANA2000 2005 Academy of Sciences of the Czech republic 16. Oszlanyi, G. and Suto, A., Acta Crystallographia 2004, A60, 134–141 17. Palatinus, L. and Chapuis, G., Journal of Applied Crystallography, 2007, 40, 786–790 18. Boström, M and Lidin, S., Journal of Alloys and Compounds, 2004, 376, 49 19. Lidin, S. and Bostrom, M., Abstracts of papers of the American Chemical Society, 2003, 226, U724–U724

Chapter 9

Solid State Transformations in Crystalline Salts Susan A. Bourne, Nikoletta B. Báthori, and Lesego J. Moitsheki

Abstract Two examples are described of reactions which proceed in the crystalline state. In the first, a metal-organic salt ŒCo .H2 O/6 X2 2 .bpdo/ 2 .H2 O/ .X D Br ; Cl / transforms at room temperature into a coordination polymer ŒCoX2 .bpdo/ .H2 O/2 H2 O with different connectivity. The process can be followed by powder x-ray diffraction. In the second example, we observed sublimation/dissociation and recrystallisation under ambient pressure when a single crystal of 4-(1-hydroxy-1,2-diphenylethyl)pyridinium chloride was heated and the pure organic moiety crystallized on the mother crystal surface providing an excellent example of molecular structure – macroscopical property relationship which can be explained by partial isostructurality. Under similar conditions the nitrate salt of the same compound, 4-(1-hydroxy-1,2-diphenylethyl)pyridinium nitrate sublimed and recrystallised without dissociation. The two crystal structure of the salts are isostructural but the Hirshfeld surface analysis shows significant differences between the intermolecular interactions which can explain the different thermal behavior of them in the crystalline phase while the computational studies explained their behavior in gas phase.

9.1 Introduction The process of crystallisation is influenced by many factors and elucidation of such structure-determining factors remains a source of great interest to those working in industrial crystallisation, polymorphism and crystal engineering [1–6]. Several authors have proposed reasons for a specific molecular arrangement to occur in a crystal structure, with support from theoretical calculations [7–9].

S.A. Bourne (), N.B. Báthori, and L.J. Moitsheki Centre for Supramolecular Chemistry Research, Department of Chemistry, University of Cape Town, Rondebosch 7700, South Africa e-mail: [email protected]


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In turn, reactions which proceed in the absence of, or presence of only catalytic amounts of solvent have generated enormous interest in recent years. Typically, these reactions require the close contact of reactants in mechanochemical grinding [10], “solvent-drop” grinding [11] or microwave-promoted reactions [12]. In some cases, reactions may also occur by the interactions of vapour with the solid state [13, 14]. We are interested not only in the synthesis of new materials by reactions without solvent [15], but also in the solid phase transformation from one crystalline solid form to another. Several other authors have studied such crystal transformations. For example, the thermochromic compound, 1,5-bis(hydroxyethylamino)-2,4dinitrobenzene (BDB) exists in two crystalline forms which differ in their hydrogen bonding networks. The thermochromic transformation from one form to the other is reversible and can be followed by X-ray diffraction and DSC [16]. The removal and readsorption of guest molecules was responsible for the crystal transformation in 2D coordination networks of [Co(NCS)(3-pia)2] (where 3pia is N-(3-pyridyl)isonicotinamide) which could be followed by EPR and IR spectroscopy [17]. Kepert et al. correlated the transition from ferromagnetic to antiferromagnetic behaviour with the dehydration-hydration reaction in a coordination framework [18]. However, these authors did not correlate the structural changes they describe with crystal morphology.

9.2 Solid State Transformation in Some Metal-Organic Salts As part of a larger study [19–21] into the coordination compounds of transition metals with 4,40 -bipyridine-N; N 0-dioxide (bpdo), we prepared the salts ŒCo .H2 O/6 Br2 2 .bpdo/ 2 .H2 O/ (1) and ŒCo .H2 O/6 Cl2 2 .bpdo/ 2 .H2 O/ (2), which transform over days into 1D coordination polymers ŒCoBr2 .bpdo/ .H2 O/2 H2 O (1b) and ŒCoCl2 .bpdo/ .H2 O/2 H2 O (2b) (Fig. 9.1 and Table 9.1). These two structures, while not isostructural, have identical packing motifs so only 1 is illustrated. Figure 9.2 shows the packing of 1, in which it is evident that the structure takes the form of a layered organic–inorganic hybrid complex. The ˚ ŒCo .H2 O/6 2C ion is octahedral with Co-O distances between 2.075 and 2.148 A. Two ŒCo .H2 O/6 2C cations are linked by bridging bpdo molecules held in place by hydrogen bonds between Co-O-H. . . O-N-(bpdo). The remaining coordinated water molecules hydrogen bond to a guest water molecule, which in turn engages in an O-H. . . X interaction with the bromide (in 1) or chloride ion (in 2). Adjacent bpdo ˚ in 1, 3.83 A ˚ in 2). molecules stack to give offset : : : interactions (3.79 A Standard fixed heating rate thermogravimetry (TG) and differential scanning calorimetry (DSC) for these compounds (Fig. 9.3) shows that 1 decomposes in two steps. Between 80ı C and 180ıC there is a two-step mass loss in the TG which correlates to two endothermic peaks in the DSC and is attributed to the loss of both coordinated and lattice water molecules (observed mass loss 14.62%; expected mass loss for 8 waters from 1 14.57%). At ca. 300ıC, the complex decomposes

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Fig. 9.1 Schematic diagram of metal-organic salts 1 and 2 and their corresponding 1D coordination polymers Table 9.1 Crystal data for 1 and 2 1 Molecular formula ŒCo .H2 O/6 Br2 . 2 .bpdo/:2 H2 O Formula weight 739.25 (g mol1 ) Space group P 21 =c ˚ a (A) 10.3728(2) ˚ b (A) 6.6329(1) ˚ c (A) 20.0945(4) ’ .ı / 90 “ .ı / 93.366(1) ” .ı / 90 ˚ Volume (A) 1,378.58(4) Z 2 Goodness of fit on 1.171 F2 Final R indices, R1, 0.0439, 0.1117 wR2 (I > 2¢I) Max peak and hole 0.924, 3:105 ˚ 3 ) (e A

2 1b ŒCo .H2 O/6 Cl2 . ŒCoBr2 .bpdo/ .H2 O/2 . 2 .bpdo/:2 H2 O H2 O 650.33 459.97

2b ŒCoCl2 .bpdo/ .H2 O/2 . H2 O 371.05

P 1N 6.7328(2) 10.2841(3) 10.6577(3) 85.200(1) 70.023(1) 91.103(1) 690.21(3) 1 1.102

C 2/c 23.958(5) 5.695(1) 10.862(2) 90 108.60(3) 90 1,404.5(5) 4 1.121

C 2/c 24.114(5) 5.618(1) 10.751(2) 90 109.16(3) 90 1,375.7(5) 4 1.101

0.1055, 0.2736

0.0458, 0.1259

0.0691, 0.2115

0.936, 0:783

1.018, 1:059

0.976, 0:572

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Fig. 9.2 Crystal packing in 1 (that of 2 is identical)

Fig. 9.3 Thermal analysis (TG, DSC and hot stage microscopy) of 1

exothermically. These changes can also be followed on the hot-stage microscope (see inset photographs in Fig. 9.3). When left on an open glass slide, within a week dry crystals of compounds 1 and 2 transform into the 1D coordination polymers 1b and 2b (see Table 9.1). These compounds are isostructural with respect to their similar unit cell parameters and atomic coordinates. The structure of 1 comprises a cobalt (II) ion coordinated to two bromides (in the trans configuration), two water molecules and two bpdo molecules. The octahedral symmetry is slightly irregular with bond angles ranging from 86:6ı

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Fig. 9.4 Crystal packing in 1 (that of 2 is identical)

Fig. 9.5 Powder x-ray diffractograms of 1 transforming to 1b

to 93:4ı . Bond lengths are all within expected ranges. The bpdo ligand functions as a bridge to connect two cobalt ions, giving a 1D coordination polymer, shown in Fig. 9.4. Adjacent polymer chains are connected by C-H. . . O hydrogen bonding between bpdo molecules and a guest water molecule. We attempted to follow this transformation using powder x-ray diffraction (attempts to observe the transformation in single crystals were unsuccessful). A powdered sample of 1 was kept in the dark at room temperature (ca. 20ı C) for a period of 2 weeks. The powder diffraction pattern was measured every few days and showed an increased intensity for peaks corresponding to 1b, while those for 1 decreased in intensity (shown schematically in Fig. 9.5).

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9.3 Sublimation and Dissociation in Simple Salts of an Organic Compound Sublimation has long been used as a simple technique to purify solid materials. Several authors have investigated the kinetics of sublimation of simple salts such as ammonium chloride [22, 23] or ammonium perchlorate [24]. More recently, Zhu et al. proposed that these processes involve three steps consisting of a surface reconstruction of the crystal, proton transfer between the ion pair followed by their desorption from the relaxed surface to the gas phase and, finally, the dissociation into neutral species.[25, 26]. In our study, we found two simple salts of 4-(1-hydroxy-1,2-diphenylethyl) pyridine, 3, which both sublime but then differ in their behaviour in the gas phase. While 3HC :NO3 retains its identity and recrystallises as the identical salt, 3HC :Cl decomposes in the gas phase into its constituent parts and the recrystallised product is 3. Moreover, the recrystallisation of 3 can be observed to occur on a large crystal of 3HC :Cl but occurs preferentially on equivalent faces of the mother crystal.

9.3.1 Crystal Structures and Isostructurality Bond lengths and angles of 4-(1-hydroxy-1,2-diphenylethyl)pyridine are similar in the three structures but the conformation changes dramatically on salt formation: the torsion angle C4-C7-C9-C10 is 58:3ı in 3 but 169:7ı in 3HC :Cl and 174:6ı in 3HC :NO3 . This is illustrated in Fig. 9.6, which also shows the atom labelling used. Table 9.2 gives data for all three crystal structures.

Fig. 9.6 Crystal structures of 4-(1-hydroxy-1,2-diphenylethyl)pyridine (3) and its chloride and nitrate salts. Thermal ellipsoids are drawn at 50% probability level and H atoms shown as spheres of arbitrary radius

9


Table 9.2 Crystal data for 3 and its salts 3 Molecular formula C19 H17 NO 275.34 Formula weight (g mol1 ) Space Group P 21 =c ˚ a (A) 9.345(2) ˚ b (A) 10.612(2) ˚ c (A) 15.267(3) ’ .ı / 90 “ .ı / 107.70(3) ” .ı / 90 ˚ Volume (A) 1,442.2(5) Z 4 Goodness of fit on F2 1.04 Final R indices, R1, wR2 0.0370, 0.0932 (I > 2¢I) 0:19, 0.17 Max peak and hole ˚ 3 ) (e A

225

3HC :Cl C19 H18 NOCl 311.80

3HC :NO 3 C19 H18 N2 O4 338.35

P 1N 6.322(1) 8.448(2) 15.349(3) 102.22(3) 92.54(3) 106.21(3) 764.6(3) 2 1.04 0.0333, 0.0895

P 1N 6.317(1) 8.197(2) 16.497(3) 100.78(3) 91.20(3) 100.44(3) 823.9(3) 2 1.04 0.0501, 0.1181

0:22, 0.27

0:20, 0.40

The packing of 3 (Fig. 9.7) involves head-to-tail chains linked by O8-H8. . . N1 ˚ hydrogen bonding. These chains connect via weak O8: : :N1 D 2:851.2/ A

˚ . The packing of 3HC :Cl C. . . O hydrogen bonds C13: : :O8 D 2:708 .2/ A and 3HC :NO3 are similar, both forming 1D chains in which the anion links ˚ and hydroxyl the pyridyl (N1: : :Cl1 D 3:388 .2/ or N1: : :O2 D 2:892 .2/ A) ˚ or O8: : :O1 D 2:748 .2/ A) ˚ groups (see Fig. 9.8). There (O8: : :Cl1 D 3:098 .1/ A are : : : interactions between the pyridyl rings in both; however the distances ˚ in 3HC :Cl is significantly shorter than between the offset parallel planes of 3.63 A C ˚ observed for 3H :NO3 . The phenyl and benzyl groups of adjacent the 4.08 A chains interdigitate to form a zipper-like motif. The three structures have similar packing coefficients (3: 69.1%, 3HC :Cl : 71.9%, 3HC :NO3 D 70:4%). The unit cell similarity .˘ D 0:0341/ and the isostructurality indices I v D 90:6%, Ivmax D 97:2%) show that the crystal structures of the two salts are isostructural [27, 28].

9.3.2 Thermal Analysis Despite their isostructurality, we found that the two salts of 3 have very different behaviour when they are heated. Figure 9.9 shows the differential scanning calorimetry (DSC) traces. Crystals of 3 melt at 190ı C while crystals of 3HC :Cl start to sublime at ca. 170ıC and decomposition was observed at ca. 240ıC. The DSC of 3HC :NO3 has an endothermic peak at 215ıC immediately followed by an exothermic peak due to recrystallisation and a slow sublimation until decomposition occurs at ca. 300ı C.

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Fig. 9.7 Packing motif in 3. Hydrogen bonds between pyridyl and hydroxyl moieities form one dimensional chains parallel to [001] while weak C-H. . . O interactions connect the chains

We studied these processes further using hot-stage microscopy (HSM). Doing so, we realised that both salts sublime and recrystallise on the cover slip. We were able to recover small crystals from the top cover slip which could be analysed using both powder and single crystal x-ray diffraction. Interestingly, while the sublimed product of the nitrate salt is still 3HC :NO3 , that of 3HC :Cl is the pure organic parent, 3. In order to obtain crystals of good quality we repeated the experiment using a large single crystal of 3HC :Cl and maintaining the temperature at 200ı C for 30 min. During this time, relatively large, good quality crystals were observed to grow preferentially on one face of the mother crystal (Fig. 9.10). These columnar crystals were subjected to DSC and single crystal X-ray diffraction analysis which confirmed that they were compound 3. In order to study the crystal transformation of 3HC :Cl to 3, we selected a large crystal .8 3 1:5 mm/, heated it to 200ı C for 30 min and then examined it using Scanning Electron Microscopy (SEM). Figure 9.11 shows the outcome. On the top surface and the long side of the mother crystal we did not observe crystal growth while on the short side many small crystals are apparent (Fig. 9.11a). Cutting the crystal perpendicular to the growth direction, the new surface was perfectly smooth (Fig. 9.11b). To identify this new surface we used BFDH morphology prediction

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Fig. 9.8 Crystal packing in 3HC :Cl . Hydrogen bonded chloride ions link the molecules into chains, while the phenyl and benzyl substituents form a zipper motif, also parallel to the b-axis

Fig. 9.9 DSC traces of 3, 3HC :Cl and 3HC :NO3

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Fig. 9.10 HSM pictures of the sublimation/decomposition process. (a) A crystal of 3HC :Cl before heating (note prismatic morphology). Maintaining the temperature at 200ı C for 30 min

allows crystals of 3 to grow on the surface of the mother crystal 3HC :Cl . (b) Black arrows indicate the columnar crystals of 3 which could be subjected to single crystal X-ray diffraction

Fig. 9.11 SEM pictures of 3HC :Cl . (a) The surfaces of the mother crystal show new crystal growth only on the short sides (left and right in figure). (b) Surface of the mother crystal after it was broken. (c) Comparing the SEM result and the BFDH predicted morphology result of crystal 3HC Cl

[29] which agrees well with the crystal shape and the face indexing performed on a single crystal of 3HC :Cl (Fig. 9.11c). These results show the chloride-layer in the crystal structure running parallel with the top surface ((001) plane). We propose a mechanism for the reaction of 3HC :Cl to 3 according to Zhu et al. as follows: (i) Sublimation of 3HC :Cl by

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the breaking of weak intermolecular interactions between phenyl and benzyl groups (‘unzipping’), from the (001) and (00–1) planes; (ii) Loss of HCl (g) in the direction of the (010) and (0–10) planes; (iii) recrystallization of product 3 on the (100) and (100) planes of the mother crystal. This mechanism is consistent with both the morphology prediction and the observation that no recrystallization occurs on the (001), (00–1) and (010), (0–10) planes. A very similar synthon formed by a pair of molecules can be recognised in both crystal structures of 3HC :Cl and 3. This is shown in blue in Fig. 9.12. With the sublimation and the escape of HCl the type and direction of the strong secondary interactions change in the sublimate (3), so that the newly formed O-H. . . N interaction is approximately perpendicular to the N-H. . . Cl that was present in 3HC :Cl . This requires a small re-arrangement of the molecules in the crystals, although the synthon remains unchanged. The internal arrangement corresponds well with the crystal morphology: 3HC :Cl are bulky prisms while 3 forms columnar crystals. ˚ in 3HC :Cl and 15.267(3) A ˚ in 3) run parallel The similar c cell axes (15.349(3) A along the synthons in the two crystal structures. Macroscopically this is likely to be the direction of the attachment of the mother and the sublimate crystal. This partial isostructurality explains why new crystal columns are grown on specific faces (100 and –100) of the mother prism and not on other sides of the bulky crystal.

Fig. 9.12 A pair of pyridine derivative molecules form the synthon that occurs in both crystal structures of 3 and 3HC :Cl . Two such synthons are highlighted in blue on each figure. (a) Molecular arrangement in 3 (dotted red lines indicate the direction of the O-H. . . N intermolecular interactions). (b) Molecular arrangement in 3HC :Cl showing the direction of the N-H. . . Cl interactions. The synthon formed by the blue molecules requires little rearrangement between the two structures

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9.3.3 Comparison of 3H C :C l and 3H C :NO3 Given the almost isostructural crystal structures but different thermal behavior for of the two salts we considered the Hirshfeld surface analysis of both [30–32]. Fingerprint plots are shown in Fig. 9.13 where de and di are defined as the distances from the surface of the nearest atom external and internal to the surface. We generated the Hirshfeld surface of the organic cations (Fig. 9.13a and b) and the ion pairs when they are hydrogen bonded through the hydroxyl group to the anion (Fig. 9.13c and d). Comparing the fingerprint plots it is clearly visible that the cations of compound 3HC :Cl and 3HC :NO3 shown a similar asymmetrical arrangement of interactions because of their identical hydrogen donor feature. Comparison of H: : :Cl 1 2 (spike ) and H: : :NO 3 (spike ) interactions of the cations shows only a difference 3 in their lengths while the ‘chicken wing’ ( ) on the fingerprint plot of 3HC :NO 3 indicate prominent C-H. . . interactions between the aromatic rings. When we compare the fingerprint plots of the cations to the ion pair in structure 3HC :Cl

Fig. 9.13 2D Fingerprint plots of 3HC :Cl and 3HC :NO 3

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(Fig. 9.13a and c) there is little difference as the shape of the plots are very similar, the extra spike is related to the hydrogen bond acceptor feature of the ion pair 1 and there is no significant difference between the length of the hydrogen bonds ( ). On the other hand, comparing the fingerprint plots of the nitrate salt (Fig. 9.13b and d) shows a significant increase in the H: : :NO 3 distance. The differences between Fig. 9.13 [(a) and (b)] versus [(c) and (d)] and in particular the greater difference observed between [(b) and (d)] suggests that the 3HC :NO 3 pair is more cohesive and interacts less strongly with the external environment (procrystal). Hence we expect that this ion pair will be more stable than 3HC :Cl . The interaction of the chloride and nitrate ion with the hydroxyl hydrogen of O8 was analyzed in order to investigate the strength of dissociation of one of these protonated species from the organic complex. Interaction between the N1 hydrogen with the anions was not considered, as this was deemed to be the stronger interaction due to the increased electrostatic component resulting from the pyridinine moeity being protonated, and therefore not the energetically limiting step in the dissociation. We used a simplified representation of the complex where both the phenyl and pyridinyl rings were substituted with methyl groups, to give uncharged tertiary butanol. The validity of this approximation was shown by comparison of the electron density (through Mulliken atomic partial charges) at the C7-O8-H8 centers using both the full cationic complex and the resultant neutral simplified species. The Cl. . . HO hydrogen bond (19:9 kcal mol1 ) is stronger than the O2 NO: : :OH interaction (17:1 kcal mol1 ) by 2.8 kcal mol1 . Although the chloride anion is a weaker hydrogen bond acceptor than nitrate, it is smaller and has a higher charge density, giving overall larger interaction strength due to the enhanced electrostatic interaction. This stronger interaction is also reflected in the dissociation energy of HCl and HNO3 from t-BuOH ŒCl and t-BuOH ŒNO3 . This process represents the physical behaviour that is observed for 3HC :Cl upon heating of the complex. Dissociation to give HCl and t-BuOH is endothermic requiring 65.4 kcal mol1 . On the other hand, HNO3 dissociation requires 69.3 kcal mol1 . The more favourable dissociation of HCl, which can in part be substantiated by the stronger affinity of chloride for the hydroxyl hydrogen, lies at the heart of the observed dissociation/sublimation of HCl and recrystallization of the organic complex, that is observed for 3HC :Cl . Figure 9.14 summarises the thermal behaviour of the two salts (adapted from Zhu [26]). In Fig. 9.14, c refers to crystal environment, s refers to relaxed surface, g refers to the gas phase. For the sublimation/decomposition reaction of crystals of 3HC :Cl the proposed reaction scheme is: (1) 3HC :Cl .c/ ion pair move to the reC laxed surface of the crystal 3H :Cl.s/ ; (2) the ion pair undergoes on proton transfer

3: : :HCl.g/ and desorbs from the surface as a pair 3: : :HCl:::.g/ and (3) dissociates in gas phase to 3.g/ and HCl.g/ . The dissociation of 3: : :HCl.g/ can be occur because of the relatively high interaction energy between the hydrogen atom of the OH group and the Cl and the relatively low dissociation energy of the 3: : :HCl.g/ ion pair. In the final step 3 will crystallize back to the (100) and (100) planes of the mother crystal.

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Fig. 9.14 Schematic diagram of the thermal behavior of 3HC :Cl and 3HC :NO 3

In case of 3HC :NO 3 crystal the proposed reaction scheme differs in step (3). The calculated interaction energy of ion pair 3HC :NO 3 .g/ is lower than in 3: : :HCl.g/ while the dissociation energy of the nitrate ion pair is higher. Hence crystals of 3HC :Cl will sublime and decompose while crystals of 3HC :NO 3 will sublime and recrystallize without decomposition. Acknowledgments The authors gratefully acknowledge financial supported from the South African National Research Foundation and the University of Cape Town Research Committee.

References 1. Braga, D.; Brammer, L.; Champness, N. R. CrystEngComm 2005, 7, 1–19. 2. Braga, D.; Grepioni, F. Making Crystals by Design. Wiley-VCH Verlag GmbH & Co., Weinheim, 2007. 3. Desiraju, G. R. Angew Chem Int Ed 2007, 46, 8342–8356. 4. Price, S. L.; Price, L. S. Struct Bonding 2005, 115, 81–123. 5. Bernstein, J. Chem Commun 2005, 5007–5012. 6. Minguez Espallargas, G.; Brammer, L.; Sherwood, P. Angew Chemie Int Ed 2006, 45, 435–440. 7. Hulme, A. T.; Johnston, A.; Florence, A. J.; Fernandes, P.; Shankland, K.; Bedford, C. T.; Welch, G. W. A.; Sadiq, G.; Haynes, D. A.; Motherwell, W. D. S.; Tocher, D. A.; Price, S. L. J Am Chem Soc 2007, 129, 3649–3657. 8. Price, S. L. Phys Chem Chem Phys 2008, 10, 1996–2009. 9. Ganguly, P.; Desiraju, G. R. Chem – Asian J 2008, 3, 868–880. 10. Kaupp, G. CrystEngComm 2009, 11, 388–403.

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11. Braga, D.; Giaffreda, S. L.; Rubini, K.; Grepioni, F.; Chierotti, M. R.; Gobetto, R. CrystEngComm 2007, 9, 39–45. 12. Keglevich, G.; Dudás, E. Synth Commun 2007, 37, 3191–3199. 13. Nakamatsu, S.; Toyota, S.; Jones, W.; Toda, F. Chem Commun 2005, 3808–3810. 14. Braga, D.; Giaffreda, S. L.; Grepioni, F.; Chierotti, M. R.; Gobetto, R.; Palladino, G.; Polito, M. CrystEngComm 2007, 9, 879–881. 15. Bourne, S. A.; Kilkenny, M.; Nassimbeni, L. R. J Chem Soc, Dalton Trans 2001, 1176–1179. 16. Lee, S. C.; Jeong, Y. G.; Jo, W. H.; Kim, H-J.; Jang, J.; Park, K-M.; Chung, I. H. J Mol Struct 2006, 825, 70–78. 17. Uemura, K.; Kitagawa, S.; Kondo, M.; Fukui, K.; Kitaura, R.; Chang, H-C.; Mizutani, T. Chem – Eur J 2002, 8, 3586–3600. 18. Kurmoo, M.; Kumagai, H.; Chapman, K. W.; Kepert, C. J. Chem Commun 2005, 3012–3014. 19. Bourne, S. A.; Moitsheki, L. J. CrystEngComm 2005, 7, 674–681. 20. Bourne, S. A.; Moitsheki, L. J. Polyhedron 2007, 26, 2719–2727. 21. Bourne, S. A.; Moitsheki, L. J. J Chem Crystallogr 2007, 37, 359–367. 22. Chaiken, R. F.; Sibbett, D. J.; Sutherland, J. E.; van de Mark, D. K.; Wheeler, A. J Chem Phys 1962, 37, 2311–2318. 23. Knacke, O.; Stranski, I. N.; Wolff, G. Z. Phys Chem 1951, 198, 1157. 24. Jacobs, P. W. M.; Russell-Jones, A. J Phys Chem 1968, 72, 202–207. 25. Zhu, R. S.; Wang, J. H.; Lin, M. C. J Phys Chem C 2007, 111, 13831–13838. 26. Zhu, R. S.; Lin, M. C. J Phys Chem C 2008, 112, 14481–14485. 27. Kálmán, A.; Párkányi, L.; Argay, G. Acta Crystallogr 1993, B49, 1039–1049. 28. Fábián, L.; Kálmán, A. Acta Crystallogr 1999, B55, 1099–1108. 29. Macrae, C. F.; Bruno, I. J.; Chisholm, J. A.; Edgington, P. R.; McCabe, P.; Pidcock, E.; Rodriguez-Monge, L.; Taylor, R.; van de Streek, J.; Wood, P. A. J Appl Cryst 2008, 41, 466–470. 30. McKinnon, J. J.; Spackman, M. A.; Mitchell, A. S. Acta Crystallogr 2004, B60, 627–668. 31. Spackman, M. A.; McKinnon, J. J. CrystEngComm 2002, 4, 378–392. 32. McKinnon, J. J.; Jayatilaka, D.; Spackman, M. A. Chem Commun 2007, 3814–3816.

Chapter 10

Influence of Size and Shape on Inclusion Properties of Transition Metal-Based Wheel-and-Axle Diols Alessia Bacchi and Mauro Carcelli

Abstract It is widely recognized that molecular shape has a key role in orienting and modulating crystal packing efficiency and it is consequently also crucial in determining host–guest properties of solid state materials. This chapter is focused on inclusion propensity of transition metal-based systems designed to have a wheeland-axle shape, which has shown to favour the inclusion of small guest in the solid state. The wheel-and-axle transition metal-based molecules are built by combining a vast library of wheels and axles: the terminal wheels are ligands of different shapes, and the linear axles are made by using metals of different coordination stereochemistry. These systems generally assemble in flexible dynamic frameworks, which can create pores on demand to accommodate small guest molecules. The framework is able to switch between two similarly stable states: the apohost, sustained by host–host contacts, and the solvate form, sustained by host–guest interactions. The transition between the two states is reversible, so that the process can be recycled. In this chapter the role of modifications of size and shape induced by changing metal stereochemistry and wheel hindrance are discussed, showing that both axle linearity and wheel bulkiness are needed to obtain inclusion properties.

10.1 Shape and Packing It is generally accepted [1–4] that molecular shape has a key role in orienting and modulating the crystal packing efficiency, defined as the volume of the molecules in the unit cell relative to the volume of the unit cell [5]. The densest packing of identical spheres, the fcc lattice, occupies 74% of the available volume, while disordered arrays of spheres can pack with efficiencies between 64% and 70% [5], and liquids close to their freezing points reach packing efficiency of 60% [6].

A. Bacchi () and M. Carcelli Dipartimento di Chimica Generale ed Inorganica, Chimica Analitica, Chimica Fisica, Università di Parma, V.le G.P.Usberti – Campus Universitario, 43124 Parma, Italy e-mail: [email protected]; [email protected]


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In molecular crystals, based on hydrogen bond and van der Waals interactions, the crystal packing efficiency is surprisingly constant. Gavezzotti [7], following the seminal work of Kitaigorodskii [8], has shown that organic molecules mostly possess packing coefficients between 60% and 80%, with slightly reduced values for molecules whose shape is irregular and perturbed by substituents [7]. It has been suggested that, when the shape of the molecule is too complex to allow efficient selfrecognition, host–guest inclusion compounds (clathrates) are preferentially formed, since the potential voids are filled by (small) guests [9]. In fact, the probability of solvate formation is positively correlated with molecular volume, which can be considered a rough indication of shape complexity [10]. A lot of work was done with “natural” hosts such as cholic acid [11], cyclodextrins [12], cyclic peptides [13], or with synthetic molecules such as the Dianin’s compound (4-p-hydroxyphenyl-2,2, 4-trimethylchroman) [14], tetraaryl porphyrins [15], calixarenes [16], helical tubuland diols [17] and, last but not least, with the so-called “wheel-and-axle” hosts (waah), that is molecules with bulky terminal groups at both ends of a rigid axle [18]. Coordination chemistry has given a great contribution to the realization of new classes of host molecules: besides microporous coordination networks [19], Werner complexes [20], cyanometallate (Hoffmann-type compounds) [21] and metal dibenzoylmethanates [22] have to be remembered. As previously mentioned, waahs [18] possess a shape that make them good candidates for hosting small guests in the crystal lattice: they are bulky, rigid and they can contain functional groups, which can interact with the guest, and so, in accordance to the general rules of Weber [23], it is probable that close packing results. Effectively, two different types of structure can be considered waahs: one is a plane penetrated by a rod,1 while in the other, as already sketched, there are two bulky end groups (wheels), connected by a linear rigid link (axle) [24]. The latter, sometimes called “dumb-bell” molecules, are discussed in this paper. Typical end groups are triptycyls, di- or triaryls, while common links are aromatic rings, azo, allenyl, or alkynyl functionalities [10,18,25] (Scheme 10.1). The wheels can also be decorated by hydrogen bonding groups, that define an anchoring point for the guests, and that, together with halogen–halogen, aryl–aryl or C-H: : : interactions [26] contribute to the formation of cavities suitable for guest entrapment. Worth of note is the innovative idea of Garcia-Garibay to use some ad hoc synthesised waahs as “molecular machines” [27]. New types of axles were obtained by using the supramolecular approach [28] and, in some cases, metal ions were introduced [24, 29]. If hydroxyl groups are placed at both ends of the axle, the remarkable class of “wheel-and-axle diols” (waad) is obtained; these hosts form crystalline clathrates with various organic guests (aldehydes, ketones, esters, ethers, amides, : : :) [30].

1

In this sense the terms “axle” and “wheel” are used to describe the structure of pseudorotaxanes and rotaxanes, where a linear “axle” interpenetrates a cyclic “wheel” [46].

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237

AXLE

Axles S *

n

*

*

n

*

*

S

n

*

Wheels

OH

OH

OH

Scheme 10.1 Examples of organic wheel-and-axle components

10.2 Metallo-organic Frameworks: Transition Metal-Based Wheel-and-Axle Diols Our efforts in the field of crystal engineering of host–guest compounds were recently oriented to exploit the possibilities offered by coordination chemistry to synthesize new “wheel-and-axle metallo-organic diols” (waamod, Scheme 10.2) [31–36]. In particular, the use of a metal and of suitable ligands allows to obtain molecules with a long principal axle, without the laborious procedures of organic synthesis; the metal could became a centre of chemical and photochemical reactivity; it is possible to make use of the structural [31] and hydrogen bonding possibilities of the anions [33]. In contrast to host molecules that possess an intrinsic concavity and crystallize with the guest inside the cavity, as cyclodextrins or calixarenes, waamods can

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HO

N

METAL

N OH

H-bond

R

N

OH

R

R=H

LOH

R = N(CH3)2

LOH2

HO LOH3

N N CH3

LOH4

H OH

N

Scheme 10.2 Transition metal based wheel-and-axle diols

include guests by leaving cavities, channels or layers, to accommodate the guest in the lattice during self assembly [37]. The long axle, realized by coordinating a metal cation to appropriate ligands, two bulky wheels, that frustrate the packing, and two terminal OH groups, able to interact with the guest, make waamods good candidates to realize flexible “dynamic frameworks” [38], that is, framework that can create pores “on demand” to accommodate small guests [16, 39]. In this sense, following Kitagawa’s view [40], waamods can be considered as third-generation hosts, because they can rearrange reversibly in response to the presence of guests. Following this classification, first-generation materials have a microporous framework that collapses on removing the guest molecules, and second-generation materials exhibit a permanent porosity also in absence of included guests (for example, the metal-organic frameworks [41]). As it was recently and persuasively discussed by Leonard Barbour [42], the use of terms as voids, porosity, porous or non-porous networks in crystal engineering and host–guest chemistry requires care. Even if the distinction between conventional

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porosity, porosity “without pores” and virtual porosity [42] is accepted, what is possible to describe with the definition “porosity without pores” is a matter of debate. Operatively, perhaps, it is possible to say that a crystal (organic or metalloorganic) is porous, even if there are no evident channels in the packing, when it adsorbs vapour (liquid) and the transformation aphost,solvate is a crystal to crystal conversion, with retention of crystallinity. It is evident that “dynamic networks” and “porosity without pores” are connected: a material, even if it is not intrinsically porous, could become porous in response to an external or internal stimulus if its structure can rearrange without significant stress. A reversible reorganization between the non-solvate and solvate phases requires two conditions: (i) a bistable network, that can switch between two states, through a low-cost structural rearrangement, represented by the initial close (self-mediated) and the final open (guest-mediated) host frameworks; (ii) the formation of an easily accessible migration path for the outcoming and incoming guest molecules. The first class of waamod that we have synthesized is formed by trans-palladium complexes Pd.LOH/2 X2 of a triarylcarbinol ligand (LOH, ligand; X, anion); they have shown suitable structural requisites to give reversible host–guest properties [33]. We will see in the following section that the reversibility of guest uptake/release is interpretable according to a model (Scheme 10.3) where, alternatively: (1) the host molecules may pack in arrays held together by hydrogen bonds between the terminal –OH groups and the anions coordinated to the metal (close, self-mediated frameworks), or (2) the host molecules may use the –OH functions to catch guest molecules (open, guest-mediated frameworks), disentangling the –OH: : :X arrays [33, 34]. The conversion is realized by simple oscillation of the molecules around their centers of mass.

= Pd(LOH)2X2

Solvate layer – Guest mediated

= -OH

Non solvate layer – Self mediated Guest

θθ

Scheme 10.3 Oscillation of host molecules goes with guest uptake and release for waamods

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10.2.1 Structural Analysis of Trans-palladium(II) Complexes of Triarylcarbinol Ligands: A Class of Transition Metal-Based Wheel-and-Axle Diol The extensive characterization of numerous members of the family of waamods ŒPd.LOH/2 X2 .LOH D ’-(4-pyridyl)benzhydrol, Scheme 10.2; XDCl, I, CH3 , CH3 COO) and of several corresponding solvates, containing hydrogen bond acceptor guest molecules ŒPd.LOH/2 X2 nG (n D 1, 2; GDacetone, THF, DMSO, DMF, 1,4-dioxane), has allowed to identify the structural requisites to give a bistable framework of host molecules capable of guest inclusion and release [33, 34].

10.2.1.1 Identification of the “Bistable Framework” All the solvate forms ŒPd.LOH/2 X2 2G, with XDCl, CH3 and I, are organized in layers with common metrics, consisting in arrays of parallel columns, made by stacked ŒPd.LOH/2 X2 2G units inclined by ™ 54ı relatively to the column axle (Fig. 10.1, Scheme 10.3). This arrangement, that is mostly based on host. . . guest hydrogen bonds, leaves space to include guest molecules, and it is therefore described as guest-mediated network. By contrast the structures of the non-solvate compounds ŒPd.LOH/2 X2 are based on –OH: : :X hydrogen bonds, which again generate columns of parallel units, arranged in layers (Fig. 10.1): this is described as a self-mediated network, since it involves solely host: : :host contacts. The selfmediated network is related to the metrics of the solvate one by a rotation of about 30ı of the complex molecules within the layer plane, until the complex long axis makes a tighter ™ angle with the column axis; the Pd: : :Pd separations are only slightly altered.

Fig. 10.1 Guest-mediated solvate (left) and self-mediated non solvate (right) layers for ŒPd.LOH/2 X2 2G (left) and ŒPd.LOH/2 X2 (right), respectively (here X D Cl, G D acetone; hydrogens omitted)

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solid/gas process [Pd(LOH)2X2]

T, 4h

G(g) desolvation [Pd(LOH)2X2] .2G

G(l)

[Pd(LOH)2X2] .2G

recrystallization

G(g)

[Pd(LOH)2X2] solid/gas process

Scheme 10.4 Reversible guest release/uptake for ŒPd.LOH/2 X2 2G; crystallinity along the process is checked by X-ray powder diffraction

In all cases the non-solvate form is unique and it is completely converted into the corresponding crystalline solvate forms by exposure to the vapour of the guest. Conversely, it is quantitatively recovered from the solvate upon removal of the guest by mild conditions (Scheme 10.4), without any observable transient amorphous phase during desolvation. On the basis of the structural data already described, it is proposed that the conversion between solvate and nonsolvate states is based on a concerted rotation of the complex molecules in the layer plane, in concomitance with the solvent migration through the lattice. The reversibility of the desolvation/solvation process is possible because the displacements required for the single host molecules are minimal, and the reorientation for their molecular long axes is modest [33]. This model is strongly supported by the structural analysis of [Pd.LOH/2 .CH3 COO/2 ], and of its THF monosolvate form ŒPd.LOH/2 .CH3 COO/2 .THF/ [33]. The overall organization of the complex units in Pd.LOH/2 .CH3 COO/2 and Pd.LOH/2 Cl2 is similar: the –OH: : :O .CO/ CH3 hydrogen bonds simply replace the –OH: : :Cl interactions. However, the molecular orientation within the chains is intermediate (™ D 36ı ) between Pd .LOH/2 Cl2 nonsolvate and solvate forms, so that some space is left between the chains within the layers (Fig. 10.2). The uptake of THF in ŒPd.LOH/2 .CH3 COO/2 occurs in these preformed pores, without any host–guest hydrogen bonding, and the host framework is practically unaltered. This suggests that the first step of the solid/gas solvation process may imply the clathration of one molecule of guest between the aryl rings, and this successively triggers the collective reorientation of the host molecules. By contrast, desolvation should proceed by a collective oscillation of the host molecules around the metal centers, that induces the conversion from the guest-mediated to the self-mediated network. This molecular rearrangement opens the space for guest migration inside the packing.

242


Fig. 10.2 Intermediate orientation .™ D 36ı / for layers of ŒPd.LOH/2 .CH3 COO/2 (left) and ŒPd.LOH/2 .CH3 COO/2 THF .right/

Fig. 10.3 Exo and endo sites for guests in ŒPd.LOH/2 X2 2G (edge-on view of the layers)

10.2.1.2 Inclusion Sites and Guest Migration In waad and also in waamod inclusion generally occurs by hydrogen bonding between the terminal –OH groups and the acceptor atom on the guest. However the guest molecules can be located in two solvation sites: one is placed inside the embrace of the terminal phenyl rings between two columns within the layer (exo site), the other is placed between the aromatic groups and the anions of two adjacent layers (endo site, Fig. 10.3). The comparison of the position of the guests over the whole family of known solvates shows that the two sites can communicate by reorientation of the phenyl rings (Fig. 10.4). This observation is reinforced by the analysis of the structure of ŒPd.LOH/2 I2 : 3=2(1,4-dioxane) [34], which presents the common layer metrics and where both solvation sites are occupied.

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Fig. 10.4 Hypothetical snapshot sequence of guest migration path, by sliding of the guest between exo and endo sites, with the assistance of conformational rearrangement of the aromatic rings indicated by arrows. The structure of ŒPd.LOH/2 I2 3=2 (1,4-dioxane) (central inset) suggests a structural continuity for the process, in fact it can be viewed as the combination of ŒPd.LOH/2 .CH3 COO/2 THF (top left) and ŒPd.LOH/2 I2 2DMSO (bottom left)

The substructure built by the guest domains in the different solvates has been estimated by visualizing the extension and shape of the crystal volume enclosed by the Hirshfeld surfaces of the guests (Fig. 10.5) [43]. The occupation of the exo site may be attained by an array of isolated guest molecules along the intracolumnar space in the monosolvates, or by a dimeric pattern based on pairs of guest molecules belonging to adjacent columns in the disolvates. Consecutive dimers are separated by aromatic rings. Conversely, the occupation of the endo sites generates a continuum of guest domains giving rise to ‘guest channels’ between the layers. The spatial communication between the two different sites is ruled by the position of the aromatic rings of the host molecules, and, as mentioned before, it is attained in ŒPd.LOH/2 I2 3=2(1,4-dioxane), where a guest chain is generated by the contact between exo and endo units, which run diagonally across the layers. We may regard the collection of the substructures of the different guests as snapshots of a possible path for solvent migration (Fig. 10.4). This model of guest migration by sliding across the layers, through channels formed by fusion of exo and endo sites, has been

244


Fig. 10.5 Hirshfeld surfaces of guest domains for solvate structures: (a) exo sites, (b) endo sites, (c) exo/endo sites, (d) exo/endo sites running across the layers

also supported by the observation that the crystal faces corresponding to the exit directions of the channels are preferentially damaged upon heating [34].

10.2.2 Robustness of the Pattern with Increasing Shape Complexity It has been suggested that both organic and metallo-organic dumb-bell-shaped molecules present a general tendency to pack in columnar arrays of parallel molecules, offset by a fraction of the axle length (Scheme 10.5) [44]. In the previous paragraph it has been demonstrated that the family of waamod ŒPd.LOH/2 X2 (LOHD’-(4-pyridyl)benzhydrol; XDCl, I, CH3 COO; CH3 ) shows reversible inclusion properties thanks to the particularly favourable molecular shape, that allows

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SOGGIE

XISPOE

KUVWON FIFHAE

D Scheme 10.5 Typical interactions between pairs of dumb-bell shaped molecules exemplified by the crystal structures indicated with CSD refcodes. Parallel molecules are offset by a fraction of molecular length as schematized below

the formation of a bistable network with dynamic porosity. The conversion of the host framework between two states (self-mediated , guest-mediated), realised by molecular oscillations, effectively generates channels, which can be used by the guest for migration through the crystal during desolvation processes. The robustness of this pattern was subsequently checked by analysing the packing propensity of different waamods, built by varying the external decoration of the wheels, the hindrance of the X groups, and also by changing Pd(II) at the centre of the axle with another metal.2 The new ligand bis(4-dimethylaminophenyl)-4-pyridylmethanol (LOH2, Scheme 10.2), obtained by a slight revision of literature method [45], reacts with

2

Crystals of 1, 2 and 3 were obtained by recrystallization of Pd.LOH2/ .CH3 COO/2 and Sn .LOH/2 Cl4 from DMSO, p-xylene and dichloromethane, respectively. Crystal data: (1) ˚ C52 H68 N6 O8 PdS2 ; MW D 1; 075:64; a D 11:43 .1/ ; b D 13:095 .5/ ; c D 9:194 .9/ A, ’ D 94:01 .4/ ; “ D 94:02 .9/ ; ” D 92:87 .6/ı , triclinic, P-1, R1 .I > 2s .I// D 0:0631, wR2 .I > 2s .I// D 0:1749. CCDC 732407. (2) C72 H86 N6 O6 Pd, MW D 1; 237:87; a D ˚ ’ D 106:879 .1/, “ D 98:178 .2/, ” D 7:7578 .7/ ; b D 15:082 .1/, c D 15:162 .1/ A, 98:960 .2/ı , triclinic, P-1, R1 .I > 2s .I// D 0:0472; wR2 .I > 2s .I// D 0:1206. CCDC 732408. ˚ (3) C38 H36 Cl8 N2 O2 Sn, MW D 954:98, a D 7:4427 .6/, b D 18:841 .1/, c D 15:160 .1/ A, “ D 96:662 .1/ı , monoclinic, P21 =c, R1 .I > 2s .I// D 0:0436, wR2 .I > 2s .I// D 0:1168. CCDC 732409.

246


palladium(II) acetate giving, in good yield, the familiar Pd(LOH2).CH3 COO/2 complex. The solvates ŒPd.LOH2/ .CH3 COO/2 2DMSO (1) and ŒPd.LOH2/ .CH3 COO/2 1.5(p-xylene)(2) are obtained by recrystallization from DMSO and p-xylene, respectively. The comparison of 1 and 2 with the parent ŒPd.LOH/2 .CH3 COO/2 and ŒPd.LOH/2 .CH3 COO/2 THF highlights the robustness of the columnar pattern, against an increase of functional and shape complexity of the wheels, obtained with the insertion of the dimethylamino groups on the terminal aromatic rings. The supramolecular arrangement of the columnar pattern in 1 and 2 (Fig. 10.6) evidences the two ways in which the host can be assembled in the bistable framework. In presence of the hydrogen-bonded DMSO, the host generates a guest-mediated framework, with the alignment of the canonical ŒPd .LOH2/2 X2 2G units, assembled by host–guest hydrogen bonds ˚ O-H: : :O D 175 .6/ı and stacked by ŒOH: : :O .dmso/ O: : :O D 2:831 .6/ A, shape complementarity, so that the bulky wheels are flanked to the slim axles. The inclusion of p-xylene in 2 occurs, obviously, without the possibility of forming host-guest hydrogen bonds. As a consequence, the host adopts a self-mediated network and associates by hydrogen bonds between the carbinol ˚ groups and the acetate ligands ŒOH: : :OAc .-x-1; -y; -z/ O: : :O D 2:849 .6/ A,

Fig. 10.6 Columnar arrangement (dashed) forming layers in the host frameworks of 1 (top, left) and 2 (top, right), compared to ŒPd.LOH/2 .CH3 COO/2 (bottom, left) and ŒPd.LOH/2 .CH3 COO/2 THF (bottom, right). Hydrogens and guests molecules omitted for clarity

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Fig. 10.7 Solid representation of the solvent accessible surface of the dynamic pores created upon solvation in 1 (left) and 2 (right). Layers are reported in edge-on projection and the pores run through parallel layers

O-H: : :O D 160:4 .3/ı , giving the arrangement typically observed for non-solvate compounds. Remarkably, the bulky guests are arranged in channels, running through the columnar packing of the host, mimicking the last step proposed for desolvation, i.e., guest migration along a path created by reorientation of the host molecules (Fig. 10.7). Worth of note is that the bistable columnar pattern found in the waamods with LOH2 is capable of sustaining different degrees of solvation. In fact, 1 and 2 are, respectively, di- and 1.5 solvate, whilst disolvate forms were generally observed for the basic ŒPd.LOH/2 X2 family, with the appearance of one monosolvate, ŒPd.LOH/2 .CH3 COO/2 THF [33], and one 1.5 solvate, ŒPd.LOH/2 I2 3=2(1,4dioxane) [34]. This is a consequence of the existence of the two solvation sites, which we previously have called exo and endo, both accessible by the –OH group of the host, which become part of the migration channels, when the host molecules switch from the guest-mediated to the self-mediated networks. In 1 the DMSO guests occupy the endo sites, whilst in 2 both sites are filled (Fig. 10.8). From the analysis of the crystal structures of 1 and 2, it is possible to see that the variations of the peripheral substituents on the wheels do not affect substantially the packing properties of the compounds. Parallelly, the influence of changing the –PdX2 – linker of the axle has been tested by using a different metal ion. When the usual ligand LOH is reacted with SnCl4 in CH2 Cl2 , ŒSn.LOH/2 Cl4 2CH2 Cl2 is isolated (Fig. 10.9). This solvate is isostructural with the members of the ŒPd.LOH/2 Cl2 2G series (G D DMF, acetone, DMSO) and, in particular, the CH2 Cl2 molecules occupy the same solvation site as in the corresponding DMF ˚ derivative ŒOH: : :Cl .CH2 Cl2 / O: : :O D 3:454 .6/ A]. The inclusion propensity has been further tested by increasing the shape complexity of the ligand. The new iminic ligand, 2,6-diphenylphenol 4-pyridyl aldimine (LOH3,Scheme 10.3), is realised to increase the length of the complex unit and the hindrance of the terminal groups (Scheme 10.2). The iminic function could provide a new acceptor site for the terminal –OH groups in the self-mediated network, while the larger molecular dimensions and anisotropy should enhance the propensity to include small guests. The palladium(II) complex of LOH3 gives indeed solvates, but the stoichiometry of the species depends on the anion [36]. The examination

248


Fig. 10.8 Top view (left) and edge-on view (right) of the different occupation of the endo and endo (orange)/ exo (green) solvation sites by DMSO and p-xylene in 1 (top) and 2 (bottom), respectively. It is shown that p-xylene fills both the sites, in analogy with ŒPd.LOH/2 Cl2 1:5 dioxane

Fig. 10.9 Comparison of the top view (left) and edge-on view (right) of solvation layers in the packing arrangements of 3 (top) and ŒPd.LOH/2 Cl2 2DMF (bottom)

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249

of the solvates ŒPd .LOH3/2 Br2 nG .n D 1; G D THF; CHCl3 ; n D 2, G D tertbutyl methyl ether, EtOH), along with the non-solvate parent compound, shows that these more complex waamod molecules are assembled by shape complementarity between the wheels and the axle (Fig. 10.10). The resulting supramolecular bundles expose the terminal –OH groups at the external ridges. These structural moduli are connected by a zipper of host–host OH. . . OH hydrogen bonds in the non-solvate structure. The guests are inserted inside the zipper in the mono- and di-solvate forms, without altering significantly the host framework (Fig. 10.11). Consequently, the desolvation path may be viewed as the progressive breaking of the host–guest hydrogen bonds followed by guest sliding between the bundles and immediate formation of spatially preorganised host–host interactions. Replacing bromine with chlorine brings a different hydrogen bond involvement of the anion, and consequently determines a remarkable variation in the assembly of the hosts. The anion, as hydrogen-bond acceptor, competes with G for OH, and both the self-mediated and the guest-mediated frameworks are in principle feasible. In fact a hybrid network is realized [36]: supramolecular ŒPd.LOH3/2 Cl2 2 dimers,

Fig. 10.10 Structural moduli based on shape complementarity (top) along the axle for ŒPd .LOH3/2 Br2 . Bottom: columnar alignments of waamods, viewed along b (left) and c (right). OH groups are exposed at the ridge of the molecular bundles

Fig. 10.11 In ŒPd .LOH3/2 Br2 nG .n D 1; 2/ guest inclusion occurs by insertion of one or two molecules of G between the OH arrays by OH. . . G interactions, with minor framework changes

250


Fig. 10.12 Hybrid supramolecular assembly of ŒPd.LOH3/2 Cl2 2 2G compared to the selfmediated (left) and guest-mediated (right) networks of ŒPd.LOH/2 Cl2 and ŒPd.LOH/2 Cl2 2 acetone

assembled by OH. . . Cl hydrogen bonds, coordinate two guest molecules at the free OH extremities (Fig. 10.12). These ŒPd.LOH3/2 Cl2 2 2G .G D THF, CHCl3 , tertbutyl methyl ether, toluene) units are stacked in columnar arrays, similar to those observed for the smaller waamod ŒPd.LOH/2 Cl2 , but they are not very stable and they have the tendency to release the guest; on thermal desolvation they give a non-solvate form that is amorphous. After desolvation, neither ŒPd.LOH3/2 Br2 nor ŒPd.LOH3/2 Cl2 2 can reabsorb guest by vapour-solid exposition, in contrast to the previously described behaviour of the analogue but smaller waamod. The marked length and shape anisotropy of the present waamod could hinder the rotations and librations needed for a dynamic network rearrangement.

10.2.3 Validation of the Wheel-and-Axle Shape The importance of wheel hindrance and axle linearity in determining the inclusion propensity of waamod has been further tested by designing complexes in which either the geometry of the axle was deformed or the bulkiness of terminal groups was reduced (Fig. 10.13). Effectively, none of these new systems afforded solvate forms.

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251

X

X

X H

HO

N

Pd

H3C

N

C H3

N

Zn

N

OH H

HO

OH

X

Fig. 10.13 Validation of wheel-and-axle shape by modification of the molecular structure: assembly by supramolecular squares for ŒPd.LOH4/2 X2 (left) and ŒZn.LOH/2 X2 (right), preventing the formation of a bistable network

The geometry of the axle of the waamod has been modified by considering the coordination preferences of the metal ion. A family of bent molecules ŒZn.LOH/2 X2 .X D Cl; Br/, obtained by coordination of LOH to zinc halogenides, was considered [35]. These compounds with the Zn(II) cation tetrahedrally coordinated, are accommodated in quadrangular networks based on –OH: : :X hydrogen bonds, which would be impossible to obtain with a square planar stereochemistry on the metal, due to reciprocal hindrance of the aromatic rings in the middle of the supramolecular squares (Fig. 10.13, right). The steric demands of the wheels were further explored by synthesizing the family of slimmer complexes ŒPd.LOH4/2 X2 (Scheme 10.2, LOH4 D .1S /-1(4-pyridinyl)ethanol; X D Cl; Br; I), where the two aromatic rings at the wheels are

252


replaced by less bulky groups (one methyl and one hydrogen) [36]. The solid state organization of these compounds follows a quadrangular pattern based on –OH: : :X hydrogen bonds, in analogy to the one observed for the above described zinc complexes ŒZn.LOH/2 X2 (Fig. 10.13, left). In ŒPd.LOH4/2 X2 the planar arrangement of the supramolecular squares is permitted by the modest steric demands of the terminal substituents, that can be easily accommodated without the need of puckering the hydrogen bonded layer. Probably, the bistable network sketched in Scheme 10.3 is possible in presence of a significant steric hindrance around the carbinol groups and of a linear stereochemistry of the axle: the release of the steric tensions by bending the axle (Zn complexes) or by reducing the wheels complexity (complexes with LOH4) allows the formation of quadrangular networks, without any clathrating properties.

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Index

A Angular overlap model (AOM), 23 Artificial neural networks (ANNs), 92–93 Associative solvents definition, 7 ions, 14–17 methanol advantages, 10 Jorgensen three-site rigid methanol model, 11 pair distribution function (PDF), 12–13 reactions quantum mechanical and molecular mechanical methods, 17–18 reaction coordinate definition, 18–19 water distance dependent free energies, 8–9 Protein Data Bank (PDB) structures, 9 spatial distribution functions (SDFs), 8 TIP5P model, 10

B Bioinorganic systems corrin force field B12 derivatives, 93 cobalt corrins structure, 94–96 force fields extension artificial neural networks (ANNs), 92–93 Cambridge structural database (CSD), 91 metal ions, 89–90 molecular mechanics (MM) method, 88–89 porphyrin force field 4-aminoquinoline antimalarial drugs, 97–98 arylmethanol antimalarial pharmacophore, 98 Cinchona alkaloids, 99–100, 104

Fe(III)-alkoxide bond, 100 hydrogen bonding, 101, 103 molecular dynamics (MD) simulations, 101 Plasmodium falciparum, 96–97 ‘points-on-a-sphere’ model, 100 strain energy surfaces, 103–104 three-point model of interaction, 104–105 C Cation– interactions, 188 Corrin force field B12 derivatives, 93 cobalt corrins structure, 94–96 Crystal field stabilisation energy (CFSE), 22 Cup-stacked carbon nanotubes (CSCNTs), 116 Cytidine-rich i-motif, 186–187 D Dimethylsulfoxide (DMSO) reductase single molybdenum cofactor, X-ray crystal structure, 152–153 sodium dithionite reduction, 153 X-band EPR spectra, 153 2,6-Diphenylphenol 4-pyridyl aldimine, 247 E Electron donor–acceptor ensembles with covalent bonding electron donor–acceptor dyads, 118–120 multi-step electron transfer, 113–115 nanocarbon materials, 116–118 without covalent bonding phthalocyanines, 127–130 porphyrin nanochannels, 124–127 – interactions, 121–124 Electron Zeeman interactions, 134

255

256 F Figure of merit, 198 Fine structure interaction, 134 Free energies from adaptive reaction coordinate forces (FEARCF) method associative solvents definition, 7 ions, 14–17 methanol, 10–14 reactions, 17–19 water, 8–10 molecular associations molecular dynamics (MD) computer simulations, 5 statistical mechanics, 3–4 potential of mean force (PMF), 6–7 weighted histogram analysis method (WHAM), 7

G g-Tensor anisotropy, 58–61

H Hirshfeld surface analysis, 230 Homo-DNA crystal structure, 184 inter-strand base stacking characteristics, 185 L-cyclohexanyl nucleic acid (L-CNA), 184 pairing stability, 185 4-(1-Hydroxy-1,2-diphenylethyl)pyridine and salts crystal structures and isostructurality bond lengths and angles, 224 crystal data, 224–225 crystal packing, 225–227 torsion angle, 224 3HC Cl and 3HC NO 3 , comparison 2D fingerprint plots, 230 thermal behaviour, schematic diagram, 231–232 recrystallisation, 224 thermal analysis crystal transformation, 226 differential scanning calorimetry (DSC) trace, 225, 227 hot-stage microscopy (HSM), 226, 228 synthon formation, 229 Hyperfine interaction, 135

Index I Intermetallic thermoelectrics electron crystal-phonon glass, 198 incommensurate structure analysis modulations, 200–201 mosaicity, 200 q-vector, 199–200 satellite reflections, 199–201 super space group symbol, 200 modulated rock-salt like compounds Bi4 Se3 , 202 Bi2 Te3 , 201 electron density maps, 204 phase diagram, system Bi–Se, 202, 203 phase diagram, system Bi–Te, 201 phase diagram, system Sn–Sb, 202–204 real space structures, pure Sb, 204, 205 stistaite, 202 Peltier effect, 197 Sb–Zn system Bi-doped single crystal, 209 electron density map, 210 13-fold superstructure, 211 pentagonal antiprisms, 213 phase diagram, 206 reconstructed reciprocal lattice images, 207, 208 Sb13 icosahedra arrangement, ˜-Zn3 Sb2 , 214–215 single crystal diffraction pattern, 208 temperature-polymorphic, 207 -Sb2 Zn3 , Sb substructure, 213 -Zn3 Sb2 , Sb-arrangement, 214 Seebeck effect, 197 skutterudites and Ba8 Ga16 Ge30 inorganic clathrate, 198

J Jahn–Teller effects elongations, barriers, 39–40 Mexican hat potential surface, 34–35 theoretical treatment, 37–39 truly compressed complexes, 41–42 warped Mexican hat, 35–37 Jorgensen three-site rigid methanol model, 11

L Ligand field density functional theory (LFDFT), 54, 55, 63, 82 Ligand field molecular mechanics (LFMM) Cu(II) bis-oxazoline complexes, 33–34 dinuclear copper centres, 45, 47–49

Index d orbital molecular mechanics, 28 Jahn–Teller effects elongations, barriers, 39–40 Mexican hat potential surface, 34–35 theoretical treatment, 37–39 truly compressed complexes, 41–42 warped Mexican hat, 35–37 [MCl4 ]2 complexes, 31–32 simple coordination complexes, Cu(II) amines Cu–N bond lengths and chelate bite angles, 30–31 steric effects, 30 structural diagrams, 31 spin-state effects, 41–42 stretching and angle bending, 27–28 type 1 copper enzymes, 42–45

M Magnetic anisotropy, [Fe(CN)6 ]3 Jahn–Teller coupling vs. spin-orbit coupling directional cosines, principal axes, 62 distorted configurations and geometric parameters, 55, 56 "g and 2g octahedral vibrations, 55 energy level diagram, trigonal distortion, 57, 58 energy profile, 55–57 Franck-Condon energy, 57 g-tensor anisotropy, 58–61 Kramers doublet and quartet states, 57 single crystal magnetic susceptibilities, 61, 62 2 T2g ground state splitting, 57, 58 vibronic coupling constants, 61 linear trinuclear Cu–NC–Fe–CN–Cu complexes

T vs. T diagram, 72 energy level diagram, 72, 73 magnetic susceptibility, 71 magnetization vs. field plot, 72 oligonuclear complexes, degenerate ground states angular distortions, 82 average-of-configuration (AOC) procedure, 75 effective ligand field Hamiltonian, 78 electronic excitations, 76–77 exchange coupling tensors, 79 g-tensor values, 80–81 kinetic exchange energy, 76 Kohn-Sham (KS) orbitals, 77

257 MO coefficients, 75 oligonuclear spin clusters, 79 orthogonal eigenvectors, 77 positive Heisenberg integral, 76 spin energy gaps, 79 spin-Hamiltonian, 74 regular (C4v / vs. distorted (Cs /, Fe-Ni pair Kramers degeneracy, 66 spin energy gap parameters, 67, 68 spin energy levels and spin functions, 65–66 Zeeman splitting, spin levels, 66 spin-orbit coupling and strain, FeIII subunit angular distortions, 68 anisotropic and antisymmetric exchange parameters, 70 qualitative rules, rational design, 70–71 single energy parameter, 68 spin energy gap parameter, 69 theory Born-Oppenheimer Hamiltonian, 63 effective g-tensors, 65 electronic states, FeIII –NiII exchange pair, 64 LFDFT, FeIII –CN–NiII exchange pair, 63 2 T2g ground state and Zeeman operators, 64 Merck molecular force field (MMFF), 25 Molecular associations molecular dynamics (MD) computer simulations, 5 statistical mechanics, 3–4 Molecular mechanics (MM), transition metal complexes angular overlap model (AOM), 23 CFSE, 22 density functional theory (DFT), 24 hydration enthalpies, 22 ligand field molecular mechanics (LFMM) Cu(II) bis-oxazoline complexes, 33–34 dinuclear copper centres, 45, 47–49 d orbital molecular mechanics, 28 Jahn–Teller effects, copper(II) complexes, 34–41 [MCl4 ]2 complexes, 31–32 simple coordination complexes, Cu(II) amines, 30–31 spin-state effects, 41–42 stretching and angle bending, 27–28 type 1 copper enzymes, 42–45 nephelauxetic effect, 23 octahedral crystal field theory d-orbital splitting diagram, 21, 22

258 shortcomings points on a sphere (POS) approach, 27 valence angles, central atom, 23 valence shell electron pair repulsion (VSEPR), 27 total potential energy, 24–25 Molecular Sophe (MoSophe) coherence pathways, 148–149 density matrix, 147, 148 Floquet harmonics, 148 graphical user interface, 146 Mosaic Misorientation Linewidth model, 147 paramagnetic materials, 3-D molecular characterization, 145 superpropagator, 148 transverse magnetization, 148 Morse function, 25, 27 Mosaic misorientation linewidth model, 147 Multifrequency EPR spectroscopy angular anomaly, 138–139 copper(II) cyclic peptide complexes marine cyclic peptides, 156–160 westiellamide and synthetic analogues, 160–164 Fourier filtering and numerical differentiation, 141 geometric and electronic structure ab initio approach, 144 computer simulation, 143–144 molecular modeling, 144 Molecular Sophe (MoSophe), integrated approach, 145–149 traditional approach, metal ion binding sites, 142–143 g-value resolution and orientation selection, 136–137 high resolution techniques, 142 MoV complexes and mononuclear molybdenum enzymes crystal field description, spin Hamiltonian parameters, 151 density functional theory, 151–152 DMSO reductase, 152–153 high-g unsplit type-1 and 2 species, 154–155 molybdopterin (MPT), 152 purple acid phosphatases (PAPs) dinuclear manganese species, 165–166 electron spin and numerical coefficients, 167 FeMn-spPAP active site, 165 MnMn-spPAP enzyme, 165–166, 168 Molecular Soph (MoSophe), 169

Index redox active FeIII FeIII=II center, 164 transition roadmap, resonant field positions, 169–170 zero field splittings, MnII center, 169 spin Hamiltonian interactions, 134–135 parameter distribution, 139–141 state mixing, 138 X-band frequencies, 136

N Nephelauxetic effect, 23 Nogalamycin, 181 Nuclear Zeeman interaction, 135

O Oligo-20 , 30 -dideoxy-ˇ-D-glucopyranose nucleic acid. See Homo-DNA

P Pair distribution function (PDF), 12–13 Phenyl-ribonucleotide pairing, 182 Photosynthetic reaction center electron donor–acceptor ensembles with covalent bonding electron donor–acceptor dyads, 118–120 multi-step electron transfer, 113–115 nanocarbon materials, 116–118 electron donor–acceptor ensembles without covalent bonding phthalocyanines, 127–130 porphyrin nanochannels, 124–127 – interactions, 121–124 photosynthesis, 112–113 Porphyrin-functionalized cup-shaped nanocarbons (CNC–H2 P)n / laser photoexcitation, 117–118 synthesis of, 116 transmission electron miscroscopy (TEM), 117 Porphyrins force field 4-aminoquinoline antimalarial drugs, 97–98 arylmethanol antimalarial pharmacophore, 98 Cinchona alkaloids, 99–100, 104 Fe(III)-alkoxide bond, 100 hydrogen bonding, 101, 103

Index molecular dynamics (MD) simulations, 101 Plasmodium falciparum, 96–97 ‘points-on-a-sphere’ model, 100 strain energy surfaces, 103–104 three-point model of interaction, 104–105 nanocarbon materials, 116–118 nanochannels, 124–127 Soret bands, 127 Potential of mean force (PMF), 6–7 Pseudoknot RNA (pk-RNA), 189–190 Purple acid phosphatases (PAPs) dinuclear manganese species, 165–166 electron spin and numerical coefficients, 167 FeMn-spPAP active site, 165 MnMn-spPAP enzyme, 165–166, 168 Molecular Soph (MoSophe), 169 redox active FeIII FeIII=II center, 164 transition roadmap, resonant field positions, 169–170 zero field splittings, MnII center, 169

Q Quadrupole interaction, 135

R Reaction coordinate in ammonia, 18–19 definition, 6 two dimensional, 17

S Single-walled carbon nanotubes (SWCNTs), 116 Solid state transformations [Co(H2 O)6 ]Br2 2(bpdo)2(H2 O) [CoBr2 (bpdo) (H2 O)2 ]H2 O, 220 crystal packing, 220, 222 powder x-ray diffractograms, 223 schematic diagram, 221 thermal analysis, 220, 222 [Co(H2 O)6 ]Cl2 2(bpdo)2(H2 O) [CoCl2 (bpdo) (H2 O)2 ]H2 O, 220 crystal packing, 220, 222 schematic diagram, 221 sublimation and dissociation crystal structures and isostructurality, 224–225

259 3HC Cl and 3HC NO 3 , comparison, 230–232 thermal analysis, 225–229 Spin Hamiltonian parameter, 151 computational chemistry, 144 crystal field description, 151 CuII complexes, patellamide D, 158–160 high-g unsplit type-2 species, 155 metal ion center, 136 mononuclear copper(II) complexes, 162 Stacking interaction base-backbone inclination and sugar-base stacking amino acid-nucleobase stacking, 185–186 homo-DNA, 183–185 cation- interactions, 188 cytidine-rich i-motif, 186–187 DNA and RNA, 178 electrostatic contribution, 177 intra- and inter-strand base stacking C30 -endo pucker and 20 -deoxyribose, 179 50 -CpG-30 step, 178, 180 pairing stability, 180 lone pair– and anion– interactions 20 -deoxyribose of cytidine, 189–190 H– interaction, 189 ribosomal frameshifiting pseudoknot RNA, 189–191 spermine and magnesium, 189 U-turn RNA tertiary structural motif, 191 Z-DNA, 189–191 parallel and perpendicular intercalating agents acridine orange and ethidium bromide dyes, 180 bis-intercalating drug ditercalinium, 181 cofacial vs. edge-on stacking, 182–183 electrostatics and van derWaals interactions, 180 nogalamycin, 181 Stilbene diether moiety conformations, 183 Superhyperfine interaction, 135

T TATA-motif major groove, 191–192 Transition metal-based wheel-and-axle diols host–guest compounds, 237 host molecule oscillation, 239

260 pattern robustness, shape complexity bis(4-dimethylaminophenyl)-4pyridylmethanol, 238, 245 2,6-diphenylphenol 4-pyridyl aldimine, 247 dumb-bell shaped molecule, typical interactions, 244–245 hybrid supramolecular assembly, 250 inclusion propensity, 247 packing propensity, 245 solvent accessible surface, dynamic pores, 247 structural moduli, 249 supramolecular arrangement, columnar pattern, 246 porosity, 238–239 shape and packing crystal packing efficiency, 235 molecular machines, 236 organic wheel-and-axle components, examples, 236–237 trans-palladium(II) complexes bistable framework identification, 240–242 inclusion sites and guest migration, 242–244 wheel-and-axle shape validation inclusion propensity, 250

Index molecular structure modification, 251 steric hindrance, 252 Trans-palladium(II) complexes bistable framework identification guest-mediated network, 240 intermediate orientation, layers, 242 reversible guest release/uptake, 241 self-mediated network, 240 inclusion sites and guest migration exo and endo sites, 242 Hirshfeld surfaces, 243–244

W Weighted histogram analysis method (WHAM), 7

Z Zn4 Sb3 blocks, 211 electron density map, 210 13-fold superstructure, 211 idealized structure, 209 low temperature resistivity, 207 structural model, 212 triclinic b-axis, 211, 212

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