Magnetism: Molecules to Materials II: Molecule-Based Materials: 2

Magnetism: Molecules to Materials II: Molecule-Based Materials. Edited by Joel S. Miller and Marc Drillon c 2002 Wiley-V...

Author: Joel S. Miller | Marc Drillon

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Magnetism: Molecules to Materials II: Molecule-Based Materials. Edited by Joel S. Miller and Marc Drillon c 2002 Wiley-VCH Verlag GmbH & Co. KGaA Copyright ISBNs: 3-527-30301-4 (Hardback); 3-527-60059-0 (Electronic)

Magnetism: Molecules to Materials II

Edited by J. S. Miller and M. Drillon


Further Titles of Interest

J. S. Miller and M. Drillon (Eds.) Magnetism: Molecules to Materials Models and Experiments 2001. XVI, 437 pages Hardcover. ISBN: 3-527-29772-3

J. H. Fendler (Ed.) Nanoparticles and Nanostructured Films 1998. XX, 468 pages Hardcover. ISBN: 3-527-29443-0

P. Braunstein, L. A. Oro, and P. R. Raithby (Eds.) Metal Clusters in Chemistry 1999. XLVIII, 1798 pages ISBN: 3-527-29549-6


Magnetism: Molecules to Materials II Molecule-Based Materials Edited by Joel S. Miller and Marc Drillon


Prof. Dr. Joel S. Miller University of Utah 315 S. 1400 E. RM Dock Salt Lake City UT 84112-0850 USA

Prof. Dr. Marc Drillon CNRS Inst. de Physique et Chimie des Matériaux de Strasbourg 23 Rue du Loess 67037 Strasbourg Cedex France

This book was carefully produced. Nevertheless, editors, authors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for A catalogue record for this book is available from the British Library. Die Deutsche Bibliothek - CIP Cataloguing-in-Publication-Data A catalogue record for this publication is available from Die Deutsche Bibliothek ISBN 3-527-30301-4 © WILEY-VCH Verlag GmbH, Weinheim (Federal Republic of Germany). 2001 Printed on acid-free paper. All rights reserved (including those of translation in other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition: EDV-Beratung Frank Herweg, Leutershausen. Printing: betz-druck GmbH, Darmstadt. Bookbinding: Wilh. Osswald + Co. KG, Neustadt Printed in the Federal Republic of Germany.


Contents

1

Nitroxide-based Organic Magnets . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Unconjugated Nitroxides . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Mono-nitroxides . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Oligo-nitroxides . . . . . . . . . . . . . . . . . . . . . . . 1.3 Conjugated Nitroxides . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Mono-nitroxides . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Oligo-nitroxides . . . . . . . . . . . . . . . . . . . . . . . 1.4 Nitronyl Nitroxides . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Mono-nitronyl Nitroxides . . . . . . . . . . . . . . . . . 1.4.2 Oligo-nitronyl Nitroxides . . . . . . . . . . . . . . . . . 1.4.3 Co-crystallization of Nitronyl Nitroxides . . . . . . . . . 1.5 Imino Nitroxides . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Poly(nitroxides) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1 1 5 5 10 12 12 14 18 18 35 40 44 46 49 51

2

Magnetic Ordering in Metal Coordination Complexes with Aminoxyl Radicals . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Aminoxyl Radicals . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Electronic Structure and Basicity . . . . . . . . . . . . 2.2.2 Aminoxyl Radicals with Another Basic Center . . . . 2.2.3 High-spin Di- and Poly(aminoxyl) Radicals . . . . . . 2.3 Magnetic Interaction between Transition Metal Ions and Aminoxyl Radicals . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Indirect Coupling (Extended Superexchange) . . . . . 2.3.2 Complexes with Direct Metal-Aminoxyl Coordination 2.3.3 Cyclic Complexes . . . . . . . . . . . . . . . . . . . . . 2.4 Design Strategy for Various Crystyl Structures . . . . . . . . . 2.5 Preparation of 3d Transition Metal-Poly(aminoxyl) Radical Complexes . . . . . . . . . . . . . . . . . . . . . . . . 2.6 One-dimensional Metal-Aminoxyl Systems . . . . . . . . . . 2.6.1 Structure and Magnetic Properties of Ferrimagnetic 1D Chains Formed by Manganese(II) and Nitronyl Nitroxides . . . . . . . . . . . . . . . . . . . .

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2.6.2

Structure and Magnetic Properties of Ferrimagnetic 1D Chains Formed by Manganese(II) and Triplet bis-Aminoxyl Radicals . . . . . . . . . . . . . 2.7 Two-dimensional Metal-Aminoxyl Systems . . . . . . . . . . 2.7.1 Structure and Magnetic Properties of Ferrimagnetic 2D Sheets Formed by Manganese(II) and Nitronyl Nitroxides . . . . . . . . . . . . . . . . . . . 2.7.2 Structure and Magnetic Properties of Ferrimagnetic 2D Sheets Formed by Manganese(II) and High-spin tris-Aminoxyl Radicals . . . . . . . . . . . 2.7.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Three-dimensional Metal-Aminoxyl Systems . . . . . . . . . 2.8.1 Crystal and Molecular Structure of the 3D System . 2.8.2 Magnetic Properties of the 3D System . . . . . . . . 2.8.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Summary and Prognosis . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

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Organic Kagome Antiferromagnets . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Inorganic Kagome Antiferromagnets . . . . . . . . . . . . . . . . . . 3.2.1 SrGa12-x Crx O19 (SCGO(x)) . . . . . . . . . . . . . . . . . . . 3.2.2 Jarosite, AM3 (OH)6 (SO4 )2 (A = Na+ , K+ , Rb+ , Ag+ , NH+ 4, H3 O+ , etc., and M = Fe3+ or Cr3+ ) . . . . . . . . . . . . . . . 3.3 Organic Kagome Antiferromagnet, m-MPYNN · X . . . . . . . . . . 3.3.1 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Magnetic Susceptibility . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.4 Positive Muon Spin Rotation . . . . . . . . . . . . . . . . . . 3.3.5 Distorted Kagome Lattices . . . . . . . . . . . . . . . . . . . . 3.3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

109 109 110 110

Magnetism in TDAE-C60 . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Synthesis and Structure . . . . . . . . . . . . . . . . . . . 4.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 The Lattice Structure . . . . . . . . . . . . . . . . 4.3 The Electronic Structure . . . . . . . . . . . . . . . . . . 4.4 The Magnetic Properties . . . . . . . . . . . . . . . . . . 4.4.1 The Bulk Magnetic Properties . . . . . . . . . . . 4.4.2 The Spin-glass Behavior of α -TDAE-C60 . . . . 4.4.3 Electron-spin Resonance . . . . . . . . . . . . . . 4.4.4 Ferromagnetic Resonance . . . . . . . . . . . . . 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 124 124 126 128 130 130 134 135 137 144 145

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111 111 111 113 115 116 117 120 120

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5

Triarylmethyl and Amine Radicals . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 5.2 Monoradicals (S = 1/2) . . . . . . . . . . . . . . . . . 5.3 Diradicals (S = 1) . . . . . . . . . . . . . . . . . . . . 5.4 Triradicals (S = 3/2) . . . . . . . . . . . . . . . . . . . 5.5 Monodisperse High-spin Oligomers (S = 2 – ca. 10) . 5.6 High-spin Polymers (up to Sn = ca. 48) . . . . . . . . 5.7 Conclusions and Prospects (Beyond S = ca. 48?) . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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149 149 149 153 161 163 179 182 185

6

High-spin Metal-ion-containing Molecules . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Self-assembly of Molecular Clusters . . . . . . . . . . . . . . 6.2.1 Competing Interactions and Spin Frustration . . . . 6.2.2 The Carboxylate Family . . . . . . . . . . . . . . . . 6.2.3 The Hydroxypyridonate Family . . . . . . . . . . . . 6.3 Host-Guest Approach . . . . . . . . . . . . . . . . . . . . . 6.3.1 Hexanuclear Iron(III) Rings . . . . . . . . . . . . . . 6.3.2 Hexanuclear Manganese Rings . . . . . . . . . . . . 6.4 Step-by-step Rationale Approach . . . . . . . . . . . . . . . 6.4.1 Complex as Ligand and Complex as Metal . . . . . . 6.4.2 Predicting the Spin Ground State . . . . . . . . . . . 6.4.3 Antiferromagnetic Approach . . . . . . . . . . . . . 6.4.4 Ferromagnetic Approach . . . . . . . . . . . . . . . . 6.4.5 Role of the Organic Ligand . . . . . . . . . . . . . . 6.4.6 Molecules with Two Shells of Paramagnetic Species 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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189 189 190 190 192 197 201 202 203 204 206 207 208 211 214 217 223 223

7

Electronic Structure and Magnetic Behavior in Polynuclear Transition-metal Compounds . . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Phenomenological Description of Exchange Coupling: the Heisenberg Hamiltonian . . . . . . . . . . . . . . . . . . . . 7.3 Qualitative Models of the Exchange Coupling Mechanism . . . 7.3.1 Orthogonal Magnetic Orbitals . . . . . . . . . . . . . . . 7.3.2 Natural Magnetic Orbitals . . . . . . . . . . . . . . . . . 7.4 Quantitative Evaluation of Exchange Coupling Constants . . . 7.4.1 Perturbative and Variational Calculations of State Energy Differences . . . . . . . . . . . . . . . . 7.4.2 Ab initio Calculations of State Energies . . . . . . . . . 7.4.3 Calculations using Broken-symmetry Functions . . . . . 7.5 Exchange Coupling in Polynuclear Transition-metal Complexes 7.5.1 Homodinuclear Compounds . . . . . . . . . . . . . . . . 7.5.2 Heterodinuclear Compounds . . . . . . . . . . . . . . .

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236 240 242 249 249 261

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7.5.3 Polynuclear Compounds . . . . . . . . . . . . . . . . . . . . . 263 7.5.4 Solid-state Compounds: The Case of Cu2 (OH)3 NO3 . . . . . 266 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 8

9

Valence Tautomerism in Dioxolene Complexes of Cobalt . . . . . . . . . 8.1 Introduction – Bistability, Hysteresis, and Electronically Labile Materials . . . . . . . . . . . . . . . . . . . 8.1.1 Bistability and Hysteresis . . . . . . . . . . . . . . . . . . . . 8.1.2 Electronically Labile Materials . . . . . . . . . . . . . . . . . 8.2 Valence Tautomerism in Dioxolene Complexes of Cobalt . . . . . . 8.2.1 Valence Tautomerism – A General Chemical Description . . 8.2.2 Valence Tautomerism – A Simplified MO Description . . . . 8.2.3 VT Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Experimental Determination of Thermodynamic Parameters 8.2.5 Dependence of K V T Equilibrium on Ancillary Ligands . . . 8.2.6 Pressure-induced VT . . . . . . . . . . . . . . . . . . . . . . . 8.2.7 Light-induced VT and Rates of VT . . . . . . . . . . . . . . . 8.2.8 VT Complexes of Other Quinone Ligands and Redox Chemistry of VT Complexes . . . . . . . . . . . . 8.2.9 Polymeric VT Materials . . . . . . . . . . . . . . . . . . . . . 8.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecule-based Magnets Derived from NiII and MnII Azido Bridging Ligand and Related Compounds . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Synthetic Procedures . . . . . . . . . . . . . . . . . . . . . . 9.3 Exchange-coupling Parameter . . . . . . . . . . . . . . . . . 9.4 Molecular-based Magnetic Materials . . . . . . . . . . . . . 9.5 One-dimensional Systems . . . . . . . . . . . . . . . . . . . 9.5.1 With 1,3-Azido Bridging Ligands (AF, Uniform) . . 9.5.2 With 1,3-Azido Bridging Ligands (AF, Alternating) 9.5.3 With 1,1-Azido Bridging Ligands (Ferromagnetic) . 9.5.4 With 1,3-N3 and 1,1-N3 bridges . . . . . . . . . . . . 9.6 Two-dimensional Systems . . . . . . . . . . . . . . . . . . . . 9.6.1 With Only Azido as Bridging Ligand . . . . . . . . . 9.7 Three-dimensional Systems . . . . . . . . . . . . . . . . . . . 9.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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281 281 281 281 284 284 287 288 290 292 297 299 300 302 303 304

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307 307 308 309 309 312 312 313 316 319 322 322 329 334 335

10 Oxalate-based 2D and 3D Magnets . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Basic Principles of Specific 2D and 3D Network Configurations 10.3 Structural Studies on 2D Oxalato Bridged Compounds . . . . . 10.4 Magnetic Studies on 2D Oxalato Bridged Compounds . . . . . 10.5 Structural Studies on 3D Oxalato Bridged Compounds . . . . .

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339 339 339 344 346 349

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10.6 Magnetic Studies on 3D Oxalato Bridged Compounds . . . . . . . . 352 10.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 11 Hybrid Organic-Inorganic Multilayer Compounds: Towards Controllable and/or Switchable Magnets . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Hydroxide-based Layered Compounds . . . . . . . . . . . . . . . 11.3 Anion-exchange Reactions . . . . . . . . . . . . . . . . . . . . . . 11.4 Influence of Organic Spacers in Hydroxide-based Compounds . . 11.4.1 The Cu2 (OH)3 X Series . . . . . . . . . . . . . . . . . . . . 11.4.2 The Co2 (OH)3 X Series . . . . . . . . . . . . . . . . . . . . 11.4.3 Dipolar Interaction and Long-range Magnetic Order . . . 11.5 Difunctional Organic Anions Connecting Magnetic Layers . . . . 11.6 Metal-radical-based Layered Magnets . . . . . . . . . . . . . . . 11.7 Controllable Magnetic Properties of Layered Copper Hydroxides 11.7.1 Solvent-mediated Magnetism . . . . . . . . . . . . . . . . 11.7.2 Photoisomerism of Azobenzenes in Layered Copper Hydroxides . . . . . . . . . . . . . . . 11.8 Layered Perovskite Ferromagnets . . . . . . . . . . . . . . . . . . 11.8.1 High-pressure Effects . . . . . . . . . . . . . . . . . . . . . 11.8.2 Spontaneous Magnetization in Layered Perovskite Ferromagnets . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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357 357 358 360 361 361 364 367 370 376 380 380

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12 Intercalation-induced Magnetization in MPS3 Layered Compounds . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Introduction and Scope . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Structural and Electronic Aspects . . . . . . . . . . . . . . . . . . . 12.3 Magnetic Properties of the Pristine MPS3 Phases (M = Mn, Fe, Ni) 12.4 Ion-exchange Intercalation into the MPS3 Compounds . . . . . . . 12.5 The Magnetic Properties of the MnPS3 Intercalates . . . . . . . . . 12.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5.2 X-ray and Neutron-diffraction Study of Selected Intercalates . . . . . . . . . . . . . . . . . . . . . 12.5.3 A Ferrimagnetic Model of the MnPS3 Intercalates: Imbalancing of Spins . . . . . . . . . . . . . . . . . . . . . . 12.6 The Magnetic Properties of the FePS3 Intercalates . . . . . . . . . 12.6.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6.2 Spectroscopic Characterization of the FePS3 Intercalates . 12.6.3 Discussion on the Role of Intercalation into FePS3 . . . . . 12.6.4 Magnetic Properties of Iron-diluted Fe1−x Cdx PS3 Compounds . . . . . . . . . . . . . . . . . . . 12.6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.7 The NiPS3 -Cobaltocene Intercalation Compound . . . . . . . . . .

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12.8 Multi-property Materials: Associating Magnetism and Non-linear Optics . . . . . . . . . . . . . 420 12.9 Conclusion and Perspectives . . . . . . . . . . . . . . . . . . . . . . . 421 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 13 Transition Metal Ion Phosphonates as Hybrid Organic–Inorganic Magnets . . . . . . . . . . 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 13.2 Synthesis of the Ligands . . . . . . . . . . . . . . . 13.3 Vanadium Phosphonates . . . . . . . . . . . . . . . 13.3.1 Preparation . . . . . . . . . . . . . . . . . . 13.3.2 Crystal Structures . . . . . . . . . . . . . . . 13.3.3 Magnetic Properties . . . . . . . . . . . . . 13.4 Divalent Metal Phosphonates . . . . . . . . . . . . 13.4.1 Synthesis . . . . . . . . . . . . . . . . . . . . 13.4.2 Crystal Structures . . . . . . . . . . . . . . . 13.4.3 Magnetic Properties . . . . . . . . . . . . . 13.5 Metal(II) Diphosphonates . . . . . . . . . . . . . . 13.5.1 Synthesis . . . . . . . . . . . . . . . . . . . . 13.5.2 Crystal Structures . . . . . . . . . . . . . . . 13.5.3 Magnetic Properties . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . .

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425 425 426 426 426 427 427 430 430 432 437 449 449 450 452 454

14 Magnetic Langmuir-Blodgett Films . . . . . . . . . . . . . . . 14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 14.2 The Langmuir–Blodgett Technique . . . . . . . . . . . . 14.2.1 Fabrication of Langmuir–Blodgett Films . . . . . 14.2.2 Structural and Physical Characterization of Langmuir and LB Films . . . . . . . . . . . . . 14.3 Magnetic Systems: A Molecular Approach . . . . . . . . 14.3.1 Hybrid LB Films with Magnetic Clusters . . . . . 14.3.2 Spin-transition Systems . . . . . . . . . . . . . . . 14.3.3 Comments on Molecular Magnetism in LB Films 14.4 Extended Systems and Cooperative Effects . . . . . . . 14.4.1 “Literally Two-Dimensional Magnets” . . . . . . 14.4.2 Metal Phosphonate LB Films . . . . . . . . . . . 14.4.3 Organic and Inorganic “Dual Network” Films . . 14.4.4 Bimetallic Compounds . . . . . . . . . . . . . . . 14.5 Comparison with Other Lamellar and Colloidal Systems 14.5.1 Hybrid Lamellar Systems . . . . . . . . . . . . . 14.5.2 Self-organized Media . . . . . . . . . . . . . . . . 14.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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457 457 459 459

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461 462 462 465 468 469 469 470 473 475 478 479 480 481 482

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485


List of Contributors

Pere Alemany Center de Recerca en Qu´ımica Teorica ` (CeRQT) Departament de Qu´ımica Inorganica ` and Departament de Qu´ımica F´ısica Universitat de Barcelona Diagonal 647 08028 Barcelona Spain Santiago Alvarez Center de Recerca en Qu´ımica Teorica ` (CeRQT) Departament de Qu´ımica Inorganica ` and Departament de Qu´ımica F´ısica Universitat de Barcelona Diagonal 647 08028 Barcelona Spain

Kunio Awaga Department of Basic Science The University of Tokyo Komaba, Meguro Tokyo 153-8902 Japan Carlo Bellitto CNR-Istituto di Chimica dei Materiali Area della Ricerca di Montelibretti Via Salaria Km. 29.5 C.P.10 00016 Monterotondo Staz Rome Italy Robert Blinc Josef Stefan Institute P.O. Box 3000 Jamova 39 1001 Ljubljana Slovenia

David B. Amabilino Institut de Ciencia ` de Materials de Barcelona (CSIC) Campus Universitari de Bellaterra 08193 Cerdanyola Spain

R. J. Bushby School of Chemistry University of Leeds Leeds LS2 9JT UK

Denis Arcon Josef Stefan Institute P.O. Box 3000 Jamova 39 1001 Ljubljana Slovenia

Rene´ Clement ´ Laboratoire de Chimie Inorganique UMR 8613, Bt 420 Universite´ Paris XI 91405 Orsay France

XII


Roberto Cortes ´ Departamento de Qu´ımica Inorganica ´ Universidad del Pais Vasco Apartado 644 48040 Bilbao and Apartado 450 01080 Vitoria Spain Silvio Decurtins Department of Chemistry and Biochemistry University of Berne Freiestrasse 3 3012 Berne Switzerland Pierre Delhaes Center de Recherche Paul Pascal CNRS Universite´ Bordeaux I Avenue du Dr A. Schweitzer 33600 Pessac France Marc Drillon Institut de Physique et Chimie des Materiaux ´ UMR 7504-CNRS 23 rue du Loess 67037 Strasbourg France Albert Escuer Departament de Qu´ımica Inorganica ` Universitat de Barcelona Diagonal 647 08028 Barcelona Spain Wataru Fujita Department of Basic Science The University of Tokyo Komaba, Meguro Tokyo 153-8902 Japan

Mohamed A.S. Goher Chemistry Department Faculty of Science Alexandria University Alexandria 21321 Egypt Tamotsu Inabe Division of Chemistry Graduate School of Science Hokkaido University Sapporo 060-0810 Japan Katsuya Inoue Institute for Molecular Science 38 Nishigounaka Myodaiji Okazaki 444-8585 Japan Hiizu Iwamura National Institution for Academic Degrees 4259 Nagatsuta-cho Midori Yokohama 226-0026 Japan Anne Leaustic ´ Laboratoire de Chimie Inorganique UMR 8613, Bt 420 Universite´ Paris XI 91405 Orsay France Luis Lezama Departamento de Qu´ımica Inorganica ´ Universidad del Pais Vasco Apartado 644 48040 Bilbao


Talal Mallah Laboratoire de Chimie Inorganique UMR CNRS 8613 Universite´ Paris-Sud 91405 Orsay France

Ales Omerzu Josef Stefan Institute P.O. Box 3000 Jamova 39 1001 Ljubljana Slovenia

Arnaud Marvilliers Laboratoire de Chimie Inorganique UMR CNRS 8613 Universite´ Paris-Sud 91405 Orsay France

Melanie Pilkington Department of Chemistry and Biochemistry University of Berne Freiestrasse 3 3012 Berne Switzerland

Carlo Massobrio Institut de Physique et Chimie des Materiaux ´ 23 rue du Loess 67037 Strasbourg France Mark W. Meisel Departments of Physics and Chemistry University of Florida Florida 32611 USA Dragan Mihailovic Josef Stefan Institute P.O. Box 3000 Jamova 39 1001 Ljubljana Slovenia Christophe Mingotaud Center de Recherche Paul Pascal CNRS Universite´ Bordeaux I Avenue du Dr A. Schweitzer 33600 Pessac France Montserrat Monfort Departament de Qu´ımica Inorganica ` Universitat de Barcelona Diagonal 647 08028 Barcelona Spain

XIII

Yann Pouillon Institut de Physique et Chimie des Materiaux ´ 23 rue du Loess 67037 Strasbourg France Pierre Rabu Institut de Physique et Chimie des Materiaux ´ UMR 7504-CNRS 23 rue du Loess 67037 Strasbourg France Joan Ribas Departament de Qu´ımica Inorganica ` Universitat de Barcelona Diagonal 647 08028 Barcelona Spain Antonio Rodr´ıguez-Fortea Center de Recerca en Qu´ımica Teorica ` (CeRQT) Departament de Qu´ımica Inorganica ` and Departament de Qu´ımica F´ısica Universitat de Barcelona Diagonal 647 08028 Barcelona Spain

XIV


Teofilo ´ Rojo Departamento de Qu´ımica Inorganica ´ Universidad del Pais Vasco Apartado 644 48040 Bilbao Eliseo Ruiz Center de Recerca en Qu´ımica Teorica ` Departament de Qu´ımica Inorganica ` and Departament de Qu´ımica F´ısica Universitat de Barcelona Diagonal 647 08028 Barcelona Spain Taketoshi Sekine Department of Basic Science The University of Tokyo Komaba, Meguro Tokyo 153-8902 Japan David A. Shultz Department of Chemistry North Carolina State University North Carolina 27695-8204 USA Daniel R. Talham Departments of Physics and Chemistry University of Florida Florida 32611 USA

Jaume Veciana Institut de Ciencia ` de Materials de Barcelona (CSIC) Campus Universitari de Bellaterra 08193 Cerdanyola Spain Ramon Vicente Departament de Qu´ımica Inorganica ` Universitat de Barcelona Diagonal 647 08028 Barcelona Spain Nobuo Wada Department of Basic Science The University of Tokyo Komaba, Meguro Tokyo 153-8902 Japan Isao Watanabe Muon Science Laboratory The Institute of Physical and Chemical Research (RIKEN) Hirosawa, Wako Saitama 351-0198 Japan


Subject Index

A3 Cu3 (PO4 )4 39 ab-initio calculations, spin distribution 325, 329–350, 360, 361, 363, 366, 368, 370, 372, 375 AgVIII P2 S6 59, 67, 69, 74, 78, 83–85 alkyl nitroxides 346 amorphous materials 257 anisotropy 3, 4, 9, 10, 41, 42, 53, 373 – coupling 3, 5, 44 – local 64, 193 – magnetocrystalline 44, 211, 216–232 – nonaxial 71 – single ion 50, 54, 55, 57, 71 – XY 50 antiferromagntic coupling prediction, orbital model 62 Ba2 CaMnFe2 F14 20, 21 Ba2 MnCoAl2 F14 42 BCPTTF salts 115, 118, 121 BDT 124 BEDT-TTF, see ET salts bielectronic exchange integral 62 bimetallic chain 1 – Co 32 – CoCu 32 – CoNi 18–19, 35, 36 – Cu 367–370 – CuGd 28 – CuIr 10, 12 – CuMn 24 – CuNi 359–361 – CuPt 10, 12 – MM 15, 16, 35 – Mn 22 – MnCo 34, 35 – MnCu 24, 26–28, 34, 361–367 – MnNi 15, 18, 370–372 – Ni 35 – ring 10

biphenyl radical anion 407 biquadratic exchange 28, 50–52 – spin 3 bis(acetylacetonato)nickel 417 bis(benzene)metal 409 bis-µ-(hydroxo)dinuclear Cu(II) unit 61 bis(2-phenyl-4,4,5,5-tetramethyl-4,5-dihydro-1H -imidazolyl-1-oxyl-3-oxide)copper(II) 351 Bonner-fisher 8, 96, 108, 117, 120, 121 C60 203, 252 Ca3 Cu3 (PO4 )4 40, 41 CaMnO3 315 carboxylate bridges 15 – ligands 1 (CH3 )4 NNi(NO2 )3 59, 70 chain, alternating 2, 9, 64, 95 – anisotropic 54 – bimetallic, see bimetallic chain – classical spin and quantum system 17, 27 – cluster chains 1 – connected 1 – 1-D 95 – ferro- and antiferromagnetic coupling 43 – infinite 43 – linear 2, 8, 43 – mixed valent 203–206 – nonuniform 57, 64 – spin 43 – triangular 1, 9, 22 – uniform 2, 4, 5, 63, 64 charge disproportionation 109 – delocalization 321 – ordering 300, 308–320 4-(4-Chlorobenzylideneamion)-2,2,6,6tetramethylpiperidin-1-oxyl) 342–343

432

Subject Index

circularly polarized light 211 classical approximation 3 classical spin 3–5, 12, 13, 17, 29, 30, 35, 41 CNMR 119 cobalt hexacyanoferrate 258, 261, 270, 272, 291 coercivity 286 Co[N(CN)2 ]2 250 [Co(NH3 )5 (OH2 )][Cr(CN)6 ] 358 Co(OH)(NO3 )H2 O 37, 38, 40 Co(phen)(3,5-DTBSQ)2]L 288–291 Compton scattering 211 conducting polymers 236, 245 conductivity, frequency-dependant 111 – optical 113 contact shift 388–390 cooperative effect 264–266, 269, 290 correlation length 5, 17, 29, 37, 44, 49, 53–54, 73, 77, 78, 98, 120 co-semiquinone 258 Coulomb exchange 340 – interaction 137, 138, 199, 203, 204, 205 – repulsion 121, 192, 193, 206 coupling, electron-nuclear 381 – electron-phonon 95, 117, 121, 122 – exchange coupling 219 – ferromagnetic 158 – Heisenberg, 2D 43 – Heisenberg 3, 4, 17, 21, 24, 28, 29, 42, 49, 50, 163, 175, 176, 189 – Ising coupling 3, 4, 17, 18, 30–41 – isotropic coupling 5, 164, 178 – spin-spin coupling 87 – through-bond 379–380 – through-space 379, 386 – XY 42 cluster 372–375 – CrNi 148–149 – Fe3 S4 186, 189, 190 – single molecule magnet, see single molecule magnet Cr(Benzyl)(C5 H5 )(PEt3 )Cl 403 Cr{(CN)Mn(TrispicMeen)}6 ](ClO4 )9 148 Cr{(CN)Ni(tetren)}6 148 III CrII 1.5 [Cr (CN)6 ] · 5H2 O 271, 272 III [Cr (CN6 ]3− 358

Cr y [Cr(CN)6 ] 257 critical domain 44 – exponent 249 – field 57, 80 crossover, see Spin crossover CsCr1−x Mgx Cl3 87 III Cs0.83 CrII 1.10 [Cr (CN)6 ]3 271–279 III Cs2 K[Cr (CN)6 ] 357 CsNiCl3 58, 59, 77–78, 86 Cs[NiII CrIII (CN)6 ]2H2 O 137–144 Cu(bipy)(OH)2 Cu(bipy) 368 Cu(bipy)(OH)2 Cu(bipy)(OSO3 ) 368 Cu(hfac)2 NitMe 350, 351 Cu(salen)Ni(hfac)2 360 Cu2 (t-Bupy)4 (N3 )2 ](ClO4 )2 369, 370 CuCl2 (NitPh)2 351–353 CuGeO3 87, 96–110, 118, 124 – impurity-doped 105–112 – phase diagram 103–105 – structure 98, 99 Cu2 O(SO4 ) 39–41 CuMn(S2 C2 O2 )2 23 CuII (salen)NiII (hfac)2 359 cyanophenyl nitronyl nitroxide 248 DAP(TCNQ) 115–118 DCNQI 252 density matrix renormalization 366 density wave 115 di-µ-azido copper(II) 367, 369 dihydrobenzotriazinyl radicals 406–408 1,2-Dihydro-2-methyl-2-phenyl-3H-indole-3-oxo-1-oxyl 331 dimerization-induced gap 97 dimers, asymmetric 164, 165 dioxygen 61 diphenylpicrylhydrazyl 405 dipolar coupling 385, 386 – shift 388–390, 419 direct exchange 157 direct transfer 157 DMR 367 domain 118, 286, 311 double chain 1, 2, 9, 37, 38, 43 double-exchange 155, 156, 158–166, 175–186, 188, 190–197, 199–201, 203–207, 300 – anisotropic 166 double spinon 99

Subject Index DPPH 406 DTDA 349 Dzialoshinski coupling 3, 42 easy magnetization axis 50, 373 elastic neutron scattering 83 electron spin resonance, see EPR electron transfer 159–160, 197, 199, 200, 207 – salt 252 ENDOR 382, 406 energy gap 110 entropy 288 EPR 72, 79, 81, 82, 86, 101, 107, 110, 124, 240, 245, 372, 382–383 ESR, see EPR ET salts 115, 116, 121, 123, 237, 251, 252 2-(6-Ethynyl-2-pyridyl)-4,4,5,5-tetramethylimidazoline-1-3-oxide 346 [Et3 NH]2 [Mn(CH3 CN)4 (H2 O)2 ] [Mn10 O4 (biphen)4 Br12 ] 373 exchange transfer 183, 184 Faraday effect 212 far-infrared 101–102, 113 [Fe(C5 Me5 )2 ][TCNE] 249 [Fex (Co1−x (btr)2 (NCS)2 ] 261, 262, 266, 267, 269 Fe2 O3 41 [Fe8 O2 (OH)12 (tacn)6 ]Br 374 Fe3 S4 cluster 186, 189, 190, 193, 194 ferrimagnetic chain 4, 5 – Ising 32–37 – linear 5–8, 14, 24, 39, 40 – random 14 ferrimagnetism, 1-D, topoligical 2, 20, 37, 38 ferrimagnets 5, 40 ferrites 257 ferromagnetic metal 310 Fisher model 12–14, 18 frustration 95–97, 181 g factor 217 [Gd2 (ox)][Cu(pba)]3 [Cu(H2 O)5 ] glavinoxyl radical 406–407 haldane spin chain 49–88 half-filled magnetic shells 41 hard axis 218

28–29

433

heat-capacity 100 Heisenberg antiferromagnet 49, 86 – chain 4, 5, 17, 43, 54, 72, 84, 87, 88, 95, 104, 108, 250 – alternating 8, 10, 11 – antiferromagnet 103 – classical-spin 12–22 – ferrimagnetic chains 23–29 – ferromagnetic 6, 7 – quantum spin 8–11 – random 19, 107 – uniform 8 – double chain 29 – ladder 88 – model 76 hexacyanometallates, spin distribution 420–421 high-field magnetization 80 4-hydroxy-2,2,6,6-tetramethyl-1-piperidinyloxy 346 hydroxyhenyl nitronyl nitroxide 248 hyperconjugation 402, 407 hyperfine couplings 382 – interactions 421 hysteresis 314 – light-induced optical 265, 268 – light-induced presure 265, 267 – light-induced thermal 265 2-imidazoline-1-oxide radicals 406–408 incommensurate structure 311 indirect transfer 157 indolinonic nitroxide 332 inelastic 70 – light scattering 99 – neutron scattering 54, 72–75, 79–82, 84, 100, 108, 110, 372 infrared 112, 117, 121 intervalence absorption 169, 179, 271, 258 iron(II)bis(hydrotris(pyrazol-1-yl)borate) 391 Ising anisotropy 50 – chains 30–41 – ferrimagnetic 32–37 – ferromagnetic 34 – model 3, 100 isotropic 42, 55 itinerant electron 156 Jahn-Teller effect 185–187, 194, 202, 308

434

Subject Index

Kagome antiferromagnet 251 K0.2 Co1.4 [FeII (CN)6 ] 270 Kerr effect 212 KFeIII [FeII (CN)6 ] 270 kinetic energy 183, 194 kinetic exchange 183 Knight shift 101, 421, 422 IV (Lax Ca1−x )(MnIII x Mn1−x )O3 156 Ladder chains 1, 9, 37, 38, 108, 109, 114 Langevin function 14, 15 Langmuir-Blodgett films 124, 264 Larmor energy 83 – precession 239 LB films, see Langmuir-Blodgett films LIESST 257, 261, 262, 268, 269, 289 light-induced – excited spin state trapping, see LIESST – ferrimagnetism 258 – magnetic pole inversion 258, 271 light-stimulated magnetic after effects 257–292 linear chain, see chain linear long-range order 44, 51, 52, 71

MAE, see magnetic after effects magnetic after effect, photo stimulated, see light-stimulated magnetic after effects magnetic after effects 257, 278 magnetic circular dichroism, X-ray 133–151, 211–232 magnetic dimers 155 magnetic dipole 215 magnetic domain 216 magnetic dots 216 magnetic exchange 193, 200 magnetic excitations 101 magnetic fluctuations 73, 84 magnetic force microscope 216 magnetic metastability 258, 291 magnetic orbitals 359, 379 magnetic scattering 211 magnetic sensors 124 magnetic storage 124 magnetic structures 325 magnetism, 1-D 1–45, 49–88

magnetization density 325 magnetocrystalline anisotropy, see anisotropic, magnetocrystalline magnetoelastic 95, 112, 117 magnetoresistance, colossal 156, 300–306 magnetostatic 13 magnetostriction 100, 104, 312 magnons 72 – phonon interactions 3 manganites 156, 300, 315 – change ordering 300, 308–320 – CMR 300–306 – doping 320–322 – rare earth 259, 300–322 maxent 328, 333, 334, 338 maximum of entropy 327, 359 – method 373, 374 McConnell mechanism 249, 381, 410 MEM(TCNQ)2 115, 116, 250, 251 metal alkyl 415 metal porphyrins 399, 400, 418 metal to insulator transition 315, 321, 322 metallocenes 392–396, 401, 403, 409–414 metallocenium tetracyanoethenides 249, 380 metallophthalocyanines 204–207, 357 metalloproteins 151 – MCD 150 2-(3-N -Methylpyridium)-4,4,5,5-tetramethyl 251 mexican hat 185 mixed valence 288 – clusters 197, 198 – dimers 156–180 – tetramers 190–196 – trimers 180–190 Mn12 O12 (CH3 CO2 )16 (H2 O) 253, 372, 373 [MnTEtOPP][TCNE] 258 molecular-beam epitaxy 224 motional narrowing 243 [MPYNN][BF4 ] 251 multilayers 216, 219 – Cox Pt1−x thin film 224–232 – Fe/Cu/Co magnetic multilayers 215 muon spin rotation 117, 235–253

Subject Index mixed valent – clusters 199, 201, 206, 207 – compounds 168 – dimers 158, 160–167, 169, 171, 173–176, 178, 180, 181, 183, 184, 196, 203–205, 207 – asymmetric 164 – orbital degeneracy 165 – tetramer 191–195 – trimers 182, 183, 185–189 muon spin resonance, see muon spin rotation muon spin rotation 235–254 naphthyl nitronyl nitroxide 248 NaV2 O5 96, 108–116, 124 NC(C6 F4 )(CNSSN) 249 Neel ´ state 6, 51, 56, 58, 71, 115 NENF 64, 70 NENP 62–65, 70, 73–76, 78–81, 83, 84, 86 – Cu-doped 85 neutron diffraction 139, 146 – scattering 70, 71, 74, 95, 99, 106, 107, 117, 325–353, 357-376 – spin polarized 150, 217, 325–353, 357–376 59, 62, 65–67 Ni(C2 H8 N2 )2 NO+ 2 Ni(C3 H10 N2 )2 N+ 59 3 59 Ni(C3 H10 N2 )2 NO+ 2 59 Ni(C5 H14 N2 )2 N+ 3 NiL(diamine)2 64 Ni[N(CN)2 ]2 250 Ni(NH3 )4 (NO2 )2 372 Ni1−x Mgx NiCl3 86 NiII (NH3 )4 (NO2 )2 357 Ni nitroprusside 258 NINAZ 63, 64, 69, 70, 78, 79 NINO 62, 63, 64, 70, 73 6-NitPy(C≡C−H) 346, 347 nitronyl nitroxides 246–249, 334, 336, 343–347, 350, 380, 383, 384, 389, 406–408 nitroxides 249, 331, 346, 394 NMR, see nuclear magnetic resonance nonaxial anisotropy, see anisotropy, nonaxial nonlinear optical solids 124 nonorthogonalized magnetic orbitals 62

435

m-NPIM, 2-(3-nitrophenyl)-4,4,5,5-tetramethyl4,5-dihydro-1H -imidazol-1-oxyl 338, 339 p-NPNN, 2-(4-nitrophenyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H -imidazol-1oxyl-3-oxide, 246–248, 340, 341 nuclear magnetic resonance 72, 73, 83, 100, 101, 109, 116, 118, 120, 240, 383–392 – spin distribution determination 381–422 occupation correlation 20 one-dimensional ferromagnetism 205–206 optical 118 – information storage 257 – mesurements, under pressure 102 – spectroscopy 102, 121, 139, 169 orbital-ordering 300 order induced by disorder 87 organic radicals 406 orthogonalized magnetic orbitals 62 4-oxo-2,2,6,6-tetramethyl-1-piperidinyloxy 331 Peierls transition, electronic 122 Perovskite manganites 300 perpendicular magnetocrystalline anisotropy, PMA 224 perylene 122–123 2-phenyl-4,4,5,5-tetramethyl-4,5-dihydro1H -imidazol-1-oxyl-3-oxide 333 photobleaching 262 photochromic 258 photodarkening 261, 262 photoemission 108 photoexcited state 257 photoinduced excited spin state trapping, see LIESST photoinduced ferrimagnetism, see light-induced ferrimagnetism photoinduced magnetic after effects, see light-stimulated magnetic after effects photoinduced magnetic pole inversion, see light-induced magnetic pole inversion photoinduced optical hysteresis, see hysteresis, light-induced optical

436

Subject Index

photoinduced pressure hysteresis, see hysteresis, light-induced pressure photoinduced thermal hysteresis, see hysteresis, light-induced thermal photoisomerizable 258 photo-tunable magnet 271 Piepho, Krausz, and Schatz model 155, 166–168, 170, 171, 173–175, 178, 179, 185–187, 194, 201, 202, 208 Piepho model 169, 170, 176, 178, 186, 187, 194 piezochromic 258 point-dipole model 386 polarized neutron diffraction, see neutron diffraction 150, 217, 325–353, 357–376 polyacetylene 245 polyoxometalates 197–203 potential exchange-transfer 184 prussian blue structured magnets 137–146, 258, 261, 263, 270–280, 291 – analogs 258, 291 pyrene 406–407 pyrene2 {M[S2 C2 (CN)2 ]2 } 115, 116, 121–124 quantum field theory 79 quantum magnetic fluctuations 49 quantum spin 4, 5, 12, 17, 24, 26, 29, 30, 35, 158 – classical spin 24, 35, 36 – chains 49–88 – tunneling 253 3-quinolyl 248 Raman scattering 98, 104, 108, 112 Rbx Co[FeII (CN)6 ] y 263, 271, 280 relaxation rate 83 remanent magnetization 273 resistivity 122 RKKY 244 R2 NiO5 87 second nearest neighbors 10 Seiden model 23 semimagnetic semiconductors 257 short-range order 44 single ion anisotropy, see anisotropic, single ion single molecule magnet 253, 372–375

soliton 99, 120 – excitations 116 specific heat 33, 38, 69, 70, 80, 101, 116 – high field 80 spin, correlated 56 spin crossover 44, 257–261, 265–267, 269, 288, 289, 291 spin delocalization 330, 333, 357, 358, 363, 370, 399–405, 412, 417 spin density, see spin distribution spin density wave 252 spin distribution 151, 325, 332, 334, 335, 339, 340–346, 349–352, 353, 357–360, 362, 364, 366, 368–375 – negative 335, 343, 361, 362, 370, 381 – NMR 379–422 – wave 242, 251 – transition metal complexes 357 spin dynamics 74–85 spin echo 100 spin flop 106 spin fluctuations 49 spin frustration 2, 22, 39 spin glass 244 spin pairing 124 spin Peierls 57, 63, 87, 95–124, 250 spin polarization 333–336, 357, 358, 396–398 spin population, see spin distribution spin state trapping 257 spin transfer 359, 402 spin wave 6 spin zero defect 80 spinels 257 spin-change 258 spin-lattice relaxation 241, 385 spin-orbit coupling 28, 60, 137, 142, 143, 148, 216–219, 221–223 spin-phonon coupling 105, 111, 117 spin-spin correlation 14, 15, 20, 51 spin-spin relaxation 241 Sr3 CuPt1−x Irx O6 9 SrMnO3 315 structural relaxation 257 superconductors, organic 236, 237 superexchange interaction 157, 308, 379 superparamagnetism 253 superstructure 310 synchrotron radiation 131, 211

Subject Index tanol suberate 249, 250 TCNE 249, 258, 338, 410, 422 TCNQ 96, 115–118, 250, 251, 422 [TDAE][C60 ] 252 tempo 249, 331, 342, 346 – spin distribution 332 tempone 331, 346 – spin distribution 332 thermal conductivity 110, 111 thermochromic 258 thermodynamic 288 thin films 211, 216, 217, 219, 224–232 2-(4-thiomethylphenyl)-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide 343 through-bond coupling, see coupling, through-bond through-space coupling, see coupling, through-space TMMC 85, 241 TMNIN 63, 64, 70, 83, 85, 86 TMTSF, superconductor 118, 251 [TMTSF]2 [PF6 ], superconductors 242 [TMTTF]2 PF6 115, 116, 118–120 topological 1D ferrimagnetism, see ferrimagnetism, 1-D, topological transfer frustration 181, 193 transfer integral 156, 157 transfer-matrix method 30–32 triangular chain, see chain, triangular triarylaminium cations 406–408 triazolinyl radicals 406–408 tricritical behavior 111 trimers 39 triple chain 2 TTF 96, 115, 116, 422

437

uniform chain, see chain, uniform valence-localized 175 valence tautomerics 258, 259, 288–291 Van Vleck 216 – equation 195 – paramagnetism 24, 27, 166 V[CrIII (CN)6 ]z magnets, MCD 144–146 Verdazyl radical 406, 407 vibronic coupling 168, 174–177, 179, 186, 195, 203, 208 – effects 167 – interaction 164, 166, 170, 185, 189, 194 – model 170 weak ferromagnetism 41 XANES 271 x-ray absorption spectroscopy 131–133, 140, 211 x-ray diffraction 120, 372 x-ray diffuse scattering 98 x-ray neutron diffraction 312 x-ray scattering 107 XY anisotropy, see anisotropy, XY XY coupling, see coupling XY XY magnet 249 Y2 BaNiII O5 59, 67, 69 YBANO 63, 74–76, 78, 79, 83, 84, 86 ZN-doped YBANO 86 zero-field splitting 30, 60


1

Nitroxide-based Organic Magnets David B. Amabilino and Jaume Veciana

1.1

Introduction

Nitroxides [1] are arguably the group of organic radical molecules [2] which have found most application in the study of molecular magnetism [3], as materials in their own right [4] or in combination with paramagnetic metal ions [5]. The reason for their appeal stems from their relative synthetic accessibility, stability, and versatility, which gives rise to a wide range of magnetic behavior, not to mention other properties [6]. In the vast majority of all the nitroxides reported to date, the NO group carrying the free electron is safeguarded sterically by methyl groups attached to the adjacent carbon atoms, endowing persistency upon the radical. The four most widely studied families of radicals (Fig. 1) are the unconjugated nitroxides (derivatives of TEMPO (1)), the conjugated nitroxides (such as phenyl N -t-butyl N -oxides (2)), the nitronyl nitroxides (3), and the imino nitroxides (4). These divisions of open-shell compounds differ dramatically in the distribution of the free electron in the molecule, as determined experimentally [7] and theoretically [8]. While in the simple nitroxides 1 the NO group bearing the free electron is comparatively isolated from the rest of the molecule by saturated hydrocarbon groups and therefore bears the vast majority of the spin density of the free electron (as represented by the singly occupied molecular orbital, or SOMO), in the nitronyl nitroxides

Fig. 1. Four of the general types of nitroxide: derivatives of TEMPO (1), phenyl N -t-butyl N -oxides (2), the nitronyl nitroxides (3), and the imino nitroxides (4), and the SOMOs of the last two cases.

2

1 Nitroxide-based Organic Magnets

(3) the electron is delocalized across the ONCNO group, with a node located at the central carbon atom. In contrast, in the imino nitroxides (4) the carbon atom of the NCNO moiety is not necessarily a node of the SOMO and in principle there is no reason for its spin population to be small or negative [9]. Experimentally, negative spin population is observed on this carbon atom [9, 10]. Nevertheless, the effect is less pronounced than in the radicals of type 3. In the latter, the effect is purely a result of spin polarization while in the imino nitroxides it is the result of competition between spin polarization and spin delocalization that determine the sign and magnitude of the spin on this atom. The degree of dispersal of electron density is clearly a key factor in the determination of magnetic interactions between the magnetic moments of the radicals in the condensed state because the most important interactions arise from the magnetic exchange mechanism. Exchange magnetic interactions between spins S1 and S2 located on organic units are described in this chapter by the effective Heisenberg Hamiltonian H = −2J S1 S2 , that has an isotropic nature and where J is the exchange interaction energy, traditionally given either in cm−1 or, as we shall use, in K as J/k (where k is the Boltzmann constant), this constant taking positive values for ferromagnetic interactions. Perhaps the most appealing (and elusive) goal in the area of organic magnetic materials is the preparation of a bulk ferromagnet [11]. The first indication that an organic radical might display bulk ferromagnetism was in the diradical tanol suberate (5) [12, 13], although it was later reported that the material is in fact a metamagnet [14]. The target was reached unequivocally for the first time by Kinoshita and colleagues with 4-nitrophenyl nitronyl nitroxide (4NPNN, 6) [15]. Interest in the magnetic properties of organic magnetic materials underwent a boom in the early part of the 1990s as a result of this revelation.

As in all magnetic materials, three main factors contribute to the overall magnetic behavior, two of them molecular, i. e. molecular topology [16] and molecular conformation, and the third supramolecular (beyond the molecule) [17], the packing of the molecules in the condensed phase. The first two factors govern the distribution of the free electron in the molecule and interaction between the spins if there is more than one free electron, and the third the magnetic interactions through space and/or non-covalent bonds. These themes will recur during the course of this essay. For unpaired electrons to interact ferromagnetically the overlap integral of their orbitals must be close to zero, a situation favored by orthogonal orbitals (according to Hund’s rule developed for atoms) [3, 18], while the exchange integral must be

1.1 Introduction

3

large. The effects of molecular topology [4, 16] on intramolecular magnetic interactions are adequately described employing either molecular orbital or valence bond theories. As far as intermolecular magnetic interactions are concerned, the most frequently-applied model is “McConnell I” which was first put forward to prophesy ferromagnetic interactions between π -conjugated hydrocarbon radicals [19] and implies the spin-polarization of adjacent nuclei. This model predicts a ferromagnetic interaction between two moieties if the π -orbital overlap between atoms with spin densities of opposite sign dominates over others with the same sign. However, this model or mechanism has been called into question very recently as a result of theoretical work [20] and statistical studies [21]. Another mechanism that has also (although less frequently) been used to explain interactions is the so-called “McConnell II” that implies charge transfer between different molecular units producing an admixture of ground and excited state configurations with distinct spin multiplicities [2–4, 22]. Once an intermolecular ferromagnetic interaction between molecules has been achieved, it is necessary to propagate it, or an interaction of similar sign and magnitude, in all three directions of space (Fig. 2) [3]. In order to comply with this condition, a three-dimensional packing of the molecules is essential. The tendency of organic molecules to form one-dimensional chains or two-dimensional sheets often acts as an impediment to achieving this feat, since although ferromagnetic interactions could be propagated within the chain or sheet (Fig. 2), often the interaction between the chains or sheets is antiferromagnetic. It is therefore necessary to control completely the packing of the molecules in the whole of the crystals, an obstacle which is largely unsolved at the present time, although considerable effort is being expended to overcome it [23]. The packing of organic molecules in the solid state is governed by non-covalent bonds acting between them, and the area of supramolecular chemistry which is concerned with this phenomenon has become known as crystal engineering [24]. The non-covalent bonds which are of particular importance in the realm of the nitroxide magnets are hydrogen bonds [25]. They have proven to be involved in the transmission of magnetic interactions in inorganic complexes [26], and, as we shall see, are often invoked to explain the magnetic behavior of purely organic materials. As far as the nitroxides are concerned, there are principally three important types of hydrogen bonds (Fig. 3): (i) those formed by the oxygen atom of the N–O group with donors of hydrogen bonds (R–X–H), be they hydroxyl groups, amines, or the like; (ii) those formed by the hydrogen atoms attached to the methyl groups “protecting” the radical and acceptors of hydrogen bonds, such as basic nitrogen or oxygen atoms; and (iii) those formed by the latter acceptor and hydrogen atoms attached to aromatic rings. The Csp3 –H· · ·O hydrogen bonds [27] often include those formed with the NO group of the radical. Since the hydrogen atoms of these methyl groups have negative spin density, because of spin-polarization, the McConnell I mechanism has been applied frequently to implicate this non-covalent interaction as one which encourages ferromagnetic interactions. As we shall see throughout the course of this chapter, there is a tight relationship between hydrogen bonding and ferromagnetic interactions in nitroxide-based organic molecular materials [4]. In the following sections, we will discuss the most outstanding results attained in the area of purely organic nitroxide magnets in general, and reflect upon these

4


Fig. 2. Schematic representation-the dots represent the radicals that contain the spins in the magnetic system-of magnetic interactions in a one dimensional system, wherein J1 is much bigger than J2 and J3 , a two dimensional system, in which the exchange couplings J1 and J2 are larger than J3 , and a three dimensional magnetic system, where J1 , J2 and J3 are of similar magnitude.

achievements, the limitations associated with their behavior and interpretation of it, and discuss the possible ways in which we foresee that research will advance. The results are divided into the four structural groups according to Fig. 1 and the materials will be introduced in this order for mono and oligo radicals. Finally the sticky problem of polymeric nitroxide materials will be treated, and we shall reflect upon the state of the art in the area.

1.2 Unconjugated Nitroxides

5

Fig. 3. Some of the hydrogen bonds which drive the assembly of crystals of nitroxide radicals.

1.2

Unconjugated Nitroxides

Interest in applications of the nitroxides of the TEMPO type (1) and related compounds initially revolved around their use as spin probes [28], as a result of their extremely simple EPR spectra – three lines resulting from the coupling of the unpaired electron with the nitrogen nucleus – and the development of theory explaining changes in their line shapes. They were also the first group of organic radicals to be studied in depth regarding their magnetic behavior in their condensed phases.

1.2.1

Mono-nitroxides

The radical 2,2,6,6-tetramethyl-4-piperidinol-1-oxyl, more colloquially known as TANOL (7) [29], was shown very early on in the history of magnetism of free radicals to follow a one-dimensional Heisenberg model in the temperature range 1.8 to 300 K, with an exchange constant J/k of −6.0 K [30]. The molecular material also orders

6


antiferromagnetically at lower temperatures as a result of inter-chain interactions, having a Neel ´ temperature (TN ) of 0.49 K [31], which rises upon application of pressure to the sample as a result of the softness of the material [32]. The structure of the compound is characterized by a one-dimensional chain of molecules with a hydrogen bond between the hydroxyl group of one molecule and the NO group of the next [33]. Acrylic and methacrylic ester derivatives of the compound have been claimed to show antiferro- and ferromagnetic intermolecular interactions, respectively [34]. The methacrylic ester is a metamagnet below 0.16 K [35], and the methacrylamide derivative also shows similar behavior [36].

A very similar radical to TANOL structurally is the 4-hydroxyimino derivative of TEMPO 8, which also forms hydrogen-bonded chains in its crystals [37], and shows a transition to bulk ferromagnet [38]. The critical temperature for the material is 0.25 K, and it has a Weiss constant of +0.43 K at higher temperatures [39]. A detailed study of the compound and its perdeuterated homologs while having no effect on the critical temperature, did allow a detailed analysis of the spin density distribution in the compounds through solid-state NMR studies [40]. The negative hyperfine coupling constants in both the NOD group and the axial methyl groups of the radical, which form hydrogen bonds to the NO group and thereby unite the chains of molecules, indicated to the authors that these two non-covalent interactions result in ferromagnetic interactions in the two directions [41].

Perhaps the group of organic radicals which have the largest “success rate” – judged by the relation between materials showing ferro- and anti-ferromagnetic interactions – are the arylmethyleneamino-2,2,6,6-tetramethylpiperidin-1-oxyl radicals (9, Table 1), because at the last count [42] 52 of 165 radicals exhibit ferromagnetic [43] interactions. In addition to that, six of these molecular materials (summarized in Table 1) show transitions to bulk ferromagnets in their crystalline states, and another six show metamagnetic behavior (Table 2) [42]. The first of the family to be characterized as a bulk ferromagnet was PhATEMPO (9, R = Ph) [44], which exhibits a typical hysteresis curve, and displays a relatively high coercive force of 106 Oe [45]. While both 4PhPhATEMPO (9, R = 4-PhPh) [46]

7

1.2 Unconjugated Nitroxides Table 1. Formulas and properties of ferromagnetic nitroxides 9. Code Space group Z

Curie temperature Weiss constant

Ref.

PhATEMPO P21 /c 4

TC = 0.18 K θ = +0.74 K

45

4ClPhATEMPO P21 /c 4

TC = 0.4 K θ = +0.69 K

47

4IPhATEMPO P21 /c 4

TC = 0.4 K θ = +0.71 K

42

4MeSPhATEMPO P21 /c 4

TC = 0.34 K θ = +52 K

52

4PhPhATEMPO P21 /c 4

TC = 0.4 K θ = +0.62 K

46

4PhOPhATEMPO Pbca21 8

TC = 0.20 K θ = +0.39 K

52

and 4ClPhATEMPO (9, R = 4-ClPh) [47] display slightly higher Curie temperatures than the first example, their hysteresis curves indicate only very small coercive forces (10 and 5 Oe, respectively). The more recently reported 4IPhATEMPO (9, R = 4-IPh) [42] appears to have a coercive force of approximately 100 Oe. Zero-field muon spin rotation (µ+ SR) experiments confirmed the spontaneous magnetization in 4ClPhATEMPO [48] and indicated a mean internal field of 75 G [49]. In their crystals, 4ClPhATEMPO, 4IPhATEMPO, and 4PhPhATEMPO are isostructural [50], and all the ferromagnetic radicals have certain features in common [51]. The hydrogen atoms of the methyl or methylene groups at β-positions with respect to the NO moiety form hydrogen bonds with the oxygen atom which bears the unpaired electron. The spin-polarization of these hydrogen atoms, giving rise to spin-alternation in the backbone as shown schematically in Fig. 4, was proposed [52] as the mechanism which operates in these nitroxides, as well as in TANOL suberate (5), the authors having ruled out the possibilities of direct magnetic interactions, such as direct exchange, or dipole-dipole interactions. The proposed hypothesis has been backed-up by theoretical studies [53].

8


Table 2. Formulas and properties of metamagnetic nitroxides 9. Code Space group Z

Neel ´ temperature Critical magnetic field for spin-flip induction (at temperature)

Ref.

2PyATEMPO n.r.*

TN = 0.26 K 10–20 Oe (0.05 K)

42

4PyATEMPO P21 /c 4

TN = 0.12 K 110 Oe (0.09 K)

42

2NATEMPO Pna21 4

TN = 0.12 K 180 Oe (0.04 K)

54

35ClPhATEMPO Pbca 8

TN = 0.12 K 20 Oe (0.05 K)

42

34ClPhATEMPO n.r.*

TN = 0.10 K 20 Oe (0.04 K)

42

26ClPhATEMPO n.r.*

TN = 0.20 K 20 Oe (0.04 K)

42

* Crystal structure not reported.

The 2-naphthyl derivative’s metamagnetic behavior was also described appealing to the spin polarization mechanism through the hydrocarbon network, since a stack of radicals forms along one axis of the crystals united by the weak hydrogen bonds described previously [54]. Particularly interesting is the magnetization curve for this compound – magnetic hysteresis was observed at 40 mK when the ferromagnetic phase was entered (Fig. 5), but on decreasing the applied field from this condition, magnetization remained then dropped suddenly as zero field was approached, presumably as a result of the formation of an antiferromagnetically ordered ground state. Similar behavior is observed when the field is applied in the opposite direction. While the exact mechanism of the change in magnetization was not clear, the authors suggested ferromagnetic interactions (J/k = +0.2 K) in the column or stack


9

Fig. 4. Schematic representation of the proposed spin-polarization mechanism present along the b axis of crystals of PhATEMPO (9, R = Ph) [52].

Fig. 5. Illustration of the magnetization curve at 40 mK for the purely organic metamagnet, 2-naphthylmethyleneamino TEMPO [54].

of radicals, while interchain interactions, whose route is not clear, are weakly antiferromagnetic (J/k = −0.02 K). The formation of salts of nitroxides functionalized with carboxylate groups is proving to be an interesting way to try and influence magnetic interactions in these materials by using crystal engineering tools. The sodium and potassium salts of 4-carboxy-TEMPO (10) show ferromagnetic interactions present in their crystals, as determined by susceptibility (Fig. 6) as well as magnetization experiments [55], whereas the parent acid shows antiferromagnetic interactions. Fitting of the susceptibility data to the Bleaney–Bowers equation gave values of J/k of +0.17 and +0.18 K for the sodium and potassium salts, respectively, and Weiss constants of +0.5 and +0.6 K when the high temperature data were fitted to the Curie-Weiss law. The

10


Fig. 6. Magnetic susceptibility data for the sodium (crosses) and potassium salts (dots) of 4-carboxy-TEMPO (10) along with best fits using linear chain (dashed line) and Bleaney Bowers (solid line) models, and the network of sodium ions coordinated to carboxylates and NO groups [55]. Reproduced by permission of The Royal Society of Chemistry.

crystal structure of the sodium salt revealed that the shortest distance between NO groups is through Na2 O2 parallelograms (Fig. 6), and the authors proposed that they may play an important role in the magnetic coupling in the material. Crystallization of salts formed between 2,2,5,5-tetramethyl-3-carboxypyrroline-1oxyl (11) and benzamidinium cations (12) results in solids with sheet-like structures in which the components are linked by strong hydrogen bonds forming a salt bridge [56]. The magnetic interactions between the radicals are weakly antiferromagnetic. Incorporation of a water molecule into one of the salts reduced dramatically these interactions, implying that the hydrogen bonds aid the transmission of exchange interactions.

1.2.2

Oligo-nitroxides

In general, the unconjugated oligo-nitroxide radicals present little or no appreciable through-bond coupling of the free electrons in the molecule. The aforementioned tanol suberate (5) prepared by Rassat and colleagues [57] is a classic example of this phenomenon, and is representative of the majority of the oligo-nitroxides derived from TEMPO [58], since the magnetic interaction through the hydrocarbon skeleton


11

is extremely small, all the spin density being located equally on the nitrogen and oxygen atoms [59]. The diester 5 has ferromagnetic interactions in the solid within planes [60] containing the radical moieties from different molecules, which interact antiferromagnetically between them [14]. Therefore, the covalent linker serves only to influence crystal packing and hence relative arrangements of spins. A more recent and interesting example is the tetraradical 13 which has recently been shown to have ferromagnetic interactions (θ = +0.71 K) present in its crystals, wherein two centrosymmetric molecules are present in the unit cell [61]. Relatively short distances are observed both inter- and intramolecularly, with near orthogonality of the SOMOs, which was taken as the motive for the ferromagnetic interactions in the material.

An efficient approach to the generation of ferromagnetic interactions within a molecule is to ensure that the SOMO orbitals are orthogonal to one another [62]. Rassat and Chiarelli designed a family of diradicals meeting this condition because of the incorporation of a rigid adamantane-type skeleton in the molecules [63]. In all of the family, intramolecular ferromagnetic interactions are present, as ascertained by studies in solution [64]. However, while radicals 15 and 16 show dominant antiferromagnetic interactions in the bulk state, the diradical 14 (which a priori is the most symmetric (D2d ) of the derivatives) is a bulk ferromagnet [65], with the highest Curie temperature (TC ) of all the reported compounds containing only carbon, hydrogen, oxygen and nitrogen, at 1.48 K, and having a Weiss constant of +10 K. As dictated by the small magnetic anisotropy of this compound no hysteresis could be observed, which is the expected magnetic behavior of a “soft” magnet. Two crystalline phases have been detected for the compound but only one – the α-phase – is

12


a bulk ferromagnet [66]. In the ferromagnetic α-phase the NO groups of the radicals are arranged intermolecularly in a head-to-tail manner along one direction with the intramolecular interaction being perpendicular to this chain. Polarized neutron diffraction studies revealed that the spin density is located mainly in the ( orbitals of the nitrogen and oxygen atoms, although some is also detected on the contiguous CH2 groups [67]. The alternation of the sign of spin density of the carbon atoms linking the two NO groups was taken as an indication that the intramolecular ferromagnetic coupling is a consequence of exchange through the weakly polarized carbon framework. Interestingly, in its crystals, the molecules of 14 are not D2d symmetric as result of a non-planar conformation of the NO group, which therefore finds itself in a chiral (C2 ) situation [68].

1.3

Conjugated Nitroxides

The family of nitroxides having an aromatic ring directly attached to the nitrogen atom of the radical have also provided a rich variety of magnetic behavior. One of the most important features of this family of radicals is the extensive delocalization of the free electron over the aromatic ring, because it provides a pathway for it to interact magnetically with its neighbors. The most representative examples of this type of conjugated radicals are summarized below.

1.3.1

Mono-nitroxides

The di- p-anisyl nitric oxide radical (DANO, 17) was the first member of this type of open-shell molecular material in which the magnetization was studied in detail. The radical has characteristics of an isotropic, nearly two-dimensional quadratic, magnetic system with antiferromagnetic interactions [69], with a ratio of interplane and intraplane exchange interactions of the order of 10−3 , in line with the solid-state structure of the compound which consists of sheets of NO groups, each with four nearest neighbors. The coupling within the molecular sheets J/k was estimated as −2.45 K, and the sample exhibited an antiferromagnetic spin ordering at 1.67 K [70]. The absence of an anomaly in the EPR spectrum at the Neel ´ temperature was taken as an indication of short-range magnetic ordering [70].

1.3 Conjugated Nitroxides

13

A radical which is closely related to DANO is 9,9-bis(4-tolyl)-9,10-dihydroacridin10-yloxyl (BTAO, 18), which forms a dimer in its crystals with the acridine parts of the molecule π-stacked in such a way that the expected magnetic coupling is ferromagnetic according to the McConnell I mechanism [71]. The observed magnetic behavior does indeed show intradimer ferromagnetic coupling (J/k = +8.85 K), while inter-dimer interactions are antiferromagnetic with J /k = −0.16 K, assuming that inter-dimer interactions occur along two directions only among the four nearest neighbors.

A very interesting recent development is the report by Reznikov and colleagues of vinyl nitroxides, owing to its exemplification of a manner to augment the strength of intermolecular magnetic interactions in purely organic compounds through enhanced delocalization of the free electron [72]. The compound 19 (Fig. 7) exhibits extremely strong antiferromagnetic interactions perhaps because it crystallizes forming chains with short distances between the oxygen atom bearing the spin and the vinyl bond in the heterocyclic ring. The authors implied this feature to account for the magnetic behavior of the material, fitted to a Heisenberg one-dimensional model, with J/k of −101 K. Calculation of the spin densities by ab initio methods suggested localized spin density on the vinyl carbon atom bearing the cyano group (Fig. 7), implying a pathway for the interaction.

Fig. 7. Views of the calculated spin density of a model for the vinyl nitroxide 19. (a) Truncated (two-radical) model system. (b) General view of the spin density distribution of the model system [72]. Reproduced by permission of The Royal Society of Chemistry.

14


Although much work has been performed on the solution-state properties of monophenyl N -t-butyl N -oxides (2), to the best of our knowledge, this depth of investigation has not been matched in the solid state. In contrast, the oligo-radicals have found great interest in the study of intramolecular magnetic coupling, an area which is discussed in the next section.

1.3.2

Oligo-nitroxides

One important goal in the field of organic molecular magnetism is to prepare synthetically a compound incorporating more than one unpaired electron with appreciably large ferromagnetic coupling between them, resulting in a molecule which has a triplet (S = 1) or higher (S > 1) ground state [73]. One of the principle interests in such robust high-spin organic molecules is to employ them as magnetically active ligands with paramagnetic transition metal ions with the purpose of preparing coordination compounds which exhibit magnetic ordering at the highest possible temperatures. A chapter concerning this pursuit will be presented in this book. The engendering of ferromagnetic coupling within a molecule relies on certain moieties capable of sustaining such an interaction, and more often than not the spacer is conjugated. The classic example of this type of ferromagnetic coupler is m-phenylene [74]. In 1969, the bis-nitroxide 20 was shown to possess a triplet ground state [75], although the compound is extremely unstable.

In attempts to improve the stability of this bis-nitroxide skeleton, the groups led by Rassat [76] and Iwamura [77] prepared independently the radicals 21 and 22, respectively. In both these radicals, the ground state of the molecule has been shown to be a singlet. The reason for the breakdown of the expected topological rule appears to be the extremely distorted conformation adopted by the NOtBu groups [78], which are bent out of the plane of the benzene ring, as revealed in the X-ray structure of 22 in which the two NO groups point to the same “side” of the molecule, i. e. in a syn conformation [77]. Indeed, Rassat and coworkers managed to separate conformational isomers of radical 21 thereby demonstrating unambiguously that both isomers have intramolecular antiferromagnetic interactions of J/k = −33 and −40.5 K [76], respectively, similar to that of the syn isomer of 22 (J/k = −36.9 K) [77].


15

In an extension of their work, Iwamura and coworkers prepared the triradical 23 with the aim of studying “competing magnetic interactions and/or spin frustration in the context of molecular magnetism” [79]. The molecule exhibits an EPR spectrum in which signals attributable to both the quartet and doublet states were observed, the former being thermally populated with a small energy gap between the two magnetic states. In the solid state, the NO groups are oriented virtually perpendicularly to the plane of the central benzene ring. Magnetic susceptibility data of the crystals indicated that the ground state is indeed a doublet, with dominant antiferromagnetic interactions between two pairs of neighboring free electrons which force the ferromagnetic alignment of the remaining pair. It was claimed as the “first demonstration of an organic triradical showing competing interactions” [79]. Ab initio calculations of model compounds showed an angular dependence of the magnetic interaction through the m-phenylene coupler, and correctly reproduced antiferromagnetic coupling when the NO group is highly twisted out of the plane of the benzene ring, implying disjoint molecular orbitals as the origin of this phenomenon [80]. Very recently, the same group reported a triradical which presents curiously a doublet ground state, and concluded that not only topology but number of π -electrons is important in the determination of ferromagnetic couplers [81].

One of the aims concerning the propagation of ferromagnetic interactions within a molecule is the preparation of polymers consisting of coupled spins [82]. Towards this goal, Ishida and Iwamura prepared and studied the triradical 24 as a model of poly[(oxyimino)-1,3-phenylenes] [83]. The molecule does indeed have a quartet ground state. While EPR spectral intensity followed the Curie-Weiss law, and no half-field ( m S = 2) or third-field ( m S = 3) signals were observed, magnetic measurements on a Faraday balance revealed that the effective magnetic moment

16


of the micro-crystalline solid presented a maximum 3.53 ÌB at approximately 140 K, consistent with an energy gap between the lowest excited doublet and the quartet ground state of +240 K. This value plummeted on lowering the temperature as a result of intermolecular antiferromagnetic interactions, the Weiss constant being −19 K. To the best of our knowledge, no information concerning the conformation of the molecule in the solid is available, while in solution, EPR spectra suggest the presence of several conformers in accord with the complex conformational space available to this molecule as a result of its four torsional degrees of freedom. Trimethylenemethane (TMM) has proved to be another extremely efficient ferromagnetic coupler of unpaired electrons [84], and the preparation by Iwamura and colleagues of a bis-nitroxide with diphenylethylene spacers between the radical centers proved its worth [85]. When the nitroxide groups are located in the 4-positions of the benzene ring as in 25 (predicted to be a triplet by the through-bond topology rules) magnetic susceptibility measurements of microcrystalline samples revealed an increase of the effective magnetic moment between 40 and 10 K, followed by its decrease. The authors ascribed this effect to intramolecular ferromagnetic interactions with antiferromagnetic interactions between molecules. The energy gap between the triplet and singlet states was estimated as 15.3 K from fitting of the magnetic data to the Bleaney–Bowers equation. The corresponding molecules with the phenyl rings substituted at the 3-positions revealed a singlet ground state, in consonance with the disjoint nature of the molecular orbitals of the two groups. More recently, Shultz and coworkers have studied [86] the properties of various derivatives with TMM couplers in order to study the effects of conformation on the electronic coupling, which are in line with the π -conjugation in the molecules. Solution state EPR measurements of the half-field signal ( m S = 2) at variable temperature on fluid and frozen solutions of the radicals showed that for compounds 25–28 and 30, the intensities obey the Curie-Weiss law, indicating that either the triplet is the ground state, or that there is triplet-singlet degeneracy. The completely planar compound 30 (expectedly) showed the highest conjugation as judged from its UV-visible absorption spectrum, while the other compounds all contain twisted conformations. Indeed, the compound 31 which does not contain the TMM-type moiety also obeys the Curie-Weiss law in the temperature range studied by the authors, and the through space dipolar interaction between the two electrons, measured by the zero-field splitting parameter D, was similar to the other compounds reflecting similar effective spin density distribution for these derivatives. The behavior of compound 29 is radically different. The intensity of the half-field signal drops rapidly upon decreasing the temperature, indicating a singlet ground state well separated from the triplet state. This observation serves to emphasize the dramatic effects that conformation can have on intramolecular magnetic interactions. Solid state magnetic data for these radicals has yet to be reported. Oligo(1,2-phenylenevinylene) has also shown to be an efficient spin coupler that might be interesting for preparing super-high-spin polymers. The diradicals 32 and 33 have triplet ground states, with J/k values of +48 and +2.1 K, respectively, and antiferromagnetic coupling between molecules in the solid state samples used for these estimates [87]. The value of the magnetic coupling in 32 is approximately 1.5 times that of the similar compound 34 [88]. The authors suggested that the motive


17

for the increased coupling is a result of the lowering of the potential energy gap between the non-bonding molecular orbitals as a result of conjugation, an assertion supported by theory. The authors implied that the presence of spin defects might not be so important in super-high-spin polymers containing these fragments than in other polyradicals. Experimental evidence for such a proposal will be highlighted later.

18

1.4


Nitronyl Nitroxides

This group of radicals is perhaps the one which has received most attention in the realm of molecular magnetism, from the point of view of purely organic as well as coordination compound materials. The synthesis of the radicals was first reported by Ullmann and co-workers in the late 1960s [89], and most of today’s studies use their established routes to the compounds [90], in spite of the problematic and erratic nature of the preparation of some of the radical precursors. The orders of spin density in the molecules determined by polarized neutron diffraction [91], different spectroscopic techniques (EPR [90, 92], NMR [93], ENDOR [94]) and ab initio calculations [7] agree that in the nitronyl nitroxide unit the free electron in the singly occupied molecular orbital (SOMO) is distributed mainly over the two oxygen and two nitrogen atoms of the ONCNO conjugated system. The central carbon atom of this moiety is a node in the SOMO, a situation which limits delocalization of this electron over the substituents located at the 2-position of the imidazolyl moiety but permits the spin polarization phenomenon thereby creating an alternating spin density on the pendant group. It is well known that the properties of the nitronyl nitroxides are determined principally by the nature of the substituent located at this position and more importantly by the spin density on their atoms As a result of this situation, great effort has been expended recently in order to study in detail by EPR and NMR spectroscopies the spin distribution on the substituents, and to elucidate how this delocalization is influenced by the molecular conformation, as well as the molecular surroundings (solvent, neighbors, etc.) both in solution and the solid state [7h, 95].

1.4.1

Mono-nitronyl Nitroxides

An extremely wide range of nitronyl nitroxides have been prepared and studied, the majority of them being aromatic derivatives, as a result of their high stability and crystallinity. All the bulk ferromagnetic nitronyl nitroxides described so far are presented in approximate chronological order in Table 3, along with crystallographic information and most pertinent magnetic data. As shall be appreciated during the discussion that follows, the balance between ferro- or anti-ferromagnetic intermolecular interactions is an extremely delicate one, which can be influenced drastically by small changes in crystal structures. For this reason, it is convenient to discuss the radicals in comparison with their most similar chemical cousins. The structurally most simple nitronyl nitroxides are those in which a single atom or small group is attached to the carbon atom at the 2-position of the imidazolyl ring, the parent molecule being HNN (35) [90]. In both its crystalline phases reported so far, the molecule forms non-covalent dimers in the solid state of the type shown in Fig. 8, in which the hydrogen atom at the 2-position of the imidazolyl ring forms a hydrogen bond with one oxygen atom [96]. In the α-phase [97], these dimers pack into sheets by virtue of trifurcated Csp3 –H· · ·O hydrogen bonds [98], and the sheets stack with the carbon atoms at the 2-positions of the imidazolyl ring of one plane located

19

1.4 Nitronyl Nitroxides

Table 3. Structures and magnetic properties of nitronyl nitroxides with ferromagnetic ordering.

†

Code Space group Z

Curie temperature Magnetic coupling constants (θ or J/k) Mean internal field

Ref.

4NPNN (6) (β-phase) Fdd2 8

TC = 0.60 K θ = +1.2 K 160 G

15, 100, 101

3QNN (37)† P21 2

TC = 0.21 K J/k = +0.28 K 60 G

107, 109

4PYNN (38) C2/c 4

TC = 0.09 K J/kB = +0.27 K 120 G

114, 116

4MeSPNN (46) P21 /a 4

TC = 0.20 K θ = +0.36 K n.a.*

127

2OHPNN (47) (α-phase) Pbca 8

TC = 0.45 K θ = +0.62 K 140 G

131, 133

2,5OHPNN (52) (α-phase) P21 /n 4

TC = 0.50 K J/k = +0.93 K θ = +0.46 K n.a.*

138, 139

2FPNN (56) (α-phase) Pbca 8

TC = 0.30 K θ = +0.48 K n.a.*

145

canted ferromagnet, * Data not available.

on top of the NO groups in another. The observed antiferromagnetic coupling was fitted to the Bleaney Bowers equation giving a J/k of −11 K, but which direction these interactions operate in is as yet unclarified. In the β-phase, the sheets contain bifurcated Csp3 –H· · ·O hydrogen bonds and the orientation between planes locates NO groups on top of and antiparallel to one another, in slightly different orientations for the four pairs of molecules formed by the eight crystallographically-independent molecules [97]. The magnetic data of the β-phase was fitted to a model with two

20


Fig. 8. Schematic representation of the non-covalent dimer formed by HNN (35) in the solid state and its packing in the α- and β-phases (only one of the two types of NO· · ·NO interaction is shown) [97, 98].

exchange constants taking into account these four interplanar dimers, and giving J/k of −33 K and J /k of −1.5 K, these values being considered averages. Given the considerable differences in the antiferromagnetic interactions between the two phases, the non-covalent dimer was judged to be magnetically irrelevant. The derivative radicals with either iodine or bromine atoms or a cyclopropane group at the central carbon atom of the ONCNO unit all have honeycomb structures, and thus present similar magnetic behavior to each other, with competing ferro- and antiferromagnetic interactions, the latter compound exhibiting an antiferromagnetic ordering at 1.5 K [99]. The magnetic susceptibility data was fitted to a dimer model with intra- (J/k) and interdimer (J /k) interactions, giving the following exchange interaction energies: J/k = −5.3 and J /k = +4.0 K for the iodo derivative, J/k = −4.5 and J /k = +2.6 K for the bromo compound, and J/k = −1.8 and J /k = 0.4 K for the cyclopropane derivative. As previously highlighted, the first fully characterized organic ferromagnet is from the family of nitronyl nitroxides, concretely the β-phase of 4-nitrophenyl derivative 4NPNN (6), and it sparked the initiation of many research programs on this type of radical. The magnetic behavior of this crystalline phase along with those of the other three known phases of this radical will be discussed in more detail in another chapter in this series by its discoverer. However, for comparison purposes, we mention here that the critical temperature of the β-phase is 0.60 K [100], which is given along with a small fraction of the detailed magnetic data obtained in Table 3 [101]. The structure in the crystals is three dimensional [102], with non-covalent interactions between the oxygen atoms of the two NO groups and the nitrogen atom of the nitro group (presumably of a Coulombic nature) in one direction and the hydrogen atoms of the phenyl ring in another. Structurally related to 4NPNN, in the sense that radicals are arranged in a headto-tail manner as a result of Coulombic interactions, is the 4-cyanophenyl nitronyl nitroxide (4NCPNN (36), Fig. 9) [103]. The oxygen atoms of one molecule are located over the NCN unit of an adjacent molecule, while a short distance between an oxygen atom of the second molecule is located close to the CH group in the 3-position of the


21

phenyl ring of the first. However, unlike the β-phase of 4NPNN, this compound has a two dimensional structure formed by sheets of nitronyl nitroxides with their long axis perpendicular to the ac plane, forming a square-lattice-type magnetic structure in which each molecule interacts with its four nearest neighbors (Fig. 9). Magnetic susceptibility data indicated ferromagnetic interactions within the molecular sheets, which were fitted to a square-lattice Heisenberg model affording J/k = +0.75 K. The two dimensional nature was confirmed by plotting the experimental C/χ T value against z J/kT with those predicted by one-, two-, and three-dimensional (Curie– Weiss) models, using J/k = +3.0 K (Fig. 9). The authors suggested that the short NO to aryl or CN distances could be possible sources of the ferromagnetic interactions.

Fig. 9. Views of the two-dimensional solid state structure of 4NCPNN (36) and the plot of experimental C/χ T against z J/kT along with those predicted by one-, two-, and threedimensional (Curie–Weiss) models with J/k = 3.0 K [103]. Reproduced by permission of The Royal Society of Chemistry.

22


The material showed no evidence for a magnetic phase transition down to 0.5 K according to a. c. susceptibility measurements. More recently, however, zero-field Ì+ SR experiments revealed the presence of an ordered magnetic state below 0.17 K [104], although details of the nature of this state were not derived. A number of heterocyclic nitronyl nitroxide derivatives have been reported, many of which display interesting magnetic properties on their own, and especially when complexed with transition metal ions [105]. It has been shown by ENDOR and TRIPLE spectroscopy that correct positioning of the heteroatoms in the heterocyclic substituent can enhance negative spin density on the pendant group when compared with hydrocarbon analogs [106]. This enhanced negative spin density is produced if the heteroatom is at a π-site that is positively polarized. The radical 3QNN (37, Table 3) crystallizes [107] in a non-centrosymmetric space group, and has a three-dimensional structure which is maintained by hydrogen bonds between the hydrogen atoms of the methyl groups in the nitronyl nitroxide moiety and both oxygen atoms of the same fragment in neighboring molecules as well as the nitrogen atoms of the pendant heterocycle. Paramagnetic susceptibility data of the compound reveal ferromagnetic interactions which were fitted [108] between 300 and 5 K to the Curie–Weiss law, giving θ = +0.27 K. Below 0.21 K this radical exhibits an ordered magnetic state when observed by zero-field Ì+ SR experiments [109]. Close examination of a.c. susceptibility data show a shallow dip at approximately 0.21 K which indicated a magnetic transition that, along with the lack of fitting of magnetic data at low temperature to conventional models for purely ferromagnetic interactions implied the presence of some antiferromagnetic interactions, suggesting, therefore, that the system is a canted ferromagnet [110]. This hypothesis is supported by the fact that the internal field of the sample experienced by the muons in the Ì+ SR experiments (60 G) is approximately half that of the other known ferromagnets of this family (150 G), and seems to be parallel to the c axis of the crystals in accordance with the theoretical estimation [109]. In contrast, the homologous 4-quinoline derivative presents antiferromagnetic interactions, which were interpreted in terms of an alternating 1D antiferromagnetic Heisenberg model with J/k = −7.8 K and α = 0.5 [111]. These antiferromagnetic interactions were ascribed to the close approach of two NO groups within the dimers present in the crystals. The family of nitronyl nitroxide with either 2-, 3-, or 4-pyridyl as substituent show antiferromagnetic interactions in the case of the first two [112], of which the 3-derivative apparently orders at 1.35 K [113], and ferromagnetic interactions for the latter, 4PYNN (38) [114]. This latter compound crystallizes to form a sheet-like structure [115], in which chains of molecules pack in a head-to-tail arrangement, this disposition being maintained by hydrogen bonds between the oxygen atom of the radical unit and the hydrogen atoms of the pyridyl ring, as represented in Fig. 10. The magnetic data was initially fitted to a model which assumed a one dimensional ferromagnetic chain with a J/k = 0.27 K, but zero field Ì+ SR experiments later revealed the appearance of an ordered state at less than 0.1 K with an internal field of 120 G [116], whose origin is as yet uncertain. The extremely low temperature of the transition has been ascribed to weak π -orbital overlap in the direction perpendicular to the chains shown schematically in Fig. 10.


23

Fig. 10. A schematic representation of the one-dimensional ribbons of molecules formed by 4PYNN (38) in the solid state [115].

Substitution at the 6-position of the 2-pyridyl nitronyl nitroxide radical with a bromine atom (6Br2PYNN, 39) and subsequently with an alkyne group (6A2PYNN (40), Fig. 11) gives crystalline materials which show, according to fitting to the CurieWeiss law, dominant antiferro- (θ = −0.18 K) and ferromagnetic (θ = +1.24 K) interactions, respectively [117]. Both molecular structures have a high twist angle between the component rings, presumably because of repulsive electrostatic interactions between the oxygen and nitrogen atoms of the radical and pyridyl units, respectively. Interestingly, in 6A2PYNN, a strong intermolecular hydrogen bond between the alkyne proton and an NO group leads to the formation of zigzag chains (Fig. 11) which are pulled together by Csp2 –H· · ·O hydrogen bonds from the 3position of the pyridyl ring to the other NO group. The packing results in an angle of 98◦ between nearest radical moieties. The ferromagnetic interactions, confirmed

Fig. 11. The radicals 6Br2PYNN (39) and 6A2PYNN (40) and a schematic view of the hydrogen-bonded chains formed by the latter [117].

24


by magnetization experiments, were analyzed using a one-dimensional Heisenberg chain model, with a J/k of +1.40 K and a weak coupling between the neighboring chains of z J /k of −0.27 K, where z is the number of interacting chains. The spin density distribution in the crystals was probed using polarized neutron diffraction, revealing a significant spin population on the alkyne hydrogen atom involved in the hydrogen bond to the NO group, whose oxygen atom has depleted spin density [118]. It was therefore proposed by the authors that the hydrogen bond is involved in the transmission of the ferromagnetic interaction, though no detailed pathway was suggested. The 5-pyrimidinyl nitronyl nitroxide displays ferromagnetic interactions in its crystals at higher temperatures, while antiferromagnetic interactions compete strongly below 14 K, giving rise to a maximum in the plot of χ T against T [119]. These data were fitted nicely to a regular one-dimensional Heisenberg chain model, with a ferromagnetic exchange constant J/k of +26.2 K, corrected with a mean molecular field approximation J /k of −1.1 K assuming that the number of nearest neighboring chains is 4. The correlation of these interactions with the structure indicated that the chains of molecules formed by the radicals are responsible for the ferromagnetic interaction, since an oxygen atom of one NO group is located very close (2.92 Å) to the central carbon atom of the ONCNO moiety of another molecule, an intermolecular arrangement which is favored by π –π stacking of the pyrimidine moieties. This interpretation based on spin-polarization arguments was appealed to since analysis of the structure shows that direct interaction between NO groups is not likely because the associated orbitals are far from being orthogonal. Interestingly, the stacking of the pyrimidinyl rings could also be invoked using the McConnell I theory because of the staggered arrangement between them. The authors claimed that the magnitude of the magnetic interaction was much smaller than expected given these two pathways for interaction, and implied that direct interaction between NO groups cancels a large part of the ferromagnetic coupling. The family of nitronyl nitroxide radicals with five-membered heterocyclic rings containing nitrogen atoms as substituents display a wide range of particularly interesting magnetic properties (Table 4). In particular, Kahn’s group has reported the preparation and properties of three triazole-derived nitronyl nitroxides. The 4methyl-1,2,4-triazole derivative 4MTNN (41) behaves as a weak ferromagnet [120]. The field-cooled (0.2 Oe) magnetization shows a break at 0.6 K, characteristic of a spin canting phenomenon which is compatible with the space group to which the crystals pertain. The molecule packs so that weak hydrogen bonds form between the methyl groups and oxygen atoms bearing the spin. These bonds lead to a zigzag chain in which the molecules are arranged in a head-to-tail fashion, which unite giving a parquet-like structure. The magnetic susceptibility data obtained for this compound were quantitatively interpreted in line with the structural features using a one-dimensional Heisenberg model, corrected with a mean field approximation accounting for interchain antiferromagnetic interactions. The intrachain interaction J/k was found to be +0.65 K while the interchain one (J /k) was −0.14 K assuming four interacting neighboring chains. The nitrogen atom at the 2-position of the triazole ring has negative spin density (according to polarized neutron diffraction data) and is located very close to one of the nitroxide oxygen atoms with positive spin

25


Table 4. Properties of nitronyl nitroxides bearing five-membered nitrogen-containing heterocycles. Code Space group Z

Magnetic behavior and data

Ref.

4MTNN (41) P21 21 21 4

Weak ferromagnet J/k = +0.65 K J /k = −0.14 K

120

4,5DMTNN (42) P21 21 21 4

Metamagnet θ = +0.45 K TN = 330 mK HC = 0.7 kOe

121

5MTNN (43) P21 /c 4

Strong ferro- and weak antiferromagnetic interactions J/k = +10.6 K z J /k = −1.4 K θ = +8.9 K

122

2BimNN (44) Pbca 8

Strong ferro- and weak antiferromagnetic interactions J/k = +17.3 K* θ = +8.2 K

123

2ImNN (45) P21 /a 4

Antiferromagnetic interactions J/k = −89 K

123– 125

* Value of weak antiferromagnetic interactions not determined.

density, and was therefore implied as the route for the dominant ferromagnetic interactions, although the authors insisted that it is not clear if this negative spin density is a cause or a consequence of these interactions. The short contact between NO groups of neighboring chains could be responsible for the antiferromagnetic interactions. The decrease in χ T exhibited by this compound at very low temperatures is also shown by the metamagnetic 4,5-dimethyl-1,2,4-triazole derivative 4,5DMTNN (42) [121], which packs in a very similar way to 4MTNN, although the distances between nitroxide groups are somewhat longer. The presence of Csp3 –H· · ·O hydrogen bonds

26


Fig. 12. Crystal structure and magnetic susceptibility curve for 5MTNN (43) [122].

which put atoms of opposite spin density close to one another may be important in the transmission of the ferromagnetic interactions. Unlike the aforementioned triazoles, the 5-methyl-1,2,4-triazole derivative 5MTNN (43) has extremely strong hydrogen bonds – between the NH group at the 2-position of the triazole ring and a spin-bearing oxygen atom – linking the molecules in the crystal so as to form a one-dimensional molecular chain (Fig. 12) [122]. The molecule is a lot flatter than the other triazoles mentioned (angle between heterocycle planes of 23.3◦ ) and the nitroxide groups are twisted by 34◦ between molecules, i. e. they are not orthogonal. The material has susceptibility data which follow the Curie–Weiss law with θ = +8.9 K (above 5 K) showing the presence of extremely strong ferromagnetic interactions, with weak antiferromagnetic interactions superimposed. The magnetic behavior can be interpreted by a one-dimensional Heisenberg model with J/k = +10.6 K and z J /k = −1.4 K using the appropriate mean-field correction. While the origin of the strong interaction was considered by either spin-polarization effect or by an admixture of ground and excited state configurations, the exact reasons for the tremendous ferromagnetic interaction are as yet unclear [122]. A similarly strong magnetic interaction accompanied by strong hydrogen bonds of a similar type has been observed in the crystals of the 2-benzimidazole nitronyl nitroxide 2BimNN (44) [123]. In this case however, the symmetry of the chain which forms is somewhat different, since the molecules are related by a translation and not by a screw axis. The magnetic susceptibility measurements (which gave a maximum of χ T at 3.2 K, consistent with the presence of dominant ferromagnetic interactions along with weak antiferromagnetic interactions) indicated a magnetic coupling similar in magnitude to that of 5MTNN (Table 4). In addition, magnetization isotherms at 2.8 and 4 K were fitted to Brillouin function curves of a system with an effective S of 9/2. In contrast, the 2-imidazolyl derivative 2ImNN (45) has strong antiferromagnetic interactions [123, 124] (Table 4) as a consequence of the closeness of the spin-carrying oxygen atoms of two radical molecules which form a dimer. In the


27

crystals of this compound, the NH group does not form a hydrogen bond with this oxygen atom, but rather with the basic nitrogen atom in a neighboring imidazolyl ring [125]. Finally, it is worth mentioning that this family of nitronyl nitroxides bearing five-membered heterocyclic rings on the whole shows relatively strong magnetic interactions, which could be a consequence of the enhanced spin polarization provoked by the heterocyclic ring. Given that the interaction between NO groups having a positive spin density and phenyl groups having opposite spin density was calculated to give rise to ferromagnetic interactions [126], Gatteschi and coworkers prepared the compound 4MeSPNN (46, Table 3) – a bulk ferromagnet with a TC of 0.20 K – with the idea that the SMe group would increase the spin density on the phenyl ring and have a relatively large spin density on the sulfur atom [127]. The solid state structure of the compound reveals a twisted conformation for the molecule which packs into dimers that form two-dimensional sheets of molecules. Evidence of “NO-phenyl” interactions, as well as short distances between the NO groups and the SMe substituent in addition to S· · ·HCsp3 interactions between planes were highlighted by the authors [128]. The magnetic susceptibility data at high temperature were fitted to the Curie–Weiss law (θ = +0.36 K), given that EPR studies implied a three-dimensional propagation of interactions between spins. Alternative fitting of the data to a square planar Heisenberg model for S = 1/2 ferromagnetically coupled spins with an additional correction for interplanar interactions gave J/k = +0.35 K in the plane and J /k = +0.04 K between them. The low dipolar interaction energy provoked the researchers to suggest the interplanar interactions as the driving force for the magnetic transition. Interest in the group of hydroxyphenyl nitronyl nitroxides was spurred initially by the suggestion that hydrogen bonds are implicated in the transmission of magnetic interactions in inorganic complexes [26], as well as for the potential controlling role that hydrogen bonds could fulfil in the crystallization of the molecules [129]. The family has provided an extremely interesting assortment of magnetic behavior [130] – the monohydroxyphenyl derivatives, 2OHPNN (47, Table 3) in the α-phase is a bulk ferromagnet [131], 4OHPNN (48) presents ferromagnetic interactions in two dimensions [132] and 3OHPNN (49) has a three-dimensional network of predominantly antiferromagnetic interactions (Fig. 13) [131]. The crystal structure of the α-phase of the bulk ferromagnetic radical 2OHPNN reveals a molecular structure in which the OH group forms a strong intramolecular hydrogen bond with one of the oxygen atoms of the nitronyl nitroxide moiety, causing a high twist angle between the planes formed by the ONCNO moiety and the phenyl ring (ca. 40◦ ). The molecule packs to generate a three dimensional structure in which the NO groups of the open shell moiety form weak hydrogen bonds with hydrogen atoms in the aliphatic part of the molecule as well as the aromatic ring. The Curie– Weiss susceptibility above 4 K gave θ of +0.62 K. Hysteretic M–H behavior with a very small coercive field was observed below 0.41 K, a feature characteristic of a soft ferromagnet [133]. Zero-field muon depolarization experiments (Fig. 14) support the three-dimensional model of magnetism, and provide a value of the internal field (140 G) similar to that of the radical 4NPNN. A similar conclusion about its magnetic dimensionality was accomplished by low temperature heat capacity measurements. The β-phase of 2OHPNN has a completely different structure that is dominated

28


Fig. 13. Magnetic properties of the mono-hydroxyphenyl nitronyl nitroxides 3OHPNN and 2OHPNN, as revealed in the plots of χ T against T and the a. c. susceptibility of 2OHPNN.

Fig. 14. Time evolution of the muon polarization in zero-field muon spin rotation experiments on 2OHPNN [133].


29

Fig. 15. A view of the crystal structure of 4OHPNN (48).

by a chain of molecules, and accordingly with this feature its magnetic behavior is reproduced by a one-dimensional Heisenberg chain model corrected with a mean field approximation [130b]. The intrachain interaction J/k was −1.31 K while the interchain one J /k was +0.70 K, assuming that there are four interacting neighboring chains. The positioning of the hydroxyl group in the 4-position of the phenyl ring in 4OHPNN (48) results in a completely different crystal structure to that of the αand β-phases of 2OHPNN. Strong intermolecular hydrogen bonds dominate, leading to the formation of chains of molecules in which hydrogen bonds are given by the hydroxyl group and received by one of the oxygen atoms of the radical moiety (Fig. 15) [132]. In turn, these molecular chains are united through two Csp3 –H· · ·O hydrogen bonds from diametrically opposite methyl groups in one radical moiety and the otherwise free NO group of a molecule in the adjacent chain. The resulting two-dimensional sheet is virtually flat. Indeed, the ferromagnetic interactions are quasi-two-dimensional, as revealed by EPR studies on oriented single crystals, and are suggested to be transmitted through these hydrogen bonds [134]. The compound shows two successive magnetic transitions at 700 and 100 mK, as revealed by zero-field Ì+ SR experiments [133]. The first is suggested to correspond to the ferromagnetic ordering in the plane of the sheets, while the second could come about because of ordering between them although the nature of the final magnetic state is as yet unclear. The radical 3OHPNN (49) forms non-covalent dimers (Fig. 16) in both the solution [135] and solid states [131]. In the latter it presents predominantly antiferromagnetic

30


Fig. 16. Schematic representation of parts of the crystal structures of 3OHPNN (49), 3,4OHPNN (50), and 3,5OHPNN (51).

interactions as a result of closeness of SOMOs of radicals in different dimers. While the placement of chlorine atoms in the aromatic ring of the hydroxyphenyl nitronyl nitroxides has so far given materials with a variety of antiferromagnetic interactions [136], additional hydroxyl groups do give materials with ferromagnetic interactions. Two of these constitutional isomers – 3,4OHPNN (50) and 3,5OHPNN (51) – contain the same “supramolecular synthon” [24] as that present in 3OHPNN: that is the head-to-tail hydrogen bonded dimer, as one can appreciate in Fig. 16. This motif is therefore a robust one which can be manipulated in a variety of structures, but it is not apparently very significant magnetically, since the three materials which incorporate the unit do not have the same dominant features. Thus, 3,4OHPNN presents competing ferro- and antiferromagnetic interactions [137], which were fitted to a one-dimensional Heisenberg spin chain with alternating signs of exchange interactions JF /k = +9.3 K, JAF /k = −0.38 K with weak interchain interactions (J /k = +0.34 K). The strong ferromagnetic interaction arises most likely from the head-to-tail overlapping of molecules in contiguous layers, appealing to the charge transfer mechanism. On the other hand, the radical 3,5OHPNN presents dominantly antiferromagnetic interactions as a result of overlapping between parallel SOMOs of molecules in stacked hydrogen-bonded ribbons [130b, 138]. The 2,5-dihydroxyphenyl nitronyl nitroxide (2,5OHPNN, 52) also has two known polymorphs, the first of which presents bulk ferromagnetism [139]. The molecular structure of the α-phase is dominated by a strong intramolecular hydrogen bond between the hydroxyl group at the 2-position of the phenyl group and one of the NO oxygen atoms, which results in a lengthening of the latter bond compared with


31

Fig. 17. Schematic representation of part of the crystal structure of 2,5OHPNN (52) [138].

its usual state, and consequently has a non-planar conformation (angle between rings is 37◦ ). Presumably for this reason the crystalline synthon observed in 3OHPNN, 3,4OHPNN, and 3,5OHPNN is not present in these crystals. The molecules are pulled together in all three dimensions by significant intermolecular hydrogen bonds: (i) between the “free” hydroxyl group acting as a donor to the other hydroxyl group which acts as an acceptor forming molecular chains (Fig. 17); (ii) dimerization of these chains through a bifurcated hydrogen bonded system involving the hydroxyl groups at the 2-position of the phenyl ring (Fig. 17); and (iii) union of these sheets by weak Csp3 –H· · ·O–N bonds. Magnetic susceptibility data gave a plot of χ T against T which increased monotonously as the temperature decreased, and was fitted to the singlet-triplet (ST) model, which suggested two ferromagnetic interactions (Table 3). A magnetization curve at 80 mK showed hysteresis, with a small coercive force (200 Oe). The bulk nature of the transition was also confirmed by heat capacity measurements [138]. Deuteration of the OH groups in 2,5OHPNN afforded crystals (70% deuteration) which had slightly lower χ T at 1.8 K than the protonated sample, and heat capacity measurements showed a decrease in the Curie temperature. This result was interpreted as a lengthening of the distances between non-covalently interacting groups, thereby supporting the contention that these bonds assist the transmission of ferromagnetic interactions. The dimer formation between the sheets is considered to result in ferromagnetic interactions, and McConnell’s theory was also invoked to explain the magnetic interactions in all three directions. Semi-empirical and ab initio calculations indicate that the hydrogen bonds present in the structure act as accomplices in the transmission of the ferromagnetic interactions in the crystals [140]. When the OH group at the 2-position is absent in the calculation, an antiferromagnetic interaction was predicted between the electrons on the two proximal NO groups. The phenyl boronic acid radical 4BAPNN (53, Fig. 18) also has a crystalline structure dominated by strong hydrogen bonds, and low dimensional ferromagnetic interactions exist between the unpaired electrons [141]. The molecules form chains linked

32


Fig. 18. Schematic representation of the crystal structure of 4BAPNN (53) which has the four possible pathways of spin-spin interaction: AB, AC, AD, and BC.

by complementary hydrogen bonds in the manner schematized in Fig. 18. Thus, molecules form head-to-tail dimers by virtue of BOH· · ·ON hydrogen bonds, and these dimers are linked in turn by dimerization of the boronic acid moieties. The magnetic susceptibility data was fitted to a dimer model, giving J/k of +0.71 K. Three possible routes for this coupling were considered by the authors, all of which involve strong hydrogen bonds: between the spins A and B in the head-to-tail dimer, between spins A and C, and then the longer pathway A to D and B to D (the alternative route A to D was not considered). The first of these pathways was suggested as the active one based on distance criteria and charge transfer arguments. The corresponding 3-substituted boronic acid isomer follows the Curie–Weiss law (θ = −0.82 K) indicating the presence of dominant antiferromagnetic interactions [141], although its structure has not yet been reported. Several halophenyl nitronyl nitroxides have been reported, many of them showing ferromagnetic interactions. A three-dimensional structure is formed by 4FPNN (54) radicals in the solid state in such a way as to favor relatively strong ferromagnetic interactions [142]. The molecules form head-to-tail dimers (Fig. 19) by virtue of Csp2 –H· · ·O hydrogen bonds (the H–O distance is less than the sum of the van der Waals radii), similar to 4PYNN and 4NPNN, except that a polymeric chain does not result. Instead, the dimers come together about a fourfold screw axis (Fig. 19), which leads to a quite short distance (3.54 Å) between the free oxygen atoms and the carbon in the center of the ONCNO moiety [143]. A strong ferromagnetic interaction is observed, which above 25 K can be described by a θ of +2.5 K. The formation of a triplet species below approximately 10 K was implied by the value of the susceptibilities, which were near to those predicted by the Curie law (C = 0.5 emu K mol−1 ). However, in the plot of χ T against T below 4 K, the value exceeds that for a triplet, a situation indicative of further ferromagnetic interactions. A model involving two ferromagnetic interactions was derived to fit the data, which gave J/k = +5.0 K, and J /k = +0.02 K, and were assigned to intra- and inter-dimer exchange, respec-


33

Fig. 19. Structural formulas of 4FPNN (54) and 4BrNN (55) and a view of the crystal structure of projected on the bc plane, with the plot of magnetization M against H T with the predicted Brillouin function for ideal S = 1/2 and S = 1 paramagnetic systems [143]. Reproduced by permission of The Royal Society of Chemistry.

tively. The weaker interaction was said to be characteristic of the approach of one of the oxygen atoms to the central carbon atom of the ONCNO moiety. It should be noted that variable temperature EPR and X-ray diffraction experiments indicated that there is a lowering of crystal symmetry at temperatures below 100 K, which is a relatively gradual change [143]. It was concluded that the dimer structure was still present, since the cell parameters do not change drastically. The bromo analog

34


4BrPNN (55) presents similar ferromagnetic interactions to the fluoro compound, which were ascribed to the dimer structure in the solid state [142], which is a distorted form of the ones formed by 4FPNN. The halogen atoms have not been implied to play any significant role in the packing or transmission of magnetic interactions. Indeed, the chloro-derivative presents antiferromagnetic interactions [142]. The corresponding 2-halophenyl nitronyl nitroxides have twisted molecular conformations resulting from steric interactions between the halogen and oxygen atoms [144]. The angles between the phenyl and imidazolyl rings is 55◦ for the fluoroderivative and 60◦ for the chloro-derivatives which show positive (θ = +0.48 K) and negative (θ = −2.00 K) Weiss constants, respectively, while the bromo- and iodo-derivatives (whose X-ray structures are not available) both present antiferromagnetic interactions (θ = −3.32 and −3.36 K, respectively) [145]. The 2-fluorophenyl nitronyl nitroxide 2FPNN (56, Table 3) is a bulk ferromagnet, with a Curie temperature of about 0.3 K, as revealed by ac susceptibility data and magnetic heat capacity measurements at very low temperatures [145]. The latter results show a broad hump distinctive of a one-dimensional Heisenberg ferromagnet, the model for which gave an intrachain J/k = +0.6 K. The ratio of interchain to intrachain coupling was estimated from mean field theory, using the TC and J/k value, to be between 1/4 and 1/10. The structure of the radical reveals the typical Csp3 –H· · ·O hydrogen bonds between the head-to-tail packed radical moieties, which was used to argue for a spin-polarization mechanism that would explain the intermolecular ferromagnetic interaction. Also present in the structure are two Csp2 –H· · ·O hydrogen bonds proceeding from the 4- and 3-positions of the aromatic ring. This latter non-covalent bond is also present in the structure of the 2-chloro-derivative, in which the molecules are arranged head-to-head, and was used to argue the case for the antiferromagnetic interaction in the crystals [145]. Antiferromagnetic interactions are observed in the crystals of the multiply-halogenated phenyl nitronyl nitroxides that have been reported – 3,5-difluoro- and pentafluoro [144, 146]. In the vast majority of solid state structures of phenyl nitronyl nitroxides, an appreciable torsion angle exists between the ONCNO plane and the adjoined aromatic ring. However, in the radical 2-phenylbenzimidazol-1-yl N ,N -dioxide [147] (PBIDO (57), Fig. 20), in which the –CMe2 CMe2 – group is replaced by an ortho-substituted benzene ring, this angle is only 10.3◦ , and the molecule has a practically planar shape [148]. The absence of a twisting force in the imidazolyl unit in this structure would seem to favor a low inter-ring angle, and indicate that the reason for the favored pseudo-eclipsed geometry is the presence of a molecule with a flat shape in the crystal, in line with the ideas put forward about three decades ago by Kitaigorodskii [149]. Dimers of the molecules form in the crystal, and these dimers are in turn arranged in a herringbone-type manner, giving a largely two-dimensional system, a fact borne out by EPR measurements, that has a similar form to the κ-phase formed in some molecular superconductors. The magnetic behavior of the compound is quite complex, with two maxima in the plot of susceptibility against temperature, one at 45 K and the other at approximately 3 K (Fig. 20). The magnetic susceptibility data were fitted in a limited temperature range to give intradimer (J/k ≈ −40 K) and interdimer (J/k ≈ −10 K) antiferromagnetic exchange constants, although the values are approximate because of the complexity of the system. The number of spins


35

Fig. 20. Chemical formula of PBIDO (57) and the temperature dependence of the magnetic susceptibility of the compound represented as a log plot of χ T against T [148]. Reproduced by permission of The Royal Society of Chemistry.

responsible for the anomaly at the lowest temperatures was ascribed to one fiftieth of the spins, and EPR revealed (fine structure satellites and half field signal) that it results from spin-multiplet states [148]. A group of radical salts derived from nitronyl nitroxide radicals which have generated much interest are the alkyl pyridinium salts of 4PYNN (38) and its constitutional isomer with the pyridyl ring substituted at the 3-position [150], especially because one of their exotic magnetic behavior. One of the latter salts is a possible kagomé antiferromagnet [151], while another salt has been claimed as a molecular spinladder, in which the radical component is not part of the ladder (which is formed by nickel(II)dithiolthionethiolate anions), but which interacts ferromagnetically within the layers it forms [152]. The exotic properties of these compounds will form the subject of another chapter in this series presented by their inventor.

1.4.2

Oligo-nitronyl Nitroxides

As for the simple nitroxides, ferromagnetic coupling units have been employed to prepare molecules with triplet or higher ground states [153]. The diradical 3phenylene bis(nitronyl nitroxide) (1,3PBNN, 58A) is expected to have, and in reality exhibits, a triplet ground state, as determined by variable temperature EPR spectroscopy [154]. Very recently, Turek and Catala have determined by EPR spectroscopy that the exchange coupling in this diradical (and other related ones), both in frozen solution and in a polymeric matrix, is J/k = +30 K [155]. In the complicated magnetic behavior of this compound in crystalline form, however, antiferromagnetic interactions dominate ferromagnetic intramolecular interactions [156]. The complicated behavior is partially a result of a reversible phase change in the crystals below 100 K, which causes non-equivalence of the centrosymmetric dimers formed by the

36


Fig. 21. A representation of the molecular dimers formed by 1,3PBNN (58A) in the solid state and the magnetic model used to explain the magnetic behavior of the material [156].

molecules in the solid (Fig. 21). After a fitting of the magnetization data at 1.8 K to an eight spin model, which allows for two kinds of dimers, intramolecular ferromagnetic interactions (J/k) of the order of +30 K were found. The related diradical 2,6-pyridyl bis(nitronyl nitroxide) (2,6-PyBNN, 58B) also shows complicated magnetic behavior resulting from competing ferro- and antiferromagnetic interactions [157]. More recently a bis-nitronyl nitroxide based on phenyl pyrimidine PPyrBNN (59) was characterized as a triplet ground state compound which has antiferromagnetic interactions between the molecules in its crystals as a result of a close O· · ·O contacts [158]. The estimated intramolecular ferromagnetic coupling was of J/k = +3.5 K. An extremely interesting compound (preceding these examples) is that reported for the first time by Dulog and Kim, in which three α-nitronyl nitroxide moieties are located at the 1,3, and 5 positions of a benzene ring (PTNN, 60) [159], and which (in principle at least) has a quartet ground state. Very little EPR data concerning the compound has appeared in the literature. A broad spectrum was presented in the original article which implied “strong intramolecular spin–spin interaction”, but no information on the ground state was presented. The magnetic susceptibility data of a powdered sample, which was repeated by Sugawara’s group [160], showed predominantly antiferromagnetic interactions in the material, whose crystal structure has not been solved. The latter group formulated an ingenious way of revealing the intramolecular magnetic interactions using a supramolecular chemical approach [161]


37

(See co-crystallization of nitronyl nitroxides below), showing that the intramolecular exchange coupling, mediated by 1,3-phenylene units, is J/k = +23 K. Building on their work concerning nitroxides attached to thienothiophene rings [162], Iwamura and co-workers reported the preparation of the diradicals TTBNN (61) and TTTBNN (62), which both show singlet ground states, with very small singlet-triplet gaps [163]. On the other hand, 2,4-thiophene bis-nitronyl nitroxide (2,4TBNN, 63) has a triplet ground state [164], with a coupling determined by magnetometry of J/k = +40 K, while the corresponding 2,5-analog is a ground state singlet. The crystals of both materials are dominated by strong antiferromagnetic interactions at low temperatures, as are those of the 2,2 -bithienyl derivatives [164]. Very recently, metallocenes have been shown to behave as magnetic couplers between radical centers [165]. In solution, the bis(nitronyl nitroxide)s MCBNN (64, M = Fe; 65, M = Ru) have singlet ground states, as revealed by a study of the temperature dependence of the m S = 2 transition in the EPR spectra of the radicals in dilute solution, with exchange coupling constants J/k of −29 (M = Fe) and −27 K (M = Ru), respectively (Fig. 22). The magnetic susceptibility data for crystals of the com-

38


Fig. 22. Formula of MCBNN (64, M = Fe; 65, M = Ru) diradicals, the X-ray structure of the ferrocene derivative, and the temperature dependencies of the m S = 2 transition in the EPR spectra of the two [165].

pounds confirmed the presence of antiferromagnetic interactions both within and beyond the molecule, the exchange interactions being Jintra /k of −3.2 and Jinter /k of −4.2 for the ferrocene derivative, whose crystal structure was determined. Unusually, the ferrocene unit adopts a syn geometry in which the two substituents are located on the same “side” of the molecule, held in this position by two complementary Csp3 –H· · ·ON hydrogen bonds, a situation also pertains in solution, as determined from the zero-field splitting parameters from EPR spectra. In the crystal, chains of molecules are formed by virtue of further Csp3 –H· · ·ON hydrogen bonds. Iwamura’s group has recently reported the synthesis of triradicals exhibiting quartet ground states. The molecular materials incorporate two 4-phenyl nitronyl nitroxides coupled to either a nitroxide [166] or a carbene group [167]. In the case of the nitroxide coupled phenyl nitronyl nitroxide NOBPNN (66, Fig. 23) the χ T value of the microcrystalline sample at room temperature was characteristic of three uncoupled spins, but rose upon cooling to reach a maximum at approximately 80 K before decreasing as a result of intermolecular antiferromagnetic couplings. The intramolecular coupling in NOBPNN is aided by the possibility of conjugation, as exemplified by the existence of quinoid resonance structures NOBPNNA and NOBPNNB, resulting in an extremely strong exchange coupling between the central nitroxide and the terminal nitronyl nitroxides of J/k = +231 K. The mixed nitronyl-imino nitroxide and bis-iminonitroxides were also prepared and shown to exhibit quartet states. These results build on previous studies by the same group on a diradical [168] with a triplet ground state because of strong coupling (lower limit of J/k of +450 K) between a nitronyl nitroxide and a 4-substituted phenylnitroxide through a quinoid state, although this state is not very evident in the solid state. Antiferromagnetic intermolecular interactions were also observed in this compound. All the bis-nitronyl nitroxides mentioned up to this point have had appreciable intramolecular magnetic coupling between them, even though without exception the intermolecular interactions are antiferromagnetic. There are also examples of nonconjugated nitronyl nitroxides, for example the diradicals BABPNN (67) [169, 170]


39

Fig. 23. The resonance forms of triradical NOBPNN [166].

and PBIMBNN (68) [171]. The former presents competing intermolecular ferroand antiferromagnetic interactions in what can be described as a an alternating onedimensional Heisenberg chain with JAF /k of −3.9 K, and JF /k of +1.2 K [170]. The compound PBIMBNN has both short intra- and intermolecular distances between SOMOs, and its magnetic behavior in the solid state can be described as a one dimensional antiferromagnetic alternating Heisenberg chain, with J/k of −158 K

40


and α of 0.22 [171]. The magnetic interactions are considered not to be throughbond because of the large torsion angles within the molecules.

1.4.3

Co-crystallization of Nitronyl Nitroxides

While the crystallization of pure radicals may result in somewhat disappointing properties, an interesting supramolecular approach is to take advantage of the interactions of the open shell molecules with other compounds – of diamagnetic or paramagnetic nature – to generate new relative orientation of the radical units and therefore altered magnetic behavior. The area of supramolecular chemistry which applies most to this objective is that of crystal engineering [24] – the use of non-covalent intermolecular bonding interactions to influence solid state arrangements of molecules. Perhaps the most simple approach appeals to simple acid-base chemistry. For example, the radicals 3PYNN (69, Fig. 24) and 4PYNN (38) when treated with HBr(g) form micro-crystals which incorporate two molecules of radical for each hydrogen bromide ion pair [172]. The (3PYNN)2 HBr adduct presents ferromagnetic interactions (while the parent radical has antiferromagnetic ones), which according to the authors is a result of the type of stack shown in Fig. 24, in which two pyridine nitrogen atoms complex one proton, and these units pile up, although there is no hard structural evidence for this argument. According to this model, the fairly strong ferromagnetic interactions (J/k = +5.7 K) in the stack are counteracted by weak antiferromagnetic interactions (J /k = −0.24 K) between them [173]. In contrast, the salt of 4PYNN of the same stoichiometry shows antiferromagnetic interactions that seem to extend in three dimensions (θ = −2.3 K) while in the parent compound they are ferromagnetic. Co-crystallization of 4PYNN independently with three diacids has produced zerodimensional supramolecules in the form of 2:1 radical/acid hydrogen bonded complexes of different topologies depending on the hardness of the acid (Fig. 25) [174]. When the acid is soft, as in the case of hydroquinone, the acidic hydrogen atoms form hydrogen bonds with the spin-bearing oxygen atoms, while in the case of harder acids the pyridinic nitrogen atom accepts the hydrogen bond. All the complexes showed antiferromagnetic interactions of varying degrees of strength which were correlated

Fig. 24. A representation of the molecular dimer formed in the (3PYNN)2 HBr salt and the stacks of dimers assumed to exist in the solid state [172].


41

Fig. 25. Zero-dimensional hydrogen-bonded complexes of pyridine-derived nitronyl nitroxides [174, 175].

with the packing of the complexes, which were governed by weak interactions. The combination of the aforementioned basic nitronyl nitroxides (3PYNN and 4PYNN) with the complementary 4-benzoic acid-derived nitronyl nitroxide (4HOOCPNN, 70) also leads to similarly zero-dimensional complexes (Fig. 25), materials which also show antiferromagnetic coupling between the spins [175]. In turn, this acid has been crystallized as its lithium, sodium and potassium salts [176]. While the pure 4HOOCPNN [177] and the sodium and potassium salts show antiferromagnetic interactions, the lithium salt, which crystallizes with two molecules of methanol, shows strong ferromagnetic interactions (J/k = +15.9 K) which take place between the dimers formed in the crystals wherein the nitroxide oxygen atom of one molecule is in close proximity to the carbon atom between the same residues in another molecule [176]. The ability of the spin-bearing oxygen atoms of the nitroxide radicals to accept hydrogen bonds has been exploited by Kobayashi and coworkers for the preparation of three 1:1 complexes of nitronyl nitroxides with boronic acids (Fig. 26) [178]. All the complexes reported show moderate ferromagnetic couplings accompanied by weaker antiferromagnetic ones. The structures of the two crystals incorporating phenyl nitronyl nitroxide have been solved, and are almost isostructural [178], the magnetic behavior and structure of the phenyl boronic acid complex [179] being shown in Fig. 27. The complexes consist of hydrogen bonded one-dimensional helical chains of molecules with alternation of the two molecular components. The

42


Fig. 26. One-dimensional hydrogen bonded 1:1 complexes of phenyl nitronyl nitroxides with boronic acids and their magnetic exchange constants, where J/k and J /k are the intra- and inter-chain exchange coupling constants [178].

Fig. 27. The magnetic susceptibility (presented as plots of χ T against T ) and views of the crystal structure (helical chain and close approaches between radicals in different chains) of phenyl nitronyl nitroxide and phenyl boronic acid [179]. Reproduced by permission of The Royal Society of Chemistry.


43

NO· · ·HOB(R)OH· · ·ON unit was proposed as the ferromagnetic interaction route. However, the shortest NO to NO distance (approximately 4.6 Å) is between helical chains (Fig. 27). This approach was assigned to the weak antiferromagnetic interaction, with the rational that the SOMOs are relatively close and there is some overlap between them. The orientation of this packing was slightly different in the two structures, and was inferred to explain the small differences in the exchange interactions. Buchachenko proposed, twenty years ago, an ingenious strategy for the preparation of materials with the potential behave as ferrimagnets that is based on cocrystallization of radicals with different spin multiplicities [180]. Following this idea, Sugawara and coworkers prepared several very interesting complexes [181]. Firstly, they managed to co-crystallize the triradical PTNN (60) with trinitrobenzene, which forms a material with molecular stacks containing the two components in alternating fashion, and thereby confirm that the open shell molecule has a quartet ground state, with an intramolecular exchange coupling J/k of +23 K [161, 182]. At low temperatures, weak intermolecular antiferromagnetic interactions become evident. The same driving forces used in the crystallization, which are Coulombic and π –π stacking interactions [183], were used for the preparation of a material containing stacks of compounds with spin multiplicities of S = 1 and S = 1/2 [184]. The bisnitronyl nitroxide 1,3PBNN (58A) with S = 1 and the mononitroxide 3,5BNO2PNN (71) with S = 1/2 are the components, which pack in alternating fashion forming a column (Fig. 28), with intercalated benzene molecules of crystallization between the stacks. The ferrimagnetic material which was the goal of the work was not achieved, because the monoradical interacts magnetically with one of the two radical moieties in the diradical preferentially, giving rise to a doublet pair. This phenomenon was witnessed in the magnetic susceptibility data, which at room temperature has a χ T value corresponding to independent three spins, a value which decreases on lowering the temperature down to 10 K as a result of antiferromagnetic interactions. The magnetic data in this temperature range is well reproduced by a model which has an intramolecular coupling J1 /k of +20 K within the diradical and an intermolecular coupling J2 /k of −30 K between neighboring 1,3PBNN and 3,5BNO2 PNN components along one direction. Between 4 and 6 K the χ T value is almost constant with a value somewhat larger than that expected for an S = 1 system, suggesting a short-range magnetic spin coupling. Below 3 K further antiferromagnetic interactions are evident. Surprisingly, the spin remaining at low temperature behaves basically independently of the other radical moiety in the molecule, as evidenced by EPR measurements which show two broad lines below 10 K as a result of the change in spin state [185]. One line corresponds to the antiferromagnetically coupled spins, and is most intense in the direction of the molecular columns, while the other has the same intensity in all directions and corresponds to the other spin in the diradical. The conclusion of this work is that the magnetic degree of freedom in the triplet molecule precludes the success of this approach to ferrimagnetic materials, and the criteria for equal coupling of the two spins in the triplet to the singlet are not met [186].

44


Fig. 28. Structure of the 1,3PBNN (58):3,5BNO2 NN (71) co-crystal and its magnetic susceptibility behavior [181].

1.5

Imino Nitroxides

The imino nitroxides are directly derived from the nitronyl nitroxides, and are often obtained by accident as a consequence of over-oxidation of the latter, but have received more interest for their coordination chemistry than for their inherent magnetic behavior, perhaps because many of the radicals in their pure state show predominantly antiferromagnetic interactions [119, 125, 162-164]. This situation is somewhat disparaging, given that in principle the spin density is able to delocalize more in these compounds onto the substituent at the 2-position of the imidazolyl ring than in the nitronyl nitroxides since there is no node at the carbon atom at the 2-position of the imidazolyl ring (Fig. 1) [9, 10].

1.5 Imino Nitroxides

45

Fig. 29. A representation of the molecular chains formed by EPIN (72) and its low temperature dependence of the susceptibility (M/H) cooled in a 3.7 G field [187].

Ferromagnetic order has been observed in the 2-ethynylpyridine imino nitroxide EPIN (72, Fig. 29) [187]. As in the corresponding nitronyl nitroxide derivative [117], the compound packs forming hydrogen-bonded chains linked by the alkyne hydrogen atom and the nitroxide oxygen atom, an interaction which was implicated in the ferromagnetic exchange. Fitting of the magnetic susceptibility data to a onedimensional Heisenberg chain model gave a J/k of +0.50 K. Application of a mean field correction didn’t improve the fit. Spontaneous magnetization was observed below 0.2 K (Fig. 29), with a saturation value of magnetization close to 1 ÌB /molecule. No hysteresis was observed, field dependence of the magnetization shows that the sample is very easily saturated, which prompted the authors to infer a bulk ferromagnetic order. The 4- and 3-benzoic acid imino nitroxides have also recently been reported [188]; in these the interactions are ferromagnetic and, it has been proposed, are propagated by the intermolecular hydrogen bonds which unite the molecules in the crystals. The same compounds have also been used in interesting ferromagnetic organic–inorganic composites with layered cobalt hydroxides [189]. Several of the bis(nitronyl nitroxides) described above were also used to prepare the corresponding bis(imino nitroxide) and combined imino-nitronyl bis nitroxide

46


derivatives by deoxygenation. In general the magnetic properties of the resulting compounds do not differ dramatically from their precursors [155, 163, 190], although the strength of the exchange interaction is somewhat lower, an effect ascribed to the lower extent of spin polarization occurring in imino nitroxides [155].

1.6

Poly(nitroxides)

One of the most conceptually-appealing ways to generate an organic ferromagnet is in the form of a polymer [191], in which radicals are spaced equally along the polymer skeleton with ferromagnetic coupling units between them (Fig. 30), as in this way ferromagnetic interactions within the covalent skeleton can in principle be extended over extremely large distances. Nevertheless, the extension of the ferromagnetic interactions in two- or three-dimensions, a fundamental requirement for achieving a bulk ferromagnet [4a], can only be attained with two- or three-dimensional polymer networks containing millions of radical centers and in which each spin-containing unit is ferromagnetically coupled with at least three (preferably more) nearest neighbor units. The apparently simple objective of achieving a super-high-spin macromolecule, as laid out in ideal manner here, has received a great deal of attention, and yet has met with extremely limited, not to say no, practical success. Following the controversy surrounding a family of polymerized diacetylene-linked bis(TEMPO) derivatives [192], which in principle might present ferromagnetic interactions through space within the across the monomeric units in the polymer chains as in A in Fig. 30, work has concentrated on the preparation of polymers in which a ferromagnetic coupler is used to link radical moieties, as in B in Fig. 30. Iwamura and coworkers presented a cunning approach to poly(1-phenyl-1,3butadiyne)s based on the solid state polymerization of co-crystals of diacetylene derivative 73 and radical 74, given that the pure radical had a solid state structure

Fig. 30. Two approaches to polymer radicals with ferromagnetic interactions between spins: A in which the spins interact principally through-space in the polymer side-chains and B in which the spins are coupled through-bonds by a ferromagnetic coupler (FC).

1.6 Poly(nitroxides)

47

unsuitable for polymerization [193]. The resulting material suffered drastically from loss of spin, the surviving radicals being predominantly paramagnetic, whereas 10% appeared to be coupled ferromagnetically, but which showed loss of spin below 250 K, perhaps as a result of contraction of the crystals causing recombination.

Various poly(1,3-phenyleneethynylene) radicals have been prepared (Fig. 31), all showing less than perfect number of spins per repeat unit of the polymer, and all presenting antiferromagnetic interactions in their condensed phases. The polymers 75–77 all show weak antiferromagnetic interactions [194–196], for example in the polymer 77 which incorporates two distinct radical moieties, the Weiss constant was −1.5 K, and was attributed to through-space interactions between polymers, since the in-chain magnetic interaction was said to be extremely weak [197]. Given that all

Fig. 31. Structure and properties of poly(1,3-phenyleneethynylene) radicals.

48


Fig. 32. Structures and properties of poly(1,2-diethynylphenyl) and poly(1,3-diethynylphenyl) radicals.

these polymers were prepared using the palladium catalyzed coupling if acetylenes with aromatic iodides, one has to ask whether some of the nitronyl nitroxide units had been converted to imino nitroxides, since this process has precedent. It is known that these polymers, in the absence of radical groups, have high conformational flexibility, but this aspect was not highlighted in these polymers, unlike the group of polymers which follows. The poly(1,2-diethynylphenyl) and poly(1,3-diethynylphenyl) radicals 78–81 (Fig. 32) show either paramagnetic or slightly antiferromagnetic coupling between radicals. Nitronyl nitroxide polymers 78 [198] and 79 [199] have elevated spin contents, but in the former case shows paramagnetic or weak antiferromagnetic coupling between spins according to the processing conditions. Indeed, one might expect this kind of morphology-dependent behavior (relatively common in polymers in general) since it is analogous to polymorphic behavior of crystals. Polymer 79 showed a large rise in the χ T curve above 100 K in one sample, probably indicative of paramagnetic impurity. The polymer 80 was paramagnetic in the temperature range studied (like the precursor monomer), while 81 showed weak antiferromagnetic interac-

1.7 Outlook

49

tions which had Weiss constants varying between −6.2 and −5.0 K depending on the preparation and precipitation conditions [200]. Following their studies concerning phenylenevinylenes [87], Nishide, Tsuchida and co-workers prepared the polyradical 82, which contains nitronyl nitroxide radicals at the 4-position with respect to the linking alkene unit in the stereoregular macromolecule [201]. The spin content of this radical was claimed to be 97% of the maximum possible value, and in addition the polymer shows ferromagnetic interactions with a J/k of +21 K (using the Bleaney–Bowers equation) in solution, although there are antiferromagnetic interactions present. The value of the ferromagnetic coupling far exceeds that of a model diradical and points to cooperative interactions. However, in the powder form, the radical presents antiferromagnetic coupling pointing to significant through-space interactions which were also seen to a lesser degree in solution.

Among the various causes that thwart the valiant efforts at preparing polymeric magnets are: (i) the preparation of the polymers can result in either the loss of radical centers or incomplete radical formation during the synthesis, giving rise to diamagnetic defects incapable of sustaining the required long-range ferromagnetic interactions; (ii) the conformation of the polymer chain is generally irregular, giving rise to occasional null or to antiferromagnetic interactions, thereby generating domains which can cancel one another; (iii) the polymer chains have ferromagnetic interactions between the spins, but between polymer chains the interaction is usually antiferromagnetic; (iv) usually, a modest number (no more than a few tens) of ferromagnetically-coupled spin units is obtained instead of the gigantic number (millions) required; and (v) the difficulties in reproducing the synthesis, the conformational stereoregularity, and characterizing completely the end products.

1.7

Outlook

Nitroxide magnets’ prime limitation is their uniformly low critical temperatures (below 2 K), which results from the extremely weak magnetic exchange interactions within and between the organic molecules currently being prepared. In turn, these

50


open-shell molecules show a weak spin–orbit coupling which results in very isotropic Heisenberg-type spin systems in the purely organic molecules incorporating only light elements. This characteristic makes the presence of ferromagnetic interactions between radicals in three-dimensions essential, otherwise no ferromagnetic ordering is possible. The strict electronic and structural requirements implicit in this condition undoubtedly hinder enormously the development of this kind of magnetic material. The low magnetic anisotropy of nitroxide units also makes it difficult to chance upon canted ferromagnets, since when an antiferromagnetic interaction is established between two units it leads to a complete compensation of the two spins because of their isotropic nature. It is clear that there is relative dominance over intramolecular magnetic interactions, whatever their strength. Synthetic organic chemistry has guided the preparation of various high-spin molecules with triplet or higher ground states. However, the situation beyond the molecule is not so controlled, and intermolecular magnetic interactions are as yet a relatively untamed beast. It is also clear from the work discussed in this chapter that in order to progress in this area efforts in the following directions are necessary: – Development of experimental methods for characterizing the spin density distribution of open-shell organic molecules both in solution and the solid states, and for determining the mechanisms, pathways, and dimensionalities of intermolecular magnetic interactions. – Development of theoretical models that reproduce and correctly interpret the magnitude and dimensionality of experimental magnetic interactions, and for calculating with high precision intermolecular magnetic interactions and magnetic anisotropy of organic molecules. – Preparation of new organic molecules with highly delocalized spins that does not imply a loss of their persistence, and/or that present a large spin polarization over the whole structure. – Alternative methods to enhance the magnetic anisotropy in molecules containing only light elements, and the discovery of new tricks for increasing the strength of magnetic exchange interactions between molecules united by either covalent or non-covalent bonds. – New ways of organizing the compounds to form new molecular materials, for example in the form of thin films by Langmuir-Blodgett techniques [202] or chemical vapor deposition [203]. – Synthesis of new molecules incorporating new crystal engineering synthons that control relative dispositions of molecules in the solid state which have strong ferromagnetic interactions. While all of these aspects are unlikely to raise the transition temperatures of the nitroxide materials the orders of magnitude which would be necessary for applications in today’s technology, they are bound to provide important messages for chemistry and physics concerning the interactions of free electrons [204].

References

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Acknowledgments We thank our coworkers who have contributed to our own research: Joan Cirujeda, Merce´ Deumal, Robert Feher, Esteve Hernandez, ` Oriol Jurgens, ¨ Maria Minguet, Concepcio´ Rovira, J. Vidal-Gancedo, and especially Juan J. Novoa for his enthusiastic collaboration. This work was supported by grants from the DGICyT, Spain (Proyecto no. PB96-0862-C0201), and the 3MD Network of the TMR program of the E.U. (Contract ERBFMRXCT 980181).

References [1] The nitroxides are more properly named aminoxyls, according to IUPAC, although we have maintained the former term because of its prevelence in the literature. For a few of the many general reviews concerning nitroxides, along with references cited therein, see: (a) A.R. Forrester, J.M. Hay, R.M. Thomson, Organic Chemistry of Stable Free Radicals, Academic Press, New York 1968; (b) J.F.W. Keana, Chem. Rev., 1978, 78, 37–64; (c) M. Dagonneau, E. S. Kagan, V. I. Mikhailov, E. G. Rozantsev, V. D. Sholle, Synthesis, 1984, 895–916; (d) L. B. Volodarsky, Janssen Chim. Acta, 1990, 8, 12–19; (e) M.-E. Brik, Heterocycles, 1995, 41, 2827–2873. [2] P. M. Lahti, (Ed.), Magnetic Properties of Organic Molecules, Marcel Dekker, New York 1999. [3] (a) Magnetic Molecular Materials, D. Gatteschi, O. Kahn, J. S. Miller, F. Palacio (Eds.): NATO ASI Series E Vol. 198, Kluwer, Dordrecht 1991. (b) O. Kahn, Molecular Magnetism, VCH, Weinheim, 1993. [4] For reviews concerning the application of nitroxides in the realm of molecular magnetism, see: (a) F. Palacio, in Magnetic Molecular Materials, D. Gatteschi, O. Kahn, J. S. Miller, F. Palacio (Eds.): NATO ASI Series E Vol. 198, Kluwer, Dordrecht 1991, p. 1–34; (b) M. Baumgarten, K. Mullen, ¨ Top. Curr. Chem., 1994, 169, 1–103. (c) J. Veciana, J. Cirujeda, C. Rovira, J. Vidal-Gancedo, Adv. Mater. 1995, 7, 221–225; (d) S. Nakatsuji, H. Anzai, J. Mater. Chem., 1997, 7, 2161–2174. [5] (a) A. Caneschi, D. Gatteschi, R. Sessoli, P. Rey, Acc. Chem. Res., 1989, 22, 392–398. (b) D. Gatteschi, R. Sessoli, J. Magn. Magn. Mater., 1992, 104–107, 2092–2095. (c) A. Caneschi, D. Gatteschi, R. Sessoli, Mol. Cryst. Liq. Cryst., 1996, 279, 177–194. (d) H. Iwamura, K. Inoue, N. Koga, T. Hayamizu, in Magnetism: A Supramolecular Function, O. Kahn (Ed.), pp. 157–179, NATO ASI Series C Vol. 484, Kluwer Academic Publishers, Dordrecht, 1996. (e) K. Fegy, K. E. Vostrikova, D. Luneau, P. Rey, Mol. Cryst. Liq. Cryst., 1997, 305, 69–80; (f) P. Rey, D. Luneau, in Supramolecular Engineering of Synthetic Metallic Materials, J. Veciana, C. Rovira, D.B. Amabilino (Eds.), pp. 145-174, NATO ASI Series C Vol. 518, Kluwer Academic Publishers, Dordrecht, 1999. [6] For example, NLO properties: (a) J.-F. Nicoud, C. Serbutoviez, G. Puccetti, I. Ledoux, J. Zyss, Chem. Phys. Lett., 1990, 175, 257–261; (b) G. Puccetti, I. Ledoux, J. Zyss, NATO ASI Ser., Ser. E, 1991, 194, 207–213. (c) S. Yamada, M. Nakano, S. Kiribayashi, I. Shigemoto, K. Yamaguchi, Synth. Met., 1997, 85, 1081–1082; (d) S. Yamada, M. Nakano, I. Shigemoto,

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[7]

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2

Magnetic Ordering in Metal Coordination Complexes with Aminoxyl Radicals Hiizu Iwamura and Katsuya Inoue†

2.1

Introduction

Several different approaches are currently used in order to design and synthesize free radical-based materials exhibiting spontaneous magnetization. Obviously there are three conditions necessary for its appearance at finite, preferably high, temperature: (i) assemblage of unpaired electrons in high concentration; (ii) operation of strong exchange interactions aligning the spins, and (iii) formation of magnetic domains in which all the spins are ordered in two- or three-dimensional network in mesoscopic scale. To satisfy these conditions, a purely organic approach has a number of drawbacks. There is a density limitation; a number of non-magnetic atoms are necessary to stabilize the unpaired electrons kinetically and/or thermodynamically. A network structure may not be a problem if an appropriate crystal design is made. However, since the exchange coupling between neighboring molecules through van der Waals force, hydrogen bonds, hydrophobic interaction, etc. is not necessarily strong, it is difficult to expect strong intermolecular magnetic coupling. It is therefore a strong design strategy to make extended structures by assembling free radicals by means of magnetic metal ions. Such polymeric complexes satisfy the above three conditions [1–3]. In this chapter are discussed magnetic materials made up of coordination complexes of magnetic metal ions with aminoxyl radicals.

2.2

Aminoxyl Radicals

To make free radicals as ligands for a magnetic metal ion, it is necessary for the radicals to have enough coordinating ability. Such radicals are classified into two groups: those having a basic radical center or amine and phosphine donors having a radical center as a substituent. In the former the interaction with the meat ions is direct, while it is indirect, through-bonds, and the mechanism may be called “extended superexchange” in the latter. Aminoxyl radicals alias “nitroxide radicals” are representatives of the former examples. o-Semiquinone radicals serve as bidentate ligands but are less stable under ambient conditions and have not been used to prepare coordination complexes having extended structures.

62

2.2.1

2 Magnetic Ordering in Metal Coordination Complexes with Aminoxyl Radicals

Electronic Structure and Basicity

Aminoxyl radicals are isoelectronic with ketyl radicals. Whereas the ketyl of di-tbutyl ketone is red and stable in deoxygenated solution, di-t-butylaminoxyl is a red oil stable under ambient conditions. Aminoxyl radicals happened to be the first organic ferromagnets ever discovered in the early nineties. The above three conditions for molecular-based magnets appear to be realized by special arrangement of the radical molecules in crystals [4, 5], although TC is quite low (300 >300 +80 ± 4 ≥300 +6.8 ± 0.1 +5.3 ± 0.1 ∼300, +67 ± 5 ≥300 +240 ± 20

Orange crystals Orange crystals Orange crystals Black block crystals Red-purple crystals Red crystals Isolated in Tween 40 Isolated in PVC Reddish yellow crystals Orange crystals

32, 33 57, 80, 82 57, 80, 82 35 37 34 34 36 34 33

ion in the cis or trans configuration. An examination of the bond lengths around the metal ions reveals that the N(1)–Mn-N(1 ) bonds are on the elongation axes and correspond to the dz orbital of Mn(II). The elongation axes lie along O(1)–Cu–O(1 ) bonds in three copper complexes, indicating that the lobes of the magnetic orbital are directed toward the O(2)s of the hfac units and N(1)s of the pyridine units. The magnetic susceptibility data of these metal-radical complexes are obtained in the temperature range 2–300 K at a constant field of 100–800 mT on a SQUID susceptometer/magnetometer. Typical results of the temperature-dependence of the molar paramagnetic susceptibility χmol and their analysis are exemplified by [M(hfac)2 ( pNOPy and mNOPy)2 ] in Fig. 2. A χmol T value of 1.29 emu K mol−1 obtained at 300 K for [Cu(hfac)2 ( pNOPy)2 ] is close to a theoretical 1.13 emu K mol−1 calculated for three isolated S = 1/2 spins {χmol T = 0.125 × g × 2[3S(S + 1)] = 0.125 × 2 × 2(3/2(1/2 + 1))}. As the temperature is decreased, χmol T values (open circles in Fig. 2a) increase gradually, reach a maximum at 36 K, and rapidly decrease

2.3 Magnetic Interaction between Transition Metal Ions and Aminoxyl Radicals

67

Fig. 1. ORTEP drawings of [Cu(hfac)2 .( pNOPy)2 ] and [Mn(hfac)2 .( pNOPy)2 ].

Fig. 2. Plots of χmol T against T for crystalline samples of: (a) [Cu(hfac)2 .( pNOPy)2 ] (◦) and [Cu(hfac)2 .(mNOPy)2 ] (•) and (b) [Mn(hfac)2 .( pNOPy)2 ] (◦) and [Mn(hfac)2 .(mNOPy)2 ] (•). Solid curves are the best theoretical fit.

below 10 K. A maximum χmol T value of 1.69 emu K mol−1 is slightly smaller than a theoretical 1.87 emu K mol−1 calculated for S = 3/2. A linear three-spin model suggested by the X-ray crystal and molecular structure was adopted for analyzing the temperature-dependence of the observed χmol T values more quantitatively. Its spin Hamiltonian is written as Eq. (1): H = −2J (S1 S M + S M S2 )

(1)

68


A Boltzmann distribution among the spin states given by the Eigenvalues of Eq. (1) for three spins with S1 = S2 = SM = 1/2 was assumed and the theoretical equation thus derived was fitted to the experimental data by means of a least-squares method. The Weiss constant, θ , was used to represent by a mean-field theory a weak intermolecular interaction expected from the short contact of 5.85 Å in the crystal packing of the complex. The best-fit parameters are: J/kB = 60.4 ± 3.3 K, g = 2.048 ± 0.0091, and θ = −3.58 ± 0.09 K, where all symbols have their usual meaning. The fitted theoretical curve is presented by a solid curve in Fig. 2. A χmol T value for [Cu(hfac)2 (mNOPy)2 ] was ca. 0.6 emu K mol−1 at 300 K and gradually decreased to 0.43 at 10 K with decreasing temperature (filled circles in Fig. 2a). The observed values are close to a theoretical 0.37 emu K mol−1 for S = 1/2. Cancellation of the two spins of the aminoxyl radicals by a strong antiferromagnetic interaction between the neighboring complexes is suggested by the X-ray crystal structure of [Cu(hfac)2 (mNOPy)2 ]. It appears from plots of χmol T against T that the copper complex has no aminoxyl radical units. In the case of pairs of 1:1 mixed-ligand complexes of (tetraarylporphyrinato)chromium(III) chloride with NOPy, the complementarity between the mNOPy and pNOPy is obvious (Table 2). The results of the other magnetic measurements and analyses are summarized in Table 2. The observed exchange interaction of the magnetic metal ions with N -tertbutylaminoxyl radicals (Table 2) through the 4-pyridyl ring clearly demonstrates that its sign is determined by the kind of the metal ions: positive for copper(II) and negative for manganese(II) and chromium(III). Nature of the magnetic orbitals of the metal ions appears to play an important role in governing the sign of the coupling. In 4NOPy the spin density at the pyridyl nitrogen atom due to the presence of the aminoxyl radical at the 4-position is estimated to be 0.09 [19]. Whereas there are π-type 3d magnetic orbitals in Cr(III) and Mn(II) that can overlap with the 2pπ orbital at the pyridyl nitrogen, the magnetic orbital is dx 2 −y 2 and orthogonal to this Table 2. The exchange coupling parameters J/kB (K) in M(NOPy) [38, 54]. M

Mn(II) S = 5/2 Cu(II) S = 1/2 Cr(III) S = 3/2

−12.4 K in [Mn( pNOPy)2 (hfac)2 ] −10.2 K in [Mn( pNOPy)2 (acac)2 ] −11.3 K in [Mn(pNOPy)(hfac)2 ]2 60.4 K in [Cu( pNOPy)2 (hfac)2 ] 58.6 K in [Cu(pNOPy)(hfac)2 ]2 4.3 K in [Cu(4NOIm)2(hfac)2 ] −77 K in [Cr(TPP)( pNOPy)Cl] −86 K in [Cr(TAP)( pNOPy)Cl]

? in [Mn(mNOPy)2 (hfac)2 ] 0}. Dimension of the complexes as well as sign and magnitude of the exchange coupling between the adjacent spins may be readily tuned in this strat-

76


Fig. 6. Continued.

egy [1, 2, 64]. A bis-monodentate diradical with a triplet ground state (S = 1), e. g., BNO, would form with coordinatively doubly unsaturated metal ions a 1:1 complex having a 1D infinite chain structure (Fig. 6b). Figs. 6a and 6b differ in the occurrence of one and two kinds of exchange coupling parameters, respectively. Since the exchange coupling between the ligands and the directly attached transition metal ions is typically antiferromagnetic {J (coordination) 0} and the 2p and 3d spins tend to cancel each other out, a residual spin would be established for the repeating unit unless the spin of the latter is 1/2. A ferromagnetic exchange coupling is not impossible if the magnetic orbitals become orthogonal to each other as found in

2.5 Preparation of 3d Transition Metal-Poly(aminoxyl) Radical Complexes

77

discrete complexes of copper(II). Anyway, such a 1D array of spins cannot order at finite temperature without interchain interaction. It would become an antiferro-, meta-, or ferromagnet depending on the nature of the interchain interaction. Since this interaction between the 1D chains is much weaker compared with the intrachain interaction, the critical temperatures (TC ) for exhibiting macroscopic ordering of the spins will consequently be very low. For a triplet diradical such as bis-nitronyl nitroxide ThBNIT in which each radical center can serve as a bis-monodentate bridging ligand [35], complexation would give rise to a ladder polymer as in Fig. 6c. The spin ordering in these systems should be less vulnerable to defects than that in purely 1D systems because there will be a detour available for the exchange coupling through bonds between the two parts of the polymer molecule separated by a chemical defect. Tris-monodentate diradical BNOP with a doublet ground state and triradicals TNOs with quartet ground states (S = 3/2) in which the radical centers are arranged in a triangular disposition would form 3:2 complexes with a coordinatively doubly unsaturated 3d metal ions M. In an ideal case, a 2D hexagonal network structure would be generated (Fig. 6d). A Tshaped quartet triradical carrying two inequivalent ligating sites, e. g., TNOP, would form a 1D chain by using two terminal aminoxyl groups. The middle aminoxyl group might then be used to cross-link the chains to form a 2D (Fig. 6e) or a 3D network structure (Fig. 6e ) depending on whether the second bridging takes place between the same chains as cross-linked by the first bridging. The spin alignment in these systems would be very much stabilized and is expected to give higher-TC magnets.

2.5

Preparation of 3d Transition Metal-Poly(aminoxyl) Radical Complexes

The complex formation is a kinetically and/or thermodynamically controlled self assemblage of the reactants. Typical procedures are as follows. A suspension of manganese(II) bis(hexafluoroacetylacetonate) dihydrate, [Mn(hfac)2 2H2 O], in nheptane is refluxed to remove water of hydration by azeotropic distillation. To the resulting cooled solution is added BNO in n-heptane. The mixture is concentrated under reduced pressure and the concentrated solution is allowed to stand to give black needles of [Mn(hfac)2 BNO] from a deep brown solution. It is preferable to carry out the reaction in inert atmosphere and anhydrous conditions, sometime in a refrigerator. The reaction is completed by precipitation. Some can be recrystallized but others are dissociated in solution. Excess of either one of the components can give complexes of different composition. For example, the reaction of [Mn(hfac)2 ] with tris(aminoxyl) TNOP is complex; while an equimolar mixture in ether containing n-hexane at −10◦ C gives black blocks of 1:1 complex [{Mn(hfac)2 }TNOP] · n-C6 H14 , a mixture containing [Mn(hfac)2 ] in 1.7 molar excess in n-heptane-ether gives black blocks of 3:2 complex [{Mn(hfac)2 }3 TNOP2 ] in ten days at 0◦ C. The complex [{Mn(hfac)2 }3 TNOPB2 ] · n-

78


C7 H16 is obtained by dissolving [Mn(hfac)2 2H2 O] in a mixture of diethyl ether, n-heptane and benzene followed by addition of TNOPB in benzene. Black blocks are formed from a deep violet solution. While [Mn(hfac)2 ] gave similar black violet 3:2 complexes with tris(aminoxyl) TNOB and bis(aminoxyl) BNOP, TNO did not form any complex probably because of steric congestion around the ligand molecule. Diradical ThBNIT gave with [Mn(hfac)2 ] dark green powders of complex [{Mn(hfac)2 }3 ThBNIT2 ]CH2 Cl2 · the expected 2:1 complex was not obtained. A 1:1 complex [Mn(hfac)2 TNOP] was obtained as orange bricks from a solution of [Mn(hfac)2 ] and TNOP in n-heptane/CH2 Cl2 containing a small amount of methanol. Dark greenish brick-like crystals of [Cu(II)(hfac)2 TNOP] were obtained similarly in benzene/CH2 Cl2 /CH3 OH. Recently a notorious side reaction has been elucidated leading to undesired byproducts that have unique [3 + 3] benzene-dimer structures [65]. 1D ferrimagnetic complexes, [Mn(hfac)2 BNOR ]n (R = Cl or Br), are typically obtained by the reaction of Mn(hfac)2 with BNOR . When it takes a few days for crystallization, however, black solutions often turn yellow in about one day and do not afford the expected, black polymer complexes. Instead yellow crystalline precipitates are obtained under these conditions (Scheme 5). An X-ray structure analysis revealed that [Mn(hfac)2 BBNOR H2 O]2 · CH2 Cl2 has a [3 + 3] benzene-dimer structure {R = Cl or Br; BBNOR = 3,10-dihalo-5,8,11,12-tetrakis(N -tert-butylimino)tricyclo[5.3.1.12,6 ]dodeca-3,9-diene N ,N ,N ,N -tetraoxide} (Fig. 7). Two crystal-

Fig. 7. A ball-and-stick X-ray structure of the [3 + 3] benzene dimer.

2.5 Preparation of 3d Transition Metal-Poly(aminoxyl) Radical Complexes

79

lographically equivalent manganese(II) ions have an octahedral coordination and are coordinated with four oxygen atoms of two hfac ligands, one oxygen atom of water, and one oxygen atom of O(1) of BBNOBr . Whereas the dimer complex is chiral, both enantiomers are contained in each unit cell (Scheme 6). The BBNOCl complex is isostructural to the bromine derivative.

Scheme 5

Scheme 6

80


Resonance structure BNOBr must be responsible for the reaction leading to the dimer complex (Scheme 7); either dimerization of BNOBr or attack of BNOBr to free and complexed BNOBr . Whereas the 1D ferrimagnetic complex [Mn(hfac)2 BNOBr ]n is a kinetic product and precipitates out of the solution at the earlier stage of the reaction, the yellow crystal of [Mn(hfac)2 BBNOBr H2 O]2 . CH2 Cl2 appears to be a thermodynamic product.

Scheme 7

Another interesting feature of this work is the liberation of dimer ligand BBNOBr free from manganese ions by dissolving the complex in ether. Two water molecules of hydration appears to be crucial for the stability of BBNOBr · 2H2 O; it is stable in water at 100◦ C but starts to decompose by dissociation even at −78◦ C in CH2 Cl2 when dehydrated by molecular sieves.

2.6

One-dimensional Metal-Aminoxyl Systems

One of the first one-dimensional polymeric transition metal complexes with aminoxyls was [Cu(hfac)2 TEMPOL] [19]. Coupling between the aminoxyl radical and copper(II) is ferromagnetic with 2J/kB = 19 ± 7 K and this S = 1 pair couple with the adjacent pairs through rather lengthy superexchange paths of the σ -bonds of TEMPOL by 2J = −78(2) mK. Since Gatteschi et al. reported a polymeric transition metal complex with nitronyl nitroxide (NIT) in 1986, quite a few one-dimensional polymeric transition metal complexes with nitronyl nitroxides [39, 46, 66–78] and with 1,3-phenylenebis(aminoxyl) derivatives (BNO) [1, 55–58, 64, 79–84] have been documented (Table 3). Bis-monodentate nitronyl nitroxides with doublet states (S = 1/2) and bis-monodentate 1,3-phenylenebis(aminoxyls) with triplet ground states (S = 1) form with coordinatively doubly unsaturated paramagnetic metal ions 1:1 complexes having one-dimensional infinite chain structures. The coupling is such as to align the neighboring spins either parallel or antiparallel to each other along the chain, thereby producing one-dimensional ferromagnets or ferrimagnets, unless the size of the spins matches each other in the latter. The paramagnetic susceptibility values of both kinds of materials are expected to diverge at low temperatures, as a result of lengthening of the correlation of the spins along the

81

2.6 One-dimensional Metal-Aminoxyl Systems Table 3. Metal-aminoxyl-based one-dimensional complexes. 2J/kB (J /kB )

Formula

Type of Sequence

Cu(hfac)2 (NITR)

37.0 K, TN < 1 K J < 0 (R = Me) 35.4 K, TC < 1 K J < 0 (R = i-Pr) –Mn-NIT-Mn-NIT– −340 to −475 K TC = 7.6 K (R = i-Pr) TC = 8.1 K (R = Et) TC = 8.6 K (R = n-Pr) –Ni-NIT-Ni-NIT– −610 K TC = 5.3 K (Ferrimagnet) –Eu-NIT-Eu-NIT– −23.4 K –Gd-NIT-Gd-NIT– –Zn-NIT-Zn-NIT– −17.6 K Antiferromagnetic chain –Mn–BNOH – TN = 5.5 K –Mn–BNOF – TN = 5.3 K –Mn–BNOCl – TC = 4.8 K –Mn–BNOBr – TC = 5.3 K –Mn–TNOP– TN = 11.0 K

R = Me, i-Pr Mn(hfac)2 (NITR) R = Me, Et, i-Pr, n-Pr, Ph Ni(hfac)2 (NITMe) Eu(hfac)3 (NITEt) Gd(hfac)3 (NITEt) Zn(hfac)2 (NITi-Pr) Mn(hfac)2 (BNOH ) Mn(hfac)2 (BNOF ) Mn(hfac)2 (BNOCl ) Mn(hfac)2 (BNOBr ) Mn(hfac)2 (TNOP )

TC or TN (magnetism) Ref.

–Cu-NIT-Cu-NIT–

39, 46, 68, 77

67, 69 72 73 70 71 71, 76 78 55 84 82 82 58

chain. Depending on the nature of the additional interchain interaction, the chain polymers become an antiferromagnet or a ferri/ferromagnet. In these magnets, the interchain magnetic interactions are much weaker than the intrachain interaction, and therefore the transition temperatures to three-dimensionally ordered states are relatively low.

2.6.1

Structure and Magnetic Properties of Ferrimagnetic 1D Chains Formed by Manganese(II) and Nitronyl Nitroxides

Manganese(II) ions form with various NITR (R = i-Pr, Et, n-Pr) crystalline chain complexes in which Mn(II) is hexacoordinated with four oxygen atoms of two hfac molecules and two oxygen atoms of two different NIT radicals. The other oxygens of the two NITR radicals are coordinated to the adjacent Mn(II) ions (Scheme 8). All the complexes are ferrimagnetic and order at ca. 8 K. Quantitative analyses of the magnetic susceptibility data are performed by using a model of classical-quantum chains [66-78]. The results are summarized in Table 3.

Scheme 8

82

2.6.2


Structure and Magnetic Properties of Ferrimagnetic 1D Chains Formed by Manganese(II) and Triplet bis-Aminoxyl Radicals

Let us explain the molecular and crystal structures of the metal complexes with BNO derivatives in some detail [55–58]. Their structures are solved in the monoclinic P21/n space group (No. 14) with Z = 4. The crystal structure data are listed in Table 4. The analyses reveal that the manganese(II) ions have octahedral coordination with four oxygen atoms of two hfac anions and two oxygen atoms of two different BNO molecules. The latter is bound to the Mn(II) ion in cis configuration. As a result, the Mn ions and biradical molecules form a helical 1D polymeric chain structure along the crystal b axis. All the hexacoordinated Mn(II) ions have either or configuration along a given chain. Two tert-butylaminoxyl groups are rotated out of the phenylene ring plane in a conrotatory manner but with different angles; each BNO molecule in the crystal has no symmetry element and therefore chiral, i. e., R or S. The 1D polymeric chains are therefore isotactic as all units of the same chirality reside on a given chain (Fig. 8). The crystal lattice is as a whole achiral due to the presence of an enantiomeric chain. The nearest neighbor interchain distances of Mn(II)-Mn(II) and Mn(II)-carbon atoms of the aminoxyl moiety in the three complexes are listed in Table 5. The 1D complexes [Mn(hfac)2 BNOH ] and [Mn(hfac)2 BNOF ] have antiferromagnetic ground states due to a negative intersublattice exchange interaction. Their saturation magnetization values, MS = 3 µB /f.u. agree well with a theoretical limit assuming the antiferromagnetic coupling between the Mn(II) and radical spins. The magnetization of [Mn(hfac)2 BNOH ] was studied using a single crystalline sample. In Fig. 9 the M(H ) curves are given along the three principal axes at 1.8 K. While Mb , the magnetization projection on the b-axis, rises linearly with increasing field,

Fig. 8. A view of a 1D chain formed by [Mn(II)(hfac)2 ] with bis-aminoxyl BNOF .

C24 H24 N2 O6 F12 Mn 719.38 9.212(3) 16.620(3) 20.088(2) 98.46(1) 3042(1) 4 0.30 × 0.15 × 0.95 mm3 Rigaku AFC5R 1.571 Refined 3256 434 0.055 0.058 1.90

C24 H23 N2 O6 F13 Mn 737.37 9.351(4) 16.626(3) 20.167(3) 100.01(2) 3087(1) 4 0.10 × 0.10 × 0.50 mm3 Rigaku AFC7R 1.586 Fixed calc. 3420 415 0.069 0.064 2.96

Mn(II)(hfac)2 (BNOF ) C24 H23 ClN2 O6 F12 Mn 753.83 8.953(4) 17.020(4) 20.094(5) 98.66(2) 3027(1) 4 0.05 × 0.10 × 0.10 mm3 Rigaku Raxis-IV 1.654 Fixed calc. 2844 415 0.106 0.122 2.95

Mn(II)(hfac)2 (BNOCl )

8.499(1) (55402)* 9.11(3) (44402)*

8.5679(6) (65502)* 9.457(8) (65501)*

Mn(II)(hfac)2 (BNOF )

8.953(4) (65501)* 8.86(1) (45502)*

Mn(II)(hfac)2 (BNOCl )

* Symmetry operators: (1) X, Y, Z ; (2) 1/2 − X, 1/2 + Y, 1/2 − Z ; (3) −X, −Y, −Z ; (4) 1/2 + X, 1/2 − Y, 1/2 + Z

¨ Mn(II)-Mn(II) distance (A) ¨ Mn(II)-C distance (A)

Mn(hfac)2 BNO H )

9.244(4) (65502)* 9.01(1)(55602)*

Mn(II)(hfac)2 (BNOBr )

C24 H23 BrN2 O6 F12 Mn 798.28 9.244(4) 17.155(5) 20.431(7) 99.56(3) 3195(1) 4 0.20 × 0.20 × 0.40 mm3 Rigaku AFC7R 1.662 Fixed calc. 1771 415 0.064 0.026 2.51

Mn(II)(hfac)2 (BNOBr )

Table 5. The nearest neighbor interchain Mn(II)-Mn(II) and Mn(II)-carbon atom distances as shown in Fig. 8.

Empirical formula Formula wt. ¨ a (A) ¨ b (A) ¨ c (A) b (◦ ) ¨ 3) V (A Z Crystal dimensions Diffractometer dcalc (g cm−3 ) Hydrogen Observations Variables R Rw GOF

Mn(hfac)2 (BNOH )

Table 4. Crystallographic data for [Mn(hfac)2 BNOR ]n complexes (R = H, F, Cl, or Br).

2.6 One-dimensional Metal-Aminoxyl Systems

83

84


Fig. 9. (a) The magnetization curves for [Mn(hfac)2 BNOH ] at 1.8 K. (b) Orientation of the magnetization vectors M in the ac-plane in [Mn(hfac)2 BNOH ].

sharp metamagnetic transitions occur at 250 and 450 Oe along the c- and a-axes, respectively. From the M(H ) curves MS was concluded to lie perpendicular to the b-axis. Its orientation in the ac-plane was determined considering the projections Ma and Mc of the magnetization vector on the a- and c-axes extrapolated to zero external field: Ma = 1.2 µB /f.u. and Mc = 2.5 µB /f.u. (it crystallizes in a monoclinic structure with a = 9.212 Å, b = 16.620 Å, c = 20.088 Å and β = 98.46) [85]. These values are very close to the projections of MS = 3.0 µB /f.u. on the crystal axes in case Ms values are oriented along the four {101}-type directions (Fig. 9b). At zero external field, all the orientations [101], [101], [101], and [101] are equivalent, and the total magnetization is compensated. When the magnetic field is applied along the c-axis, [001], the metamagnetic transition corresponds to the re-orientations of the magnetization vector M[101] → M[101] and M[101] → M[101] , thus giving a cprojection Mc = 1.5(cos 25.94◦ + cos 23.02◦ ) µB = 2.73 µB . Similarly, for H//a-axis the metamagnetic transition corresponds to the re-orientations M[101] → M[101] and M[101] → M[101] and Ma = 1.5(cos 72.53◦ + cos 58.51◦ ) µB = 1.23 µB . With further increasing field the two magnetization vectors smoothly rotate to give a saturation at ca. 30 kOe. The low-field susceptibilities of the [Mn(hfac)2 BNOH ], [Mn(hfac)2 BNOF ], [Mn(hfac)2 BNOCl ] and [Mn(hfac)2 BNOBr ] complexes with ferrimagnetic ground state as a function of temperature are shown in Fig. 10. The TC values were determined as 4.8 and 5.3 K for complexes of BNOCl and BNOBr , respectively. Below


85

Fig. 10. Temperature-dependence of the low-field susceptibility (5 Oe) for the ferrimagnetic complexes: (a) [Mn(hfac)2 BNOH ], [Mn(hfac)2 BNOF ], and (b) [Mn(hfac)2 BNOCl ], [Mn(hfac)2 BNOBr ].

Fig. 11. Magnetization curves for [Mn(hfac)2 BNOCl ] (O) and [Mn(hfac)2 BNOBr ] () at 1.7 K. Inset shows the low-field cycling.

TC the magnetic behavior of both the complexes is very similar to each other. The magnetization at 1.8 K shows saturation at about 30 000 Oe with a maximal value of ca. 3 µB (Fig. 11), which corresponds to the antiparallel alignment of the Mn(II) and NO group spins. The compounds show narrow hysteresis with the coercive force less than 20 Oe (Inset of Fig. 11). Above TC , the product of the molar paramagnetic susceptibility and temperature, χmol T , for all the BNOR complexes increases steadily with decreasing temperature and passes over a maximum at 8–9 K. These dependencies coincide with the paramagnetic range, therefore only the data for [Mn(hfac)2 BNOH ] are displayed in Fig. 12.

86


Fig. 12. Temperature-dependence of the product χmol T for the [Mn(hfac)2 BNOH ] complex (circle symbols). The solid line is a fit by the use of Eq. (2). The best-fit parameters are listed in the inset table for this compound and for those of the complexes with BNOF , BNOCl and BNOBr .

The [Mn(hfac)2 BNOR ] compounds under consideration have three-spin periodicity along the 1D chains and the extensive analysis of intrachain exchange interactions requires numerical calculations using the spin Hamiltonian: H = −2J1 (s3i−2 s3i−1 + s3i−1 s3i + αs3i S3i+1 ) i

where α = J2 /J1 and s and S are the NO group and Mn(II) spin operators, respectively. However, considering the high temperature value of χmol T and lowtemperature saturation magnetization, some preliminary conclusions can be made about the strength of the intrachain magnetic couplings [86]. As a matter of fact, taking the saturation magnetization value in the ordered state into account, we may consider two configurations: (i) ferrimagnetic chains formed by the 2/2 total spins of biradicals antiferromagnetically coupled with the 5/2 spins of Mn(II) ions, and (ii) ferromagnetic chains formed by the pseudo-spins consisting of two NO groups of different biradicals bridged by Mn(II) ions, i. e., S = 3/2 ferromagnetic chains. The former configuration should yield a characteristic high temperature minimum in plots of χmol T against T with the value approaching to 5.38 emu K mol−1 , while the high temperature value of 1.875 emu K mol−1 is expected for the latter. The observed χmol T values at 300 K vary between 2.2 and 2.4 emu K mol−1 , which is slightly larger than the theoretical limit 1.88 emu K mol−1 expected for S = 3/2 ferromagnetic chain compounds. Hence, the basic intrachain exchange interaction in [Mn(hfac)2 BNOR ] compounds can be determined assuming a ferromagnetic chain structure with S = 3/2. A classical-spin approximation was employed for the analysis and the experimental χmol T dependencies were treated by the expression [87]: χmol T = N

g 2 µ2B 1 + U (T /T0 ) S(S + 1) 3kB 1 − U (T /T0 )

(2)

where U (T /T0 ) = coth(T0 /T ) − T /T0 , T0 = (2J/kB )S(S + 1) and the other symbols have their usual meaning. A comparative analysis of the behavior on the basis of a classical and quantum ferro- or ferrimagnetic chains [88] showed that both the approaches yield similar values for the exchange interaction at elevated temperatures T > 2J/kB . Therefore, Eq. (2) was first fitted to the experimental plot of χmol T


87

against T in the high-temperature region, then the fits were extended down to ca. 50 K. The effective exchange coupling value 2J/kB between the pseudo-spins was found to be 23 K for all the four [Mn(hfac)2 BNOR ] compounds with R = H, F, Cl and Br. Using this value, the interchain exchange parameters of ferrimagnetic compounds [Mn(hfac)2 BNOCl ] and [Mn(hfac)2 BNOBr ] were then evaluated. Near TC , T0 /T > 10. Thus, taking U (T /T0 ) = 1 − T /T0 , and introducing the interchain exchange interaction by χtot = 1/(1/χmol − λ ), one obtains: T1 =

3TC2 2T0 − TC

(3)

where T1 = (2z J /kB )S(S + 1). This equation reduces to that given by Richards [89] when neglecting TC in the denominator. The evaluated values of 2J /kB are +0.018 K and +0.022 K for [Mn(hfac)2 BNOCl ] and [Mn(hfac)2 BNOBr ], respectively. For the metamagnetic complexes [Mn(hfac)2 BNOH ] and [Mn(hfac)2 BNOF ] these values are −0.018 K and −0.010 K [90], respectively. Thus, the ratios |J/J | are ∼ 10−3 for all the complexes studied. The Mn complexes with BNOCl and BNOBr have topologically the same crystal structure with the complexes of BNOH and BNOF . From the observed intermolecular distance, the strongest interchain interaction in [Mn(hfac)2 BNOR ] is judged to arise from the Mn–Mn and Mn–Cmiddle distance (Table 5). From the dipole-dipole interaction term, magnetic interaction between nearest neighbor magnetic moments is always antiferromagnetic (Fig. 13). This argument can be confirmed by the fact that 2J /kB does not exhibit a regular change throughout the [Mn(hfac)2 BNOR ] series, but changes abruptly in sign when the nearest interacting pair is changed. Polycrystalline samples of [Mn(hfac)2 BNOR ] showed broad singlet EPR spectra at room temperature with H pp = 303 G, g = 2.0055 for R = H, H pp = 315 G, g = 2.0095 for R = Cl and H pp = 158 G, g = 2.018 for R = Br. The temperature dependencies of H pp are shown in Fig. 14. The large H pp values indicate that the low dimensional exchange interaction dominates in these crystals [91–93].

Fig. 13. (a) Schematic drawing of the magnetic structure of [Mn(hfac)2 BNOCl ] and [Mn(hfac)2 BNOBr ], and (b) [Mn(hfac)2 BNOH ] and [Mn(hfac)2 BNOF ]. Broken lines show the antiferromagnetic interaction between the ferro/ferri-magnetic 1D chains. Solid lines show the ferromagnetic interchain interaction.

88


Fig. 14. Temperaturedependence of H pp for the [Mn(hfac)2 BNOR ] complexes (R = H, Cl, or Br).

2.7

Two-dimensional Metal-Aminoxyl Systems

In principle, there are no difficulties in the design of materials that undergo magnetic phase transitions at higher temperatures: the magnetic network of coupled metal ions and radicals should be extended from one to two or three dimensions, and the strong magnetic coupling between the spin centers would ensure high transition temperatures (see also three conditions given in Introduction) [94]. One of the first two-dimensional structures is a series of copper(II) β-diketonate complexes [95– 101]. The coordination of the oxygen atoms of the aminoxyl groups of neighboring molecules completes the distorted octahedra around the Cu(II) ions. Temperaturedependence of the magnetic susceptibility for these complexes fits a theory of isolated ferromagnetic coupled pairs. Enaminoketones of 3-imidazolin-1-oxyl form layered polymeric structures with Cu(II), Co and Ni [102–105]. However, whereas all these complexes have extended structures, the magnetic coupling is limited to the directly bonded metal-aminoxyl couples. Table 6. Metal-aminoxyl-based two-dimensional complexes. Formula

Crystal or powder

{Mn(pfbz)2 }2 (NITR) R = Me, Et {Mn(pfpr)2 }2 (NITR) R = Me, Et {Mn(hafc)2 }3 (NITBzald)2 · 0.5CHCl3

Powder

{Mn(hafc)2 }3 (TNOPB)2 · n-C7 H16 {Mn(hafc)2 }3 (TNOP)2

J/kB (J /kB )

TC or TN (magnetism)

Ref. 74

Crystal

TC = 24 K TC = 20.5 K TC = 24 K TC = 20.5 K TC = 6.4 K (Ferrimagnet) TC = 3.4 K

Crystal

TC = 9.5 K

Powder Powder

−149.6 K (0.075 K) −367 K

104 105 106 56 57 36

2.7 Two-dimensional Metal-Aminoxyl Systems

89

Thus the problem is not only how to control the construction and the structure of extended systems in a desired fashion in order to extend the properties from the individual building blocks to the whole lattice, but also how to maintain strong magnetic coupling throughout the extended structure. Moreover, there is much difficulty in making single crystal of the complex which have high dimensionality. Therefore, there are still few examples of aminoxyl-metal ion-based two-dimensional magnetic complexes (Table 6) [36, 56, 57, 74, 106–108]. The flexibility of the ligands are important to make good crystals of two- or three-dimensional complexes. In the metal-nitronyl nitroxide systems, there are limitations to make two or three dimensional complexes topologically. The approach by high spin oligo-aminoxyls and transition metal complexes has a greater advantage than metal-nitronyl nitroxide systems Table 6.

2.7.1

Structure and Magnetic Properties of Ferrimagnetic 2D Sheets Formed by Manganese(II) and Nitronyl Nitroxides

Some ferrimagnetic 2D manganese(II)-nitronyl nitroxide systems are synthesized by the complexation of manganese (II) bispentafluorobenzoate (Mn(pfbz)2 ) or manganese (II) bispentafluoropropionate (Mn(pfpr)2 ) with 2-alkyl nitronyl nitroxide (NITR, R = Me, Et) (Fig. 15). None of the complexes gave single crystals amenable for an X-ray crystal structure analysis. It is assumed that 2D sheet structures are formed in these complexes. The complexes of [{Mn(pfbz)2 }2 (NITR)] (R = Me, Et) and [{Mn(pfpr)2 }2 (NITR)] (R = Me, Et) are ferrimagnetic, and the transition into ordered states occurs at ca. 23 K. The quantitative analysis of the magnetic susceptibility of these complexes was performed by using a model of a Heisenberg classical-quantum spin system (see Table 6).

Fig. 15. Scheme of the supposed magnetic interactions in (a) [Mn(pfpr)2 (NITMe)] and (b) [{Mn(pfbz)2 }2 {NITR)].

90

2.7.2 2.7.2.1


Structure and Magnetic Properties of Ferrimagnetic 2D Sheets Formed by Manganese(II) and High-spin tris-Aminoxyl Radicals Crystal and Molecular Structure of 2D Systems

[{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 The X-ray crystal structure of the complex reveals that the manganese(II) ion has an octahedral coordination with four oxygen atoms of two hfac anions bound to the metal ion in the equatorial plane, while the axial positions are occupied by the two oxygen atoms of the two aminoxyl groups. Six triradical molecules and six Mn ions make a hexagon from which an extended honeycomb network is constructed by sharing its edge (Fig. 16a). A disordered n-heptane molecule is contained in each hexagonal cavity. The 2D network sheets form a layered structure in which the adjacent layers are slide by a radius of the hexagon from the superimposable disposition with a mean inter-plane distance of 3.58 Å (Fig. 16b). On the basis of the spin density and distance, the strongest inter-plane spin–spin interaction is judged to arise from the carbons (3.78 Å apart) of the benzene rings para on the one hand and meta on the other to the aminoxyl groups (Fig. 16b ). This type of interaction is expected to be ferromagnetic as dictated by the McConnell’s theory [109, 110]. [{Mn(hfac)2 }3 (TNOB)2 ] While satisfactory analytical data were obtained [36], the complex does not give a single crystal amenable for an X-ray crystal structure analysis. It is assumed that, while a 2D sheet structure is formed, the reduced symmetry of TNOB relative to TNOPB must be responsible for the difficulty in growing single crystals. It may be assumed that a 2D-heterospin system consisting of a ferromagnetically coupled triradical TNOPB serving as a tris(monodentate) bridging ligand and attached to a paramagnetic transition metal ion Mn(II) in an antiferromagnetic fashion would be realized. The 2D network is schematically given in Fig. 17. As in TNOB, the network may be stacked ferromagnetically across the layer.

2.7.2.2

Magnetic Properties of 2D Systems

Below T C [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 When the measurement was carried out in a low field, the magnetization values showed a sharp rise at TC = 3.4 K (Fig. 18). The low-field susceptibility at 3 K is extremely large, as expected for a ferro/ferrimagnet. The spontaneous magnetization was observed below TC , demonstrating the transition to a bulk magnet. The field dependence of the magnetization for [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 is shown in Fig. 19. When the measurement was carried out at 1.8 K, its magnetization reaches to ca. 9 µB at 30 000 Oe and becomes saturated. If the interaction between the Mn(II) and TNOPB is antiferromagnetic (J2 < 0 in Chart I (b)), the saturated magnetization value is expected to be 9 µB (5/2 × 3 − 3/2 × 2 = 9/2), in good agreement with the observed value. Note that, when a single-domain state is reached, the low tem-


91

Fig. 16. (a) View along the c axis of a layer showing the hexagons made of six tris-aminoxyl TNOPB and six manganese complexes Mn(hfac)2 . (b) View of the shortest contact between the layers.

92


Fig. 17. Schematic drawing of the estimated 2D network structure for [{Mn(hfac)2 }3 (TNOB)2 ].

Fig. 18. Plots of magnetization against T for the complex [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 measured at a field of 1 Oe (◦) and spontaneous magnetization (•).

Fig. 19. Field dependence of the magnetization of [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 measured at 1.8 K (◦) and 10.8 K (+).


93

perature (1.78 K) magnetization curve of [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 can satisfactorily be described above 6 kOe by the B3/2 (x) Brillouin function with the molecular field coefficient λ ≈ 0.28 emu mol−1 . The latter mainly includes the inplane interactions. Proceeding from this analysis, we cannot evaluate the weakest inter-plain exchange interaction parameter, which seems mainly responsible for the occurrence of 3D long-range order in this complex. [{Mn(hfac)2 }3 (TNOB)2 ] The low-field magnetization measurements carried out in 5 Oe, showed a sharp rise at TC = 9.2 K (Fig. 20). The low-field susceptibility at 9 K is extremely large, as expected for a ferro/ferrimagnet. The field dependence of the magnetization for [{Mn(hfac)2 }3 (TNOB)2 ] are shown in Fig. 21. The spontaneous magnetization was observed below TC , demonstrating the transition to a bulk magnet. When the measurement was carried out at 1.8 K, the magnetization for [{Mn(hfac)2 }3 (TNOB)2 ] reaches to ca. 9 µB at 30 000 Oe and becomes saturated. If the interaction between the Mn(II) and TNOB is antiferromagnetic (J2 < 0 in Chart I (b)), the saturated magnetization value is expect to be 9 µB (5/2 × 3 − 3/2 × 2 = 9/2) in good agreement with the observed value.

Fig. 20. Plots of magnetization against T for the complex [{Mn(hfac)2 }3 (TNOB)2 ] measured in a field of 5 Oe (◦) and spontaneous magnetization (•).

Fig. 21. Field dependence of the magnetization of [{Mn(hfac)2 }3 (TNOB)2 ] measured at 1.8 K (◦), 5.0 K (♦), and 15.0 K (×).

94


Above T C [111] [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 The magnetic susceptibility of [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 as, represented by a plot of χmol T against T , is shown in Fig. 22. With increasing temperature, this dependence is first characterized by a sharp maximum at 2.5 K followed by a smooth minimum in the range 80–140 K, which rather resembles a plateau. The value of χmol T = 5.71 emu K mol−1 within this interval is very close to the theoretical limit, 5.625 emu K mol−1 , which is expected for three stable non-interacting S = 3/2 spins per mole. According to Fig. 16a, this spin configuration can be considered as formed by one S = 5/2 spin of the Mn(II) ion coupled antiferromagnetically with two 1/2 spins of two different triradicals TNOPB. Any other stable spin configuration, either two S = 3/2 TNOPB and three S = 5/2 Mn(II) spins or six decoupled S = 1/2 spins of TNOPB and three S = 5/2 spins of Mn(II), yield much higher values of χmol T (>15 emu K mol−1 ). With further increasing temperature, χmol T shows however a substantial increase. This circumstance points to the contribution of the thermal excitations of the 3/2 spin species above about 140 K. Owing to low TC , the in-plane inter-trimer interaction, J1 ,

Fig. 22. The temperature-dependence of χmol T for the layered complex [{Mn(hfac)2 }3 (TNOP)2 ] · n-C7 H16 . Open circles are the experimental data, and the solid and the dashed lines are the least squares fits by the use of Eq. (5) for 2D and 3D lattices, respectively. The fits performed for stable trimers below 120 K coincide with the corresponding 2D and 3D fits for unstable trimers and are not shown in the Figure. The inset shows details of the low temperature behavior as a plot of χ/T against λ /T .


95

is suggested to be weak compared to the intra-trimer interaction, JTR , which mainly governs the high temperature properties of the [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 complex. Then, the temperature variation of χmol T can be analyzed by the expression for an isolated ferrimagnetic (1/2, 5/2, 1/2) linear trimer modified accordingly by introducing weak inter-trimer interactions. The energy level scheme of this trimer was calculated using the isotropic spin Hamiltonian H = −2JTR (s1 S2 + S2 s3 ). The eigenvalues E(ST , S13 ) of this Hamiltonian are E(3/2, 1) = 7JTR , E(5/2, 1) = 2JTR , E(5/2, 0) = 0 and E(7/2, 1) = −5JTR (here ST = S2 + S13 and S13 = s1 + s3 ) and give the susceptibility in the form [112]: N g 2 µ2B 15 4 5e5JTR /kB T + 5e7JTR /kB T + 16e12JTR /kB t (0) χmol = 1+ 3kB T 4 5 2 + 3e5JTR /kB T + 3e7JTR /kB T + 4e12JTR /kB T (0)

= χ0 mol Q(JTR /kB T )

(4)

(0)

where χ0 mol = (N g 2 µ2B /3kB T )(15/4) and the other symbols have their usual meaning. For negative JTR , the product STR (STR + 1) is equal to 15/4 and starts to increase near TTR = JTR /kB . Therefore, at low temperatures this magnetic system can be considered as a 2D honeycomb-like network formed by stable S = 3/2 spins. Within the scope of this approximation the paramagnetic susceptibility of the complex [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 was analyzed below 120 K by using the hightemperature power series expansion up to order eight for a 2D honeycomb lattice [113]. A satisfactory fit to the experimental temperature variation of χmol T was possible down to 18 K only, with the in-plane interaction parameter J1 /kB = +0.225 K. From this analysis it was concluded that the contribution from the inter-plane exchange interaction becomes important below ca. 20 K. In the range 4.5–120 K a good fit was possible within(0)the scope of the molecular field approximation, i. e., taking (0) χmol = χ0 mol / 1−λ χ0 mol with λ = +0.333 emu mol−1 . In Fig. 22, where the results of these two analyses are shown as plots of χmol T against T ; the curves corresponding to both fits are indistinguishable above 20 K. This fact can point that in the ratio between the inter-plane and in-plane exchange integrals, J2 /J1 , is not so small as, e. g., for typical 2D systems with J2 /J1 = 10−2 –10−3 [114]. At higher temperatures (0) effect of the strong intra-trimer interaction can be taken into account putting χmol (0) instead of χ0 mol in the expression for the paramagnetic susceptibility χmol . Hence, in the molecular field approximation one obtains: (0)

χmol =

χ0 mol

(0)

Q −1 (JTR /kB T ) − λ χ0 mol

(5)

The dashed line in Fig. 22 is the fit to the experimental data over the whole temperature range 4.5–280 K made by the use of Eq. (5). As seen, the experimental data can well be described within this approximation both at high and low temperatures thus proving the importance of the thermal excitations within the (1/2, 5/2, 1/2) trimers for the complex [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 . The best agreement was obtained at JTR /kB = −176.4 K and λ = +0.333 emu mol−1 . The power series

96


expansion for the 2D honeycomb network [113], with STR (STR + 1)/(15/4) replaced by Q(JTR /kB T ), also gives a good fit within the range 18–280 K. The fit parameters for this approximation are JTR /kB = −175.4 K and J1 /kB = +0.226 K. The low temperature behavior of the paramagnetic susceptibility is plotted in the inset in Fig. 22 as C/T against λ /T (C being the Curie constant). As can be seen, the effect of low-dimensionality is not essential in [{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 . [{Mn(hfac)2 }3 (TNOB)2 ] The temperature-dependence of the molar magnetic susceptibility χ for [{Mn(hfac)2 }3 (TNOB)2 ] was investigated at several magnetic fields. When the measurement was carried out in a magnetic field of 5000 Oe, the product of the molar susceptibility and temperature (χmol T ) increased with decreasing temperature, and showed a maximum at 10 K (Fig. 23). The value of χmol T = 7.1 emu K mol−1 is larger than the theoretical limit, 5.625 emu K mol−1 , which is expected for three stable noninteracting S = 3/2 spins per mole. According to Fig. 17, this spin configuration can be considered as formed by one S = 5/2 spin of the Mn(II) ion coupled antiferromagnetically with two 1/2-spins of two different triradicals TNOB. Any other stable spin configuration, either two 3/2 (TNOB) and three 5/2 (Mn(II)) spins or six decoupled 1/2 spins of TNOB and three 5/2 spins of Mn(II), yield much higher values of χmol T (>15 emu K mol−1 ). The ESR spectrum of the complex consisted of a single line (g = 2.0057 and H pp = 392.4 G at room temperature). The temperature-dependence of the g and H pp values is shown in Fig. 24. The g value decreased with decreasing temperature and the decrease leveled off at TC down to 5.9 K. This g value behavior indicates that the internal magnetic field increases with decreasing temperature. The signal narrowed with decreasing temperature, reached a minimum width at ca. 15 K, and then broadened at lower temperature. These temperature dependencies indicate that the effect of the internal magnetic field becomes substantial below 15 K. While clearly separated g and g were not observed in the ESR spectra, the upfield shift appeared to be mostly due to g and the shift of g appeared to lag behind. A 1D

Fig. 23. Plot of χmol T against T for the complex [{Mn(hfac)2 }3 (TNOB)2 ] measured in a field of 5000 Oe.

2.8 Three-dimensional Metal-Aminoxyl Systems

97

Fig. 24. The temperature-dependence of g (◦) and H pp (•) for [{Mn(hfac)2 }3 (TNOB)2 ].

ferrimagnetic chain would have exhibited a much larger g anisotropy. The H pp value is reasonable for a 2D spin structure [91–93].

2.7.3

Conclusion

It is shown that perfect 2D ferrimagnetic sheets with heterospin ferromagnetic (J1 > 0)-antiferromagnetic (J2 < 0 in Chart I (b)) networks together with ferromagnetic stacking of the layers are realized in the metal–aminoxyl radical systems. While the kinetic instability of the triradical TNOB did not allow us to study the magnitude of the intramolecular ferromagnetic exchange coupling, it is expected to be considerably greater in TNOPB. The interaction in TNOB leads by its symmetry to an isosceles triangular relation. One between the two nitroxide radicals at positions 3 and 5 of the same benzene ring is estimated from that of m-phenylenebis(N -tertbutylnitroxide) and the analogs to be J/kB = 200–500 K. The other interaction between the 4 and 3 (and 5) aminoxyl radical centers is estimated to be ca. 67 K. Altogether, the intramolecular ferromagnetic coupling in TNOB is estimated to be stronger than in TNOPB and contributes to the higher TC value of 9.5 K compared to 3.4 K in the latter when self-assembled with the aid of Mn(II) ions.

2.8

Three-dimensional Metal-Aminoxyl Systems

In Sections 6 and 7 we described one- and two-dimensional complexes, respectively. For one-dimensional complexes, the transition temperatures to ferri-ferromagnets are about 5–6 K, while for two-dimensional complexes TC grows up to ca. 9 K. In order to make complexes with higher transition temperature, the dimensions of the spin network must be raised. The flexibility of the ligands is more important to make good crystals of three dimensional complexes than two dimensional systems. Owing to these difficulties, only one well-defined three-dimensional complex has been reported in the metal-aminoxyl systems.

98

2.8.1


Crystal and Molecular Structure of the 3D System

An X-ray crystal structure analysis of an orthorhombic crystal of the complex reveals the formation of a parallel crosses-shaped 3D polymeric network (Fig. 25). The oxygen atoms of the terminal aminoxyl groups of triradical bis{3-(N -tertbutyloxylamino)-5-tert-butylphenyl}aminoxyl (TNOP) are ligated to two different manganese(II) ions to form a 1D chain in the b/c plane of the crystal. Since any manganese ion in an octahedral position is attached to the two aminoxyl oxygens from two different triradical molecules in a trans disposition, the triradical molecules are in zigzag orientation along the chain. The diarylaminoxyl unit is in a chiral propeller conformation and the R and S forms alternate along the chain. The middle aminoxyl group of the ligand TNOP molecule on one chain is used to link its oxygen with that of the same chirality in the adjacent chains extended in the b/ − c diagonal direction through a third Mn(II) ion in an octahedral position with the intersecting angle of 54.4◦ , establishing a parallel crosses-shaped 3D polymeric network (Fig. 26). The three-connected nets of the intersecting angle of 0 and 90◦ would have produced lattices corresponding to graphite and the silicon sublattice of thorium silicide, respectively.

Fig. 25. Crystal structure of the 3D metal-radical complex [{Mn(hfac)2 }3 (TNOP)2 ]. For clarity the CF3 and (CH3 )C groups are not shown. a, b and c denote the orthorhombic crystal axes. The Mn(1) and Mn(2) ions are shown by filled circles.


99

Fig. 26. Schematic drawing of the crystal of the 3D metal-radical complex [{Mn(hfac)2 }3 (TNOP)2 ].

2.8.2 2.8.2.1

Magnetic Properties of the 3D System Below T C

The temperature-dependence of the magnetization M for a single crystalline sample of [{Mn(hfac)2 }3 (TNOP)2 ] was investigated at 5 Oe. When the sample was cooled within the field of 5 Oe, the field-cooled magnetization showed an abrupt rise at TC = 46 K (Fig. 27). The field dependence of the magnetization at 5 K showed two important features. First, the magnetization rose sharply at low field, reached a value of ca. 9 µB (50 000 emu G mol−1 ) at 220 Oe and became saturated. The saturation value is in good agreement with a theoretical one of 9 µB (5/2 × 3 − 3/2 × 2 = 9/2) expected for the antiferromagnetic coupling between the d5 Mn(II) ion and S = 3/2 triradical TNOP. Secondly, a conspicuous magnetocrystalline anisotropy was found in which the easy axis of magnetization lies along the c axis of the crystal lattice and the hard axis lies perpendicular to it (Fig. 28).

2.8.2.2

Above T C

The temperature-dependence of the molar magnetic susceptibility χmol was investigated at a field of 5000 Oe (Fig. 29). The χmol T value of 8.64 emu K mol−1 at 300 K is larger than a theoretical value of 5.63 emu K mol−1 expected for a short-range antiferromagnetic ordering of six 1/2 spins of TNOP and three 5/2 spins of d5 Mn(II) for [{Mn(hfac)2 }3 (TNOP)2 ]. As T is lowered, χmol T value increased monotonically in proportion to the increase in the correlation length within the network. Together with

100


Fig. 27. The temperature-dependence of the magnetization of the single crystal of [{Mn(hfac)2 }3 (TNOP)2 ]. (a) The field cooled magnetization (FCM, ◦), the zero field cooled magnetization (ZFC, ) along c-axis ; (b) The field cooled magnetization (FCM, ), the zero field cooled magnetization (ZFC, ♦) along the b-axis.

Fig. 28. Magnetization curves for [{Mn(hfac)2 }3 (TNOP)2 ] at 1.8 and 25 K along the three principal crystallographic axes.


101

Fig. 29. Temperature-dependence of the product χmol T of the [{Mn(hfac)2 }3 (TNOP)2 ] complex in the paramagnetic temperature range. The open circles are the experimental data, and the solid and dashed lines are calculated for the fixed trimer spin STR = 3/2 in the quantumclassical and classical-classical approximations, respectively.

the lack of a minimum at lower temperature, the room temperature χmol T value also points to the operation of strong (more negative than −300 K) antiferromagnetic coupling between the Mn(II) ion and the nitroxide radical of TNOP in which the onset of the intramolecular ferromagnetic coupling is meaningful. In the low-temperature range, the magnetic behavior is qualitatively equivalent to a 3D ferromagnetically coupled network of S = 3/2 spins consisting of the S(1/2) − S(5/2) − S(1/2) units. The exchange interactions determining the isotropic magnetic properties of the [{Mn(hfac)2 }3 (TNOP)2 ] compound were evaluated from analysis of the temperature-dependence of the paramagnetic susceptibility. All the attempts to describe this dependence within the frame of 3D ferro- or ferrimagnetic models by combining different magnetic sublattices made up either from Mn(II) and TNOP molecules or (1/2, 5/2, 1/2) species formed by Mn(II) and nitroxide groups were unsuccessful (See Fig. 29). This was accounted for the effect of a magnetic low dimensionality the [{Mn(hfac)2 }3 (TNOP)2 ] compound exhibits at least in the paramagnetic region. Although this complex forms a well defined 3D network with respect to the chemical bonding, the spin–spin couplings between Mn(II) and triradical species can be different along different directions, which can in turn modify essentially the paramagnetic behavior of χmol (T ) in the temperature range below 300 K. The paramagnetic susceptibility of [{Mn(hfac)2 }3 (TNOP)2 ] was examined by a model in which the triradicals were assumed to form 1D-ferrimagnetic chains with the Mn(1) ions in positions 1a and 1b (Fig. 25), while the Mn(2) ions in positions 2 link them through the exchange interaction with the middle nitroxide group of (TNOP). This assumption means that the exchange interaction between Mn(1) and the terminal nitroxide group is substantially stronger than the interaction between Mn(2) and the middle nitroxide group of (TNOP).

102


As a matter of fact, the [{Mn(hfac)2 }3 (TNOP)2 ] complex is not a true 1Dchain compound because the magnetic contribution of the Mn(2) ions linking the . . .–Mn(1)–(TNOP)–Mn(1)–. . . chains can be neither neglected nor considered as a kind of paramagnetic impurity. Moreover, the 1D-chains themselves have a four-spin periodicity which does not allow to perform any exhaustive analysis by the use of existing analytical expressions derived for ferrimagnetic chains with two-spin periodicity [60, 88, 115–119]. Therefore the approach applied to interpret the paramagnetic susceptibility of [{Mn(hfac)2 }3 (TNOP)2 ] contained some simplifications. This complex on the whole was considered as a two sublattice ferrimagnet formed by isolated Mn(2) ions and . . .–Mn(1)–(TNOP)–Mn(1)–. . . chains with a positive intersublattice exchange interaction. Then, in the molecular-field approximation, the low-field paramagnetic susceptibility of this complex can be written in the conventional form: χmol =

T2

(CMn + Cch )T + CMn Cch (2λ − λMn − λch ) − (CMn λMn + Cch λch )T − CMn Cch [(λ )2 − λMn λch ]

(6)

where λ is the intersublattice molecular-field coefficient, λMn and λch are the intrasublattice molecular-field coefficients for the Mn(2) and 1D-chain sublattices and: CMn = N

g 2 µ2B SMn (SMn + 1) and Cch = χch T 3kB

(7)

are, accordingly, the Curie constants of the Mn(2) and chain sublattices. In Eqs. (6) and (7) the intrachain exchange interaction is included in χch , which is hence a temperature dependent quantity named “constant” for convenience only. To calculate the temperature-dependence of χch T , the . . .–Mn(1)–(TNOP)– Mn(1)–. . . chain was approximated by a model in which molecular species having stable spins in the temperature region up to 300 K were isolated. According to the chain structure, two possible configurations were considered: (i) a ferrimagnetic (5/2 − 3/2) chain formed by nitroxide radicals (TNOP) with SR = 3/2 antiferromagnetically coupled with Mn(1) and (ii) a ferrimagnetic (3/2 − 1/2) chain formed by the trimeric spin species made up of one Mn(1) ion and two terminal nitroxide groups of different triradicals (STR = 3/2) antiferromagnetically coupled with the middle nitroxide group spin (S = 1/2). The (5/2 − 3/2) configuration was analyzed in the Heisenberg classical-classical spin approximation [88]. No satisfactory fit was possible with negative 2Jch /kB and positive λ values. The determination of the exchange interaction parameters for the (3/1 − 1/2) configuration was made in the quantum-classical chain approximation by using the analytical expression for the paramagnetic susceptibility of a ferrimagnetic chain derived by Seiden [60, 115]: (χch T )Qu

N µ2B 2 3 STR (STR + 1) + + = 3kB 4 1 − P(γ )

2 · STR (STR + 1)P(γ ) − STR Q(γ ) + 0.25Q (γ )

(8)


103

Table 7. Exchange parameters of [{Mn(hfac)2 }3 (TNOP)2 ]. The number of nearest neighbors for the intersublattice exchange interaction 2J /kB is taken as 2 and 6, respectively. Model

2Jch /kB [K]

λ [emu mol−1 ]

2J /kB [K]

JTR /kB [K]

Class.-Class. Quant.-Class. Quant.-Class.

−900.30 −520.20 −520.20

+5.90 +5.20 +5.10

+4.4 +3.9 +3.8

STR = 3/2 STR = 3/2 −350

where γ = −

and

2Jch STR , kB T

P(γ ) =

(1 + 12γ −2 ) sinh γ − (5γ −1 + 12γ −3 ) cosh γ − γ −1 + 12γ −3 , sinh γ − γ −1 cosh γ + γ −1

Q(γ ) =

(1 + 2γ −2 ) cosh γ − 2γ −1 sinh γ − 2γ −2 sinh γ − γ −1 cosh γ + γ −1

The best fits were found near the zero values for χMn and χch and the final fit was made with two variables, 2Jch /kB and λ . In Fig. 29 the calculated and experimental temperature-dependencies of χmol T for [{Mn(hfac)2 }3 (TNOP)2 ] are compared. They are in good agreement in a wide temperature range down to about 55 K. The corresponding parameters are given in Table 7. The results obtained show that the [{Mn(hfac)2 }3 (TNOP)2 ] complex is characterized by very strong intrachain interactions. The possibility to isolate trimeric spin species (1/2, 5/2, 1/2) in the . . .–Mn(1)–(TNOP)–Mn(1)–. . . chain indicates that the exchange interaction between Mn(1) and terminal nitroxide group exceeds essentially the interaction energy between the NO groups of the TNOP radical, which is characterized by the exchange integral 2J/kB = +480 K [33]. 2.8.2.3

Effect of Intra-trimer Interaction

Because of the strong intra-trimer exchange interaction the model with fixed STR value seems to be applicable in the temperature range up to 300 K. However, this approach will fail at temperatures higher than the intra-trimer interaction parameter JTR /k. To reveal the role of the intra-trimer interaction in the temperaturedependence of χmol T , a fitting procedure was made with STR replaced by the effec3kB tive moment of the (1/2, 5/2, 1/2) trimer µ2TR = (χTR T ) in Eq. (8). Here N g 2 µ2B χTR T for an isolated trimer is given by Eq. (4). The temperature variation of χmol T of [{Mn(hfac)2 }3 (TNOP)2 ] appeared to be unaffected by the intra-trimer exchange interaction. In fact, a change of the fit parameters lies within the accuracy of the procedure (see Table 7). Hence |JTr |/kB was estimated to be larger than 350 K.

104

2.8.3


Conclusion

It is concluded that the perfect 3D ferro/ferrimagnet with heterospin ferromagnetic (J1 > 0)-antiferromagnetic (J2 < 0) network is realized in [{Mn(hfac)2 }3 (TNOP)2 ]. Magnetic properties of the ferrimagnetic 3D metal-radical complex [{Mn(hfac)2 }3 (TNOP)2 ] can adequately be described in the Heisenberg exchange approximation assuming that two magnetic sublattices, 1D ferrimagnetic . . .–Mn(1)–(TNOP)–Mn(1)–. . . chains with four-spin periodicity and Mn(2) ions, form a collinear ferrimagnetic structure with a positive exchange coupling. Due to a strong exchange interaction between Mn(1) and terminal NO groups within the chain, it can be considered approximately as a two-spin ferrimagnetic chain made up of middle nitroxide groups (S = 1/2) antiferromagnetically coupled with the trimer spin species having spins S = 3/2.

2.9

Summary and Prognosis

The supramolecular approaches have been successfully applied to the construction of high-dimensional network structures by using magnetic metal ions with organic free radicals serving as bridging ligands. These extended structures are difficult to construct by using only covalent bonds. The method employed takes advantage of the intermolecular bonding interactions considerably weaker than conventional covalent bonds, mostly coordination bonds plus hydrogen bonds, hydrophobic interactions, van der Waals forces, etc. The products are formed under thermodynamic control rather than kinetic control. The magnetic structures correspond nicely to the crystal structure and network structures have been successfully used for making molecular-based magnets in which the spins order at finite temperature. Elsewhere such network structures are intended for making switches, host molecular cages like “organic zeolites” and enzymatic pockets, electric conductors, non-linear optical materials, etc. As far as the magnetic properties are concerned, the exchange coupling through these weaker bonds are generally rather weak. For the coupling to be strong, the unpaired electrons have to be bound to each other through one or two σ -bonds or several π-bonds. Thus the supramolecular approaches have been limited to metal coordination compounds. Design of appropriate free radical ligands, i. e., high-spin oligo-aminoxyl radicals as bridging ligands is a key to our strategy. The number and the configuration of the coordination sites in the free radical ligands control the dimensions of the magnetic structures of these metal–radical ligand complexes. A sophistication of the design of new high-spin bridging ligands should lead to magnetic materials having higher TC . Furthermore, a clear-cut one-to-one correspondence has been found between tacticity of the extended molecular structures and dimension of the crystal structures; while the isotactic polymeric chains remain one-dimensional and are difficult to have strong interchain interactions, as in [Mn(hfac)2 BNO], [Mn(hfac)2 TNOP] · nC6 H14 ]and [Mn(hfac)2 TNOPB], the syndiotactic chains have a tendency to grow

References

105

into 2D ([{Mn(hfac)2 }3 (TNOPB)2 ] · n-C7 H16 ) and 3D ([{Mn(hfac)2 }3 (TNOP)2 ]) networks by extending interchain connectivity. The ligands employed so far are conformationally labile and chiral only in the crystals. The right chirality of each ligand and the consequent tacticity have been selected during the self-assembling and crystallization processes. Furthermore, isotactic chains of opposite chirality cancel each other out and there is no net chirality exhibited by the bulk crystals. Ongoing studies should employ ligands stable with respect to chirality to dictate the dimension of the resulting metal complexes. Once such crystals are obtained, they might become chiral magnets that would show interesting photophysical behavior. The usefulness of the heterospin systems as a versatile design strategy for high TC molecule-based magnetic materials would be increased by incorporation of the chiral aspect into the complex structures.

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3

Organic Kagome Antiferromagnets Kunio Awaga, Nobuo Wada, Isao Watanabe, and Tamotsu Inabe

3.1

Introduction

Geometrical frustration in antiferromagnetic systems with triangular coordination symmetry has recently been of interest in physics. In such a triangle the two nearest neighbors to a given spin are themselves nearest neighbors and antiferromagnetic coupling among them cannot be completely satisfied. This frustration prevents long-range magnetic order from being established and enables novel kinds of lowtemperature magnetic state to develop [1–3]. The Heisenberg Kagome (named after a form of Japanese basket weaving [4]) antiferromagnet, whose lattice is shown in Scheme 1, is one of the most interesting of these frustrated systems.

Scheme 1

Whereas the number of the nearest neighbors is six in the simple triangular lattice, it is reduced to be four in the Kagome lattice. This enables more freedom for the alignment of the magnetic moments on the Kagome lattice. A possible ground state for the antiferromagnetic classical spins on a regular triangular lattice is the so-called 120◦ structure (Scheme 2a), in which the magnetic moments are all parallel to the triangular plane and the neighboring moments make an angle of 120◦ with each other. √ √ The magnetic moments in the same direction form a 3 × 3 superlattice whose unit is indicated by the broken lines. The spin alignment between the two neighbors is energetically disadvantageous to the simple antiparallel one, but the net moment becomes zero. The 120◦ structure can result in long-range magnetic order with the periodicity in the simple triangular Heisenberg antiferromagnets, indicating that it is a unique solution to spin frustration. Although it is possible to write down a coplanar

110

3 Organic Kagome Antiferromagnets

Scheme 2

120◦ structure on the Kagome lattice, as shown in Scheme 2b, the reduced number of nearest neighbors in this lattice enables non-coplanar 120◦ spin orientation, or a so-called paper Origami structure [5, 6]. Scheme 2c shows the internal spin space folded in two along the broken line. On each plane the magnetic moments have the 120◦ structure, but the moments on the different planes are not coplanar. Because continuous spin folding takes place with no energy cost, it is predicted that the classical Kagome antiferromagnet has rich, non-trivial ground-state degeneracy. The actual ground state might be governed by subtle effects, such as a quantum effect, a single-ion magnetic anisotropy, next-nearest-neighbor interactions, and so on. For these, the Kagome antiferromagnet is theoretically expected to have characteristic features – non-Neel ´ states, residual entropy at absolute zero temperature, and so on.

3.2

Inorganic Kagome Antiferromagnets

Despite the interest in the Kagome antiferromagnets, few antiferromagnetic Kagome systems have yet been studied, owing to the lack of suitable model compounds. They had, in addition, been limited to inorganic materials, before we discovered the organic Kagome antiferromagnet described in Section 3. In this section we will briefly review inorganic Kagome antiferromagnets.

3.2.1

SrGa12-x Crx O19 (SCGO(x))

This is a quasi-two-dimensional oxide containing antiferromagnetically interacting S = 3/2 Cr3+ ions in Kagome bilayers [7]. Although the antiferromagnetic Weiss constant is between −200 and −500 K, depending on the Cr concentration, there is no long-range magnetic order down to at least 1.5 K [8]. Instead hysteretic behavior, indicative of a spin-glass transition, is observed at 3.5 K [9]. Neutron scattering [8]

3.3 Organic Kagome Antiferromagnet, m-MPYNN·X

111

and muon spin rotation (µSR) [10] measurements indicate that the spins are not strictly frozen at these low temperatures with short-range antiferromagnetic correlation. Single-crystal magnetic susceptibility measurements reveal strong magnetic anisotropy at the spin-glass-like transition, suggesting that the magnetization component normal to the Kagome planes freezes completely, whereas the component parallel to the planes does not [11]. SCGO(x) suffers from a severe disadvantage as a model material, however, in that the coverage of the Kagome lattice sites is significantly less than 100% and, depending on the method of preparation, ranges from 88–95%. A significant proportion of moments also reside on a triangular lattice.

3.2.2

+ Jarosite, AM3 (OH)6 (SO4 )2 (A = Na+ , K+ , Rb+ , Ag+ , NH+ 4 , H3 O , 3+ 3+ etc., and M = Fe or Cr )

The structures of jarosite materials belong to the rhombohedral space group R3m, and are identified as a Kagome lattice in which MO6 octahedra are linked through their vertices in layers that are well-separated by hydroxide, sulphate, and hydronium groups [12, 13]. Fe-jarosite, in which the Fe3+ ions are in the ground state of 6 A1g and nearest-neighbor exchanges can approximate well to Heisenberg symmetry, has been studied extensively by magnetic susceptibility [13, 14], Mossbauer ¨ [13, 14], neutron-scattering [15] and µSR [16] measurements. Long-range magnetic order is observed below TN ≈ 50 K for the compounds in which A = K+ , Na+ , etc., with the 120◦ structure [13–16], whereas the compound with A = H3 O+ has an anomaly, characteristic of spin-glass freezing, in the magnetic susceptibility at 17 K [17]. Besides these two examples, the spin lattices in La4 Cu3 MoO12 [18] and RCuO2.66 [19] are reported to identical with the Kagome lattice. The 2D solid 3 He adsorbed on graphite has also been studied as an antiferromagnetic system [20].

3.3 3.3.1

Organic Kagome Antiferromagnet, m-MPYNN·X Crystal Structure

We recently discovered that crystals of m-N -methylpyridinium nitronylnitroxide (abbreviated m-MPYNN) have an antiferromagnetic Kagome lattice [21]. m-MPYNN · I was obtained by reaction of m-pyridyl nitronylnitroxide and methyl iodide. Recrystallization of m-MPYNN·I with the presence of excess TBA·A (TBA = tetrabutylammonium and A = BF4 , ClO4 ) gave a crystalline solid solution, m-MPYNN·Ax ·I1−x . The reaction of equivalent amounts of m-MPYNN·I and Ag·A resulted in immediate precipitation of Ag·I, leaving iodide-free m-MPYNN·A in the solution. Recrystallization of m-MPYNN·I, m-MPYNN·Ax ·I1−x , and m-MPYNN·A from their acetone solutions resulted in hexagonal single crystals containing one acetone molecule per three m-MPYNN. The crystals of the simple iodide salt, m-MPYNN·I·(1/3)(acetone),

112


Fig. 1. (a) Organic 2D layer of m-MPYNN projected on to the ab plane. (b) Bond-alternated hexagonal lattice; J1 and J2 are the intradimer and interdimer magnetic interactions, respectively. (c) Kagome lattice.

were not stable – in air they immediately turned into powder as a result of evaporation of the solvent of crystallization – whereas the crystals containing BF4 or ClO4 were stable. The structure of m-MPYNN·X·(1/3)(acetone) (X = I, BF4 , ClO4 , etc.) belongs to a trigonal space group. The m-MPYNN molecules exist as a dimer, and the dimer units form a 2D triangular lattice parallel to the ab plane. Fig. 1a shows a projection of the organic layer of m-MPYNN on to the ab plane. The radical dimer is located on each side of the triangles – in the other words the m-MPYNN molecules form a bondalternated hexagonal lattice, as schematically shown in Fig. 1b. In the intradimer arrangement there is a very short intermolecular, interatomic distance of less than 3 Å between the NO group and the pyridinium ring. This short contact is probably caused by an electrostatic interaction between the positive charge on the pyridinium ring and the negative charge polarized on the oxygen atom. In the interdimer arrangement, on the other hand, there is weak contact between the NO groups. The NO–NO contact means overlap between the singly-occupied molecular orbitals (SOMOs), which always contributes to antiferromagnetic coupling.


113

Fig. 2. Side view of the organic 2D layers. Nine m-MPYNN dimers are drawn on the surface of the hexagonal prism.

Figure 2 shows a side view of the trigonal lattice, where nine units of the mMPYNN dimers on the surface of the hexagonal prism are drawn. The unit cell includes two organic layers at the height z = 0 and z = 1/2, between which there is a big separation. One-third of the anions are in the organic layer, joining the m-MPYNN molecules; those remaining are between the layers, compensating the excess positive charge in the organic layers. The crystal solvent, acetone, is located between the organic layers at the center of the triangle.

3.3.2

Magnetic Susceptibility

The temperature-dependence of the paramagnetic susceptibility, χp , for mMPYNN·BF4 ·(1/3)(acetone) is shown in Fig. 3, in which χp T is plotted as a function of temperature.

Fig. 3. Temperature-dependence of the paramagnetic susceptibilities χp for mMPYNN · BF4 · (1/3)(acetone).

114


Fig. 4. Temperature-dependence of the ac magnetic susceptibilities, χac , for oriented single crystals of m-MPYNN · BF4 ·(1/3)(acetone).

The value of χp T increases as the temperature is reduced from room temperature to ca. 10 K, indicating that the intradimer coupling, J1 , is ferromagnetic. After passing through a maximum near 10 K, χp T decreases rapidly, suggesting that the interdimer magnetic interaction, J2 , is antiferromagnetic. The observed temperaturedependence can be readily interpreted in terms of the ferromagnetic J1 and the antiferromagnetic J2 by use of Eq. (1): χ=

4C T {3 + exp(−2J1 /kB T )} − 4J2 /kB

(1)

where C is the Curie constant and kB the Boltzmann constant. The derivation of Eq. (1) is described elsewhere [21]. The solid curve in Fig. 3 is the theoretical best fit to the data, obtained with J1 /kB = 11.6 K and J2 /kB = −1.6 K. Below |J1 |/kB K the radical dimer can be regarded as a spin-1 Heisenberg spin located at the mid point of each side of the triangle, as shown in Fig. 1c. It is expected that the interdimer antiferromagnetic coupling J2 gives rise to spin frustration among the triplet spins. The spin lattice in Fig. 1c is exactly coincident with the Kagome lattice. Therefore, the magnetic system in this organic material will he characterized as a spin-1 Kagome antiferromagnet in the temperature range below |J2 |/kB K. Figure 4 shows the temperature-dependence of the ac magnetic susceptibilities, χac , for oriented single crystals of m-MPYNN·BF4 ·(1/3)(acetone) below 0.8 K [22]. The magnetic field was parallel to the c axis. The value increases with decreasing temperature down to 0.24 K, and, after passing through a maximum approaches zero at absolute zero. We have confirmed no magnetic anisotropy in this behavior. This clearly indicates that the ground state is not an antiferromagnetic ordered state but a spin-gap state. The low-temperature data is, in fact, a good fit to the gap equation:

χ=A kB T

f

exp − kB T

(2)


115

where A is a constant and is the magnetic gap. The parameter f depends on the density of the excited states against the excitation energy, but is fixed at 1 in this analysis [23]. The solid curve in Fig. 4 is the theoretical curve obtained with A = 0.52 and /kB = 0.25 K. Spin or gap states have been observed in spin Peierls systems [24] and Haldene gap systems [25], although these precedents were 1D magnetic systems. The ground states of the spin-frustrated inorganic systems described in Section 2 are either the 3D ordered state or the spin-glass state. As far as we are aware this is the first example of a spin-gap state resulting from spin frustration. It is worth noting here that Anderson predicted the so-called resonating valence bond (RVB) state on a triangular antiferromagnetic lattice, which brought about a spin gap [26]. It is possible that the ground state of this material can be characterized in terms of the RVB state.

3.3.3

Heat Capacity

The temperature-dependence of the heat capacity, cp , of m-MPYNN · BF4 · (1/3) (acetone) has been examined down to 0.12 K [22]. The results below 3 K are shown in Fig. 5. The value of cp gradually increases with decreasing temperature. After a broad maximum at 1.4 K, cp decreases. Below 0.24 K, where χac shows the spin-gap ground state, cp increases again. The temperature of maximum cp , 1.4 K, almost agrees with |J2 |/kB . Monte Carlo calculation indicated that the heat capacity of the spin-1/2 Kagome Heisenberg antiferromagnet has maximum short-range magnetic ordering at 1.4|J |/kB [27]. The anomaly observed at 1.4 K is probably because of the short-range ordering which results from J2 . The reason of the increase in cp below 0.24 K is not clear, but it suggests another anomaly below 0.1 K. It is notable that there is no signal indicative of long-range ordering in the temperature range down to 0.1 K, which is 8% of |J2 |/kB . This is indicative of the presence of spin frustration in this magnetic system. Plots of cp /T increase gradually as the temperature is reduced to 0.12 K (not shown). We calculated the entropy change accompanying the anomaly at 1.4 K to be (S = 4.7 J K−1 mol−1 , by using the data above 0.12 K and subtracting the contributions of the lattice and the excited state resulting from J1 . Because the triplet spins on the m-MPYNN dimers lose magnetic freedom as a result of

Fig. 5. Temperature-dependence of the heat capacities cp for m-MPYNN·BF4 ·(1/3)(acetone).

116


the short-range ordering, the magnetic entropy is theoretically calculated to be Sm = (R/2) ln 3 = 4.567 J K−1 mol−1 . The observed value of S is already larger than Sm , despite S being obtained by use of data acquired above 0.12 K. This means that there is an unknown amount of freedom besides the magnetic freedom; this cooperates with the short-range magnetic ordering in this ultra-low temperature range.

3.3.4

Positive Muon Spin Rotation

We performed µSR measurements on m-MPYNN·BF4 ·(1/3)(acetone) in the temperature range down to 30 mK, to clarify whether or not magnetic transitions occur, and to confirm the non-magnetic ground state [28]. Positive muon spin rotation (µ+ SR) is a good microscopic probe for monitoring such a magnetic state of the system. A muon spin is completely polarized along a beam direction, even in the zero-field (ZF) condition, and depolarized after the stop at a potential-minimum position in the samples, interacting with a local field at a muon site [29]. Long-range or shortrange ordering of the dimer spins can be recognized as a change in the depolarization behavior of the muon spin, because a static or a dynamically fluctuating component of the internal field which is accompanied by the magnetic transition strongly affects the muon spin polarization. Figure 6 shows ZF-µ+ SR time spectra obtained at 265, 100, and 2.9 K, and at 30 mK. In this figure the asymmetry parameter of the muon spin at time t, A(t), is defined as [F(t)− B(t)]/[F(t)+ B(t)], l, where F(t) and B(t) are muon events counted by the forward and backward counters, respectively. The asymmetry at each temperature was normalized to unity t = 0, to enable comparison of differences between depolarization behavior. The depolarization behavior cannot be described either by a simple Gaussian function or a Lorentzian function. For convenience the ZF-µ+ SR spectra obtained were analyzed by means of a power function, A0 exp(−λt)β , where A0 is the initial asymmetry at t = 0 and λ is the depolarization rate. The solid curves in Fig. 6 are the best fit results obtained by use of this power function. The temperature-dependence of A0 , λ, and β was obtained from the best fit analysis. All are independent of temperature below ca 100 K, showing that the static and

Fig. 6. ZF-µ+ SR time spectra obtained for m-MPYNN·BF4 ·(1/3)(acetone) at 265 K, 100 K, 2.9 K, and 30 mK.


117

dynamic properties of the local field at the muon site are temperature-independent. This is different from other types of Kagome magnet in which strong enhancement of the rate of polarization, by the critical slowing-down behavior of magnetic moments, is observed in the region of a magnetic transition temperature [10, 16, 30, 31]. The value of λ decreases slightly above 150 K, probably because of the motional narrowing effect indicating that the muon starts to diffuse through the crystal. The half-width of the distribution of the static internal field at the muon site, H , was estimated, from the longitudinal field-dependence of the µ+ SR time spectra (not shown), to be 10 ± 2 G. It is known that a muon implanted into a crystal which contains F− ions forms a strong FµF state by hydrogen-bonding. In this case, the distance between the F- ion and the muon is similar to a nominal F− ionic radius of 1.16 Å. Assuming the distance between the stopped muon and the 19 F-nucleus in m-MPYNN-BF4 is the nominal F− ionic radius, the dipole field of the 19 F-nucleus at the muon site is estimated to be ca 8.5 G, a value comparable with the H value obtained. Although the reason for the absence of muon spin precession observed in other fluorides [32] is still unclear, it can be concluded that the implanted muon is expected to stop near the F− ion and enter into hydrogen-bonding, and that the static internal field at the muon site originates from the 19 F-nuclear dipole field. In conclusion, the temperature-independent depolarization behavior resulting from the distributed static internal field induced by the 19 F-nuclear dipoles at the muon site was observed down to 30 mK. The width of the field distribution was 10 ± 2 G. No clear long-range magnetic ordering of the dimer spins was observed. Taking into account results from magnetic susceptibility measurements, it is concluded that the ground state of m-MPYNN·BF4 is non-magnetic.

3.3.5

Distorted Kagome Lattices

In this section, we will describe the structures and magnetic properties of mEPYNN·I and m-PPYNN·I, where m-EPYNN and m-PPYNN are m-N-ethyl- and m-N -propylpyridinium nitronylnitroxides, respectively, and compare them with those of m-MPYNN·I. The materials were obtained by the same procedure as for m-MPYNN·I. Recrystallization of m-EPYNN·I and m-PPYNN·I from acetone or acetone-benzene resulted in hexagonal single crystals. Results from elemental analysis were indicative of the chemical formulas m-EPYNN·I·1.5H2 O and mPPYNN·I·0.5H2 O. Table 1 shows the unit cell dimensions of the m-R-PYNN·I series, determined by use of X-ray diffraction data in the range 20◦ < 2θ < 25◦ . Whereas the crystal of m-MPYNN · I has a trigonal structure, m-EPYNN · I and m-PPYNN · I crystallize as monoclinic systems. It was, however, found that lattice transformations for m-EPYNN · I and m-PPYNN · I led to cell dimensions quite similar to those of m-MPYNN · I. A schematic comparison between the trigonal and monoclinic cell is shown in Scheme 3. The transformed lattice constants are a = 16.14(6) Å, b = 16.19(4) Å, c = 24.02(6) Å, α = 89.5(2)◦ , β = 90.1(2)◦ , γ = 119.9(1)◦ , and V = 5440(26) Å3 for m-EPYNN·I and a = 16.30(1) Å, b = 16.30(1) Å, c = 24.71(1) Å, α = 89.7(4)◦ ,

118


Table 1. Cell and magnetic properties of m-R-PYNN·I.

Structure a (Å) b (Å) c (Å) β (◦ ) V (Å3 ) Z J1 /kB J2 /kB

m-MPYNN·I

m-EPYNN·I

m-PPYNN·I

Trigonal 15.876(5) – 23.583(6) – 5147(3) 12

Monoclinic 16.14(6) 28.07(8) 24.02(5) 91.1(2) 10876(53) 24

Monoclinic 28.153(9) 16.407(14) 24.705(11) 90.25(3) 11411(11) 24

10.2 −1.6

9.6 −1.7

6.6 −1.0

Scheme 3

β = 90.1(4)◦ , γ = 119.5(3)◦ , and V = 5709(5) Å3 for m-PPYNN·I. The lattice parameters obtained, a, b, c, and V , are slightly larger than the corresponding ones for m-MPYNN·I, but the differences between them are very small. Although we could not complete full structural analyses of m-EPYNN·I and m-PPYNN·I, probably because of positional disorders of the iodide ion and the crystal solvent, it is expected that they have a slightly distorted Kagome lattice. The decrease in crystal symmetry means distortion of the equilateral triangle to an isosceles triangle. This will significantly affect the low-temperature magnetic properties, as described later. Figure 7 shows the temperature-dependence of χp T for the m-R-PYNN·I series. The plots show quite similar temperature-dependence – the value of χp T increases as temperature is reduced from room temperature to ca 10 K. After passing through a maximum χp T decreases rapidly. This temperature-dependence is well explained by Eq. (1). Strictly speaking, m-EPYNN·I and m-PPYNN·I should include two kinds of J2 , because of the distortion of the Kagome lattice in these materials. The distortion is, however, so small we can ignore the difference. The solid curves going through the plots for the three compounds in Fig. 7 are the theoretical best fits to the data, obtained with the parameters listed in Table 1. The values of J1 and J2 decrease systematically with extension of the N -alkyl chain, presumably because of expansion of the 2D lattice. The temperature-dependence of the ac susceptibility, χac , for the three compounds are shown in Fig. 8. Although m-MPYNN·I has the regular antiferromagnetic Kagome lattice, as has m-MPYNN·BF4 , the value of χac continues to increase down to 0.05 K with no evidence of the spin-gap state. This is probably because


119

Fig. 7. Temperature-dependence of the paramagnetic susceptibilities, χp , for m-MPYNN·I, mEPYNN·I and m-PPYNN·I.

Fig. 8. Temperature-dependence of the ac magnetic susceptibilities, χac , for m-MPYNN·I, mEPYNN·I, and m-PPYNN·I.

m-MPYNN·I is chemically unstable; evaporation of the solvent gradually takes place. The dependence can be explained by the Eq. (3):

χ=A kB T

f

exp − kB T

+

Cdef T

(3)

where the first term is the same as in Eq. (2) and the second term is for the Curie contribution of lattice defects. When the data are fit to Eq. (3), the values obtained are: A = 0.64, /kB = 0.25 K, and Cdef = 0.025 emu K mol−1 (6.6%). The values of A and are very close to the corresponding values for m-MPYNN·BF4 . The temperature-dependence of the distorted Kagome materials m-EPYNN·I and mPPYNN·I is similar, but their values of χac below 0.2 K are ca. five times larger than that for m-MPYNN·I. The values are too large to be explained by the contribution of lattice defects. It is considered that their behavior is intrinsic and the spin-gap state is readily collapsed by the small distortion of the Kagome lattice.

120

3.3.6


Summary

The crystal structures and magnetic properties of the m-R-PYNN-X series have been studied. In the crystal of m-MPYNN·X the ferromagnetic dimers formed the triangular lattice with weak interdimer antiferromagnetic coupling. The magnetic system can be regarded as a spin-1 Kagome antiferromagnet at low temperatures. Single-crystal EPR revealed the 2D Heisenberg character of the spin system The low-temperature magnetic behavior was indicative of the spin-gap ground state; this was possibly identical with the RVB state. The temperature-dependence of the heat capacity showed that short-range magnetic ordering resulted from interdimer antiferromagnetic interaction, but that there was no long-range ordering down to 0.1 K. It also suggested an unknown amount of freedom which cooperated with the short-range magnetic ordering. The detection of µ+ SR revealed the temperatureindependent depolarization behavior down to 30 mK. In the other words, this study was strongly indicative of the absence of long-range magnetic ordering of the dimer spins and the non-magnetic ground state. Extension of the N -alkyl chain in the m-RPYNN·I series resulted in distortion of the Kagome lattice, and consequent collapse of the spin-gap ground state.

Acknowledgment The authors would like to thank their co-workers (Masao Ogata, Tsunehisa Okuno, Akira Yamaguchi, Morikuni Hasegawa, Masahiro Yoshimaru, Wataru Fujita, Takeo Otsuka, Hideo Yano, Tatsuya Kobayashi, Seiko Ohira, and Hiroyuki Imai) for their important contributions to the work reported herein.

References [1] [2] [3] [4] [5] [6]

P. Fazekas and P.W. Anderson, Philos. Mag. 1974, 30, 423. X.G. Wen, F. Wilczek, and A. Zee, Phys. Rev. B 1989, 39, 11413. P. Chandra and P. Coleman, Phys. Rev. Lett. 1991, 66, 100. I. Syozi, Progr. Theor. Phys. 1951, 6, 306. I. Ritchey, P. Chandra, and P. Coleman, Phys. Rev. B 1993, 47, 15342. E.F. Shender, V.B. Cherepanov, P.C. Holdsworth, and A.J. Berlinsky, Phys. Rev. Lett. 1991, 70, 3812. [7] X. Obradors, A. Labarta, A. Isalgue, J. Tejada, J. Rodriguez, and M. Pernet, Solid State Commun. 1988, 65, 189. [8] C. Broholm, G. Aeppli, G. Espinosa, and A.S. Cooper, Phys. Rev. Lett. 1990, 65, 3173; S.-H. Lee, C. Broholm, G. Aeppli, T. G. Perring, B. Hessen, and A. Taylor, Phys. Rev. Lett. 1996, 76, 4424. [9] A.P. Ramirez, G.P. Espinosa, and A.S. Cooper, Phys. Rev. Lett. 1990, 64, 2070; Phys. Rev. B 1992, 45, 2505.

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[10] Y.J. Uemura, A. Keren, K. Kojima, L.P. Le, G.M. Luke, W.D. Wu, Y. Ajiro, T. Asano, Y. Kiruyama, M. Mekata, H. Kikuchi, and K. Kakurai, Phys. Rev. Lett. 1994, 73, 3306. [11] P. Schiffer, A.P. Ramirez, K.N. Franklin, and S-W. Cheong, Phys. Rev. Lett. 1996, 77, 2085. [12] R. Wang, W.F. Brandley, and H. Steinfink, Acta Crystallogr. 1965, 18, 249. [13] M. Takano, T. Shinjo, and T. Takada, J. Phys. Soc. Jpn 1971, 30, 1049. [14] M. Takano, T. Shinjo, M. Kiyama, and T. Takada, J. Phys. Soc. Jpn 1968, 25, 902. [15] M.G. Townsent, G. Longworth and E. Roudaut, Phys. Rev. B 1986, 33, 4919. [16] A. Keren, K. Kojima, L.P. Le, G.M. Luke, W.D. Wu, Y.J. Uemura, M. Takano, H. Dabkowska, and M.J.P. Gingras, Phys. Rev. B 1996, 53, 6451. [17] A.S. Wills and A. Harrison, J. Chem. Soc., Faraday Trans. 1996, 92, 2161. [18] D.A.V. Griend, S. Boudin, V. Caignaert, K. Poeppelmeier, Y. Wang, V.P. Dravid, M. Azuma, M. Takano, Z. Ho, and J.D. Jorgensen, J. Am. Chem. Soc. 1999, 121, 4787. [19] M.D. Nunez-Regueiro, C. Lacroix and B. Canals, Phys. Rev. B, 1996, 54, 736. [20] Y.R. Wang, Phys. Rev. B 1992, 45, 12608, and references cited therein. [21] K. Awaga, T. Okuno, A. Yamaguchi, M. Hasegawa, T. Inabe, Y. Maruyama, and N. Wada, Phys. Rev. B, 1994, 49, 3975. [22] N. Wada, T. Kobayashi, H. Yano, T. Okuno, A. Yamaguchi, and K. Awaga, J. Phys. Soc. Jpn. 1997, 66, 961. [23] L.N. Bulaevskii, Soviet Phys. Solid State 1969, 11, 921. [24] I.S. Jacobs, J.W. Bray, H.R. Hart Jr, L.V. Interrante, J.S. Kasper, G.D. Watkins, Phys. Rev. B 1976, 14, 3036. [25] F.D.M. Haldene, Phys. Lett. 1983, 93A, 464. [26] P.W. Anderson, Mater. Res. Bull. 1973, 8, 153. [27] T. Nakamura and S. Miyashita, Phys. Rev. B 1995, 52, 9174. [28] I. Watanabe, N. Wada, H. Yano, T. Okuno, K. Awaga, S. Ohira, K. Nishiyama, and K. Nagamine, Phys. Rev. B, 1998, 58, 2438. [29] Y.J. Uemura, T. Yamazaki. D.R. Harshman, M. Senba, and E.J. Ansaldo, Phys. Rev. B 1985, 31546. [30] A. Keren, L.P. Le, G.M. Luke, W.D. Wu, Y.J. Uemura, Y. Ajiro, T. Asano, H. Huriyama, M. Mekata, and H. Kikuchi, Hyperfine Interactions 1994, 85, 181. [31] S.R. Dunsiger, R.F. Kiefl, K.H. Chow, B.D. Gaulin, M.J.P. Gingras, J.E. Greedan, A. Keren, K. Kojima, G.M. Luke, W.A. MacFarlane, N.P. Raju, J.E. Sonier, Y.J. Uemura, and W.D. Wu, Phys. Rev. B 1996, 54, 9091. [32] J.H. Brewer, S.R. Kreitzman, D.R. Noakes, E.J. Ansaldo, D.R. Harshman, and R. Keitel, Phys. Rev. B 1986, 33, 7813.


4

Magnetism in TDAE-C60 Ales Omerzu, Denis Arcon, Robert Blinc and Dragan Mihailovic

4.1

Introduction

The purpose of this paper is to review recent work on one of the most interesting new magnetic organic compounds this decade, namely the ferromagnetic fullerene compound tetrakis-dimethylaminoethylene-C60 (TDAE-C60 ) (Fig. 1) first discovered in 1991 by Fred Wudl and collaborators at the University of California in Santa Barbara [1]. At the time of their discovery, the Curie temperature of TC = 16 K was an order of magnitude higher than the previous record [2] and brought the research field of p-electron ferromagnetism from the realms of the esoteric into the mainstream. Very soon after the discovery of an efficient method for producing useful quantities of fullerenes using a carbon arc by Huffman and Kraetschmer [3] attempts to dope them with various dopants yielded immediate and spectacular results. Whereas a Bell Laboratories group [4] were rewarded with the discovery of fullerene superconductivity by doping with alkali metals, the efforts of the Santa Barbara group [1] in doping with the strong organic electron donor TDAE yielded a material with very unusual low-temperature magnetic properties. When TDAE (a liquid at room temperature) was mixed with C60 in solution it crystallized into small particles with could be removed as a precipitate. The result was TDAE+ C− 60 , a charge-transfer salt with a monoclinic structure quite different to the high-symmetry cubic or tetragonal ones of other doped fullerene compounds (Fig. 3). The structure contains unusually short distances between adjacent C60 buckyballs of 9.99 Å [5] which is believed to

Fig. 1. Schematic diagrams of C60 (left) and TDAE (right) molecules. Carbon atoms are shown as dark spheres, nitrogen atoms as light spheres, and hydrogen atoms as small spheres.

124

4 Magnetism in TDAE-C60

lead to coupling between spins localized on C− 60 ions and the formation of a ferromagnetically correlated spin state. Since TDAE-C60 was discovered, there has been significant experimental progress in elucidating the magnetic and electronic properties of this material. However, very few new compounds have been found to show similar behavior, and until very recently [6] TDAE-C60 remained the compound with the highest TC . For example TDAE-C70 [7] and many different TDAE-doped C60 derivatives show no evidence for a ferromagnetic (FM) state down to 4 K – which is true also when TDAE is substituted with other electron donors [8] – and although there have been some reports of possible ferromagnetism at higher temperatures [9], up until very recently such unidentified ferromagnetic organic compounds (UFOs) have so far failed the reproducibility test. The current record thus stands at 19 K, for cobaltocene-3aminophenylmethano[60]fullerene [6], which has a TC approximately ∼3.5 K higher than TDAE-C60 .

4.2 4.2.1

Synthesis and Structure Synthesis

TDAE-C60 was first synthesized in powder form by reacting either powder C60 with liquid TDAE at room temperature or C60 in toluene solution with TDAE. The synthesis was performed in oxygen-free surroundings because TDAE is highly sensitive to oxygen immediately forming diethyl urea. TDAE-C60 precipitate was then thoroughly washed and dried. A method for growing single crystals of organic charge-transfer (CT) salts has been developed in the seventies for demands of a new emerging field of low-dimensional organic conductors [10]. The method is applicable to two-component systems of donors and acceptors, both soluble in an organic solvent (usually acetonitrile or some other solvent with low dielectric constant). The resulting CT salt is no longer soluble in non-polar solvent and precipitates out from solution. For growing a single crystal of significant size, the rate of charge-transfer reaction must be very slow. For this purpose crystal growing cells are used. In these cells reactants are dissolved in two vessels separated by a suitable filter (fritted glass), or a larger space filled with a pure solvent. The separation enables slow diffusion of one reactant into the solution of another and consequently, slow growth of crystals. Soon after its discovery in 1991 a similar method has been employed for growing single crystals of TDAE-C60 but for unknown reasons these method originally failed. Later, in 1994 an adapted procedure was tried with large surplus of TDAE, so shifting the balance of the diffusion process strongly in the direction of TDAE’s diffusion into the C60 compartment. The first crystals where not of good quality, but during the next few years the method has improved and today it is possible to grow crystals of high quality for both α and α modifications (see later for explanation of the two modifications of TDAE-C60 ). A typical size of such crystals is around 1 mm.

4.2 Synthesis and Structure

125

Fig. 2. A crystal growing cell for TDAE-C60 .

This enables all important physical experiments to be performed except neutron scattering (the size of TDAE-C60 crystal for the neutron scattering should be at least 2 × 2 × 2 mm3 primarily because of diffuse scattering on protons). Sizes of crystal growing cells can be different: from 10 mL to several hundreds of milliliters. The usual size is 2 × 30 mL with additional free space of approximate 20 mL which is initially filled with pure solvent. The photograph (Fig. 2) shows the shape of a typical cell. The two compartments are connected with a narrow tube, which is divided in the middle by an additional fritted glass filter which slows diffusion. Before filling, the tube must be carefully cleaned in chromic acid, washed with deionized water and dried. The solvent (toluene) must be freshly distilled under an inert atmosphere and transferred into a glove-box with an oxygen concentration less then 1 ppm. C60 and TDAE are used as commercially shipped (C60 Hoechst gold grade 95% pure, and pure TDAE from Fluka or Aldrich). Two solutions are prepared separately in an inert atmosphere with concentrations 2 mg mL−1 and 0.3 mg mL−1 for C60 and TDAE, respectively. The solutions are filtered and then poured into two compartments of the tube. Finally, the free space between two compartments is filled with pure toluene. The tube is carefully sealed with vacuum grease and transferred to a thermostatted bath for a period from three to six months, depending on the thermostatting temperature. When crystals of the α modification are needed the growing cell should be thermostatted at temperatures between 8 and 10◦ C. For the ferromagnetic α modification, the thermostatting temperatures are between 20 and 25◦ C. When the crystal growth is completed, the tube is transferred back to a glove-box and crystals are extracted from it, washed with hexane and dried. For all experimental purposes, the crystals must be kept under vacuum or an inert gas.

126

4.2.2


The Lattice Structure

The lattice structure of powder specimens was first determined by Stevens et al. [5] to be monoclinic C2/m with one formula unit per unit cell. Later, a structural analysis performed on single crystals [11] showed the room temperature structure to be monoclinic with unit cell dimensions a = 15.858(2) Å, b = 12.998(2) Å, c = 19.987(2) Å, β = 93.37◦ and four formula units per unit cell. The space group was found to be C2/c and not C2/m as originally reported from powder data. The unit cell in fact consists of two subcells (Fig. 3) which are stacked along the c-direction so that the unit cell size in the c-direction is doubled. In one of the subcells the TDAE ions are shifted along the b-axis for about 0.02 Å and in the other by the same distance in the opposite direction. The TDAE coordinates are (0.5, 0.502, 0.75), (0.5, 0.498, 0.25), (0, 0.002, 0.75) and (0, −0.002, 0.25) with the C = C bond parallel to the c-axis, whereas the C60 coordinates are (0, 0.5, 0), (0, 0.5, 0.5), (0.5, 0, 0) and (0.5, 0, 0.5). The C60 –C60 center-to-center distance is shortest along the c axis and amounts to 9.99 Å at room temperature. The atomic coordinates are collected in Table 1, together with the isotropic displacement parameters. The C60 molecules were found to be executing large amplitude re-orientations at room temperature, so that large anisotropic thermal displacements factors of the C60 carbon atoms were found. The thermal displacement parameters for some of the C60 carbon atoms at room temperature are in fact so large that the C60 atomic coordinates may well represent only an average over one or more disordered structures involving fractional atomic occupancy. On the other hand, the TDAE N and C atomic coordinates are well defined already at room temperature. At 80 K the C60 center to center distance along the c-axis decreases to 9.87 Å and the C60 atomic coordinates are much better defined than at room temperature. At the time of writing no systematic structural analysis has yet been performed on the different modifications (ferromagnetic α or non-ferromagnetic α ) of the material, nor has there been any extensive temperature dependence structural study either at low temperatures or high temperatures.

Fig. 3. Schematic unit cell of TDAE-C60 consisting of two subcells which are stacked along the c-direction. The arrows indicate the small shifts of the TDAE molecules in the unit cell along the b-direction.

4.2 Synthesis and Structure

127

Table 1. Atomic coordinates of TDAE-C60 and isotropic displacement factors. The atoms assigned with a ‘prime’ belong to the TDAE molecule while the others form the C60 molecule. x/a C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14) C(15) C(16) C(17) C(18) C(19) C(20) C(21) C(22) C(23) C(24) C(25) C(26) C(27) C(28) C(29) C(30) N(1() N(2() C(1() C(2() C(3() C(4() C(5()

0.5596 0.5578 0.4752 0.4149 0.4827 0.6258 0.6136 0.4355 0.3441 0.4657 0.5326 0.6210 0.6909 0.6793 0.5851 0.4993 0.3524 0.3310 0.3297 0.3846 0.4048 0.4912 0.6444 0.7103 0.6918 0.6332 0.4613 0.3756 0.2863 0.2953 0.4373 0.5761 0.5033 0.3764 0.4164 0.6092 0.6292

y/b

z/c

0.0996 −0.0432 −0.0589 0.0620 0.104 0.1123 −0.0852 −0.1312 0.0309 0.1992 0.2466 0.1919 0.042 −0.0362 −0.1849 −0.2101 −0.1402 −0.0606 0.1245 0.2018 0.2467 0.2714 0.2029 0.0767 −0.1221 −0.2021 −0.2515 −0.2149 −0.0439 0.0929 0.4688 0.5340 0.5022 0.3927 0.5174 0.4815 0.6145

0.1572 0.1689 0.1684 0.1520 0.1598 0.1310 0.1456 0.1404 0.1169 0.1132 0.0673 0.0778 0.0946 0.1037 0.1139 0.1119 0.0861 0.0979 0.0693 0.0669 −0.000 0.0007 0.0287 0.0331 0.0488 0.0584 0.0563 0.0379 0.0253 0.0155 0.6727 0.6869 0.7148 0.6970 0.6067 0.6286 0.7211

U 0.166 0.171 0.148 0.150 0.197 0.118 0.145 0.130 0.123 0.127 0.106 0.266 0.229 0.199 0.088 0.092 0.175 0.217 0.194 0.109 0.070 0.062 0.166 0.124 0.098 0.087 0.075 0.092 0.138 0.142 0.0535 0.0584 0.0452 0.058 0.068 0.076 0.077

128


4.3

The Electronic Structure

Ferromagnetism in insulators is very rare, and there are not very many examples known. One would therefore expect that TDAE-C60 may also be an itinerant ferromagnet, as the discoverers originally thought [1]. However, very soon after the discovery of the material it was found from the powder infrared absorption spectra that the TDAE-C60 shows no Drude tail and exhibits no absorption at low frequencies [12]. Subsequent careful infrared work by Degiorgi et al. [13] confirmed this finding and confirmed that material is most probably an insulator. Microwave absorption measurements [14] also appeared to confirm the insulating behavior of the powder and the issue was finally unambiguously settled by DC and AC conductivity measurements on single crystals of TDAE-C60 as a function of temperature [15] , when direct electrical contacts on TDAE-C60 single crystals became possible. For the measurements the two-contact method was used, as the millimeter-size samples have resistances of ∼100 k at room temperature, much higher than the gold contacts used to attach wires on the samples. The DC conductivity as a function of temperature is shown in Fig. 4. It has an activated temperature dependence: σDC = σ0 exp(−E a /kB T )

(1)

with two activation energies E a = 0.34 for T > T0 , and E a = 0.14 for T < T0 , where T0 = 150 K is the temperature below which rotations of the C60 molecules start to slow down [36]. Below 100 K the conductance become unmeasurable and there are no evidence of a re-entrant rise of conductivity down to 4.2 K.

Fig. 4. The activated temperature dependence of DC conductivity of TDAE-C60 plotted as log σ against 1/T .

4.3 The Electronic Structure

129

Fig. 5. (a) The conductance as a function of frequency in TDAE-C60 for a number of different temperatures. (b) The frequency-dependent part of the conductance for different temperatures as a function of frequency (the DC part G 0 has been subtracted).

The frequency dependence of conductivity at several different temperatures is show in Fig. 5a. It shows a clear crossover from the frequency-independent behavior at low frequencies to a power-law dependence at higher frequencies. When the frequency-independent DC part of the conductivity is subtracted from the total conductivity only the frequency-dependent part remains with a power-law frequency dependence (Fig. 3b) σAC = Bωs

(2)

with an exponent s ≈ 1. The total conductivity can be expressed as a sum of two components: a temperature-dependent and frequency independent DC conductivity and a temperature-independent and frequency-dependent AC conductivity σ (T, ω) = σDC (T ) + σAC (ω)

(3)

where σDC and σAC are given by eq. (1) and eq. (2), respectively. The model proposed for the mechanism of electrical transport in TDAE-C60 is the following: since no real energy gap of order 0.2 eV was observed in the IR measurements, the Mott–Hubbard insulating state is ruled out and there must be another reason for the activated behavior of the conductivity. Because of the strong coupling of electrons to phonons on the C60 molecule, an electron, when added to the neutral molecule, gives rise to a relaxation of the equatorial bond conjugation

130


and reduction in energy by E b ≈ 0.1 eV [16]. Thus each electron on C60 should be considered as a small polaron confined to the C60 molecule, and we should expect classic thermally activated phonon-assisted conductivity: σ ≈ ω exp(−E b /kB T )

(4)

where E b is the polaron binding energy and ω should signify the rate of rotation of the molecule. The AC part of the conductivity can be described by intermolecular tunneling which is temperature independent. The orientational disorder in the system causes a power-law frequency dependence for the tunneling (the behavior usually observed in random systems). In summary, the macroscopic conductivity of TDAEC60 is determined by the intermolecular hopping where there is a crossover between two conductivity regimes: a low-frequency temperature-dependent phonon-assisted hopping and a high-frequency temperature-independent tunneling.

4.4 4.4.1

The Magnetic Properties The Bulk Magnetic Properties

By measuring magnetic susceptibility χ and magnetization M we get information about the nature of macroscopic magnetic state of a sample. The methods for measuring the bulk magnetic properties are roughly divided into static and dynamic ones. With static methods we measure the bulk magnetic moment of a sample in some static external field. Dynamic methods, such as AC susceptibility measurements, give information about how a sample’s magnetic moment responds to a time-varying field and is the ideal choice for measuring magnetic susceptibility. With these methods the ferromagnetic transition in α-TDAE-C60 has been directly and reliably proven [17]. In Fig. 6 we see the temperature-dependence of the real and the imaginary part of the AC susceptibility for two α-TDAE-C60 samples: a powder (left) and a single crystal (right). Considering single crystals first, a steep rise of the real part of the susceptibility and a peak in the imaginary part at 16 K indicate a ferromagnetic transition. Below TC = 16 K, the real part saturates because the measured susceptibility χ0 is not equal to intrinsic susceptibility of the material (0. They are connected by relationship: χ = χ0 /(1 + Dχ0 )

(5)

where D is the demagnetization factor, which depends only on a geometry of the sample. When χ0 diverges at ferromagnetic transition, χ saturates at value 1/D and remains at that value as long as Dχ0 1. A slight decrease in the real part of the susceptibility below 10 K is related to the hump in the imaginary part, and is due to additional phenomena observed in single crystals of α-TDAE-C60 , namely a reentrant spin glass transition [18].

4.4 The Magnetic Properties

131

Fig. 6. The real and the imaginary parts of the AC susceptibility as a function of temperature for a powder (left) and a single crystal (right) of α-TDAE-C60 .

All the features that are sharply visible in the AC susceptibility of the single crystal are smeared for the powder sample. This is mainly because of very poor homogeneity and large surface area of the nano-size crystallites in the powder sample. The temperature and the field dependence of magnetization of α-TDAE-C60 are shown in Fig. 7. The behavior of the magnetization measured in a low magnetic field are characteristic for the order parameter of the second-order phase transition. It is equal to zero above the transition temperature TC , and continuously rises below TC . The field dependence of the magnetization in the ferromagnetic phase is also characteristic of a ferromagnet: a very sharp increase with a saturation in quite low field H < 50 Oe. Although strongly non-linear, the magnetization curve shows no significant hysteresis (although some authors claim to have observed a hysteresis loop a few Oersteds wide [19]). The bulk magnetic properties of the metastable α -TDAE-C60 phase are quite different from those for the α modification. There is no sign of any ferromagnetic transition down to 2 K. The system behaves as a paramagnet. The AC susceptibility of α -TDAE-C60 crystals is shown on the left of Fig. 8. χAC is very small, corresponding to the Curie susceptibility χ = C/T of non-interacting spins (the solid line in Fig. 8). The hump below 16 K is due to a small part of the sample which has already transformed into the α modification. The paramagnetic nature of α -TDAE-C60 becomes more obvious in the static magnetization measurements. The magnetization

132


Fig. 7. The temperature-dependence of the magnetization of α-TDAE-C60 measured in a magnetic field 10 Oe (left) and the magnetization curve of α-TDAE-C60 measured in fields −100 Oe < H < 100 Oe at 2 K.

is linearly related to the magnetic field M = χ H and also obeys the Curie law (right panel of Fig. 8). When M −1 is plotted against temperature it clearly extrapolates to zero (insert). The field-dependence of magnetization is also typically paramagnetic (left of Fig. 9). It fits extremely well to the theoretical Brillouin formula for a system of non-interacting magnetic moments: M = N µ tanh(µH /kB T )

(6)

where N is the number of spins in the system, µ the magnetic moment, H is the magnetic field, kB the Boltzmann constant, and T the temperature. It is surprising to find that N corresponds to one spin per pair of ions TDAE+ -C− 60 . One would expect that both ions posses one unpaired spin but this is not the case. Following the effective number of spins up to 100 K reveals a gradual increase of the effective spin number. The same happens also in the ferromagnetic α modification (Fig. 9. (right)). As mentioned before, the α -TDAE-C60 is the metastable modification of TDAEC60 . It irreversibly transforms into the α -TDAE-C60 . These transformation can be followed by measuring the magnetization of α -TDAE-C60 after several cycles of annealing at temperatures slightly above room temperature which speeds up the transformation [20]. The transformation is not gradual as can be seen in Fig. 10. The first annealing cycle doesn’t increase the magnetization much, but the second cycle causes an abrupt change for more then two orders of magnitude. After the third


133

Fig. 8. The real (black) and the imaginary (white) part of the AC susceptibility (left) and the magnetization in a static magnetic field of 100 Oe (right) of α -TDAE-C60 as a function of temperature. The insert shows the inverse magnetization which extrapolates to zero as T → 0.

Fig. 9. The field dependence of magnetization of α -TDAE-C60 at 2 K. The solid line is the theoretical Brillouin function (left). The effective number of spins per formula unit as a function of temperature (right).

134


Fig. 10. The temperature dependence of magnetization after different numbers of annealing cycles of ((-TDAE-C60 .

cycle the magnetization is already saturated. Further annealing slowly damages the sample and it’s magnetization gradually falls again. It is important to note that the ferromagnetic transition temperature always stays at 16 K in all stages between α TDAE-C60 and α-TDAE-C60 .

4.4.2

The Spin-glass Behavior of α -TDAE-C60

In the early stage of research on the nature of magnetic ordering in TDAE-C60 , some experimental results appeared to be in contradiction with the hypothesis of a long-range ferromagnetic ordering in TDAE-C60 . In the first place, the temperature dependence of the ESR linewidth [21] showed a relatively small line broadening and no frequency shift with a non-exponential and very slow decay of the magnetization [22]. Both of these features are characteristic of random magnetic systems without a long range ordering, and naturally, it was suggested that TDAE-C60 could be a spin-glass. After a firm experimental establishment of a direct connection between orientational degrees of freedom of C60 molecules and magnetic interactions in the system [23], this hypothesis seemed to be even more plausible (these connection was later demonstrated also by theoretical calculations [24]). By freezing C60 molecules in random orientations one can obtain a distribution of exchange interactions in the system, and consequently, magnetic disorder and frustration – two essential conditions for a spin-glass. Later measurements of linear and non-linear susceptibility partly confirmed the spin-glass hypothesis [25]. The linear susceptibility χ1 exhibit a broad peak centered at 10 K and the non-linear susceptibilities χ3 and χ5 diverge at


135

the same temperature. The only feature which deviated from the spin-glass behavior was the absence of any shift of the peak position at the temperature axis with frequency, which is so characteristic for spin glasses. Obviously, TDAE-C60 possesses some characteristics of spin-glasses and some of ferromagnets and it is not impossible that both phases coexist together. This idea was shown to be essentially correct by latest measurements on single crystals of α-TDAE-C60 , where it was conclusively shown that the ferromagnetic transition at 16 K is followed by a reentrant spin-glass transition at 7 K.

4.4.3

Electron-spin Resonance

As already indicated in the previous section, electron spin resonance (ESR) is a very valuable experimental tool for the investigation of magnetic properties of materials. In the first place, with ESR we can determine the static spin susceptibility by integrating the ESR absorption spectra (the static spin susceptibility χs is directly proportional to the absorption integral). Also, with ESR we can detect very weak magnetic signals, undetectable with macroscopic techniques. From the shape and the width of the ESR absorption spectra we can get additional information about spin dynamics and eventual presence of internal fields. In Fig. 11 we can see a shape of an ESR spectrum of α-TDAE-C60 in the ferromagnetic phase which develops at temperatures below the ferromagnetic transition temperature TC = 16 K. The overall width of 80 Gauss and a complicated structure indicate the presence of internal magnetic fields due to a complex distribution of magnetic domains and shape anisotropy.

Fig. 11. The shape of ESR spectrum of α-TDAE-C60 in the ferromagnetic phase.

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Fig. 12. Temperature-dependence of the low-temperature spin susceptibility (ESR integrated intensity) for different annealing temperatures.

The ESR linewidth can be correlated with a µSR measurement which shows the existence of internal magnetic fields of similar magnitude [26]. In the powder samples we cannot observe sharp features in the spectra, and only inhomogeneous line broadening is observed below TC . The ESR technique was used for tracing the transformation from the metastable, non-ferromagnetic α modification to the stable, ferromagnetic α modification of TDAE-C60 [20]. The low-temperature spin susceptibility χs rises with the annealing temperature until 110◦ C, when the sample starts to polymerise. From the plots in Fig. 12, we can see that ferromagnetic correlations start to become significant even at temperatures much higher than TC . This effect can be attributed to the applied magnetic field of 3.4 kGauss used in the X-band ESR measurement. The ESR line-width in the paramagnetic phase gives us information about relaxation processes in the system. For TDAE-C60 , an anomaly in the temperature dependence of the linewidth centered at T0 = 160 K is characteristic (Fig. 13). The sharp decrease of the linewidth is related to slowing of rotational motion of C60 molecules which is a gradual process, but appears sharp when viewed at the ESR time-scale (10−10 s). It is interesting to note that T0 slightly shifts towards lower temperatures when a sample transforms from α to α modification. It seems that C60 molecules have more room to rotate in the ferromagnetic α modification.


137

Fig. 13. The ESR linewidth as a function of temperature for different annealing temperatures.

4.4.4

Ferromagnetic Resonance

Magnetic resonance in the magnetically ordered phase is different with respect to the ordinary electron spin resonance in the sense that one cannot deal with only one electron separate from the all the rest due to the presence of the large exchange fields between electronic spins. Instead of the usual ESR signal in the magnetically ordered phase, a coherent precession of all the electronic spins, i. e. the precession of the entire magnetization of the sample, can be excited. The relation between the resonance frequency and resonance field becomes strongly non-linear [27a] and it strongly depends on the type of the ordering [27b]. While in simple uniaxial ferromagnets only one resonance mode is predicted, in antiferromagnets and weak ferromagnets two resonance modes should be found. Here it is interesting to compare uniaxial ferromagnets and weak ferromagnets. In both when the external magnetic field is perpendicular to the easy axis one finds a resonance mode with a dip in the resonance field-resonance frequency relation at a resonance field equal to the anisotropy field. But in weak ferromagnets a high frequency antiferromagnetic type mode is present as well. The magnetic resonance in spin-glasses is very complicated and strongly depends on the thermal history like for instance that the line position for field-cooled samples when the measured field is applied parallel with respect to the case when the measured field is applied anti-parallel to the cooling field is different due to the hysteresis effects. In many ways superparamagnets behave similar to normal paramagnets and the resonance position of the observed lines depends linearly on the resonance frequency. So the (anti)ferromagnetic resonance technique is extremely sensitive technique for the determination of the ground state and microscopic parameters.

138


4.4.4.1

Ferromagnetic Resonance in TDAE-C60

Magnetic resonance experiments on TDAE-C60 single crystals were performed in a wide frequency range between 30 MHz and 245 GHz. High-frequency experiments in the microwave region (1.2 GHz, L-band; 9.6 GHz, X -band; 94 GHz, W -band; and 245 GHz) at T = 5 K < TC and a||H showed a single resonance line with some inner structure [28, 29]. It should be noted in the 245 GHz experiment no additional lines in were observed anywhere between 0 and 10 T. The same observation holds also for the X -band and L-band experiments where the largest sweep field was between 0 and 10 kGauss. The resonant frequency is linearly dependent on the resonant field in the microwave region, so no definite conclusion can be made on the basis of these experiments. Much more interesting behavior is found in the radio-frequency region. Above 110 MHz there is still only one resonant line. Below 110 MHz a new line emerges at zero field which shifts to higher resonant fields with decreasing resonant frequency. The two resonant lines merge together below 50 MHz. The dependence of the resonant frequency on the resonant field is strongly non-linear in the low frequency region (Fig. 14). A dip in the resonance frequency-resonance field relation is predicted for uniaxial ferromagnets as well as for weak ferromagnets. Since we have not observed any other resonant modes – which should be found in weak ferromagnet – at higher frequencies as well as in the experiments where the high frequency magnetic field was parallel to the external magnetic field we have to rule out the possibility of weak ferromagnetism. The strongly non-linear behavior (Fig. 14) also eliminates any possibility of a superparamagnetic state in TDAE-C60 single crystals and we conclude from the ferromagnetic resonance that the magnetic state is that of a normal Heisenberg ferromagnet. Agreement between theory and experiment becomes quantitative, if one takes into account also the demagnetizing field effects. For the anisotropy field the obtained values are HK = 29 Gauss and for the demagnetizing field Hdem = −39 Gauss. A non-linear dependence of the resonance field-resonance frequency relation disappears above the transition temperature in the paramagnetic phase (Fig. 14b). To conclude this section we would like to stress again that the resonant frequencyresonant field relation of the magnetic resonance signal observed below TC confirms

Fig. 14. Resonant frequency-resonant field-dependence in TDAE-C60 single crystal at (a) T = 5 K and a||H , and (b) T = 20 K and a||H .


139

the presence of long range magnetically ordered state below TC = 16 K. The presence of a dip in the resonant frequency-resonant field relation at H = 31 Gauss at T = 5 K and a||H , as well as the existence of a zero-field gap at 110 MHz, seem to show that TDAE-C60 single crystals below TC = 16 K described in this work were essentially Heisenberg ferromagnets. The anisotropy field appears to be rather small, which is not so unusual for a purely organic compound. Nevertheless the fact that the linewidth of the observed resonances is comparable to the shifts suggests that the distribution of the local fields is rather large and the possibility of the coexistence of a long range ferromagnetic order and short range spin-glass effects can therefore not be excluded. 4.4.4.2

Nuclear Magnetic Resonance of Powdered and Single-crystal TDAE-C60

NMR in TDAE-C60 In TDAE-C60 there are two suitable NMR probes: 1 H from the methyl groups of the TDAE molecule and 13 C mainly from the C60 and partially from the TDAE molecule. The problem with 13 C NMR is, that 13 C isotope occurs in a very small natural abundance, r = 1.108%, which makes experiments in TDAE-C60 single crystals difficult. On the other hand, the 1 H NMR probe is extremely sensitive and even experiments on 1–2 mg samples can be performed. Further, the 13 C and 1 H probes also differ in one very important aspect. While 13 C atoms are mainly on the C molecule so that their 2 p orbital contribute to the z 60 molecular t1u orbital filled with one accepted electronic spin, 1 H NMR probes come exclusively from the TDAE methyl groups, and we shall see, their different position in the crystal has some important consequences. 4.4.4.3

1 H NMR

in Powdered TDAE-C60

In powdered samples the transformation from non-magnetic α modification to ferromagnetic α modification occurs rapidly [30] even at room temperature and by the time one prepares the experiment the sample is already transformed. That is the reason why we focus in this subsection only to a well annealed powdered TDAE-C60 samples. In powdered TDAE-C60 at room temperature at a Larmor frequency ωL /2π = 270 MHz two proton NMR lines are observed [31], designated as A and B lines (Fig. 15). They are of nearly equal intensity (Fig. 15) and at room temperature they are separated by 42 kHz. The temperature dependence of the two lines is very different. The position of the A-line is nearly T -independent whereas the position of the Bline (Fig. 16) follows a Curie–Weiss law with a negative Curie temperature down to around 50 K. This means that those protons, which contribute to the B-line are close to the C60 spins and due to the hyperfine contact interaction B-line exhibit a paramagnetic shift δν. On the other hand the protons which contribute to the A-line, seem to be in a position where some sort of spin cancellation mechanism causes zero electron spin density. A trivial explanation could be that roughly half of the sample was destroyed during the sample preparation due to the high air sensitivity of the powdered TDAE-C60 samples, but additional ESR measurements disagreed with

140


Fig. 15. The temperature evolution of the 1 H NMR lines in a well annealed powdered TDAEC60 sample.

Fig. 16. The temperature-dependence of the paramagnetic shifts of the 1 H NMR A and B lines in well annealed powdered TDAE-C60 sample.


141

such a large proportion of the decomposition of the sample. Thus we believe that both line are intrinsic. They could reflect the incomplete transformation from α to α modification or two different 1 H protons of the same TDAE molecule. 4.4.4.4

1 H NMR

in TDAE-C60 Single Crystals

The transformation between the two modifications is in TDAE-C60 single crystals is much slower than in powdered samples and this fact has enabled the study of the individual properties of the ferromagnetic [32] and non-magnetic modifications respectively as well as the difference between the two modifications [33]. It was shown in the previous subsection that in powder samples the intensities of the “non-magnetic” and “magnetic” methyl proton A and B lines are nearly equal at room temperature. Approximately the same is true for well-annealed single crystal samples, which show a ferromagnetic transition. On the other hand in the nonmagnetic α samples, at room temperature the intensity of the “magnetic” line B (i. e. the line which shows a paramagnetic frequency shift following a Curie–Weiss law) is much weaker than the intensity of the “non-magnetic” A line. With temperature cycling between 200 K and 330 K one can change the relative intensities of the two lines [34]. This most probably reflects the annealing process that changes single crystals from the non-magnetic to ferromagnetic type. With decreasing temperature both the A and B lines broaden and the linewidth of the B line increases to 25 kHz at 170 K. This is the temperature range where the 13 C NMR rotational motion of the C− 60 ions freezes out as we shall see from the experiment. The protons are thus also sensitive to orientational ordering of the C− 60 ions through the coupling of the methyl protons with the unpaired electron at the C60 site. At 50 K the half-width of the B line is already about 250 kHz. Below TC , in ferromagnetic α type samples, the proton NMR spectra are several MHz broad (Fig. 17), and the ferromagnetic B-line is shifted with respect to the

Fig. 17. 1 H NMR spectra of TDAE-C60 single crystal at some representative temperatures.

142


non-magnetic A line. However as already noted in the powdered samples, the ferromagnetic B-line slowly disappeared and the intensity of the non-magnetic A-line increases. The disappearance of the B-line indicates that at low temperatures the responsible mechanism for spin-cancellation is most probably spin-pairing in agreement with the magnetization measurements and AC susceptibility. The non-magnetic A-line also approaches a double peaked line-shape at T = 5 K which is in agreement with the spin-pairing mechanism into singlet-like state. If the ground state of the non-magnetic A-line is of a density wave (either spin or charge density wave) the amplitude of the density wave should be very small, since the shifts of the two peaks of the A-line are rather small as compared with the shift of the magnetic B-line. In the non-magnetic α modification the TDAE proton NMR spectra, on the other hand, exhibit just one proton line. The observed 1 H NMR lines are narrower [34] and the position of this line is close to the proton Larmor frequency and thus coincides with the position of the A line of the modification α. Its position does not change with decreasing temperature even down to 4 K. In spite of an extensive search with a field swept (± 1000 G) superconducting magnet we were unable to find any other, more shifted B-type proton line in the modification α . More information about the dynamics of the local magnetic fields in the α modification of TDAE-C60 below 10 K can be obtained from the proton spin-lattice relaxation time T1 . The temperature dependence of the proton spin-lattice relaxation time T1 of the methyl protons of TDAE-C60 crystals of modification α is shown in Fig. 18. The proton spin–lattice relaxation rate is practically temperature independent between room temperature and 20 K. Between 20 K and 10 K the relaxation rate slowly increases with decreasing temperature whereas a dramatic decrease of the relaxation rate occurs below 10 K and the behavior is of the activated type. It was noticed that the temperature dependence of the proton T1 in modification α is somewhat similar to the temperature dependence of the T1 in mesoscopic size magnetic systems like iron clusters [35] Fe8 with a S = 0 ground state which is separated with a gap from the lowest excited S = 1 triplet state. In an attempt to describe the observed proton spin-lattice relaxation rate T1−1 quantitatively it was assumed that the ground state is a singlet state with S = 0 and that T1−1 has contributions

Fig. 18. The temperature-dependence of the 1 H spin-lattice relaxation rate of the α modification methyl proton line.


143

proportional to the probability of occupation of the excited spin energy levels; the dominant contribution being from the first excited triplet state (total spin S = 1). Using such a model a value for the singlet–triplet gap was found to be E T = 19.1 K [33]. The large methyl proton shifts of the A-line in the ferromagnetic α modification + are evidently due to hyperfine contact interactions. The C− 60 ions and the TDAE ions are thus indeed strongly exchange coupled. A part of the exchange coupling between the C− 60 ions is thus of indirect nature and takes place via the intermediate TDAE+ group. However the presence of non-shifted B-line and its temperature dependence suggests that the mechanism responsible for a spin-cancellation is some kind of pairing of spins into singlet-like ground state. On the basis of 1 H NMR one cannot exclude the possibility that we have a dimerized spin-Peierls or some sort of density wave (spin or charge) ground state. 4.4.4.5

13 C NMR

of Powdered TDAE-C60

As already mentioned, the small size of the TDAE-C60 single crystals and low natural abundance of the 13 C isotope has prevented measurements of 13 C NMR of single crystals. We thus present the results obtained on the well annealed powdered samples. The main difference between the 1 H and 13 C NMR in TDAE-C60 is the much smaller contact hyperfine interaction in the later case. This is most clearly seen when one compares the 1 H and 13 C shifts. The extremely large values of the TDAE methyl proton NMR shifts of the A-line which amount to 9000 ppm are much bigger than 13 C NMR shift of 188 ppm with respect to TMS [36]. The the relatively small C− 60 obvious explanation is that the unpaired electron spin density is non-zero at the methyl proton sites whereas at the 13 C sites the electron spin density is strongly reduced due to the fact that the unpaired electron orbital at the C− 60 ions is mainly of π-character. This has dramatic consequences in the second moment of the 13 C NMR line as well as in the spin-lattice relaxation time which are both determined by the dipolar interaction with the unpaired electron. In view of the low natural abundance of the 13 C nuclei and the fact that there are nearly ten times less TDAE than C60 carbons, the observed 13 C spectra can be 13 safely assigned to the C− 60 ions. This is also confirmed by the observed C NMR lineshift with respect to TMS which amounts at room temperature to 188 ppm. It agrees rather well with the value of 185 ppm observed for the electrochemically prepared 13 C− 60 in solution. Comparing the shifts of the C NMR lines with respect to TMS we notice that the shifts of pure C60 , C70 as well as K6 C− 60 which are all insulating with a completely filled highest occupied molecular orbital-are in the same range between 132 and 155 ppm. However, the shift of the 13 C NMR line in Rb3 C60 is very close (182 ppm) to the one observed in TDAE-C60 (188 ppm). Both compounds have in common that they have only a partially filled lowest unoccupied molecular orbital. Since in K6 C60 the t1u orbital is completely filled, the shift (12 ppm) of the line with respect to the C60 is entirely due to the chemical shift of the additional 6 electrons. We can thus estimate the contribution of each added electron in the t1u orbital to the chemical shift to be ∼2 ppm. The rest of the observed shift 43 ppm in TDAE-C60 with respect to the pure C60 is therefore due to the Knight shift – i. e. due to a non-zero

144


Fig. 19. Temperature-dependence of the second moment of the 13 C NMR line in powdered TDAE-C60 .

spin-density at the 13 C site. The non-zero spin-density at the carbon sites is a result of the curved surface of the C60 molecule. The temperature dependence of the second moment of the 13 C spectra is shown in Fig. 19. The 13 C spectra are clearly motionally narrowed by the nearly isotropic rotation of the C− 60 ion above 170 K. The spectral shape, which is Lorentzian, does not change between room temperature and 170 K. The second moment M2 amounts here to less than 1 kHz2 . Between 150 K and 70 K a 13 C linewidth transition takes place due to a freezing out of the C− 60 “isotropic” rotation on the NMR time scale. The second moment M2 increases to 160 kHz2 . The analysis [36] of the temperature dependence of the 13 C NMR linewidth transition led us to the activation energy for the C− 60 reorientation to be E a ≈ 130 meV. The 13 C NMR data summarized above demonstrate the nearly isotropic rotation of the C− 60 ions above 150 K and the existence of the orientational ordering transition between 150 K and 100 K. The question whether the resulting orientational order of the C− 60 ions is perfect, or whether there is some residual static orientational disorder at low temperatures cannot be answered by the 13 C powder line-shape data. 13 C spin-lattice relaxation data on the other hand seem to demonstrate the existence of residual disorder. The recovery of the 13 C spin magnetization after 180◦ –t–90◦ pulse sequence is definitely non-exponential due to a distribution of spin-lattice relaxation times. The stretch exponential behavior reflects either the presence of the orientational disorder of C60 molecules or the distribution of local magnetic fields which is characteristic for inhomogeneous ferromagnets or spin-glasses.

4.5

Conclusion

The macroscopic measurements presented thus far give a self-consistent picture of the electronic and magnetic properties of TDAE-C60 . All the data point towards a low-temperature insulating Heisenberg-like ferromagnetic state with low anisotropy, low magnetization (∼10 Gauss) and very small hysteresis (if any).

References

145

On the other hand, relatively little is known about the microscopic nature of the magnetic interactions leading to its rather remarkable properties. For example, the magnetic measurements appear to show that there is an interplay between the ferromagnetic long-range order and short-range glass-like behavior. Although it appears to be reasonably clear that this somehow arises from orientational disorder of the C60 molecules, until a full structural study is completed at low temperatures in both the α and α phases in correlation with the magnetic properties, the microscopic details will not be understood. It is also appears to clear by now that the ferromagnetic interactions arise between the fullerenes, and that the spins on the donor TDAE appear to be less important in relation to the low-temperature ferromagnetic state than originally thought. Since non-TDAE fullerene ferromagnets have been discovered, whose properties are virtually identical [6], we can conclude that TDAE is not essential for the positive effective exchange interaction between the fullerenes in this material. However, there are some indications that there might be structural effects due to the peculiar molecular structure of the TDAE donor, which might play a role in determining the rotational degrees of freedom of the C60 molecules. It was shown by molecular orbital calculations that the TDAE in the +1 state appears to have a nearly degenerate configurational ground state [37], and infrared measurements [37] seem to show strong non-harmonic behavior which could be considered as good evidence for the existence of such a near-degenerate ground state of the donor. Curiously, the temperature ∼130 K where C60 molecules start to slow down their rotation and where the TDAE spins start to pair up [33] appears to be close to the temperature where the non-harmonic effects start to be visible in the optical spectra [37]. It remains to be shown how much of this is coincidental, or in fact these observations are connected in some way. As already mentioned, apart from TDAE-C60 there exist a number of similar compounds with different donors exhibiting a low-temperature ferromagnetic ground state [6]. The fact that the Curie temperatures of these new compounds is very similar suggests that the fullerene ferromagnetic materials may be limited to temperatures below 20 K. However, until we understand the microscopic origin of the ferromagnetic exchange interaction in these materials, it is perilous to make predictions about the TC values of future fullerene charge-transfer compounds.

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4 Magnetism in TDAE-C60 Muller, ¨ R. K. Eick, S. M. Zahurak, R. Tycko, G. Dabbagh, F. A. Thiel, Nature (London) 1991, 350, 320–322. P. W. Stephens, D. Cox, J. W. Lauher, L. Mihaly, J. B. Wiley, P. M. Allemand, A. Hirsch, K. Holczer, Q. Li, J. D. Thompson, F. Wudl, Nature (London) 1991, 355, 331–332. A. Mrzel, A. Omerzu, P. Umek, D. Mihailovic, Z. Jaglicic, Z. Trontelj, Chem. Phys. Lett., 1998, 298, 329–333. K. Tanaka, A. A. Zakhidov, K. Yoshizawa K. Okahara, T. Yamabe, K. Yakushi, K. Kikuchi, S. Suzuki, I. Ikemoto, Y. Achiba, Phys. Rev. B 1993, 47, 7554–7559. (a) H. Klos, I. Rystau, W. Schutz, ¨ B. Gotschy, A. Skiebe, A. Hirsch, Chem. Phys. Lett. 1994, 224, 333–336; (b) A. Otsuka, T. Teramoto, Y. Sugita, T. Ban, G. Saito Synth. Met., 1995, 70, 1423–1424. Y. Li, D. Zhang, F. Bai, D. Zhu, B. Yin, J. W. Li, Z, Zhao, Solid State Commun. 1993, 86, 475–457. (a) H. Anzai, J. Cryst. Growth 1975, 33, 185–187; (b) M. L. Kaplan, ibid., 161–164. L. Golic, R. Blinc, P. Cevc, D. Arcon, D. Mihailovic, A. Omerzu, P. Venturini in Fullurenes and Fullerene Nanostructures (Eds. H. Kuzmany, J. Fink, M. Mehring, S. Roth), World Scientific, Singapore, 1996, p.p. 531–534. D. Mihailovic, P. Venturini, A. Hassanien, J. Gasperic, K. Lutar, S. Milicev in Progress in Fullerene Research (Eds. H. Kuzmany, J. Fink, M. Mehring, S. Roth), World Scientific, Singapore, 1994, p.p. 275–278. F. Bommeli, L. Degiorgi, P. Wachter, D. Mihailovic, A. Hassanien, P. Venturini, M. Schreiber, F. Diedrich, Phys. Rev B 1995, 51, 1366–1369. A. Schilder, H. Klos, I. Rystau, W. Schutz, ¨ B. Gotschy, Phys. Rev. Lett. 1994, 73, 1299– 1302. A. Omerzu, D. Mihailovic, N. Biskup, O. Milat in S. Tomic, Phys. Rev Lett. 1996, 77, 2045–2048. K. Harrigaya, J. Phys. Soc. Jpn. 1991, 60, 4001–4004. A. Suzuki, T. Suzuki, R. J. Whitehead, Y. Maruyama, Chem. Phys. Lett. 1994, 223, 517– 520. A. Omerzu, D. Mijatovic, D. Mihailovic, to be published. L. Dunsch, D. Eckert, J. Frohner, A. Bartel, K.-H. Muller, J. Appl. Phys. 1997, 81, 4611– 4613. A. Mrzel, P. Cevc, A. Omerzu, D. Mihailovic, Phys. Rev B 1996, 53, R2922–2925. P. Venturini, D. Mihailovic, R. Blinc, P. Cevc, J. Dolinsek, D. Abramic, B. Zalar, H. Oshio, P.-M. Allemand, A. Hirsch, F. Wudl, Int. J. Mod. Phys. B 1992, 6, 3947–3951. R. Blinc, P. Cevc, D. Arcon, D. Mihailovic, P. Venturini, Phys. Rev. B 1994, 50, 1–3. D. Mihailovic, D. Arcon, P. Venturini, R. Blinc, A. Omerzu, P. Cevc, Science 1995, 268, 400–402. T. Sato, T. Saito, T. Yamabe, K. Tanaka, Phys. Rev. B 1997, 55, 11052–11055. K. Tanaka, T. Sato, K. Yoshizawa, K. Okahara, T. Yamabe, M. Tokumoto, Chem. Phys. Lett. 1955, 237, 123–126. A. Lappas, K. Prassides, K. Vavekis, D. Arcon, R. Blinc, P. Cevc, A. Amato, R. Feyerhen, F. N. Gygax, A. Schenck, Science 1995, 267, 1799–1802. (a) S.V. Vonsovskii, Ferromagnetic Resonance, Pergamon Press, Oxford, 1966. (b) D. Arcon, R. Blinc, A. Omerzu, Molecular Physics Reports 1997, 18/19, 89–97. R. Blinc, K. Pokhodnia, P. Cevc, D. Arcon, A. Omerzu, D. Mihailovic, P. Venturini, L. Golic, Z. Trontelj, J. Luunik, ˆ J. Pirnat, Phys. Rev. Lett. 1996, 76, 523–527. R. Blinc, P. Cevc, D. Arcon, A. Omerzu, M. Mehring, S. Knorr, A. Grupp, A.-L. Barra, G. Chouteau, Phys. Rev. B 1998, 58, 14416–14423. D. Arcon, R. Blinc, P. Cevc, T. Jesenko, Europhys. Lett. 1996, 35, 469–472.

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5

Triarylmethyl and Amine Radicals R.-J. Bushby

5.1

Introduction

Recent work on high-spin species based on triarylmethyl radical and triarylamine radical cation building blocks has helped us to understand the rules which may ultimately lead to a proper ferromagnetic polymer [1]. Following a short discussion of the chemistry of triarylmethyl radicals and triarylamine radical cations this chapter describes their elaboration into triplet biradical, quartet tetraradical, high-spin oligomeric and ultimately polymeric systems.

5.2

Monoradicals (S = 1/2)

The study of triarylmethyl radicals goes back over 100 years to the very origins of organic free radical chemistry [2]. In 1900, Gomberg reported that, when a solution of triphenylmethyl chloride 1 (Fig. 1) in benzene was reduced with finely divided silver, an intensely yellow solution was obtained which behaved as if it contained the triphenylmethyl radical 2 [3].

Fig. 1. Gomberg’s preparation of triphenylmethyl 2 [3]. Reagents (i) Ag/toluene; (ii) air.

150

5 Triarylmethyl and Amine Radicals

For example, when this solution was exposed to the air it decolorized and when the resultant solution was evaporated the peroxide 4 was isolated. Alternatively, when the yellow solution was evaporated in the absence of air, a radical dimer was obtained. Gomberg incorrectly identified this dimer as hexaphenylethane (arising by coupling of two radicals 2 through their α-positions) and only much later was it shown to have the structure shown in formula 3 and to arise by coupling of the α-position of one radical to the para position of another [4]. The interesting story of how this mistake arose, how it was propagated for so long and how a clear understanding of Gomberg’s work eventually emerged has been reviewed in detail by McBride [5]. We now know that Gomberg’s yellow benzene solution was a mixture containing mainly the dimer 3, which is in dynamic equilibrium with a small percentage of the free radical 2. Simple resonance theory suggests that the free spin in the triphenylmethyl radical 2 will be distributed between the α, ortho and para positions and this is reinforced by HMO calculations which yield spin densities of 4/13 on the α-carbon and 1/13 on each ortho and para site. Higher levels of theory give similar positive spin densities for these sites but also predict a small negative spin density on each alternate carbon. They show that the central carbon is close to being sp2 trigonal/planar and that the benzene rings are twisted out of the plane giving a propeller-like conformation. This twisting out of the plane substantially reduces the repulsion between the phenyl ortho hydrogens whilst only slightly reducing the conjugation between the radical center and the π-orbitals of the benzene rings. For triphenylmethyl in the gas phase the tortional angle is 40–50◦ [6], for tris(para-nitrophenyl)methyl 5 in the crystal it is 30◦ [7] and for the crystalline 1:1 complex of tris(pentachlorophenyl)methyl and benzene the three rings are twisted by 46, 53 and 54◦ (Fig. 2, inset) [8]. In general one expects the introduction of bulky ortho substituents into the radical 2 to increase the tortional angle of the aryl ring, to decrease the degree of conjugation and to enhance the free spin density on the α-carbon. Substituents also profoundly affect the monomerdimer equilibrium and data for relevant compounds is collected in Table 1 [9–14]. Other factors being equal, the two main factors that influence the equilibrium are resonance stabilization of the radical and steric hindrance to dimerization. Hence, increasing the extent of the conjugated system in 2 by introducing para-phenyl substituents increases the degree of dissociation (Table 1, entries 1-4) and para nitro and methoxy groups markedly increase the degree of dissociation (entries 5 and 7). The importance of steric factors is most clearly seen in comparing compounds 6 and 7 (Fig. 3). In tris(2,6-dimethoxyphenyl)methyl 6 the ortho methoxy groups shield the radical from attack both above and below the plane and prevent dimerization. As a result the system is completely dissociated even in the solid state. The sesquixanthydryl 7 is similarly stabilized by ortho oxygens but is forced to be planar. It is much less stable and in this case the equilibrium strongly favors the dimer [13]. The most remarkable example of a stabilized triarylmethyl is that of the deep red perchlorinated radical 5 (Fig. 2). This system is completely dissociated. Also, whereas almost all other triarylmethyl radicals react rapidly with oxygen, the perchlorinated radical 5 is stable in air up to 300◦ C! The large dihedral twist of the phenyl substituents in this system means that the spin is largely localized on the α-carbon but this carbon is completely shielded by three benzenes and six ortho chlorines. Effectively the radical is in a cage [14]. Although 5 is heat and air stable, like most triarylmethyl radicals, it

5.2 Monoradicals (S = 1/2)

151

Fig. 2. Synthesis of tris(pentachlorophenyl)methyl 5 [14]. Reagents (i) BCH; (ii) Bu4 NOH; (iii) para-chloranil. Inset: Geometry of the radical taken from the X-Ray crystal structure of the 1:1 complex with benzene [8]. (Reproduced by permission of the Royal Society of Chemistry).

Fig. 3. Similarly substituted triarylmethyl derivatives but with very different geometries and degrees of steric hindrance [13].

is sensitive to light undergoing a photocyclization to give a 9-phenylfluorenyl derivative [15]. Although many triarylmethyl radicals have been made by reduction of the corresponding halide, the preparation of the perchlorinated radical 5 provides an example of the other main synthetic route: oxidation of the corresponding carbanion.

152


Table 1. Degree of dissociation of triarylmethyl dimers. The degree of dissociation of some of these systems has proved controversial with quite widely divergent figures being quoted in the literature according to which experimental method was employed and even sometimes when two laboratories have used the same experimental method. However, within the present context, the general trends are more important than the absolute values. Except as noted the figures are based on cryoscopic measurements.

a b

Entry

Radical formed

Dissociation of the dimer (%)

Conditions

Ref.

1 2 3 4 5 6

(C6 H4 )3 C• p-C6 H5 C6 H4 (C6 H5 )2 C• ( p-C6 H5 C6 H4 )2 C6 H5 C• ( p-C6 H5 C6 H4 )3 C• ( p-O2 NC6 H4 )3 C• ( p-ButC6 H4 )3 C•

2–3 15 79 100 100 57–79a ca. 100b

[9] [9] [9] [9] [9] [10] [11]

7

( p-CH3 OC6 H4 )3 C•

ca. 100b

8 9 10 11

(o-CH3 OC6 H4 )3 C• Compound 6 (Fig. 3) Compound 7 (Fig. 3) Compound 5 (Fig. 2)

ca. 100b ca. 100 ca. 0 ca. 100

5◦ C, benzene 5◦ C, benzene 5◦ C, benzene 5◦ C, benzene 5◦ C, benzene 0◦ C, toluene −30 to 100◦ C, benzene or toluene −30 to 100◦ C, benzene or toluene 5◦ C, benzene 25◦ C, benzene or ether 150◦ C, methyl benzoate Up to 300◦ C, neat

[11] [12] [13] [13] [14]

Based on magnetic susceptibility. Based on EPR measurements.

The triphenylamine radical cation 9 is also made by a one-electron oxidation; in this case of the corresponding amine 8 (Fig. 4) [16]. It is unstable, irreversibly dimerizing with the loss of two protons to give the benzidine 10. The dimerization process is second order in 9 and so involves a radical cation/radical cation coupling reaction and not the addition of a radical cation to a neutral amine molecule. Rates of dimerization give an indication of the effect of substituents on the stability of triarylamino radical cations and relevant data is presented in Table 2 [17, 18]. As shown, substituent effects mostly parallel those in the triarylmethyl series. Like the triarylmethyls, triarylamine radical cations are stabilized by extending the conjuga-

Fig. 4. Synthesis of the radical cation of triphenylamine 9 [16]. Reagents: (i) – e− ; (ii) – 2H+ .

5.3 Diradicals (S = 1)

153

Table 2. Rates of dimerization of triarylamine radical cations in acetonitrile at room temperature. Entry 1 2 3 4 5 6 7 8

System N+ .

( p-NO2 C6 H4 )(C6 H5 )2 ( p-Et2 NSO2 C6 H4 )3 N+ . (C6 H5 )3 N•+ ( p-But C6 H4 )(C6 H5 )2 N+ . ( p-C6 H5 C6 H4 )(C6 H5 )2 N+ . ( p-C6 H5 C6 H4 )3 N•+ ( p-CH3 OC6 H4 )(C6 H5 )2 N+ . ( p-CH3 CH2 OC6 H4 )3 N+ .

Rate of dimerization (M−1 s−1 )

Ref.

1.4 × 104

[16] [17] [17] [16] [16] [17] [16] [17]

4.4 × 103 1.1 × 103 1 × 102 6 × 10 2.4 × 10 6 × 10−1 8.8 × 10−2

tion with a para phenyl substituent, (entries 3, 5 and 6) or by a para alkoxy substituent (entries 7 and 8). However, unlike the neutral radicals, these radical cations are destabilized by electron withdrawing para substituents (entries 1 and 2). Even systems such as tris(para-biphenylyl)aminium, which slowly dimerize in solution, can be isolated as stable solids [18]. In general the amine radical cations are much more air-stable and thermally stable than their all-carbon counterparts and far more have been isolated. Some have found a use as “easy-to-handle chemical oxidants” [19] and tris(4-bromophenyl)aminium hexachloroantimonate is commercially available. The radical 2 and the radical cation 9 are isoelectronic and X-ray crystallography shows that they have very similar propeller-like geometries. Hence, in tris(parabiphenylyl)aminium perchlorate the dihedral angles about the central nitrogen are 43, 46, and 27◦ [20]. EPR studies show that the introduction of the nitrogen only perturbs the free spin distribution a little. Hence the EPR spectrum of the free radical 2 shows a(6H), 2.55 G, ortho-H; a(6H), 1.11 G, meta-H; a(3H), 2.78 G, para-H [21] whereas the radical cation 9, generated by treating triphenylamine with BF3 in SO2 shows a(6H), 2.28 G, ortho-H; a(6H), 1.22 G, meta-H; a(3H), 3.32 G, para-H [22]. In the light of knowledge gleaned from studies of these monoradicals, workers who have tried to construct high-spin systems based on triarylmethyl and triarylamine building blocks have generally opted for systems in which the stability of the spincarrier is enhanced by perchloro, para-phenyl, para-tert-butyl and/or ortho-alkoxy substituents.

5.3

Diradicals (S = 1)

Just as triphenylmethyl 2 was the first “stable” organic monoradical to be observed experimentally, so the closely related “Schlenk hydrocarbon” 13 (Fig. 5) was the first “stable” organic triplet diradical. Following Gomberg’s initial success [3] Stark and coworkers [23] attempted to make a metaquinonoid diradical by reduction of the dichloride 11 (Fig. 5).

154


Fig. 5. Preparation of the Schlenk hydrocarbon 13 [24, 25]. Reagents (i) Ag/benzene. Inset: EPR spectrum, frozen toluene matrix, −180◦ C [27]. (Reproduced by permission of WileyVCH.)

However, it was only when the experiments were repeated by Schlenk and Brauns [24, 25] using rigorously air-free experimental conditions that it became clear that reduction of the dichloride 11 gave first the monochloro-monoradical 12 and finally the diradical 13. Like the corresponding monoradical 2, the diradical 13 tends to selfassociate but, since 13 is “bifunctional”, this results in a complex mixture of oligomers rather than a simple dimer. These oligomers, the monoradical 12 and the diradical 13 are all extremely sensitive to oxygen which instantly discharges their color [24] giving peroxide products [26]. In solution, where the molecules are rapidly tumbling and spin-relaxation is also very rapid, EPR spectra for organic triplet species are usually too broad to be observed. However, when a solution containing the diradical 13 in toluene is frozen at −180◦ C a strong triplet EPR spectrum [27] is observed which is superimposed on a broad singlet arising from the monoradicals present (Fig. 5, inset). The triplet component of the spectrum has been fitted to a single species, with zero field splittings |D/ hc| = 0.0079 cm−1 , |E/ hc| = 0.0005 cm−1 . A study of the temperature dependence of the intensity of the EPR signal shows that the Curie Law is obeyed and this is consistent with a triplet ground state [28]. The size of the energy difference between the triplet and first excited singlet spin state is unknown and estimates have varied from as high as 1 eV (23 kcal mol−1 ) [27] down to as low as 2.6 kcal mol−1 [29]. The lower number is probably closer to the truth


155

but even this is so large that there will not be a significant population of the excited singlet state at normal temperatures. The only experimentally measured value for a compound in this family is that for metaquinodimethane for which the triplet state is favored by 9.6 kcal mol−1 [30]. The geometry of the Schlenk hydrocarbon 11 is also unknown but it seems probable that there is a mixture of diastereoisomers since the two stereogenic α-carbon centers can either be right hand helical [usually designated plus (P)] or left-hand helical [usually designated minus (M)] [31]. This has been clearly demonstrated by Vecciana for the perchlorinated Schlenk hydrocarbon 14 [32]. The synthesis of this is shown in Fig. 6.

Fig. 6. Synthesis of the perchlorinated Schlenk hydrocarbon 14 [32]. Reagents (i) CHCl3 /AlCl3 ; (ii) C6 Cl5 H; (iii) Bu4 NOH; (iv) para-chloranil; (v) chromatographic separation of meso and rac isomers.

156


Like the corresponding perchlorinated monoradical 5, the diradical 14 is thermally stable and it can be stored for months at room temperature. Indeed, it is sufficiently stable to be purified by chromatography. In this way it has been possible to separate the two diastereoisomers. In the meso isomer the helicity of the two stereogenic centers is opposed and in the rac isomer both are the same. The diastereoisomers can be interconverted by heating in MeCN/THF (G ‡ = 23.4 kcal mol−1 ). As expected they show significantly different physical and spectroscopic properties. Hence, in a frozen THF matrix at 143 K, the meso isomer shows |D/ hc| = 0.0152 cm−1 , |E/ hc| = 0.0051 cm−1 and the rac isomer |D/ hc| = 0.0085 cm−1 , |E/ hc| < 0.0003 cm−1 . Both have triplet ground states. This separation of the diastereoisomers is important result since it underlines the fact that all of the high-spin systems based on triarylmethyl radical and triarylamine radical cation building blocks are complex mixtures of diastereoisomers (up to 2(N −1) for a system comprised of N centers) [33]. Hence, the common practice of fitting spin-splitting, zero-field splitting, etc., data using a single parameter set is always an approximation. Whereas the Schlenk hydrocarbon 13 is largely oligomerized in solution this tendency to self-associate can be suppressed by suitable substitution. Derivatives 14–19 (Figs. 6 and 7) [29, 32–36] of the Schlenk hydrocarbon are all monomeric in solution and 14–17 and 19 all have triplet ground states with large singlet-triplet energy gaps. Studies by EPR spectroscopy 4–80 K and by magnetometry 2–80 K of frozen THF and Me-THF matrices of the highly substituted and presumably highly nonplanar diradical 18 show the presence of two isomers, which are probably diastereoisomers, both of which have singlet ground states. For the major isomer E ST = −0.2 kcal mol−1 and for the minor isomer −0.02 kcal mol−1 [33]. The solid diradicals 16–19 can all be stored at room temperature under vacuum or in an argon atmosphere. Solid samples of the diradicals 14 and 19 give an effective moment µeff. close to that of 2.83 µB expected for a triplet molecule [29, 35, 36] but those for 16–18 are lower (2.2–2.5 µB ) and analysis of these systems is complicated by the presence of S = 1/2 impurities [29]. In comparing the diradicals shown in Fig. 7 with the bisradical-cations shown in Fig. 8 it is reasonable to assume that the replacement of the α-carbons with αnitrogens reduces the energy difference between the singlet and triplet states [37] but unfortunately the magnitude of this reduction is not known. Certainly these amminium cations, like the corresponding hydrocarbons, have triplet ground states and the magnitudes of the zero field splittings are similar confirming that the heteroatoms only perturb the spin-distribution in quite a minor way. Most are more stable than the equivalent all-carbon diradicals. Their stability has usually been probed using cyclic voltammetry [38–41]. The simple diradical 21a [38– 40] is not very stable but these radical cations are greatly stabilized by ortho or para methoxy [41–43], phenylamino or diphenylamino [44] substituents. Diphenylamino and phenylamino substituents prove to be particularly good at stabilizing these radical cations but they also have the undesirable effect that E ST is reduced to the extent that it becomes of the order of kT or even that the ordering of the states is reversed. A potential problem in building high-spin systems based on charged triarylamine radical cation blocks rather than neutral triarylmethyl radical building blocks is


157

Fig. 7. Triplet diradical derivatives of the Schlenk hydrocarbon 15 [34], 16–18 [29, 35], and 19 [36].

the coulombic effect. A priori, it seemed possible that that cation-cation repulsion would make the polyradical polycation species either difficult to prepare or at highly unstable. However, in one system where this effect has been measured it was shown that cation–cation repulsion is moderated by the shielding from the counterions. Whilst the cation-cation repulsion can be measured it is scarcely significant [41]. It is important to note that, in all of the triplet ground-state biradicals discussed so far, the topology is that of a metaphenylene. Equivalent orthophenylene and paraphenylene species always have singlet ground states. Because metaquinodimethane hydrocarbons cannot be represented by a classical valence bond formula in which each π -electron is formally paired with one on a neighboring carbon they are called “non-Kekule´ hydrocarbons”. As in other non-Kekule´ hydrocarbons [45] the ferromagnetic spin coupling in metaquinodimethane derivatives is best understood in terms of Hund’s Rule. [46, 47]. The application of Hund’s Rule to systems such as atomic carbon (Fig. 9) is well known but, whereas Hund’s rule applies to all atomic systems, it does not apply in the same universal way to every molecular system

158


Fig. 8. Triarylamine analogs of the Schlenk hydrocarbon 20 [42], 21a [38–40], 21b [42, 43], and 22 [44].

containing degenerate or near-degenerate SOMOs. In atomic systems, Hund’s Rule depends on the fact that the co-centered singly occupied atomic orbitals are always strictly degenerate, orthogonal ( ψ1 ψ2 dτ = 0) and coextensive ( ψ12 ψ22 dτ = 0). In molecular systems the SOMOs are sometimes not quite degenerate and they may or may not be coextensive. It is this second point which is most often crucial to determining the energy difference between the spin states. In the Schlenk hydrocarbon 13 (Fig. 9) or the 3,4 -dimethylenebiphenyl derivatives shown in Fig. 10 it is clear that the SOMOs are properly coextensive (they share atoms in common) and in situations such as this the triplet state is always strongly preferred. However, in a long chain α,ω-polymethylene [• CH2 (CH2 )n CH•2 ] or the 3,3 -dimethylenebiphenyl derivatives shown in Fig. 10 the SOMOs are “disjoint”. They no longer overlap in their spatial distribution and they no longer share atoms in common. In situations such as this there is little or no interaction between the spins and the singlet and triplet states are close to being degenerate. An additional complication arises in molecular systems when changes in geometry, environment or the introduction of substituents or heteroatoms lifts the degener-


159

Fig. 9. Hund’s Rule illustrated for the case of atomic carbon and the Schlenk hydrocarbon. Note that, since the singly occupied orbitals py and ψ16 are symmetric with respect to a vertical plane and px and ψ17 symmetric we have orthogonality in both cases (ψ1 ψ2 dτ = 0) but that in each case they are also coextensive ( ψ12 ψ22 dτ = 0).

acy of the SOMOs. What is found is that non-Kekule´ α-diradicals with coextensive SOMOs are remarkably tolerant to such perturbations and the triplet state remains the ground state even when the perturbation is quite substantial. These triplets are known as “robust” triplets [48] and all attempts to build high-spin polyradicals have relied on “robust” triplet building blocks. The most frequently exploited alternative to ferromagnetic coupling 1,3 through benzene is 3,4 -coupling through biphenyl (Fig. 10). As already pointed out, this gives the required pair of degenerate coextensive orbitals and it is instructive to compare this with isomers in which there is 3,3 -coupling through biphenyl where the singlyoccupied orbitals are disjoint and there is expected to be a negligible exchange

160


Fig. 10. Ferromagnetic coupling 3,4 and 3,3 through biphenyl [41, 49]. In the 3,4 case the relevant singly occupied orbitals are both orthogonal and coextensive leading to a significant exchange interaction. In the 3,3 case they are disjoint (they occupy separate regions of space) and the exchange interaction is negligible.

5.4 Triradicals (S = 3/2)

161

interaction. The coextensive diradical 23 has a triplet ground state. However, in the isomeric disjoint diradical 24, the singlet state lies 0.1 kcal below the triplet state [49]. The situation for the corresponding biphenyldiamine diradical dications 25 and 26 appears to be similar with only the 3,4 -coupled diradical having a triplet ground state. In this series the temperature dependence of the EPR spectrum for the 3,3 coupled system 26 is complex and it has been interpreted on the assumption that there is a mixture of rotamers about the central biphenyl linkage [41]. In other diradicals coupled 3,3 through biphenyl the splitting between the singlet and triplet states is very close to zero [50]. Other alternatives to 1,3-coupling through benzene that have been explored are 1,3-coupling through triazene [51], 1,6-coupling through naphthalene [52] and 4,4 -coupling through metaterphenyl [53]. In principle, many other non-Kekule´ quinodimethane nuclei could be exploited [54].

5.4

Triradicals (S = 3/2)

The two most obvious ways of extending the triplet diradical 13 to give a quartet triradical are through the central ring as in the “Leo” triradical 27 (Fig. 11) or through one of the peripheral benzene rings as in the “linear” system 31 (Fig. 12). Although the Leo triradical 27 has been known for many years [55] and it is known to give a quartet EPR spectrum there appears to be no experimental evidence that the quartet is actually the ground state. However, the corresponding perchlorinated triradical 28 has been shown to possess a quartet ground state. Like the corresponding perchlorinated diradical 14, it is remarkably stable and different diastereoisomers have been isolated [56]. The tris-amino radical cations 29a and 29b [38, 39, 43] also have quartet ground states. There is conflicting information regarding their stability [39, 43, 57] but the tris-diphenylamine-substituted radical cation 30 is a stable, isolable solid [58]. In this case, the quartet and doublet states are comparable in energy. As usual, although “amino” substituents are very good at stabilizing these radical cations they are sufficiently strongly perturbing that they annul the splitting between the high-spin and low-spin states. All of the linear triradicals 31 (Fig. 12) have quartet ground states with negligible population of the first excited doublet state cyclic > branched/dendritic > linear. Both branched and cyclic tetraradical derivatives of the Schlenk hydrocarbon have been investigated [34, 59, 67–69]. Synthetic routes to these are shown in Figs. 15 and 16 [70]. The tetraradical 37a was obtained by oxidizing a 0.05 M solution of the tetraanion in tetrahydrofuran with two molar equivalents of iodine at −78◦ C [34, 67]. When the solution was frozen, the m = 1 region of the EPR spectrum showed the symmetrical eight peak pattern expected for a pentuplet tetraradical superimposed on a signal ascribed to a monoradical impurity. NMR measurement of the magnetic moment in the range 133–163 K gave µeff. = 4.3 µB which approaches the spin-only value of 4.9 µB . Even tetraradical 37c, the most sterically hindered of the tetraradicals shown in Fig. 15, has a pentuplet ground state with negligible thermal population of lower spin states [59] despite the fact that it must be significantly nonplanar. Attempts to prepare an equivalent perchlorinated tetraradical by treating the chlorocarbon 38 with tetrabutylammonium hydroxide and then chloranil unfortunately failed even when using a large excess of reagent and very long reaction

166


Fig. 14. The effect of the number and position of “spin defects” on the “spin value” for linear, dendritic, and cyclic arrays of ferromagnetically coupled S = 1/2 sites.

5.5 Monodisperse High-spin Oligomers (S = 2 – ca. 10)

167

Fig. 15. Syntheses of branched pentet tetraradicals [34, 67, 68]. Reagents (i) 1 mol. BuLi, −30◦ C; (ii) 4,4 -di-tert-butylbenzophenone; (iii) EtOCOCl; (iv) BuLi, −25◦ C, (MeO)2 CO; (v) EtOCOCl; (vi) Li, THF; (vii) I2 , −78◦ C. Ar = para-tert-butylphenyl.

168


Fig. 16. Syntheses of a cyclic pentet tetraradical 39 [69]. Reagents (i) 1 mol. BuLi, 5 K fits Brillouin curves 3.5 > S > 2.5 but at lower temperatures significant intermolecular antiferromagnetic interactions lead to lower values [71]. The data obtained for the dendritic heptaradical 42 is very similar. The heptaradical 43 shows a temperature dependent moment arising from the fact that it is built upon 3,4 -coupling through the biphenyl unit which is relatively weak. The field-dependence of the magnetization at 5 K fits S = ca. 3.3 compared with the expected value of 3.5 [60]. As pointed out earlier, cyclic polyradical architectures are particularly desirable. The cyclic octaradical 44 (Fig. 19) was made by a variant on the route used to prepare the tetraradical 39 [72]. A 10−3 –10−2 M solution showed no significant intermolecular interactions and the field dependent behavior cyclic > branched/dendritic > linear and clearly it is going to be very difficult to make further progress with anything other than polycyclic or networked architectures. In all cases the presence of defects means that the observed total spin values are less than the theoretical maximum because of spin imperfections inherent in the synthetic methods employed but this is only disastrous for linear and branched architectures. The requirement for strong local ferromagnetic coupling can be achieved by building on the Schlenk hydrocarbon motif and exploiting 1,3-coupling through benzene but this can conflict with the equally important need for a reasonable degree of planarity in the π system and for an acceptable level of thermal stability. Hence it has proved necessary to exploit the relatively weak 3,4 -coupling through biphenyl ( 40 at 1.8 K and at best Sn = 48, Ss ca. 66. Sn decreases steeply with increasing temperature. Samples left at room temperature for several weeks decomposed and on cooling to low temperatures 300 is reproducibly obtained. This and the AC susceptibility studies will be described in the upcoming VIIth ICMM meeting in San Antonio in the September of 2000”.


6

High-spin Metal-ion-containing Molecules Talal Mallah and Arnaud Marvilliers

6.1

Introduction

The discovery of magnetic bistability in Mn12 where the magnetization stays blocked after removing an external applied magnetic field [1] has prompted several research groups to design new polynuclear complexes bearing a low-lying high spin ground state [2]. The origin of this behavior is due to the axial magnetic anisotropy and the relatively large magnetic moment (S = 10) of the molecule [3] as for metallic or metal-oxide superparamagnetic particles [4]. The originality of the molecular systems like Mn12 is the strict monodispersion of the sample which allow to ascribe the observed phenomenon to a single molecule. One-molecule based devices for information storage may now become a reality. However, if Mn12 were to be used, the device should be refrigerated to below liquid helium temperature since above 4 K relaxation effects will destroy the induced magnetic moment. Thus, one of the challenges in this area is the synthesis of new molecules possessing very high spin ground state well separated from the first excited states and having a large magnetic anisotropy so that the blocking of the magnetic moment may be observed at high temperature. For example, Mn12 has an S = 10 spin ground state with a zero field splitting parameter due to an Ising type anisotropy D = −0.5 cm−1 [5]. This leads to an anisotropy energy barrier of 50 cm−1 (DS2z ) and hysteresis loops are observed only at temperatures lower than 3 K. If bistability is to be present at 30 K for example, the anisotropy energy barrier has to be as high as 500 cm−1 assuming everything else being equal. A high spin state is a necessary but not a sufficient condition to observe the blocking of the magnetization. Powell’s [Fe17 + Fe19 ] compound has the highest spin ground state S = 33/2 reported to date in a polynuclear system [6]. But, probably because of the very small magnetic anisotropy of the molecules, no blocking temperature had been observed down to T = 2 K. Several research programs throughout the world are devoted to the preparation of polynuclear complexes containing a large number of paramagnetic metal ions. Two approaches are mainly used leading in several cases to high spin molecules. The first approach is a “one-pot”, the second is a rational one. The paper is organized in five parts, after this introduction the three following sections are devoted to the self-assembly approach, then to the host-guest approach and finally to the rationale strategy. Within each part, the magnetic properties of the chemical systems will be presented and discussed. The last section consists of a general conclusion.

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6 High-spin Metal-ion-containing Molecules

6.2

Self-assembly of Molecular Clusters

To date it seems difficult to rationalize the synthetic approaches that have been used to prepare the polynuclear clusters by a one-pot approach. However, many beautiful reactions were performed leading to interesting new systems. The common feature of almost all the reactions and the complexes obtained is the presence of particular chelating ligands. These ligands possess the general following characteristics: (i) they have more than one coordination mode, (ii) may be terminal and bridging simultaneously, (iii) can be bidentate or tridentate in some cases without stabilizing mononuclear complexes. We focus on two families of compounds where two archetypal ligands play the key role: carboxylate and 2-hydroxypyridine derivatives. A common structural feature to most of the polynuclear complexes of the carboxylate and the 2-hydroxypyridine families is the presence of metal ions sitting at the corners of a triangle leading to competition between the antiferromagnetic interactions between the metal ions. This makes very difficult the prediction of the nature of the ground state of such molecules.

6.2.1

Competing Interactions and Spin Frustration

Let us take a simple example of three S = 2 spins sitting on the corners of an isosceles triangle as shown in Scheme 1 and see how the nature of the ground state varies as a function of the relative amplitude of the exchange interactions between the local spins. The spin Hamiltonian (Eq. 1) used to calculate the energy levels due to the interaction of the three local spins S A , S B and SC is given by:

Scheme 1

H = −J (S A · S B + S A · SC + S B · SC ) + (J − J )(S B · SC )

(1)

The expression for the energy levels (Eq. 2) is: J − J ∗ ∗ J E(S, S ∗ ) = − S(S + 1) + S (S + 1) 2 2

(2)

where S ∗ = S B + SC to |S B − SC | and S = S ∗ + S A to |S ∗ − S A |. Assuming only antiferromagnetic interactions, the ground state may be S = 2, 1 or 0 depending on the J /J ratio (if we restrict J /J in the range 0–2) as shown in Fig. 1. Figure 1 reveals other important features. For J /J = 1/2, 2/3, and 3/2, the ground state is accidentally degenerate and the system is said to be frustrated (Toulouse original

6.2 Self-assembly of Molecular Clusters

191

Fig. 1. Plot of −E(S, S ∗ ) against A for an isosceles triangle of S = 2 spins.

work referred to a square Ising-type spin topology with three ferromagnetic and one antiferromagnetic interactions) [7]. A small perturbation in the chemical surroundings of the metal ions may slightly change the J /J ratio so that degeneracy is lifted leading to a well defined ground state. A system with a non-degenerate ground state is in a situation of stable equilibrium as a result of the competition between the exchange coupling interactions. We must stress that in the particular example of three S = 2 local spins, no spin frustration occurs when J /J is equal to one (the ground state is not degenerate); the magnetic properties of the system are those of a S = 1 ground state. Many molecules prepared by the one-pot approach have spin topologies that may lead to competing interactions so that the spin ground state is difficult to predict. A very small perturbation in the chemical surroundings of some of the metal ions may slightly change the amplitude of the coupling and thus leads to a completely different spin ground state. For example, II the complexes of general formula [MnIII 2 Mn O(O2 CR)6 L3 ] where R is CH3 or C6 H5 and L is C5 H5 N or H2 O (Fig. 2), spin ground states ranging from 1/2 to 13/2 have been observed depending on the nature of R and L which induces different exchange interactions between the metal ions within the triangle [8].

Fig. 2. PLATON projection of [Mn3 O(2Fbenzoato)6 (Pyr)3 ].2MeCN, which has crystallographic C2 symmetry. Thermal ellipsoids at the 50% probability level. The F-benzene moieties and the hydrogen atoms have been omitted for clarity (reproduced with permission).

192

6.2.2


The Carboxylate Family

The triangle arrangement of the trinuclear complex shown in Fig. 2 is found in many of the FeIII , MnIII and MnIV high nuclearity clusters belonging to the carboxylate family. This is a very stable framework that can be obtained with the metal ions FeIII , CrIII , MnII , MnIII or MnIV with pyridine or/and water to complete the coordination sphere of the metal ions. Depending on the nature of the metal ion, its oxidation degree and the terminal ligands different spin ground states may be stabilized [9]. The importance of these trinuclear complexes lies in their use as starting point for the synthesis of higher nuclearity complexes. A hexanuclear complex has been prepared by the association of two fragments of the trinuclear FeIII one [10]. The addition of three molar equivalents of the chelating ligand 1,1-bis(N -methylimidazol-2yl)ethanol (Scheme 2) to one molar equivalent of [FeIII 3 O(O2 CCH3 )(C5 H5 N)3 ]ClO4 leads to the formation of a hexanuclear complex (Scheme 3) made of two fragments of the original one by displacement of some of the carboxylate ligands. For six interacting FeIII ions (S = 5/2) the spin of the ground state can take a value between 0 and 15 depending on the relative amplitude and the nature of the exchange interaction between neighboring metal ions. Competing spin interactions lead in this case to a spin ground state S = 5.

Scheme 2

Scheme 3

Starting from a similar but slightly different trinuclear complex [FeIII 3 O(O2 CCH2 Cl)(H2 O)3 ]NO3 in the presence of Fe(NO3 )3 lead to a cyclic decanuclear FeIII complex (Fig. 3) [11]. The nature of the ground state in such molecule is easy to predict; depending on the nature of the exchange coupling interaction, it may be S = 0 (antiferromagnetic) or S = 25 (ferromagnetic). Magnetization measurements show clearly a S = 0 ground state [12].


193

Fig. 3. ORTEP drawing of the planar projection of [Fe(OMe)2 (O2 CCH2 Cl)]10 with 50% probability thermal ellipsoids and atom labels; prime and unprimed atoms are related by the center of inversion. Chlorine and hydrogen atoms are omitted for clarity (reproduced with permission).

Tetranuclear manganese complexes possessing a butterfly-like core have been used as starting point to prepare high nuclearity clusters (Scheme 4); Mn(4) and Mn(3) form the body of the butterfly and the two fragments Mn(1)–O and Mn(2)–O the wings [13].

Scheme 4

Many compounds having the same core with FeIII , MnIII , and VIII exist [14]. Christou and coworkers were able to merge two Mn tetranuclear [Mn4 O2 (O2 CCH3 )7 (pic)2 ]− (pic− is the deprotonated picolinic acid) molecules into a new octanuclear one [Mn8 O4 (O2 CCH3 )12 (pic)4 ] (Fig. 4). The reaction is based on the use of the Jahn-Teller effect that permits the abstraction by (CH3 )3 SiCl of one acetate group belonging to a manganese ion of the butterfly body. Actually the structure of the tetranuclear complex shows that among the seven acetate groups only one has a long Mn-O bond distance thus

194


Fig. 4. Labeled structure of complex Mn8 O4 (OAc)12 (pic)4 . To avoid congestion, not all symmetry-equivalent atoms have been labeled. The µ3 -O atoms are O5, O5 , O6, and O6 (reproduced with permission).

Fig. 5. ORTEP representation of the anion complex Mn8 O6 C16 (O2 CPh)7 .(H2 O)− 2 at the 50% probability level. For clarity, atoms not bound to Mn are de-emphasized (reproduced with permission).

enough labile to be attacked by (CH3 )3 SiCl [15]. Replacing the acetate groups by benzoate and performing the same reaction lead to a new octanuclear compound [Mn8 O6 Cl6 (O2 CC6 H5 )7 (H2 O)2 ]− with a different structure (Fig. 5) [16].


195

The general reaction can be written: 2[Mn4 O2 (O2 CC6 H5 )9 (H2 O)]− + 8(CH3 )3 SiCl → [Mn8 O6 Cl6 (O2 CC6 H5 )7 (H2 O)2 ]− + 8(CH3 )3 SiO2 CC6 H5 + 3C6 H5 CO2 H + H+ + 2Cl− The spin ground state of this octanuclear complex has been found to be equal to S = 11. The zero field splitting parameter D was estimated to be −0.04 cm−1 . Despite the high value of the spin ground state, no blocking of the magnetization was observed above T = 2 K. Chemical oxidation in acetonitrile of the benzoate tetranuclear complex using dibenzoyl peroxide leads to the formation of a new MnIII nonanuclear complex [Mn9 Na2 O7 (O2 CC6 H5 )15 (CH3 CN)2 ] possessing a spin ground state S = 4 [16]. The elegant reactions performed by Christou and coworkers that led to these complexes by coupling two tetranuclear ones are rather rare examples of “rationale” design. Most polynuclear complexes are to date obtained by a self-assembly process where prediction is still not reliable. However, as we will see, given a stable metal-ion framework as for the Mn12 derivatives it is possible to introduce small changes that keep the overall structure but may lead to new complexes with different spin ground states.

6.2.2.1

Mn12 Derivatives

The most studied compound in the Mn-carboxylate compounds is the so called Mn12 . It was prepared in 1980 by Lis by mixing KMnO4 and Mn(CH3 CO2 )2 .4H2 O in the molar ratio 1/2.5 in a 60% solution of acetic acid. The compound has the chemical formula [Mn12 O12 (O2 CCH3 )16 (H2 O)4 ].2CH3 CO2 H.4H2 O. The structure consists III by eight µ -O2− of a central MnIV 3 4 O4 cubane core connected to a ring of eight Mn anions (Fig. 6). The 16 acetate ligands and the four water molecules complete the coordination sphere of the metal ions. The four water molecules occupy the axial positions of two MnIII metal ions [17]. Using a.c. susceptibility measurements in zero applied static field in order to avoid saturation effect shows that the spin ground state of Mn12 is S = 10 [5]. High-field EPR spectra using different frequencies lead to the conclusion that the M S = −10 component of the S = 10 ground manifold has the lowest energy. EPR provided as well a good estimation of the zero field splitting parameter (D = −0.5 cm−1 ). The imaginary component of the susceptibility (χ ) was found to be different from zero below T = 9 K with maximum values between 7 and 5 K depending on the frequency of the a. c. magnetic field. This behavior is similar to what is observed in superparamagnetic particles but with a very important difference, that is the sample of Mn12 is made of identical molecules while a sample of metallic or metal-oxide particles has a size distribution. The most spectacular behavior is the magnetic bistability observed when a field is applied to an oriented crystal of Mn12 (Fig. 7) [1]. The origin of the hysteresis cycle is purely molecular since no 3D order was observed above T = 2 K. Christou succeeded to prepare a whole new family related to the original Mn12 acetate. Replacing acetate by benzoate affords a new compound with the same

196


Fig. 6. ORTEP representation of [Mn12 O12 (O2 CPh)16 (H2 O)4 ] at the 50% probability level. For clarity, the peripheral carboxylates are de-emphasized and only one phenyl carbon atom is included (reproduced with permission).

Fig. 7. Hysteresis loops of Mn12 recorded parallel to the c axis with a SQUID magnetometer at 2.2 K (outer loop) and 2.8 K (inner loop). A whole loop was recorded in ca. 8 h. The dotted lines are a guide for the eye only (reproduced with permission).


197

molecular structure but with a different ground state. The spin ground state for [Mn12 O12 (O2 CC6 H5 )16 (H2 O)4 ] is S = 9 in zero field [3]. The substitution of four MnIII ions by four FeIII is possible when performing the reaction using FeII instead of MnII . The structure of the new Mn8 Fe4 compound is similar to that of the parent one but the substitution process induces a drastic change in the magnetic properties. The new compound has a S = 2 ground state instead of S = 10 for Mn12 [18]. Starting with a propionate-Mn12 and adding tetraphenylphosphonium iodide leads to a new monoanion Mn12 : PPh4 [Mn12 O12 (O2 CC2 H5 )16 (H2 O)4 ] [19]. Electrochemical studies show that the extra electron is located on one of the manganese atoms belonging to the external ring. The ground state has been found to be S = 19/2. Thus, keeping the same overall metal-oxide framework it was possible to prepare molecules with different spin ground states: S = 10 for Mn12 acetate, S = 9 for Mn12 propionate, S = 19/2 for one-electron reduced Mn12 propionate and S = 2 for Mn8 Fe4 acetate. The few examples given above show how the chemistry of these systems is rich but how the prediction of the structure and the nature of the ground state is still out of reach.

6.2.3

The Hydroxypyridonate Family

The richness of the chemistry of the hydroxypyridonate family lies mainly in the flexibility of the ligands [20]. These ligands are able to simultaneously act as chelating and bridging ligands. As stated by Winpenny, the 2-hyroxypyridone derivatives are a much less well-behaved ligands than the carboxylate derivatives because once deprotonated they may show six different coordination modes within the same complex; this is illustrated in Scheme 5. Few examples of polynuclear complexes involving 3d metals and a hydroxypyridonate ligand had been reported before 1987 [21]. Winpenny et al. extended the chemistry of mixed carboxylate/pyridonate complexes and prepared a new series involving almost all the 3d metal ions [20].

Scheme 5

198


Fig. 8. Structure of Co24 (µ3 -0H)14 (µ2 -OH)4 (µ3 -OMe)2 (µ3 -Cl)2 (Cl4 )(mph)22 (reproduced with permission).

One of the largest polynuclear molecule containing paramagnetic ions is the tetraicosanuclear cobalt(II) complex obtained from the reaction of CoCl2 with two molar equivalent of Namph in methanol. Recrystallization from ethyl acetate containing 0.1% water by weight leads to crystals of [Co24 (µ3 -OH)14 (µ2 -OH)4 (µ3 OMe)2 (µ3 -Cl)2 (Cl4 )(mph)22 ] (Fig. 8) [22]. The small amount of water in ethyl acetate is probably the source of hydroxides necessary to grow the core of the complex. The magnetic properties of Co24 indicate that the spin ground state in not less than S = 9 which makes this complex a good candidate to observe magnetic bistability. The structure of the core is reminiscent to that of [Co(OH)4 ]2+ cubes with one corner missing and for some metals a chloride or a methoxide replacing the OH− groups. The periphery of the molecule is made of a layer containing twenty-two 2methylhydroxypyridonate ligands that adopt three different coordination modes as those shown in Schemes 5a, 5b and 5c. The global structure of Co24 is similar to that of [Fe17 + Fe19 ] mentioned in the introduction even though the synthetic route adopted by Powell et al. is different. According to Powell, the formation of such oligomeric


199

species which are at midway between mononuclear (or binuclear) complexes and infinite 2D array of (Fe(OH)2 )+ may be controlled by the iron/polydentate ligand ratio and the pH of the solution [6].

6.2.3.1

Role of the Solvent

The solvent can occasionally play an important role in stabilizing complexes with different nuclearities; a nice example can be taken from the chemistry of NiII pyridonate/acetate. The reaction of hydrated NiII (O2 CCH3 )2 with excess Hchp at 130◦ C for 1 h, followed by removal of unreacted Hchp and acetic acid, gives a bright green solid. Extraction of the residue with methanol gives after slow evaporation of the solution green needles in 40% yield. The structure reveals a linear trimeric NiII complex: [Ni3 (chp)4 (O2 CCH3 )2 (CH3 OH)6 ] [23]. The central Ni atom is surrounded by for oxygen atoms coming from four chp ligands; the two other oxygen atoms are located in axial positions and belong to two different acetate groups (Fig. 9). Only the oxygen atom of the chp ligand is linked to the metal ions while the nitrogen atom of chp is involved in hydrogen-bonding with the methanol groups. When extracting the green solid obtained from the above reaction by THF instead of methanol, a new dodecanuclear complex of formula [Ni12 (O2 CCH3 )12 (chp)12 (H2 O)(THF)6 ] with a completely different structure has been isolated [24].

Fig. 9. The structure of the trinuclear complex [Ni3 (chp)4(O2 -CMe)2 (MeOH)6 ]. Hydrogen bonds with O· · ·N distances in the range 2.654–2.698 Å shown as dotted lines (reproduced with permission).

200


Fig. 10. The structure of the dodecanuclear complex Ni12 (O2 CCH3 )12 (chp)12 (H2 O)(THF) (reproduced with permission).

The twelve Ni atoms form a ring held by bridging acetate and chp ligands (Fig. 10). The chp ligands are all bridging by their oxygen atom while the acetate groups have two bonding modes; the external bridge two Ni atoms while the internal are trinucleating. The core structure of this compound is similar to that of Fe10 the so-called “ferric wheel” mentioned above [11]. However, the nature of the exchange coupling interaction between adjacent NiII ions is ferromagnetic while it was found to be antiferromagnetic in Fe10 . The origin of the ferromagnetic interaction can be rationalized by the small Ni– O–Ni angle of the Ni2 O2 core. The mean value of this angle found equal to 96.4 ± 1.5◦ is consistent with a ferromagnetic interaction on the basis of the experimental studies carried out by Hatfield on binuclear hydroxo-bridged CuII complexes [25]. Simulating the experimental data leads to a JNiNi value of 9.4 cm−1 based on the following spin Hamiltonian (Eq. 3): H = −JNiNi

12

Si · Si+1

(3)

i=1

The spin ground state corresponds to the sum of the local S = 1 spins leading to a value of S = 12.

6.3 Host-Guest Approach

6.2.3.2

201

Role of the Substituents of Hydroxypyridine

Winpenny and coworkers performed again the same reaction by replacing chp by mhp and recrystallized the green solid from CH2 Cl2 -diethyl ether. A new undecanuclear [Ni11 (µ3 -OH)6 (µ-O2 CCH3 )6 (mph)9 (H2 O)3 ][CO3 ] compound is formed (Fig. 11) [24]. The structure of this compound is fundamentally different from that of the other two. The dramatic change in the structure is probably the result of the presence of mhp instead of chp. The mhp ligand in Ni11 is bonded to Ni by its nitrogen and oxygen atoms whereas only the oxygen atom of chp is involved in metal ligation in Ni3 and Ni12 . The chemistry of the hydroxypyridonate derivatives is vast. We have just given few examples to show how using the same synthetic route but introducing slight changes leads to the formation of different structures. Again here, prediction is not an easy task.

Fig. 11. The structure of the undecanuclear cation of [Ni11 (µ3 -OH)6 (O2 -CMe)6 (mhp)9 (H2 O)3 ]+ . Atoms not involved in metal atom bridging are excluded for clarity (reproduced with permission).

6.3

Host-Guest Approach

Serendipity is the rule for the synthesis of most of the polynuclear complexes prepared by self-assembly. Up to now, few synthetic methods were conceived to design polynuclear molecules in a rationale way. Lippard and coworkers showed that host– guest interaction is an original and interesting route to obtain a new kind of discrete species that may possess a high spin ground state and presents the properties ascribed to a single molecule magnet.

202

6.3.1


Hexanuclear Iron(III) Rings

The structure of the first synthesized compound of formula [NaFe6 (OCH3 )12 (dbm)6 ] Cl.12CH3 OH.CHCl3 belonging to a new series that emerged only few years ago consists of a ring of six FeIII metal ions bridged by methoxides; the coordination sphere of the metal ions is completed by the bidentate dibenzoylmethane ligand (Fig. 12) [26]. The structure of this compound qualifies as an example of [12] metallacrown-6 type [27]. The important feature is the presence of a sodium cation in the octahedral cavity formed by six oxygen atoms coming from six bridging methoxides. Using 23 Na NMR, Gatteschi and coworkers gave evidence that the molecular structure is retained in solution [28]. The spin ground state of this Fe6 Na cyclic complex and that of a related one with ClO− 4 as counter anion was found to be S = 0 as expected from the antiferromagnetic interaction (JFeFe = −20.4 and −19.9 cm−1 for [Fe6 Na]Cl and [Fe6 Na]ClO4 respectively, the interaction between non-adjacent FeIII

Fig. 12. ORTEP representation of the cation [NaFe6 (OCH3 )12 (dbm)6 ]+ with atom labels. Hydrogen atoms have been omitted for clarity. An inversion center relates primed to unprimed atoms. Thermal ellipsoids enclose 50% probability (reproduced with permission).

6.3 Host-Guest Approach

203

ions is neglected) between adjacent metal ions as for the Fe10 ferric wheel. Gatteschi and coworkers succeeded for the first time to estimate the single ion anisotropy of FeIII (D = −0.2 cm−1 ) within these Fe6 Na complexes that possess a non-magnetic ground state. The origin of the compound magnetic anisotropy revealed by susceptibility measurements on single crystals of the perchlorate derivative can be explained on the basis of single ion contributions mainly. This is an important step to the understanding of relaxation effects of iron(III) oxo clusters that have a superparamagnetictype behavior.

6.3.1.1

Role of the Template

The amplitude of the antiferromagnetic interaction between two adjacent iron(III) ions depends on the Fe–O–Fe angle; in order to modulate the amplitude of the interaction Gatteschi and coworkers tried to prepare new compounds similar to Fe6 Na using Li+ and K+ as templates. The reaction with K+ does not proceed to the formation of a new Fe6 K complex. While with Li+ a new Fe6 Li complex which has the same overall structure as Fe6 Na is obtained [29]. Because of the smaller ionic radius of Li+ (0.68 Å) in comparison to that of Na+ (0.97 Å), the size of the ring given by the Fe1–Fe1 separation is smaller for Fe6 Li than for Fe6 Na: 6.272(3) and 6.425(1) Å respectively. Furthermore, the nearest-neighbor Fe-Fe separation decreases considerably from 3.2152(5) to 3.140(1) Å; the Fe–O–Fe angles are reduced by more than 2.5◦ . The investigation of the magnetic properties of Fe6 Li shows that the amplitude of the antiferromagnetic interaction is reduced by about 30% (JFeFe = 14.30 and 14.68 cm−1 for [Fe6 Li]ClO4 and [Fe6 Li]PF6 respectively) in comparison to Fe6 Na, however the spin ground state is still S = 0.

6.3.2

Hexanuclear Manganese Rings

As has already been shown in cyanide-bridged three dimensional molecular-based magnets, where changing the nature of the metal ions and keeping the overall general structure enable tuning of the exchange coupling interaction and lead to the formation of a room temperature magnet [30], for some discrete species this may represent a powerful tool to modulate their magnetic properties. Christou and coworkers showed that substituting 4 MnIII by 4 FeIII in the external ring of Mn12 acetate (S = 10) leads to the formation of a new Mn8 Fe4 acetate with a S = 2 ground state (see Section 2). A preparation method similar to that of Fe6 Na affords a new Mn6 Na complex when manganese is used instead of iron. The overall structure of the hexanuclear Mn6 Na species [NaMn6 (OCH3 )12 (dbm)6 ]+ is similar to that of Fe6 Na; the main difference comes from the presence of the Jahn–Teller d4 MnIII metal ion that leads to a tetragonal elongation along three perpendicular directions of the three crystallographically independent MnIII ions within the cyclic core [31]. The ground state was found to be equal to S = 12 due to the ferromagnetic interaction between adjacent MnIII metal ions. In a d4 tetragonally elongated octahedron, the dx 2 −y 2 orbital is

204


empty and due to the particular orientation of the axes’ distortion on the metal ions within the ring, the singly occupied dz 2 orbitals of nearest-neighbor MnIII do not overlap. The ferromagnetic interaction responsible of the stabilization of the largest spin ground state has its origin in the overlap between the semi-occupied dz 2 orbital on one center and the empty dx 2 −y 2 orbital on an adjacent one through the methoxy ligands. This mechanism was first invoked by Goodenough [32] to explain the ferromagnetic interaction in some metal-oxide three dimensional networks and later by Girerd [33] to rationalize the magnetic properties of a binuclear µ-oxo, µ-acetato MnIII complex. Another complex belonging to the same family has been obtained by the same synthetic procedure as for Mn6 Na. A MnII metal ion plays the role of the template leading to a heptanuclear Mn7 complex. Conductivity measurements confirmed the non-ionic character of the compound leading to the following mixed-valence formuIII lation: MnII 3 Mn4 [34]. The analysis of the magnetic properties is quite difficult in such complex since even though the central ion is a MnII , the position of the other two MnII is difficult to locate within the ring. On the other hand, the presence of triangular motives leads to competition between the different exchange coupling interactions making, as pointed out in Section 2, prediction of the nature of the ground state very difficult. However, the χM T value at low temperature indicates a S = 17/2 ground state. Least-squares fits of the experimental magnetization data with field data at two different temperatures leads to the conclusion that spin ground states S = 17/2 or S = 19/2 are possible and that the zero-field splitting parameter is ca. 0.25 cm−1 . As a conclusion to this part, it is important to note that the prediction of the structure and thus of the nature of the ground state is not as difficult as for the complexes reviewed in the preceding section so that the template approach may be a valuable and powerful tool to prepare new molecules with expected electronic structure. Pecoraro and coworkers designed polynuclear complexes based on the same concept using different metal ions of the first series as well as lanthanides as templates in order to tune the nuclearity of the clusters [27b].

6.4

Step-by-step Rationale Approach

The synthesis of high spin molecules has been since the middle of the eighties considered as one possible route to the preparation of genuine molecular-based ferromagnets. Kahn stated that a strategy used to prepare molecular-based ferromagnets “consists of synthesizing high-spin molecules or chains and then assembling them in a ferromagnetic fashion within the crystal lattice” [35]. To date, there are very few reports in the literature of high spin discrete species (molecules) interacting together and leading to molecular ferromagnets (see below). However, these ideas contributed in a constructive manner to the preparation of polynuclear complexes possessing a high spin ground state using a rationale approach. The important feature of the rationale approach is the possibility that the chemist has to predict the

6.4 Step-by-step Rationale Approach

205

nature of the ground state, the size of the molecule, its shape and eventually the order of magnitude of the magnetic anisotropy that plays an crucial role in determining the blocking temperature of the magnetic moment. Gatteschi and coworkers has, for instance, predicted that an oxo-bridged tetranuclear FeIII complex possessing the structure depicted in Scheme 6 would have a S = 5 ground state due to the expected antiferromagnetic interaction between the central and the three peripheral S = 5/2 FeIII metal ions. Furthermore, assuming a local zero-field splitting parameter D(FeIII ) = −0.2 cm−1 , Gatteschi predicted that the S = 5 ground state would have a D(5) parameter equal to −0.17 cm−1 . The first results on the tetranuclear [Fe4 (OCH3 )6 (dbm)6 ] complex that possess the postulated structure reveal by low temperature HF-EPR studies that D(5) is equal to −0.2 in excellent agreement with the predicted value. Gatteschi and coworkers went a step further and estimated that a decanuclear FeIII complex (Scheme 7) would have a S = 10 ground state and a D(10) zero-field splitting parameter equal to −0.12 cm−1 [28]. This compound has not been reported yet but its topology is reminiscent of dendritic-like molecules of first generation [36]. A step-by-step convergent method developed for dendrimers may be useful to realize the synthesis of this decanuclear complex by first preparing the peripheral trinuclear dendron and then assembling three such complexes around a central FeIII metal ion. This stepwise approach enables the chemist to have a good idea about the magnetic anisotropy. But, since the magnetic anisotropy of a compound depends as well on the relative orientation of the molecules within the crystal lattice, prediction may become an arduous task to fulfil.

Scheme 6

Scheme 7

To overcome this difficulty Langmuir–Blodgett technique [37] may be a useful tool to organize the molecules in mono- or multilayer films so that the anisotropy axes (assuming an axial anisotropy) of a collection of molecules may be oriented in the same direction. The first example is given by Coronado and Mingotaud who succeeded to prepare Langmuir-Blodgett films of the benzoate derivative of Mn12 [38]. Magnetic studies on one monolayer reveals that a high degree of organization

206


has been achieved with the anisotropy axes of the molecules lying perpendicular to the plane of the monolayer; when the applied magnetic field is parallel to the monolayer, the observed hysteresis loop (at T < 4 K) is softer than when the field is perpendicular to the layer.

6.4.1

Complex as Ligand and Complex as Metal

In the following text, we focus on the tactics that enabled chemists to prepare high spin molecules where it is possible to predict in most cases the nature of the spin ground state as well as the overall molecular structure of the target molecules. Two prerequisite conditions have to be fulfilled in order to put in practice the stepwise approach. Firstly, a central molecular complex (referred to as the ‘core’ in the following) that plays the role of a ligand (complex as ligand) i. e. possessing on its periphery atoms bearing lone electron pairs able to coordinate to a metal ion, should be conceived and then synthesized. This complex must be stable and inert since all reactions will be performed in solution. The second condition is the preparation of the peripheral complex which must be able to behave as a Lewis acid with respect to the central molecule (complex as metal). This may be achieved when such complexes bear ligands that can easily be substituted by the core. Furthermore, since the objective is the synthesis of a discrete molecule, the peripheral complex should possess chelating ligands that prevent the formation of extended lattices. And finally, in order to minimize intermolecular interactions at low temperature and to insure that the properties of a single molecule can be studied, bulky peripheral ligands and charged species are preferred to neutral ones so that the counter-ions may dilute the magnetic species preventing dipole–dipole interactions, for example. Within this approach, the nuclearity of the target molecule will depend on the connectivity of the core. By connectivity, we mean the number of sites that can receive metal ions; for example, trisoxalatochromate(III) has a connectivity 3 (Scheme 8), since it can coordinate to three metal ions by its six oxygen atoms. Another complex that can play the role of a core is hexacyanochromate(III) which possess a connectivity 6 due to the six nitrogen atoms present at the vertices of the octahedron (Scheme 9). The connectivity given by the core is an upper value to the number of peripheral complexes that may be attached. The number of coordination sites of the peripheral complex depends on the nature of the core. For trisoxalatochromate(III), the oxalate oxygen atoms are bidentate so that two coordination sites in cis position

Scheme 8


207

(Scheme 10) should be available within the peripheral complex in order to construct a polynuclear species; while for hexacyanochromate(III) the nitrogen atoms are monodentate and the peripheral complex must possess one available coordination site as depicted in Scheme 11. Other parameters like the nature of the solvent, the nature of the counter-ions, the relative charge of the core and the peripheral molecules or the size of the ligands may be decisive to stabilize complexes with different nuclearities other than those predicted on the simple connectivity properties of the core.

Scheme 9

Scheme 10

6.4.2

Scheme 11

Predicting the Spin Ground State

The value of the spin ground state will depend on the nature of the exchange coupling interaction between the core and the peripheral metal ions through the bridging ligands. For a given bridging ligand, the nature of the exchange interaction is greatly influenced by the nature of the two interacting metal ions and to be more precise by the number of their d electrons. It is not the object of this section to go deep in the mechanism of exchange coupling interactions, we would just like to specify the model that we will use to make prediction. The phenomenon of electron exchange interaction is expressed by the Heisenberg Hamiltonian H = −J S A · S B where S is the local spin of a metal ion taken in its ground state and J is the interaction energy. The above Hamiltonian relies on the fact that the interaction between the metal ions is weak so that the spin keeps its local properties. In the case of interacting metal ions bearing more than one electron, the semi-occupied orbitals on each metal ion are considered and J can be expressed (Eq. 4) as the sum of the individual jij interactions between the semi-occupied orbitals ai of metal ion A and bj of B taken two by two: J=

1 jij n A n B i, j

(4)

208


where n A and n B are the number of unpaired electrons on A and B respectively. The semi-occupied orbitals considered are not pure metallic orbitals but they contain a contribution from the bridging ligands as it was proposed by Anderson, Hoffmann and Kahn [39]. The parameter jij is the sum of two contributions of opposite signs: one positive jijF contributes to ferromagnetism (parallel alignment of the interacting spins) and is proportional the bielectronic exchange integral and the other is negative jijAF contributes to antiferromagnetism (antiparallel alignment of the interacting spins). Because most of the complexes obtained by the step-by-step approach are bimetallic and since the orbital analysis of the interaction is made by considering a binuclear low symmetrical unit comprising the central metal, the bridging ligand and one peripheral metal ion, we will adopt here the orbitals proposed by Kahn [39c, 40]. These orbitals are strictly localized and are built so that they may not necessarily be orthogonal to each other. In this case, the antiferromagnetic contribution is proportional to the resonance integral βij and to the overlap integral Si j between orbitals ai localized on metal A and bj localized on metal B. These orbitals are well-adapted to our systems which are generally bimetallic and to our chemical approach. Thus, the amplitude of the antiferromagnetic interaction is proportional to the degree of overlap between the semi-occupied localized orbitals; the higher the degree of overlap, the strongest the interaction is. Now, it is clear that two orthogonal ai and bj orbitals will have zero overlap so that only the ferromagnetic contribution will remain leading to the highest possible spin for the ground state.

6.4.3

Antiferromagnetic Approach

One of the first high-spin molecules designed by a step-by-step strategy was reported by Kahn and coworkers in 1986. Using the Cu(pba)2− (connectivity 2) as the core (Scheme 12) and [Mn(Me6 -[14]ane-N4 )]2+ (Scheme 10, M = Mn) as the peripheral complex, it was possible to obtain a trinuclear linear CuMn2 species [41]. The magnetic properties show clearly that the spin ground state S = 9/2 arises from the antiferromagnetic interaction between the central S = 1/2 and the two peripheral S = 5/2 local spins (Fig. 13).

Scheme 12

To enhance the value of the magnetic moment, one possibility is to use a central complex with higher connectivity. Trisoxalatochromate(III) which has a connectivity 3 is a good candidate to do so. Unfortunately, the reaction of K3 [Cr(C2 O4 )3 ] with the


209

Fig. 13. Experimental ( ) and calculated (—) plots of χM T against T for CuMn2 . The inset shows an expansion of the χM T axis in the 100–250 K temperature range, as evidence of the minimum in χM T (reproduced with permission).

above mentioned MnII complex did not lead to any well defined compound. While using a different CrIII complex possessing a tris bidentate ligand (Scheme 13, same connectivity as Cr[C2 O4 ]3− 3 ) as the core leads to a tetranuclear CrMn3 complex with a low-lying S = 6 ground state. Fitting experimental χM T data leads to JCrMn = −3.1 cm−1 (Fig. 14) [42].

Scheme 13

To increase the nuclearity of this kind of complexes and to stabilize a higher spin ground state, hexacyanochromate(III) was used as the assembling core. The peripheral MnII metal ion is chelated by a pentadentate ligand with the sixth coordination

210


Fig. 14. Experimental (◦) and calculated (—) plots of χM T against T for CrMn3 .

Fig. 15. Experimental (◦) and calculated (—) plots of χM T against T for CrMn6 .

site occupied by a water molecule which can be substituted by the nitrogen end of [Cr(CN)6 ]3− . With a connectivity 6, a heptanuclear CrMn6 complex was expected and obtained [43]. The antiferromagnetic interaction between the central S = 3/2 CrIII and the six surroundings S = 5/2 MnII leads to a S = 27/2 ground state (Fig. 15).


6.4.4

211

Ferromagnetic Approach

In 1971, Ginsberg predicted that for the CrIII –O–NiII linear sequence, the interaction between CrIII and NiII might be ferromagnetic [32b]. If we assume that this sequence is part of an extended cubic 3D network (this is what Ginsberg was referring to in his paper) where the local symmetry around the metal ions is octahedral, the CrIII has three unpaired electron in t2g orbitals and NiII has two unpaired electrons in eg orbitals. In term of the orbital model developed by Kahn, we are in the situation of strict orthogonality, the overlap integral between the CrIII t2g and the NiII eg semi-occupied orbitals is zero and the ferromagnetic contribution dominates leading to an alignment of the local spins within the ground state. Kahn et al. were the first to test this prediction by preparing a tetranuclear [Cr(oxNi(Me6 3− as the core and [14]ane-N4 ))3 ](ClO4 )3 (ox = C2 O2− 4 ) complex using [Cr(ox)3 ] 2+ [Ni(Me6 -[14]ane-N4 )] (Scheme 10, M = Ni) at the periphery [35]. The magnetic data shows that the interaction is ferromagnetic with a spin ground state S = 9/2 and an exchange coupling parameter JCrNi through the oxalate bridge equal to 5.3 cm−1 . Unfortunately, the structure of this compound has not been reported. Later, Okawa and coworkers succeeded to solve the structure of a similar complex using dithiooxalate instead of oxalate as bridging ligand (Fig. 16) [44]. The spin ground state was found, as expected, to be S = 9/2.

Fig. 16. An ORTEP view of the tetranuclear cation [Cr((C2 O2 S2 )(Ni(Me6 -[14]ane-N4 ))3 ]3+ .

212


Fig. 17. Experimental (◦) and calculated (—) plots of χM T against T for CrNi6 .

When [Cr(CN)6 ]3− is mixed with six molar equivalents of the mononuclear [Ni(tetren)H2 O]2+ (tetren = tetraethylenepentamine, M = Ni, Scheme 11), a heptanuclear CrNi6 complex with an octahedral symmetry is isolated [45]. Again in this case, as expected, the strict orthogonality of the semi-occupied orbitals on the central CrIII on one hand and on the peripheral six NiII on the other, leads to a ferromagnetic interaction stabilizing the S = 15/2 state as the ground state. The best fit parameters of the χM T = T experimental data leads to: J = 15.6 cm−1 , |D| = 0.008 cm−1 and g = 2.04 (Fig. 17). The structure of this compound was partly solved, only the position of the heavy atoms and their surroundings could be determined (Fig. 18). Shortly after, Spiccia and Murray reported the crystal structure of a very similar complex with [Fe(CN)6 ]4− as the core surrounded by six CuII ions chelated by a tetradentate ligand (Fig. 19) [46].

6.4.4.1

Dynamic Magnetic Properties of CrNi6

The dynamic magnetic properties of CrNi6 was investigated down to 200 mK using a. c. susceptibility measurements at different frequencies of the oscillating magnetic field (0.7 Oe). A maximum of the real component (χ ) of the magnetic susceptibility is observed at T = 0.38 K at a frequency of 1000 Hz (Fig. 20). Associated with the maximum, the out of phase component (χ ) increases and, on cooling, reaches a maximum at 0.24 K. This maximum may be due either to three-dimensional ordering or to a blocking of the magnetic S = 15/2 moment due to the decrease of its relaxation time at low temperature. Measurements were thus carried out at different frequencies: 1000, 300, and 30 Hz and using a different apparatus at 680 MHz [47]. The maximum of χ is found to be frequency-dependent. It shifts to low temperature when the frequency is decreased. These observations are in line with the occurrence


213

Fig. 18. Structure of the cation [Cr(CNNi(tetren))6 ]9+ . Only the first coordination sphere of the metal ions is represented (reproduced with permission).

of blocking of the magnetization as a result of superparamagnetic behavior and not because of a 3D magnetic order. The magnetic moment relaxation time (τ ) is proportional to the inverse of the frequency (f) of the applied magnetic field: τ = 1/2π f . The blocking temperature (TB ) at a given frequency corresponds to the temperature of the maximum of the χ signal. Plotting ln(τ ) against 1/TB gives a straight line (Fig. 21). The blocking phenomenon is thermally activated (Arrhenius type), as already observed in magnetic particles and in some high spin molecules [1, 3, 48]. The relaxation time can be expressed as τ = τ0 exp(E A /kTB ), where τ0 is the relaxation time at infinite temperature and E A /k is the activation energy. τ0 and E A are found equal to 1.1×10−11 s and 3.98 cm−1 respectively. Assuming an axial anisotropy, the energy barrier is given by DSz2 where Sz = 15/2. It is possible to compute the value of the zero field splitting parameter D to be 0.07 cm−1 . This value is an order of magnitude higher than the value extracted from fitting the χM T = f (T ) data (|D| = 0.008 cm−1 ). One reasonable explanation to this discrepancy is that our assumption of an axial anisotropy as responsible of the blocking of the moment at low temperature is wrong. The CrNi6 heptanuclear complex has an octahedral symmetry and the local magnetic axial anisotropy of the six NiII ions will cancel out. Nevertheless, the experimentally observed blocking of the magnetic moment is due to the presence of a kind of magnetic anisotropy which is probably cubic and not axial in this case.

214


Fig. 19. ORTEP diagram of [Fe(CN)Cu(tpa)6 ][ClO4 ]8 .3H2 O. For clarity only the atoms in Fe(CN)Cu(N4 )6 are labelled (reproduced with permission).

6.4.5

Role of the Organic Ligand

One crucial point of the approach developed above is the presence of a chelating ligand that cannot be substituted by the core. We, and others, have already shown that by changing the number of available coordination sites around the ’complex as metal’ by changing the nature of the organic ligand, it is possible to built systems with different dimensionality (structurally) and original architecture [49–51]. Murray et al. reacted ferricyanide with [Ni(bpm)2 ]2+ and obtained a pentanuclear complex of formula [Fe(CN)6 ]2 [Ni(bpm)2 ]3 .7H2 O (bpm = bis (1-pyrazolyl) methane) where three Ni(bpm)2 units bridge two ferricyanide molecules (Fig. 22)


215

Fig. 20. Plots of real (χ ) and imaginary (χ ) susceptibility against temperature at a frequency of 1000 Hz for CrNi6 .

Fig. 21. ln(τ ) = f (1/TB ) where τ = 1/2π f and f = 1000, 300, 30 Hz and 685 MHz for CrNi6 .

[51e]. The magnetic properties of the pentanuclear complex reveal at TC = 23 K a long-range ferromagnetic order due the ferromagnetic intermolecular interaction mediated by a three dimensional network of hydrogen bonds. It is worth noting here that this is one of the few examples of polynuclear complexes where the interaction between the molecules leads to a ferromagnetic long-range order. Since, in the framework of the mean field approximation, the ordering temperature of three dimensional networks is proportional to S(S + 1), a compound containing molecules with a spin state S = 16, for example, and interacting ferromagnetically in the same

216


Fig. 22. Structure of the pentanuclear complex [Fe(CN)6 ]2 [Ni(bpm)2 ]3 showing the atomlabeling scheme and 20% probability ellipsoids (reproduced with permission).

manner as in Murray’s compound would be ferromagnetic a room temperature. In order to investigate the intramolecular interaction, Murray and coworkers dehydrated the compound by heating it at 200◦ C for 36 h. Dehydration leads to the suppression of the long-range magnetic order; the magnetic properties of the dehydrated sample indicate that the ground state of the pentanuclear complex is either a S = 4 or S = 3. The structure of this compound merits some comments. It is surprising that a discrete µ-cyano assembly is obtained instead of an extended one. Actually, the few examples reported in the literature of compounds obtained from the reaction of hexacyanometallates and a mononuclear complex possessing two available sites in cis position are polymeric [51d, 52]. On the other hand, Murray mentioned in 2+ his paper that when Ni(bpm)2+ 2 is replaced by Ni(bipy)2 , a pentanuclear complex with the same structure is obtained. In order to understand the particular role of these two mononuclear NiII complexes, we attempted to built a structural model similar to that reported by Gatteschi (three dimensional) [51d] and Morpugo (one dimensional) [52] by using Corey–Pauling–Kotlun (CPK) molecular models. It was clear that an extended structure could not be built because the steric hindrance induced by the bulky bpm or bipy ligands. In order to achieve an extended structure, 2+ the hexacyanometallate must bridge more than three Ni(bpm)2+ 2 (or Ni(bipy)2 ) molecules; this turned out not to be possible when the chelating ligand has bulky groups attached on two well identified atoms coordinated to NiII and not anywhere else. This leads to the conclusion that it is possible to design the organic ligand in order to prepare complexes of expected nuclearities or extended systems with a particular architecture.


6.4.6

217

Molecules with Two Shells of Paramagnetic Species

One of the advantages of the step-by-step approach is the possibility to use the strategy developed for the synthesis of dendritic molecules in order to design polynuclear complexes containing at each generation an increased number of paramagnetic species. Let us concentrate on the method that may be used to design molecules with a central metallic core surrounded by two shells of metal ions. The same method may then be extended to molecules containing more than two shells. In the case of a core of connectivity 3, the topology of a target two-shell molecule is represented in Scheme 14. In order to prepare such molecules, one should design three kinds of complexes: the first kind is the core that as stated above should be able to play the role of a ligand towards the complexes of the first shell, the second kind is the periphery molecule, it must play the role of a metal towards the complexes of the second shell and the third kind is the complex of the first shell that should play simultaneously the role of a metal and a ligand towards the core and the peripheral complexes respectively. The core and the peripheral complexes are easy to design (see above), the difficulty resides in the design of the first shell complex which in addition to the requirements mentioned above must be able to transmit efficiently the magnetic interaction so that the low-lying spin ground state of the polynuclear complex will be well separated from the excited states.

Scheme 14

Schemes 15 and 16 show two possible examples of such molecules; Scheme 15 represents a mononuclear complex adapted to a core possessing a monodentate Lewis base like the hexacyanometallates while Scheme 16 represents a complex with a tetradentate ligand leaving two coordination sites in cis position allowing the reaction with the trisoxalatochromate(III) for example. These complexes bear two imidazol groups that once deprotonated may serve to coordinate two peripheral molecules achieving thus the synthesis of two-shell complexes.

Scheme 15

Scheme 16

218


6.4.6.1

Synthesis and Magnetic Properties of a CrNi3 Complex

The synthesis of two-shell complexes may be carried out by two different methods: the first method is convergent, it consists of preparing a trinuclear complex and then as a second step assembling six trinuclear complexes around the hexacyanochromate(III) core (or three trinuclear complexes if the trisoxalatochromate(III) is used as the core), the second method is divergent and consists of building up around the core the two shells step by step. We have used this latter approach to prepare a tetranuclear complex that can be considered as the first step towards the synthesis of a two-shell complex. The reaction between ((C4 H9 )4 N)3 [Cr(CN)6 ] and [Ni(imdipa)Cl]PF6 in acetonitrile leads to the formation of a tetranuclear complex of formula [(NC)3 Cr(CNNi(imdipa))3 ]Cl2 PF6 . The investigation of the magnetic properties shows that the spin ground state is S = 9/2 as expected from the ferromagnetic interaction between the central CrIII and NiII metal ion through the cyanide bridge. The experimental data showing the dependence of χM T on T (Fig. 23) were fitted by use of the spin Hamiltonian (Eq. 5): ∗

H = −JCrNi SCr · S + D

Sz2

S(S + 1) − + β [gCr SCr + gNi S ∗ ] H 3

(5)

where S ∗ = S N i1 +S N i2 +S N i3 and S = SCr +S ∗ , D is the zero-field splitting parameter within the ground state S = 9/2. The fit results are: JCrNi = 12.4 cm−1 , gCr = 1.98, gNi = 2.27 and |D| = 0.7 cm−1 ; the JCrNi value is in the same range as that of the heptanuclear CrNi6 complex [45] (15.6 cm−1 ). An important feature revealed by the magnetic properties measurements is the rather relatively large zero-field splitting parameter (0.7 cm−1 ) associated to S = 9/2 ground state. It is clear that this value is only a rough estimate, HF-EPR studies are needed to get a much better idea on

Fig. 23. Experimental (◦) and calculated (—) plots of χM T [(NC)3 Cr(CNNi(imdipa))3 ]Cl2 PF6 .

against

T

for


219

the amplitude of the magnetic anisotropy. However, the zero-field splitting in the tetranuclear complex is two order of magnitude larger than that found for CrNi6 (0.008 cm−1 ). This is in line with the lower symmetry of the tetranuclear complex in comparison to the octahedral heptanuclear one. We are currently working on the synthesis of the second step that will enable, by deprotonating the six imidazol functions present on the three NiII complexes, coordination of six peripheral metal complexes and thus achieve the synthesis of a decanuclear two-shell complex.

6.4.6.2

A Pentanuclear Complex with Three Different Paramagnetic Species

Another elegant way to design a molecule with two shells of paramagnetic species is to use organic radicals as chelates for the peripheral metallic complexes. The first idea was to prepare a tetranuclear complex similar to that reported by Kahn and coworkers [Cr(oxNi(Me6 -[14]ane-N4 ))3 ](ClO4 )3 [35] (see above) but by substituting the tetradentate ligand of the peripheral complex by two bidentate organic radicals. The synthesis of the mononuclear complex [Ni(IM2-py)2 (NO3 )]NO3 (IM2-py = 2-(2-pyridyl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazolyl-1-oxy, Scheme 17) was achieved. Unfortunately, the crystal structure was not solved but that of the mononuclear NiII complex with the hydroxylamine derivative of the radical was (Fig. 24). It shows that the two bidentate ligands are coordinated in cis position as required for the trisoxalatochromate(III) core; the remaining coordination sites are occupied by a chelated nitrate anion. The reaction between [Ni(IM2-py)2 (NO3 )]NO3 and the tetrabutylammonium or the potassium salt of [Cr(C2 O4 )3 ]3− leads to non-pure compounds that were identified to be a mixture of the postulated tetranuclear complex contaminated with variable amount of the trinuclear complex CrNi2 depending on the preparation procedure. Trying the perchlorate salt of the NiII complex seems to give better results but no well identified pure compound could be obtained yet.

Scheme 17

The structure of the NiII complex (Fig. 24) shows that the ligands are bulky so that the reaction with hexacyanochromate(III) may lead to a pentanuclear complex similar to that described by Murray and coworkers (Fig. 22) [51e]. Let us first see what will be the ground state of such pentanuclear complex that will contain two S = 3/2 CrIII , three S = 1 NiII and six S = 1/2 organic radicals. We have already shown that the exchange interaction between CrIII and NiII is ferromagnetic due to the orthogonality of their semi-occupied orbitals. On the other hand, Rey studied the magnetic properties of the mononuclear Ni(hfac)2 (IM2-py) (hfac = hexafluo-

220


Fig. 24. Structure of the monocation [Ni(HIM2-py)2 (NO3 )]+ .

roacetylacetonate) complex and observed a ferromagnetic interaction between NiII and the radical ligand [53]. The exchange coupling parameter JNiRad was found to be equal to 128 cm−1 . Having these results in mind, we expect that within the pentanuclear complex the interaction between the different magnetic species will be ferromagnetic leading to a S = 9 ground state. The reaction between [Ni(IM2-py)2 (NO3 )]NO3 and K3 [Cr(CN)6 ] leads, when performed in water, to the formation of a precipitate. The characterization of the compound leads to the following formula: [Cr(CN)6 ]2 [Ni(IM2-py)2 ]3 .7H2 O [54]. The new compound is soluble in most common solvents but is insoluble in water as expected for a neutral species. Unfortunately, crystals suitable for X-rays analysis have not been obtained. To give some evidence supporting our assumption of the presence of a discrete species within the compound, we recorded the UV-visible electronic spectrum and compared it to that of the mononuclear NiII complex. The UV-visible spectrum (MeOH, c = 3×10−2 M) presents a band assigned to the 3 T2g ← 3 A transition of the NiII chromophores (E = 11 363 cm−1 , ε = 35.9 L mol−1 cm−1 ) 2g which is shifted to higher energy in comparison to that of the mononuclear [Ni(IM2py)2 (H2 O)2 ]2+ complex (E = 10 416 cm−1 , ε = 45 L mol−1 cm−1 ). It has already been shown that the nitrogen end of the cyanide induces a stronger crystal field than water [55], thus the solubility of the compound is not because of decomposition of an extended network in solution but because our compound is made of discrete polynuclear species keeping the same structure (presence of bridging cyanides) in solution as found in the solid state by infrared studies. To check our assumption that the molecular species is a pentanuclear complex with a structure similar to that reported by Murray and in order to investigate the nature of the ground state, we carried out magnetization measurements on a powder


221

Fig. 25. Experimental (◦) and calculated (—) plots of χM T against T for [Cr(CN)6 ]2 [Ni(IM2py)2 ]3 .7H2 O.

sample. On cooling down χM T increases and reaches a maximum at T = 6.5 K, then decreases (Fig. 25). The value at the maximum (42 cm3 mol−1 K) is very close to the expected one for a S = 9 ground state (45 cm3 mol−1 K for an average g value of 2) which corresponds to the parallel alignment of the local spins of the eleven paramagnetic species. A calculation of χM T as a function of temperature for different values of JCrNi and JNiRad by setting the local g values to gCr = 1.98, gNi = 2.07 and gRad = 2.00 was performed. The calculated curves for JNiRad = 150 K (105 cm−1 ) and JCrNi = 9, 11, 13, 15 and 17 K are shown in Fig. 26. The best agreement between the experimental and the calculated data is obtained in the temperature range 300– 8 K, for JCrNi = 13 K (9 cm−1 ) and JNiRad = 150 K (105 cm−1 ). It is possible at this level to introduce a parameter θ that takes into account the decrease of χM T at low temperature as due to antiferromagnetic intermolecular interactions, a very good agreement is obtained with θ = −0.45 K (Fig. 25). The sign and the values of the exchange coupling parameters are in the same range as what has already been found for CrNi6 [45] (JCrNi = 15.6 cm−1 ) and Ni(hfac)2 (IM2-py) [53] (JNiRad = 128 cm−1 ). The decrease of χM T at low temperature may be due to zero-field splitting effect and not to intermolecular antiferromagnetic interaction. Unfortunately, zerofield splitting could not be included because of prohibitive calculation time. The magnetization vs. field plot (Fig. 27) (T = 2.2 K, H = 0–140 kOe) shows that the value at saturation (18.1 Bohr Magneton) corresponds to the expected S = 9 ground state. AC susceptibility measurements performed down to 100 mK show the absence of long-range magnetic order, a behavior different from the ferromagnetic order found for Murray’s pentanuclear complex [Fe(CN)6 ]2 [Ni(bpm)2 ]3 .7H2 O. The origin of the difference in behavior at low temperature is probably due to the absence of a network of hydrogen bonds in our compound linking the pentanuclear species together; this is only an assumption since the crystal structure of our compound

222


Fig. 26. Value of χM T calculated by fixing JNiRad to 150 K and varying the value of JCrNi for [Cr(CN)6 ]2 [Ni(IM2-py)2 ]3 .7H2 O.

Fig. 27. Plots of magnetization against field for [Cr(CN)6 ]2 [Ni(IM2-py)2 ]3 .7H2 O, (◦) experimental, (—) Brillouin function for S = 9 (g = 2), (- - -) sum of the Brillouin functions for six S = 1/2 (g = 2), three S = 1 (g = 2.07), and two S = 3/2 (g = 1.98).

has not been solved yet. The solubility of our compound and the presence of only two bands in the 2000–2200 cm−1 region of the infrared spectrum assigned to two kind of cyanide bonds: bridging and non-bridging is in favor of the absence of a hydrogen-bond network involving the pentanuclear species. Actually, the infrared spectrum of Murray’s complex reveals, in addition of bands assigned to bridging and terminal cyanides, the presence of bands assigned to terminal cyanides which form hydrogen-bonds with the oxygen atoms of water molecules present in the structure.

6.5 Conclusion

223

The use of organic radicals to stabilize large spin ground states may be particularly interesting within a rationale approach. We have described an example of a complex where the organic radicals are located on the periphery. Rey and coworkers showed that it is possible to use bis-bidentate radicals to bridge two metal ions and prepare an extended 2D network by a two-step reaction [56]. The organic radicals within the network are bridging the metal ions. Using the same approach, it may be possible to design discrete species where the organic radicals are located not only at the periphery but within the body of the polynuclear complex. A judicious choice of the different paramagnetic species may lead to the stabilization of a very high spin ground state.

6.5

Conclusion

The self-assembly strategy has produced a great number of new complexes, some of them possess a high spin ground state. The possibilities in this area of research are open and the results obtained in the last ten years proof that the efforts made are rewarding. On the other hand, the multistep approach that we have developed is laborious and arduous. Preparing a perfectly structured two- or three-shell high spin molecules is a challenge. The question is: is it worth the effort to try to design and prepare such systems? The answer is probably: yes. The study of the properties of a molecule made of well identified fragments (the constituent of each shell) gives valuable information on many physical parameters: magnetic anisotropy, amplitude and nature of the exchange coupling interaction, optical transitions. . . This information is crucial to our understanding of the properties of large polynuclear complexes and are of great value to perform magnetostructural correlation of such complex molecules.

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7

Electronic Structure and Magnetic Behavior in Polynuclear Transition-metal Compounds Eliseo Ruiz, Santiago Alvarez, Antonio Rodr´ıguez-Fortea, Pere Alemany, Yann Pouillon, and Carlo Massobrio

7.1

Introduction

The observed magnetic behavior of transition-metal complexes containing more than one paramagnetic metal atom often differs from that predicted by the sum of the magnetic properties of each individual unit bearing unpaired electrons [1]. This phenomenon is due to a coupling of the electron spins and is termed intramolecular antiferromagnetism or ferromagnetism, depending upon whether antiparallel or parallel spin alignment is found in the ground state, respectively. Since the discovery of intramolecular magnetic coupling in 1951 by Guha [2] and then by Bleaney and Bowers [3] in a compound known at that time as copper(II) acetate monohydrate, the mechanism of exchange coupling and its relation with the electronic structure have been the subject of a large number of experimental and theoretical studies [4, 5]. From the theoretical point of view, it was soon realized that the study of the electronic structure of magnetically coupled systems is more challenging that the problem of chemical bonding in closed-shell molecules. While simple reasoning based on molecular topology, overlap between atomic orbitals and electronegativity often allow qualitative interpretations in closed-shell systems [6], no single qualitative model is able to explain satisfactorily all features of exchange coupled systems and there are still a number of controversies about the advantages and limits of the various approaches that have been devised. The direct calculation by means of sophisticated ab initio methods of the energy differences between the ground and low lying excited spin states has been also hindered by serious computational problems: energy splittings of the order of 100 cm−1 (∼0.3 kcal mol−1 ) or even smaller must be obtained as differences between total energies which are up to seven orders of magnitude larger [7]. If one adds to this situation that the compounds of experimental interest are formed by at least 40 atoms (including two or more transition metal ones) one can understand the relative scarcity of attempts to use the ab initio approach until the last few years. The rapid development of hardware and software technologies, together with the emergence and consolidation of new ab initio methods applied to the electronic structure of molecular compounds (mainly based on density functional theory, DFT) [8, 9] in the last decade has dramatically changed the situation. Thus, the simplest cases of exchange coupled systems, i. e. dimers of transition-metal ions with a single unpaired

228

7 Electronic Structure and Magnetic Behavior

electron on each metal atom, can be treated in an almost routine way using standard quantum chemical software packages on desktop computers. The study of more complex systems, involving two atoms with more than one unpaired electron per center or compounds with more than two paramagnetic centers is nowadays the subject of an intense research and their study will be possibly affordable in a routine way soon. The availability of quantitative or semiquantitative approaches to the electronic structure of magnetically coupled systems has, on the other hand, renewed the interest on the earlier qualitative models. The exploration of their strengths and weaknesses, together with the establishment of their limits of applicability has allowed researchers in this field to use these simple methods as valuable complementary tools in the interpretation of the results obtained with the more sophisticated ab initio calculations. The conceptual simplicity of these qualitative models often provides a much deeper insight into the physical origins of exchange coupling than that obtained by using the more accurate, but also more obscure, first principles techniques. In the first part of this chapter (Sections 2–4) we will present the key concepts involved in the most widely used qualitative models and ab initio approaches to the electronic structure of magnetically coupled systems, discussing their merits and limits. In the second part (Section 5) we will show how some of these theoretical approaches have been applied to selected examples.

7.2

Phenomenological Description of Exchange Coupling: the Heisenberg Hamiltonian

The study of intramolecular exchange interactions started, as mentioned above, with the analysis of the magnetic properties of copper(II) acetate. This compound is actually dimeric, with four acetate ligands bridging two copper(II) ions (1), each bearing one unpaired electron. The magnetic susceptibility of this compound exhibits a broad maximum as a function of temperature and becomes negligible below 100 K. This behavior can be rationalized through the phenomenological Heisenberg Hamiltonian that describes the exchange interaction between the two paramagnetic centers: Hˆ = −J SÂ · SˆB

(1)

where SA and SB are the total spins on each metal ion (SA = SB = 1/2 in this case) and J is known as the exchange coupling constant [1]. With the above definition, positive values of J indicate a ground state with parallel spins, that is, a ferromagnetic interaction, while negative values correspond to an antiferromagnetic coupling. (Alternative definitions for the exchange coupling constants are also common in the literature. In some cases, the Heisenberg Hamiltonian is expressed as Hˆ = +J SÂ · SˆB , whereupon positive values of J indicate antiferromagnetic coupling, and negative ones correspond to the ferromagnetic situation. In other instances, the Hamiltonian used is Hˆ = −2J SÂ · SˆB and the reported coupling constants must be multiplied

7.2 Phenomenological Description of Exchange Coupling: the Heisenberg Hamiltonian

229

by 2 to make them comparable with those obtained using Eq. 1.) The experimental magnetic susceptibility indicates that the electron spins in copper(II) acetate are antiferromagnetically coupled with J = −296 cm−1 . If the two spins of the metal ions interact, the local spins SA and SB are not good quantum numbers and we must use the total spin: Sˆ = SÂ + SˆB

(2)

to characterize the pair states. It is relatively easy to show that the eigenvalues of the Heisenberg Hamiltonian can be expressed as a function of the total spin quantum number S: J E(S) = − S(S + 1) 2

(3)

which, for two local doublet states found in copper(II) acetate leads to singlet (S = 0) and triplet (S = 1) states separated by an energy gap of magnitude J : E S − ET = J

(4)

It is important to note here that exchange coupling constants are not determined directly from experiment. The usual procedure is to use the model Hamiltonian to derive an expression for the temperature dependence of the magnetic susceptibility and to fit the experimental susceptibility to this expression, treating the coupling constant as an adjustable parameter [4]. This procedure, which is straightforward for exchange coupled dimers is, however, difficult for many polynuclear or extended systems, for which an analytical expression for the temperature dependence of the magnetic susceptibility is still lacking. In such cases, approximate models or simulation procedures are often used to obtain the temperature dependence of the magnetic

230


susceptibility and to fit it to the experimental data [5]. The use of different models may, however, lead to significantly different “experimental” coupling constants; this makes comparison with calculated constants difficult.

7.3

Qualitative Models of the Exchange Coupling Mechanism

The Heisenberg Hamiltonian is purely phenomenological and it does not provide any information on the real mechanism of the interaction between the two unpaired electrons. The theoretical interpretation of exchange interactions has traditionally been based on ideas developed for infinite solid lattices [10–13]. Since it has been realized empirically that the bridging atoms between the metal ions bearing the unpaired electrons determine the sign and magnitude of the exchange interaction, such qualitative treatments focus on the various types of overlap between ligandcentered and metal d orbitals. Extension of these ideas to cases involving molecular, rather than atomic bridging species has lead to the two most widely used qualitative models for intramolecular exchange interactions that will be briefly reviewed here.

7.3.1

Orthogonal Magnetic Orbitals

To relate the experimentally available quantity, the coupling constant J , to the electronic structure of the compound, let us consider a centrosymmetric model system Ma –X–Mb , where Ma and Mb are two paramagnetic centers (transition metal atoms in our case) with one unpaired electron each and X is a closed-shell diamagnetic bridge (or set of bridges). The unpaired electron on each paramagnetic center occupies one of the d orbitals of the transition metal atoms, da and db . In copper(II) acetate, for example, the unpaired electrons can be found on x2 –y2 -like copper orbitals oriented toward four oxygen atoms of the acetato bridges (2).

The combination of the da and db orbitals with ligand-centered φx orbitals leads to two molecular orbitals ϕ1 and ϕ2 (see 3, where only the contributions of one of the acetato bridges are depicted for simplicity) that play a key role in the qualitative orbital models proposed to rationalize magnetic behavior of dinuclear complexes. If we restrict our analysis to the two unpaired electrons occupying molecular orbitals ϕ1

7.3 Qualitative Models of the Exchange Coupling Mechanism

231

and ϕ2 (active-electron approximation) the following many-electron configurations arise (4) [14]: S1 = |ϕ1 αϕ1 β| S2 = |ϕ2 αϕ2 β| 1 S3 = √ |ϕ1 αϕ2 β| − |ϕ1 βϕ2 α| 2 T,+1 = |ϕ1 αϕ2 α|; T,−1 = |ϕ1 βϕ2 β|; 1 T,0 = √ |ϕ1 αϕ2 β| + |ϕ1 βϕ2 α| 2

(5)

Although the energy of the lowest triplet can be evaluated for a single determinant, e.g. T,+1 , the lowest singlet state will be represented by a linear combination of S1 and S2 : S = λ1 S1 + λ2 S2

(6)

In the limit of non-interacting metal ions we have |λ1 | = |λ2 |, while in the opposite extreme, for strong metal-metal bonding, |λ1 | |λ2 |. In a centrosymmetric dimer, ϕ1 and ϕ2 belong to different symmetry species and there is no contribution of S3 to the lowest singlet state because it belongs to a different symmetry species than S1 and S2 . In what follows it will be assumed that the MOs themselves correspond to an SCF solution for the triplet state [15]. After introducing some plausible approximations, Hay, Thibeault and Hoffmann [16] proposed the following expression for the singlet–triplet splitting: 1 (ε1 − ε2 )2 E S − E T = −J12 + (J11 + J22 ) − 2 2K 12

(7)

where ε1 and ε2 are the energies of molecular orbitals ϕ1 and ϕ2 , and Ji j and K i j are the Coulomb and exchange integrals, respectively, expressed in the molecular orbital basis: −1 Ji j = ϕi (1)ϕ j (2)|r12 |ϕi (1)ϕ j (2) (8) −1 K i j = ϕi (1)ϕ j (2)|r12 |ϕ j (1)ϕi (2) (9)

232


The interpretation of experimental data is simpler if Eq. (7) is expressed in terms of two-electron integrals involving localized molecular orbitals ϕa and ϕb defined as follows: 1 ϕa = √ (ϕ1 + ϕ2 ) 2

and

1 ϕb = √ (ϕ1 − ϕ2 ) 2

(10)

Because of their orthogonality, ϕa |ϕb = 0, ϕa and ϕb are sometimes called orthogonal magnetic orbitals. The singlet-triplet splitting, Eq. (7), can be now rewritten as: E S − E T = J = 2K ab −

(ε1 − ε2 )2 Jaa − Jab

(11)

which is the key equation of the Hay, Thibeault, and Hoffmann (HTH) model relating the exchange coupling constant to the electronic structure of the compound. Because K ab , Jaa , and Jab are all positive and Jaa > Jab , both terms in Eq. (11) must be positive. The first term in this equation represents, therefore, a positive, ferromagnetic, contribution to the overall coupling constant, whereas the minus sign preceding the second term in Eq. (11) indicates an antiferromagnetic contribution to the exchange coupling constant: J = JF + JAF

(12)

JF = 2K ab

(13)

with

and JAF = −

(ε1 − ε2 )2 Jaa − Jab

(14)

If ϕ1 and ϕ2 are degenerate or nearly degenerate, the antiferromagnetic contribution vanishes and a triplet ground state results. On the other hand, a significant splitting between these two molecular orbitals will yield a singlet ground state. Eq. (11) thus suggests that we can focus on the orbital energy difference ε1 − ε2 as a measure of the singlet-triplet energy splitting for these compounds [16]. The HTH model has been mainly applied within the extended Huckel ¨ framework, [17–20] the simplest all-valence-electron model in quantum chemistry. Since twoelectron interactions are not included in this method, actual singlet-triplet energy differences cannot be calculated with such approach. One can nevertheless assume that extended Huckel ¨ calculations reproduce correctly the qualitative changes in the orbital energies as a function of the structure and the nature of the substituents [6]. Thus, the HTH model allows the study of the variation of J within a family of dinuclear compounds if one assumes that all two-electron integrals in Eq. (11) are practically insensitive to structural changes (or to changes in the non-bridging ligands) [21]. Within this approximation, that has been used to explain a large number

7.3 Qualitative Models of the Exchange Coupling Mechanism

233

of experimentally observed magneto-structural correlations [22–30], the analysis is restricted to the variation of the one electron term (ε1 − ε2 )2 in Eq. (11). Extension of the HTH model to more complex systems, such as dinuclear compounds with more than one unpaired electron on each metal atom or compounds with more than two metal atoms, is not straightforward [31]. The number of configurations that must be considered to describe the spin states of the system grows rapidly with the number of unpaired electrons and the analysis becomes more and more complex. Explicit expressions similar to Eq. (11) have been derived only for dimers with the same number of unpaired electrons on each metal atom. In these expressions, the antiferromagnetic term can be analyzed in terms of separate contributions from pairs of orbitals. In the case of a dimer with two d8 ions in local octahedral environments, for example, one must consider four molecular orbitals: ϕ1 and ϕ2 arising from the in-phase and out-of-phase combinations of the x2 − y2 orbitals of the two metals, and ϕ3 and ϕ4 involving the z2 orbitals. Two orthogonalized magnetic orbitals are now constructed from each of these pairs (ϕ1 and ϕ2 give raise to ϕa and ϕb , while ϕc and ϕd are constructed from ϕ3 and ϕ4 using expressions analogous to Eq. 10). The total coupling constant in terms of orbital energies and two-electron integrals involving the orthogonalized magnetic orbitals is, within this approximation: J = E S − ET = =

1 (E T − E Q ) 2

1 1 (ε1 − ε2 )2 1 (ε3 − ε4 )2 − (K ab + K ad + K bc + K cd ) − 2 4 Jaa − Jab 4 Jcc − Jcd

(15)

which shows that the antiferromagnetic term can be traced to the separate contributions from the x2 − y2 and z2 orbitals [16]. Here, the energy values E S , E T and E Q correspond to the spin states with S = 0, S = 1 and S = 2, respectively. Despite its success in explaining a large amount of experimental data, the shortcomings of the HTH model are evident. The model allows only to study trends within a family of compounds with the same Ma –X–Mb core. Since the actual values of the coupling constant are not directly evaluated, it is impossible to predict one of the most important properties in intramolecular magnetism, that is, the relative coupling ability of different bridging ligands. The model fails also in the case of the most interesting compounds, those exhibiting ferromagnetic coupling. Since the term (ε1 − ε2 )2 is supposed to be negligible for these compounds, changes in K i j , even if small in absolute terms, can be crucial in the study of magneto-structural correlations. An additional problem that limits the applicability of the HTH model is that the localization criterion, see Eq. (10), is only valid when the Ma and Mb centers are symmetry-related, either through an inversion center, or through a twofold axis. This fact precludes the application of the HTH model to heterodinuclear compounds which are of great interest as potential building blocks for molecule-based ferrimagnetic systems [32].

234

7.3.2


Natural Magnetic Orbitals

To remedy, at least partially, some of the deficiencies of the HTH model, an alternative approach to analyze the relationship between electronic structure and the exchange coupling mechanism was devised [4, 33]. The exchange interaction in the Ma –X–Mb system may be viewed as the borderline case of a very weak chemical bond. In this case it is appropriate to use a Heitler-London type of wavefunction: =

1 2 ) 2(1 ± Sab

χa (1)χb (2) ± χa (2)χb (1)]

(16)

where the positive sign holds for the singlet and the negative sign for the triplet state. In this approximation, χa is defined as the singly occupied molecular orbital for the Ma –X fragment in its local ground state and χb is defined in the same way with respect to the X–Mb fragment. This type of orbitals has been called natural magnetic orbitals by Kahn and coworkers [4, 33–35]. The cutting of the Ma –X–Mb system into two Ma –X and X–Mb fragments with a common bridging region X is not rigorous and constitutes certainly the weak point of this approach since too much weight of the bridge’s orbitals is introduced in this way in the wavefunctions describing each state. One way suggested to determine the natural magnetic orbital χa consists in contracting the atomic orbitals of Mb until all orbital interactions between the magnetic center Mb and its surroundings become negligible. Natural magnetic orbitals are by construction non-orthogonal and their overlap integral Sab = χa | χb

(17)

plays a key role in the qualitative orbital model devised by Kahn and coworkers to predict the magnitude of exchange interactions in magnetically coupled systems [36–45]. Considering the two states described by the Heitler-London wavefunctions (Eq. 16) the singlet-triplet splitting can be expressed as: 2 E S − E T = J = 2K + 4h ab Sab − 2Sab (2h aa + j)

(18)

where ˆ a h aa = χa |h|χ ˆ b h ab = χa |h|χ −1 k = χa (1)χb (2)|r12 |χa (2)χb (1) −1 j = χa (1)χb (2)|r12 |χa (1)χb (2)

(19)

In these expressions hˆ is the one-electron Hamiltonian that takes into account the kinetic energy of the electron and its interactions with the nuclei and with all the passive electrons. For a centrosymmetric Ma –X–Mb system, h aa = h bb .

7.4 Quantitative Evaluation of Exchange Coupling Constants

235

The 2k term in Eq. (18) is always positive, and therefore represents a ferromagnetic contribution. Assuming Sab to be small enough, Sab and h ab are of opposite sign and the second term in Eq. (18) represents an antiferromagnetic contribution to the overall coupling constant. The sign of the last term in Eq. (18) cannot be easily determined because h aa and j have opposite signs. For small enough of Sab values one can assume that the contribution of this third term to the coupling constant will be much smaller than the rest and it is often neglected in a qualitative analysis, resulting in: J = JF + JAF ≈ 2k + 4h ab Sab

(20)

In a more elaborate model one can include the contribution of the metal–metal charge-transfer configurations χa (1)χa (2) and χb (1)χb (2) to the singlet state. This treatment gives rise to an additional antiferromagnetic term stabilizing the singlet state. There is no definitive answer yet as to which of the two antiferromagnetic contributions dominates the value of J . It has been however suggested that in transition metal dinuclear compounds the metal-metal charge-transfer configurations are in general too high in energy to couple significantly with the low lying singlet state [4]. The qualitative interpretation of the exchange coupling is now based on the overlap Sab between natural magnetic orbitals. If Sab vanishes, according to Eq. (20) we should expect a triplet ground state with J = 2k. The strength of the antiferromagnetic coupling provided by different bridging ligands (or sets of bridging ligands) X can now be compared, provided that one is able to calculate Sab . This is, however, a difficult task since, as mentioned above, the definition of natural magnetic orbitals is not rigorous. This difficulty has relegated the application of this qualitative model to the cases in which Sab can be predicted to vanish for symmetry reasons. The search for compounds with orthogonal natural magnetic orbitals has lead to some success in the synthesis of molecules with “designed” ferromagnetic coupling, as in Cu(II)Cr(III)[37] or Cu(II)V(IV) complexes [39]. It is also worth to mention in this section the work of Gudel ¨ et al., who explored the exchange interaction, for instance in several transition metal oxo complexes [46, 47], using a perturbative approach to obtain the different contributions to the exchange interaction. This approach has also been employed by von Seggern et al. [48]. to study the ferromagnetic coupling in end-on azido Cu(II) complexes. The parameters needed in these calculations, such as the h ab transfer integrals are obtained from simple angular overlap approximations or extended Huckel ¨ calculations, while the orbital energy differences U are usually estimated from experimental spectroscopic data [49].

7.4

Quantitative Evaluation of Exchange Coupling Constants

Although successful qualitative predictions have been derived from the models discussed above, non-empirical calculations including electron correlation are needed to reach quantitative estimates of exchange coupling constants. As can be deduced

236


from the preceding discussion, the consideration of configuration interaction is an unavoidable step in any attempt to calculate the spectrum of the low lying states of a magnetic polynuclear compound. The precise calculation of the small energy gaps needed for the evaluation of coupling constants is a great computational challenge. In this section we will briefly review the fundamental aspects of the different approaches that have been proposed to reach this goal.

7.4.1

Perturbative and Variational Calculations of State Energy Differences

In one of the pioneering works in theoretical molecular magnetism, de Loth et al. solved this dilemma by calculating the singlet–triplet energy difference in copper(II) acetate directly [50]. For this purpose these authors devised a perturbative development up to second order of the configuration interaction problem which allowed them not only a first semiquantitative computation of the coupling constant in this compound, but also a decomposition of such parameter in different contributions that permitted a qualitative understanding of the physical mechanisms responsible for the exchange coupling phenomenon. The calculation of the coupling constant within this approach consists of two separate steps. The first is the construction of magnetic orbitals performing a restricted open-shell SCF calculation. This calculation yields two singly occupied molecular orbitals ϕ1 and ϕ2 that are then transformed into orthogonal localized magnetic orbitals ϕa and ϕb defined by Eq. (10). The M S = 0 components of the singlet and the triplet states are defined by: 1 1 0 = √ | . . . ϕi αϕi β . . . ϕa αϕb β| + | . . . ϕi αϕi β . . . ϕa βϕb α| 2 1 = √ (1 + 2 ) 2 (21) 1 3 0 = √ | . . . ϕi αϕi β . . . ϕa αϕb β| − | . . . ϕi αϕi β . . . ϕa βϕb α| 2 1 = √ (1 − 2 ) 2 where ϕi stands for one of the doubly occupied molecular orbitals and 1 , 2 are shorthand notations for the two Slater determinants involved in the above expressions. The zeroth-order singlet–triplet energy splitting is given by the well-known exchange integral: (0)

E ST = 2K ab

(22)

that represents a ferromagnetic contribution, called potential exchange, favoring a triplet ground state. The second order contribution to the singlet–triplet splitting is given by: 2 1 | Hˆ |i i | Hˆ |2 i (2) E ST = (23) E0 − Ei


237

where E 0 is the energy corresponding to 1 or 2 and E i are the energies of the determinants i which describe excited states. It is interesting to note that the number of determinants i which contribute to the second-order perturbation term of the singlet–triplet separation is reduced to those which interact with both 1 and 2 . For this reason, these determinants are much less numerous than those involved in the second order CI corrections to the energy of the singlet and triplet states. The determinants i which contribute to the second-order correction must differ, at most, by two spin orbitals from 1 and 2 to give a non-zero numerator. Fig. 1 shows a schematic representation of all types of i determinants along with the name of their contribution to the second order correction to the singlet-triplet energy splitting.

Fig. 1. Schematic representation of the determinants that interact with both 1 and 2 in the second-order correction to the singlet-triplet energy splitting.

238


Table 1. Numerical values (cm−1 ) of various contributions to the singlet-triplet energy splitting, J , for Cu(II) acetate after de Loth et al. [50]. Values in the fourth column correspond to the accumulated sum of the different contributions to J . The corresponding experimental value is −297 cm−1 [4, 51, 52]. Perturbation

Contribution

Zeroth order Second order

Potential exchange Kinetic exchange Double-spin polarization M → L charge transfer L → M charge transfer Kinetic exchange + polarization Kinetic exchange Kinetic exchange + polarization

Higher order

Ji +233.6 −204.3 −52.0 0 −5.9 −2.3

Ji +233.6 +29.3 −22.7 −22.7 −28.6 −30.9

−89.3 or −213.5 −120.2 or −244.4

As can be deduced from Table 1, the leading contributions for copper acetate are those of potential exchange Eq. (22) and kinetic exchange (second-order term, see Fig. 1). These two contributions have been shown to correspond, respectively, to J F and J AF in the qualitative HTH model Eq. (11) which therefore corresponds to the neglect of all other second and higher order terms in the perturbative expansion of the singlet-triplet gap. The actual figures in Table 1 show that the kinetic exchange barely compensates the direct exchange, bringing the singlet-triplet splitting almost to zero. This result, which has been found in all cases studied with this methodology, is rather disappointing, since earlier qualitative explanations of exchange coupling such as the HTH model had been based on just these two terms. Addition of other contributions to the second order expression (see Table 1) results in a progressive stabilization of the singlet state relative to the triplet. The value given by de Loth et al. for J at the second order level is −30.9 cm−1 , which has already the correct sign, but is still far from the experimental value of approximately −297 cm−1 [4, 51, 52]. Such disagreement led the authors to consider higher order corrections, although these are so numerous that cannot be calculated in a complete way. Considering two different ways to estimate higher order corrections, de Loth et al. arrive at much better values for J : −120.2 and −244.4 cm−1 . These two values show, however, the weak point of this perturbational approach, that is, convergence. In many cases stopping at the second order level gives just the correct sign of the coupling constant and higher order terms are needed to obtain a quantitative estimate of its value. The treatment of these higher order terms is far from trivial and different treatments can lead to quite different values for such terms. An interesting question that arises at this point is why is the HTH model able to qualitatively predict the changes in J for small structural distortions or changes in the peripheral ligands if the two terms that it retains practically cancel each other? An answer to this question can be found in the work of Daudey et al. that attempted to justify the experimentally observed correlation between the value of J and the Cu—O—Cu angle in planar hydroxo-bridged Cu(II) compounds [53]. The calculated values for J , together with its decomposition in the different zero and second-order terms, are shown in Table 2 for [Cu(tmen)OH]2 Br2 for its experimental geome-


239

Table 2. Numerical values (cm−1 ) of various contributions to the singlet-triplet energy splitting, J , for [Cu(tmen)OH]2 Br2 with its experimental geometry (left column) and with the O–Cu–O angle set to 95◦ , after Daudey et al. [53]. Contribution

Cu–O–Cu 104◦

Potential exchange Kinetic exchange Double-spin polarization L → M charge transfer M → L charge transfer Kinetic exchange + polarization Calculated value Experimental value

+1380 −1306 +11 −477 −35 −236 −393 −509

95◦ +1275 −431 +40 −492 −35 −260 +97 +161

try (Cu—O—Cu = 104◦ ) and for a hypothetical structure having Cu–O–Cu = 95◦ , for which a value of J = 161 cm−1 is predicted from the experimentally-derived magneto-structural correlation. It can be clearly deduced from the values in Table 2 that the variation of the kinetic exchange term is actually the main cause for the variation in J . All other second-order terms, although far from negligible, are much less sensitive to the structural variation analyzed. The success of the HTH model is thus related to the fact that it reduces the antiferromagnetic contribution to the kinetic exchange, which is the only second-order contribution that is strongly affected by the molecular geometry. The perturbational approach of de Loth et al. has been applied with some success to Cu(II) dinuclear complexes with acetato [53], hydroxo [53], alkoxo [54] and oxalato bridges [55], as well as to a heterodinuclear Cu(II) -V(IV) complex, in which the kinetic exchange term is found to be zero as predicted by the qualitative model of Kahn and coworkers [56]. This approach was subsequently employed by Haase and coworkers to study N -oxide [57], hydroxo [58], alkoxo/acetato [59] and terephthalato-bridged [60] Cu(II) dinuclear complexes and hemocyanin models [61]. The difficulties related to the convergence of the perturbational corrections that arise within this approach lead Miralles et al. [62–64] to propose a different strategy which tried to avoid the aforementioned problems. In the so-called differencededicated configuration interaction (DDCI) method low-order perturbation criteria are applied to select the i determinants which contribute directly to the considered energy difference. After this subspace is rationally selected, the calculation of the transition energies is treated variationally via a CI calculation. For two electrons in two active orbitals (ϕa and ϕb ), as present in exchange-coupled Cu(II) dinuclear compounds, the model space that is used consists of the two neutral valence-bond structures |ϕa αϕb β| and |ϕa βϕb α|. The corresponding list of interacting determinants (the DDCI-2 list) involves only those presenting up to two inactive orbitals (i. e. one hole and one particle, or two holes and two particles). Diagonalization of this subspace of single and double excitations permits to obtain the singlet-triplet gap as

240


the difference between the first two roots of this variational CI. It has been shown that, since the DDCI space is invariant under a unitary transformation of the active orbitals, it is also possible to generate the DDCI space using the delocalized orbitals ϕ1 and ϕ2 . The DDCI-2 method has been applied with success to different magnetically coupled dinuclear compounds involving one or more unpaired electrons per center, chloro and hydroxo doubly-bridged Cu(II) complexes [65], chloro and azido doublybridged Ni(II) compounds [66], and hydroxo-bridged Cr(III) binuclear complexes [67]. For copper(II) acetate the calculated value at this level of approximation is −77 cm−1 (see Table 3 for a comparison of calculated J values for copper acetate using various quantitative approaches) which correctly reproduces the antiferromagnetic character of the interaction, but strongly underestimates its actual magnitude. This discrepancy might come from the neglect of important contributions to the singlet state, notably the ionic valence-bond structures, |ϕa αϕa β| and |ϕb αϕb β|. If these two determinants are included in the model space, the difference dedicated CI space has to be enlarged up to a DDCI-3 list, involving configurations with two inactive holes and one inactive particle or one inactive hole and two inactive particles [68]. This list increases the size of the CI space by a factor of 50–60, but gives a much better theoretical estimate of J for copper acetate: −224 cm−1 . The DDCI-3 method, even if appealing because of the quality of results it delivers, suffers from its computational complexity, which limits its use to heavily simplified models of the actually synthesized compounds. As will be seen later in the section dedicated to some representative examples, modeling terminal or bridging ligands by substituting bulky groups by simpler ones might induce changes of up to 50–100 cm−1 in the calculated coupling constants. In such cases it is impossible to tell whether the discrepancy between theoretical and experimental values comes from the computational methodology or from the modeling of the real structure.

7.4.2

Ab initio Calculations of State Energies

The “brute force” approach, i. e. the calculation of exchange coupling constants from the energy differences of the thermally populated spin states, has also been employed by some authors. As mentioned above, an essential requirement for an estimation of J using this procedure is the availability of highly accurate energies for all the states involved in the magnetic behavior of the compound under scrutiny. Representative calculations of this type have been performed by Staemmler and coworkers employing their own methodology [69–73], and Pierloot and Ceulemans using the standard complete active space SCF method (CASSCF) with inclusion of the dynamic correlation through second-order perturbation theory (CASPT2) [74, 75]. The quantum chemical strategy proposed by Staemmler and coworkers starts with a first calculation aimed at generating molecular orbitals equally appropriate for all low-lying electronic states. These can be obtained usually from a ROHF calculation for the highest multiplicity state, although a more involved calculation may be necessary [69]. Once these orbitals have been obtained, the energy of each state can


241

be calculated by means of either a full valence configuration (VCI) treatment or a CASSCF calculation. The results show that there is virtually no difference between these two treatments since all electronic states involved are very close in energy. Dynamic correlation effects must be included in a third step on top of the VCI or CASSCF calculation. The method of choice of Staemmler and coworkers is the multiconfiguration coupled electron pair approach (MC-CEPA) [76]. This theoretical approach has been applied to different exchange coupled dimers with more than one unpaired electron per center, oxo-bridged Ti(III), V(III) and Cr(III) complexes [69– 71], and oxo- and sulfur-bridged Ni(II) complexes [72, 73]. It is interesting to remark that these authors have also been the first ones to include explicitly the important effects of spin–orbit coupling and Zeeman splitting in their study of chlorine-bridged dinuclear cobalt(II) complexes [77]. Pierloot and Ceulemans have focused on the study of the exchange interaction in [Ti2 Cl9 ]3− , including parametric expressions of metal-centered spin-orbit coupling and Zeeman splitting due to the d1 configuration of the metal atom [74, 75]. Recently, these authors have published a review of their work reporting also results for [Cr2 Cl9 ]3− [78]. The VCI or the CASSCF calculations correctly reproduce the ordering of the low lying energy states, but the inclusion of dynamic correlation effects is needed if one wants to calculate reliable values of coupling constants. The main reason is that the antiferromagnetic contribution to J is determined by the extent to which “ionic” (charge transfer) configurations are mixed into the dominant “neutral” (covalent) ones in the VCI. As long as the ionic configurations are built up from orbitals which have been optimized for covalent states and no relaxation effects are accounted for, their energies are too high and consequently their contribution to J AF is too small. The quality of results that can be obtained by such an approach can be deduced from the values in Table 3. The CASSCF calculation of the second step yields a value of −24 cm−1 for J in copper acetate, which correctly indicates a singlet ground state, Table 3. Numerical values (cm−1 ) of the singlet-triplet energy splitting, J , for copper(II) acetate calculated using some of the methods discussed in the text. For calculations performed using the broken-symmetry approach, unprojected and projected (in parenthesis, this issue will be discussed in the next section) values are indicated in the table. All data included in this table have been calculated for this review [79–81]. Method DDCI-2 DDCI-3 CASSCF CASPT2 UHF-bs Xα-bs SVWN-bs BLYP-bs B3LYP-bs Experimentala a

Ref. [51].

J −77 −224 −24 −117 −27 −848 −1057 −779 −299 −297

(−54) (−1696) (−2114) (−1558) (−598)

242


but strongly underestimates the magnitude of J , accounting for less than 10% of its experimental value (−296 cm−1 ). Consideration of the dynamic electron correlation by means of perturbation theory, as in the CASPT2 method, recovers a substantial part of the antiferromagnetic contribution to J yielding a value of −117 cm−1 that is, however, still far from the experimental one. This value is substantially improved when some bridging ligand-centered molecular orbitals are included in the active space. Despite the success of the ab initio approach in the determination of coupling constants, its weak point is doubtlessly its computational complexity. The use of the state-of-the-art programs needed for this type of calculations is not only out of reach for most experimental chemists interested in molecular magnetism, but is also severely limited by the size of the molecule that one wants to study. The ab initio approach has been only applied so far to strongly idealized models of exchange coupled systems in which bulky terminal ligands have been substituted by smaller ones and in which small structural distortions have been disregarded in order to build a model with as much symmetry elements as possible to reduce the computational burden.

7.4.3

Calculations using Broken-symmetry Functions

A possible solution to the problems outlined above was advanced by Noodleman et al. in 1981 in one of the key papers on the theoretical treatment of magnetically coupled systems [82]. Noodleman’s suggestion in this work was the use of a single configuration model containing non-orthogonal orbitals for the calculation of the coupling constant using either unrestricted Hartree–Fock theory or spin-polarized density functional theory, e. g., the Xα method [83, 84]. The crucial point of this proposal was the use of a state of mixed spin symmetry and lowered space symmetry (a broken-symmetry wavefunction). Let us briefly review the more important features of this method for a system having two paramagnetic centers with one unpaired electron each occupying orthogonal magnetic orbitals ϕa and ϕb [85–87]. Proper spin eigenfunctions for this system are given by: 1 S,0 = √ |ϕa αϕb β| + |ϕa βϕb α| 2 1 T,0 = √ |ϕa αϕb β| − |ϕa βϕb α| 2 T,+1 = |ϕa αϕb α| T,−1 = |ϕa βϕb β|

(24)

The direct calculation of the coupling constant as the energy difference between the singlet and triplet states involves therefore at least one wavefunction, S,0 that cannot be expressed as a single configuration. Noodleman’s suggestion was to use instead a broken-symmetry solution: B S = |ϕa αϕb β| (or its degenerate counterpart B S = |ϕa βϕb α|)

(25)


243

which has M S = 0 but is a state of mixed spin because it can be expressed as a combination of S,0 and T,0 : 1 B S = √ [ S,0 + T,0 ] 2

(26)

and the energy of which is given by: EBS =

1 (E S + E T ) 2

(27)

from which the following expression for the coupling constant can be deduced: J = 2(E B S − E T )

(28)

For the general case, the overlap Sab between non-orthogonal orbitals must be taken into account, and Eq. (28) rewritten as: J=

2(E B S − E T ) 2 1 + Sab

(29)

For small values of Sab (as in the case of exchange coupled dinuclear compounds) this expression reduces to Eq. (28). The use of the broken-symmetry approach in combination with the UHF method yields values for J that are in qualitative agreement with experimental data. For example, the calculated value for J in copper acetate is −54 cm−1 , indicating correctly that the two electrons are antiferromagnetically coupled. The value of J , though, is severely underestimated by this approach. Noodleman’s method can be applied also within the density functional formalism. The J values obtained for copper acetate using different functionals are summarized in Table 3 (values calculated using Eq. (28) are those given in parenthesis). All functionals tested predict an antiferromagnetic coupling in good agreement with experimental observations, even if the value of the coupling constant is strongly overestimated. The local density approximation (SVWN functional) [15, 88] gives the worst results, with a magnitude of J which is almost 10 times larger than the experimental value. Gradient corrected functionals [89, 90] and hybrid functionals strongly reduce the calculated value of J , which is still strongly overestimated. Even the best results obtained with the B3LYP functional [91], yield calculated coupling constants about twice the experimental value. This observation, which is general for all systems studied so far, has led us to propose the use of a modified broken-symmetry approach in which Eq. (28) is simply replaced by: J = E B S − ET

(30)

The use of this equation implies that, when using density functional theory to evaluate the energy of the states involved in the magnetic behavior, the energy of the

244


Fig. 2. Experimental exchange coupling constants for different families of binuclear compounds with different bridges, represented as a function of the calculated value with the B3LYP-bs method using the complete, unmodeled structure for each compound.

singlet state E S can be effectively estimated from the energy of the broken-symmetry solution E B S [92]. The calculated value J in copper acetate are substantially better when Eq. (30) is used (values without parenthesis in Table 3) in combination with density functional calculations. Our experience in this field is that the combination of Eq. (30) with the B3LYP functional gives values for the coupling constant which are in excellent agreement with the experimental data for all the compounds studied so far (Fig. 2). The use of Eq. (30) instead of Eq. (28) has lead to some controversy in the recent literature [92–97]. For wavefunction-based methods, such as UHF, it is clear that the spin-projection procedure that leads to Eq. (28) is indeed the right way to tackle the problem. When dealing with density functional calculations the playground is however somewhat different. In density functional theory, the Kohn–Sham wavefunction is only a tool used to obtain the ground state electron density from which the energy is calculated. The use of spin-projection techniques applied to the wavefunction constructed from the Kohn–Sham orbitals has been questioned recently [9]. Wittbrodt and Schlegel [98] have discussed the influence of spin projection on potential energy surfaces finding that these certainly improve UHF and UMP2 results whereas the best results from DFT methods are obtained with the energy values of the brokensymmetry state without projection. In this context it is also interesting to point to the work of Perdew et al. [99, 100] in which it is observed that the broken-symmetry function describes the electron density and the on-top electron pair density with remarkable accuracy even if it gives an unrealistic spin density distribution. These authors conclude that the broken-symmetry function is indeed the correct singledeterminant solution of the Kohn–Sham equations for these systems. For another interesting work related to the adequacy of using broken-symmetry solutions to estimate the energy of the singlet state in organic biradicals, the reader is referred to a recent article by Grafenstein ¨ et al. [101]. The use of broken-symmetry wavefunctions (either with or without the use of spin-projection) can be easily extended to dinuclear compounds with more than one unpaired electron per center [92]. For a compound with the same spin on the two centers the following equation can be used to estimate J in conjunction with DFT


245

calculations using the B3LYP method: J=

2(E B S − E H S ) S H S (S H S + 1)

(31)

where HS stands for the high-spin configuration. A similar expression applies when spin-projection is considered: J=

2(E B S − E H S ) 2 SH S

(32)

Several authors have applied the broken-symmetry approach, introducing in some cases particularities for the estimation of the energy differences between ground and excited states. We can mention as one of the first works in this field the paper of Fukutome in 1981 [102]. Hart and Rappe have applied the Hartree–Fock brokensymmetry approach to the study of oxo-bridged Ti(III) and Fe(III) complexes [103, 104]. A particular feature of these studies is the use of the ROHF method instead the usual UHF one for the calculation of the high-spin state. Ovchinnikov et al. [105] have also explored the applicability of the broken-symmetry method to the estimation of the splitting energies for simple diatomic molecules as previously done by Goursot and coworkers [106]. It is worth to note that there are significant differences between the symmetry of the SOMOs in simple diatomic molecules and in the transition-metal complexes discussed in this review. In a molecule such as O2 , its two orthogonal π ∗ SOMOs cannot be represented as a pair of localized orbitals as in the case of exchange coupled paramagnetic centers. For this type of situations DFT calculations with spin projection techniques seem to yield good results for the calculation of the singlet–triplet splitting [105]. Daul has proposed an alternative to the broken-symmetry method within the density functional theory, providing an expression to calculate the energy difference from single-determinant energies [107]. A similar approach has been developed by Filatov and Shaik, called spinrestricted ensemble-referenced Kohn-Sham method (REKS). The electron densities and energies for the selected states are represented as weighted sums of energies and densities of symmetry-adapted Kohn–Sham determinants [108–110]. An alternative procedure using the scheme based on the Lowdin ¨ annihilator has been used by Cory and Zerner to project the unrestricted Hartree–Fock wavefunction using an INDO model Hamiltonian in their study of ferredoxin models [111]. Finally, we must mention the work of Yamaguchi and coworkers who have also been using broken-symmetry functions in the context of unrestricted Hartree–Fock and MP2 calculations [112]. These authors use also spin-projection techniques to extract J through the expression: J=

2(E B S − E H S ) S 2 H S − S 2 B S

(33)

where S 2 = S(S + 1) is the expectation value for S 2 in each configuration. This expression is similar to that proposed earlier by Ginsberg [113].

246


Given the simplicity of the broken-symmetry approach compared to other methods described above, several groups have employed such methodology to study the exchange coupling and the electronic structure in polynuclear transition metal complexes. Noodleman and coworkers have carried out extensive work on complexes with biological interest, mainly in iron–sulfur clusters [85, 86, 114–127] and oxobridged manganese complexes [128–132]. They have employed local or gradient corrected density functionals that provide usually a correct qualitative energy order of the spin states but non-accurate quantitative estimations of exchange coupling constant values. It is also worth mentioning the contribution of Solomon and coworkers in the field of bioinorganic chemistry. Their work in this field is more focused on the analysis of the electronic structure and its relation with a variety of spectroscopic data rather than on the magnetic behavior. As representative examples we can mention their work on Cu(II) model complexes of active centers in blue copper proteins [133– 140] and hemocyanins [141–147], model iron complexes of hemerythrins [148–153], and manganese model complexes of catalases [154, 155]. Yamaguchi and coworkers have performed an extensive study of the magnetic properties of molecular systems, focusing on both transition-metal complexes and organic radicals [156]. They employed several methods, from Hartree–Fock and post-Hartree–Fock to those based on density functional theory. Among the systems with transition metals studied by these authors we can mention the [M2 Cl8 ]2− (M = Cr and Mo) complexes containing metal-metal multiple bonds [157–159], transition metal tetrathiolates [160, 161], iron-sulfur clusters [162–164], Prussian blue analogs [165–167], tetranuclear linear Ni–Cr–Cr–Ni complexes [168, 169], fluorobridged Cu(II), Ni(II) and Mn(II) dinuclear complexes [170], copper clusters [171] and also metalloporphyrins [172]. They have also developed a procedure to calculate the magnetization, combining path-integral and Monte Carlo methods [173–175], applying it to complex systems such as Mn12 compounds [176, 177] or the Fe12 ferric wheel [178]. Bencini and coworkers started in the eighties to apply the Xα method and the broken-symmetry approach [179] to the study of several Cu(II) dinuclear compounds with hydroxo [180], halo [181-183], oxalato-type [184], or carbonato bridges [185], and more recently azido-bridged Cu(II) complexes [186] using new functionals. These authors have also explored the electronic structure of some Fe and Co hexanuclear compounds in search for explanations of spectroscopic data reported for these systems [187–190]. They have also analyzed the influence of substitutions in dioxobenzene-bridged Mo(V) complexes on the exchange coupling constant [191]. Recently, they have extended the use of the broken-symmetry approach to mixed valence compounds by studying Fe(II)Fe(III) complexes [192], oxo-bridged Mn(III)Mn(IV) complexes [193] and the Creutz–Taube ion [194], that has also been studied by Chen et al. [195]. Caneschi et al. have deduced the structural dependence of the exchange coupling constant for hydroxo- and alkoxo-bridged complexes [196] using DFT methods. Density functional calculations were performed by Belanzoni et al. to investigate the electronic structure and exchange coupling in organometallic Fe(II) dinuclear complexes with metal-metal interactions and different types of bridging ligands [197]. McGrady and Stranger have applied DFT based calculations to perform exhaustive studies of the d3 –d3 [M2 Cl9 ]3− and [M2 Cl10 ]4− systems (M =


247

Cr(III), Mo(III) and W(III)) [198–207] and oxo-bridged Mn dinuclear compounds [208–210]. The magneto-structural correlation in dinuclear alkoxo-bridged V(IV) complexes has been explored by Plass by using the broken-symmetry approach combined with a non-local functional where a self-interaction correction has been included [211]. Blanchet-Boiteux and Mouesca have analyzed the exchange coupling in end-on azido-bridged Cu(II) dinuclear complexes and oxo-bridged Cu(II) dimers using DFT methods. Their work is centered on the relation between the exchange coupling constant and the overlap of the magnetic orbitals or the atomic spin populations [212–214]. Recently, Boca et al. have employed the Hartree–Fock method to study the electronic structure in trinuclear cobalt complexes [215]. We have studied the exchange coupling and magneto-structural correlations in several transition metal dinuclear complexes using the broken-symmetry approach and the B3LYP hybrid functional [92]. Considering a classification according to the bridging ligands, we can mention hydroxo- and alkoxo Cu(II) dinuclear complexes [216, 217], end-on azido-bridged Cu(II), Ni(II) and Mn(II) complexes [218], end-to-end azido-bridged Cu(II) and Ni(II) compounds [219], Cu(II) complexes with oxalato-type bridging ligands [220, 221], carboxylato-bridged Cu(II) dinuclear complexes [222], Cu(II) and Ni(II) cyano-bridged binuclear complexes, chlorobridged Cu(II) dimers and bis(oximato)-bridged heterobimetallic compounds [223]. Using the same approach, Castro et al. have studied the exchange coupling in dithiosquarate-bridged Cu(II) complexes [224] and the problem of orbital countercomplementarity in mixed µ-acetato and µ-hydroxo Cu(II) trimers has been explored by Gutierrez et al. [225]. In the next section we will provide a more detailed description of our work in this field. We would like to remark here that the broken-symmetry DFT approach is able to provide quantitative estimates of J that are of a similar quality to those obtained from highly sophisticated multireference ab initio calculations. The power of the brokensymmetry approach resides in its computational simplicity, which can be applied to compounds with more than 100 atoms using relatively modest computational resources and standard quantum chemistry software packages, easily available to a broad community of researchers interested in this field. The broken-symmetry method is also highly appealing because it is relatively easy to adapt for the calculation of coupling constants in higher nuclearity compounds or even to solid state materials with periodically repeating unit cells containing an arbitrary number of paramagnetic centers. In the latter case, construction of the broken-symmetry solution often requires the use of supercells to deal with the symmetry lowering with respect to the original space group of the crystal. A few considerations are in order to properly extend the ideas developed so far to the case of periodic systems, for which coupling constants are typically obtained via a procedure involving two main steps. First, total energies corresponding to distinct values of the total spin are obtained and compared, special emphasis being put on the consistency with experimental results and on the relative stability of the magnetic states under consideration. It should be remarked that, in addition to the ferromagnetic configuration, several spin configurations corresponding to the same total spin (as in the antiferromagnetic or ferrimagnetic situations) need to be taken into account. The second step consists in mapping to appropriate spin Hamiltonians the collection of

248


total energy data resulting from the spin configurations thereby obtained. So far most attempts in this direction have been based on the Unrestricted Hartree–Fock approach, implemented within the CRYSTAL code [226], refined in some cases by including the contribution of electron correlation via an a posteriori scheme based on correlation-only density functional formulas. This recipe has allowed the successful investigation of the electronic and magnetic properties of a large amount of transition metal oxides and halides [227–240]. From a methodological point of view, and focusing on the extraction of the superexchange coupling constants from a parametrization of total energy data, the case of the non-cubic Mn3 O4 spinel is particularly instructive. Apart from the ferromagnetic structure, six ferrimagnetic configurations were considered [241]. This gives rise to a system of equations relating the ferromagnetic–ferrimagnetic energy differences to four exchange coupling constants via a spin Hamiltonian which includes firstand second-neighbor interactions. The calculated J parameters were found to be about 40–50% of those derived from experimental data, mostly due to the neglect of electronic correlation in the UHF method. Nevertheless, the sign and the strength of the magnetic interactions turned out to be in agreement with experimental evidence. Solid-state compounds exhibiting interesting and mostly unexplored correlations between structural and magnetic properties may encompass systems obtained by the combined synthesis of inorganic layered networks and molecular species, as in the organic-inorganic hybrid multilayer materials [242]. In these cases, theoretical models may be used to predict structures which are not experimentally available, while ensuring a reliable description of the electronic structure. The possibility of simultaneously optimizing structural parameters and the electronic structure in the search for a configurational ground state accurately described at the density-functional level relies on the first-principle molecular dynamics technique proposed in 1985 by R. Car and M. Parrinello [243]. Within this scheme, the most important idea to be retained is that the total energy can be taken as a function of all the wavefunction coefficients of the occupied states and the positions of the atoms. Given this assumption, one is faced to the global minimization problem of finding the electronic ground state for the relaxed atomic configuration. The novelty of the approach rests on the fact that when we seek the relaxed ground state, the positions and the coefficients of the wavefunctions are varied at the same time, thereby ensuring that at the global minimum of energy the self-consistent solution will be automatically obtained. The application of this method to polynuclear transition metal compounds relevant in the area of molecular magnetism is still at its infancy [244]. However, its flexibility and the extended record of reliability achieved for other systems makes its application to molecular based magnetic materials highly promising.

7.5 Exchange Coupling in Polynuclear Transition-metal Complexes

7.5

249

Exchange Coupling in Polynuclear Transition-metal Complexes

After this short review of the computational techniques available for the study of exchange coupled systems, we discuss now in more detail the results of our own research applying one of these methods, the broken-symmetry approach in combination with B3LYP calculations, to the study of different aspects related to the magnetic behavior of magnetically coupled compounds containing transition metal atoms. We start our discussion with the study of the simplest case, i. e. dinuclear Cu(II) compounds, with only two exchange coupled electrons, and increase gradually the complexity of the system considering homodinuclear compounds with more than one electron per paramagnetic center, heterodinuclear compounds and polynuclear clusters.

7.5.1 7.5.1.1

Homodinuclear Compounds Hydroxo- and Alkoxo-bridged Cu(II) Compounds

One of the most extensively studied families of exchange coupled dinuclear compounds is that of the hydroxo- and alkoxo-bridged Cu(II) complexes. Although they provide examples of the simplest case of magnetic interaction, involving only two unpaired electrons, their magnetic behavior is quite varied, exhibiting ferro- or antiferromagnetic character depending on their molecular geometry. Hatfield and Hodgson [245] found a linear correlation between the experimentally determined exchange coupling constant and the Cu–O–Cu bond angle θ (see 5 for the definition of the most relevant geometrical parameters in these compounds). Antiferromagnetic coupling is found for complexes with θ larger than a critical value, θc = 98◦ , whereas ferromagnetism appears at smaller angles. A plot of the calculated J as a function of θ for the model compound yields also a linear correlation (dotted line in Fig. 3). The calculated critical angle θc is, however, slightly smaller (92◦ ) and antiferromagnetic coupling is predicted for the range comprising all experimental angles (96–105◦ ). A more detailed analysis of the structural data shows that a second parameter, the out-of-plane displacement of the hydrogen atom of the hydroxo group (measured by τ as indicated in 5), also affects the value of the exchange coupling constant. The computational results show indeed that the two structural parameters are correlated: if the value of θ is optimized keeping τ fixed, one finds that the

250


Fig. 3. Magnetic coupling constants, J , for Cu(II) hydroxo-bridged complexes calculated with the B3LYP-bs method using a double zeta basis set for model 5 as a function of bridging angle θ. The black circles correspond to the experimental values, the dashed line gives the calculated values (triangles) for the planar model (τ = 0◦ ). The squares represent the values calculated for the optimized θ at a fixed value of τ (circled numbers). The uncircled labels indicate the value of τ for each experimental structure [216].

out-of-plane displacement of the hydrogen atoms favors smaller values of θ (Fig. 3, squares, with the fixed τ values given in circles). The most interesting result is that in a plot of J as a function of θ for each (θ, τ ) pair (Fig. 3, solid line) a linear correlation emerges that predicts ferromagnetic coupling for large values of τ (and, hence, small values of θ). This trend is in excellent agreement with the experimental data (Fig. 3, black circles with the corresponding τ values given besides). A similar trend is also found for the related alkoxo-bridged complexes, with the main difference that in this case all compounds are predicted to be antiferromagnetic for the range of (θ, τ ) values experimentally found, although ferromagnetic behavior cannot be ruled out for the so far unknown compounds with τ values larger than 50◦ . The effect of different counterions on the exchange coupling constant can thus be rationalized considering that the position of the hydrogen atoms of the hydroxo bridges is dictated by hydrogen bonding with the counterions. The assumption of the HTH model that small changes in structural parameters affect only the one-electron contribution to the coupling constant can be checked by plotting the value of J against (ε1 − ε2 )2 when θ is varied for a fixed value of τ = 0◦ (Fig. 4). The orbital energies ε1 and ε2 in this plot are those of the Kohn– Sham SOMOs in the triplet state for the model compound shown in 5. The linear dependence expected from Eq. (11) is found for both the hydroxo- and the alkoxobridged (not shown in the figure) compounds. A similar behavior is found for the


251

Fig. 4. Singlet–triplet energy separation, J , calculated for the hydroxo-bridged model compound 5 with τ = 0◦ (B3LYPbs method) as a function of the square of the energy gap between the two SOMOs in the triplet state [216]. Table 4. Exchange coupling constants J (cm−1 ) calculated for two model compounds with different terminal ligands. The experimental J and pKb values are also included for comparison [217]. L

Calc. J

Expt. J

pKb

[CuL(µ-OH)2 CuL](NO3 )2 bipy NH3 en

+107 +81 +60

+172

8.77 4.75 4.07

[CuL(µ-OH)2 CuL]Br2 NH3 en tmeen

−354 −402 −502

−509

4.75 4.07 3.29

out-of-plane hydrogen shift at a fixed θ value. These calculations suggest, thus, that there is a sound theoretical basis for the analysis of magneto-structural correlations based on the study of changes in the HOMO–LUMO gap with geometry. Another interesting point that has been analyzed for this family of compounds is the dependence of J on the nature of the terminal ligands. The donor atoms in these ligands are usually nitrogen atoms, belonging sometimes to aromatic, sometimes to aliphatic N-donors. The conclusions regarding a series of calculations for model compounds with different terminal ligands (Table 4) shows that the strength of the antiferromagnetic coupling follows the same trend as the basicity of these ligands: tmeen > en > NH3 > bipy. Considering the J values experimentally found for this family of complexes, a sharp contrast is found between the large number of known antiferromagnetic complexes and the paucity of ferromagnetic systems. A possible strategy for the design of new ferromagnetic compounds is to search for the factors that lead to practically degenerate SOMOs, a search for which theoretical studies may be of great help. One possibility consists in introducing modifications in the bridging ligand. For this purpose, the hydroxo- and alkoxo-bridged Cu(II) compounds offer an excellent op-

252


portunity since changes in the nature of the X group bonded to the bridging oxygen atom may influence the magnetic behavior, as evidenced by the fact that alkoxobridged complexes give stronger antiferromagnetic coupling than hydroxo-bridged ones with similar composition and structure [246]. Table 5 shows the calculated exchange coupling constants for a variety of OXbridged dinuclear Cu(II) compounds with ammonia as terminal ligands. From the analysis of these values some conclusions can be drawn: (a) all the alkoxo- and phenoxo-bridged complexes show stronger antiferromagnetic coupling than the hydroxo-bridged ones, in good agreement with the experimental results; (b) substitution of the hydrogen atoms in methoxo-bridged compounds by alkyl groups weakens the antiferromagnetic coupling; (c) in general, the larger the electronegativity of the substituent, the stronger the antiferromagnetic coupling is, although there are a few exceptions to this rule. A particularly surprising result is the exceptionally strong ferromagnetic coupling constant predicted for the oxo-bridged complex of copper(II), as compared to the largest values reported in the literature for azido- and hydroxo-bridged complexes (+170 and +172 cm−1 ). A more realistic model for the oxo-bridged complex, with pentacoordinate Cu(II) atoms having an extra NH3 molecule in the fifth coordination position is also predicted to show a very strong ferromagnetic coupling, with a J value of +685 cm−1 calculated for the optimized structure. Table 5. Exchange coupling constants J (cm−1 ) calculated for [(NH3 )2 Cu(µ-OX)2 Cu(NH3 )2 ]n+ (n = 0 for OX = O, OSO3 , OBR3 and OAlR3 ; n = 4 for OX = OPy; n = 2 for all other OX). The same geometry with θ = 101◦ and τ = 0.0◦ has been taken for all model compounds. The range of experimental values of J , when known, is also included for comparison [246]. X F Me BH3 Et But Ph py H GeH3 SiH3 Ge(OH) 3 COMe NO2 Si(OH) 3 Al(OH) 3 SO3 SOMe Li –

Calc. J −1855 −778 −687 −669 −617 −587 −675 −493 −331 −278 −259 −230 −221 −202 −134 −108 +8 +100 +989

Expt. J

−1064/−65 −852/−166 −855/−242 −509/+172


7.5.1.2

253

Cu(II) Compounds with Oxalato, Oxamidato or Related Polyatomic Bridging Ligands

One of the most striking observations in intramolecular magnetism is the ability of some polyatomic bridging ligands to provide a pathway for strong exchange coupling between two paramagnetic centers that are far apart. In this regard, one of the most studied ligands is the oxalate dianion and a series of other groups that can be formally derived from it by replacing the oxygen atoms by either S or NR. Given the variety of structures found for oxalato bridged Cu(II) complexes, this family allows us to analyze the influence of the coordination environment around the metal atoms on the exchange coupling [220, 221]. In recent years, several complexes of general formula [(AA)Cu(µC2 O4 )Cu(AA)]Xn have been structurally and magnetically characterized. Owing to the Jahn–Teller plasticity of the coordination sphere around Cu(II), this ion may appear as four-coordinate, four-coordinate with a fifth ligand at a larger distance (4 + 1 coordination), or four-coordinate with two weakly bound ligands (4 + 2 coordination). In all three cases, the four short ligand–metal bonds can be found approximately in a common plane giving square-planar, square-pyramidal, or square-bipyramidal coordination environments, respectively. In all cases, the unpaired electron is located in a dx 2 −y 2 -type orbital pointing to the four atoms with short metal–ligand distances. Two different orientations of the basal plane with respect to the plane of the bridging oxalate have been identified experimentally, depending on whether they are coplanar or perpendicular. This gives rise to the three different relative dispositions of the two SOMOs indicated in 6–8. Alternatively, five-coordinate Cu(II) ions may present a trigonal bipyramidal environment. In this case, the unpaired electron is located in a dz 2 -type orbital along the pseudotrigonal axis (9). The calculated J for model compounds with these four topologies are given in Table 6. The coplanar disposition of the SOMOs provides the most effective exchange pathway for antiferromagnetic coupling, in good agreement with the available experimental data. On the other hand, the parallel disposition of the SOMOs leads to weak coupling, which can be either ferro- or antiferromagnetic depending on the nature of the terminal ligands and on the detailed geometrical features of the coordination environment around the copper atoms. For the other two topologies, moderate Table 6. Exchange coupling constants J (cm−1 ) calculated for [(NH3 )2 Cu(µ-C2 O4 ) Cu(NH3 )2 ]2+ with different topologies of the two SOMOs. The column labeled Jest corresponds to the empirical estimation of J from Eq. (34), taking the average experimental value (−370 cm−1 ) for the coplanar case as a reference value [220]. Orbital topology Coplanar (6) Perpendicular (7) Parallel (8) Trigonal-bipyramidal (9) a

See text

Jcalc −293 −86 +10 −185

Jest −370 −93 0 −165

Jexp −300 to −400 −75 +1.2 to −37 −75a

254


antiferromagnetic coupling is expected. The influence of the orbital topology on the coupling constant has also been analyzed by Julve et al. [247] using empirical rules based solely on the overlap between natural magnetic orbitals (Eq. 11). Taking Ja , the coupling constant for coplanar compounds, as a reference value, these authors suggest the following relationships between the J values in the different compounds (the subscripts correspond to the different orbital topologies in 6–9): Jb = Ja /4 Jc = 0 Jd = 4Ja /9

(34)

The values obtained using these relationships (Table 6) are in a fair agreement with both our calculated data and the experimentally determined coupling constants, showing the excellent predictive power of these empirical rules. The disagreement between the calculated coupling constant and the experimental data for the trigonal-bipyramidal topology can be attributed to the departure of the experimental coordination environment from an ideal trigonal bipyramid. A calculation for the unmodeled structure of this compound yields a coupling constant of −82 cm−1 , in excellent agreement with the experimental value. Chemical substitution at the bridging ligand is expected to have an important influence on the exchange coupling and has therefore been analyzed by performing a series of calculations for model compounds with the general formula [(NH3 )2 Cu(µC2 WXYZ)Cu(NH3 )2 ]2+ where W, X, Y, Z = NH, O, or S. The calculated exchange


255

Table 7. Exchange coupling constants J (cm−1 ) calculated for [(NH3 )2 Cu(µC2 WXYZ)Cu(NH3 )2 ]2+ with different bridging ligands and ranges of experimental values for complexes with the analogous bridges [221]. Bridge

W

X

Y

Z

−Jcalc

−Jexp

Oxalate Oxamate cis-Oxamidate

O NR NR NR NR NR S S S NR NR NR S NR NR

O O NR O O NR S O O NR S S S NR NR

O O O NR O NR O S O S NR S S NR NR

O O O O NR NR O O S S S NR S NR NR

293 312 360 347 356 358 485 465 391 504 553 473 829 98 44

284-402 400-425 242–453

trans-Oxamidate Ethylenetetraamidate cis-Dithiooxalate trans-Dithiooxalate cis-Dithiooxamidate trans-Dithiooxamidate Tetrathiooxalate Bipyrimidine Bisimidazole

305–591

523–730 >800 139–236

coupling constants, Table 7 and Fig. 5, show that antiferromagnetic coupling is predicted for all the combinations of W, X, Y, and Z. The magnitude of such coupling is strongly affected by the nature of the bridging ligand, ranging from J = −829 cm−1 for tetrathiooxalate to J = −44 cm−1 for bisimidazole. These calculations confirm the qualitative trend established by Verdaguer et al. using the HTH model [248], that progressive substitution of oxygen by less electronegative donor atoms such as nitrogen or sulfur results in increasingly stronger antiferromagnetic coupling. The exception to this rule comes from the aromatic bridging ligands bipyrimidine and bisimidazole, which show a much weaker coupling than the analogous non-aromatic ligand, ethylenetetraamidate. This fact can be explained by the delocalization of the lone pair orbitals throughout the aromatic system that results in a poorer overlap with the metal d orbitals.

Fig. 5. Ranges of experimental exchange coupling constants for different families of binuclear Cu(II) compounds with bridges of oxalato-type, represented as a function of the calculated value for the corresponding model compound (Table 7) [221].

256


Fig. 6. Dependence of the calculated J value on the electronegativity of the terminal ligands X in compounds of type 10 [220].

In contrast with the effect of substitution of the donor atoms, which accounts for changes in the coupling constant of up to 600 cm−1 , different substitution patterns for the same set of donor atoms affects the values of J by less than 90 cm−1 . Although a large part of the variation in the values of J can be associated with the electronegativity of the donor atoms, the wide range of values experimentally found for the same bridging ligands clearly indicates that other factors, such as structural distortions or changes in the nature of the terminal ligands affect the exchange coupling to a significant extent. Once the main factors concerning the role of the bridge are understood, we analyze the effect of the nature of the terminal ligands on the magnitude of the exchange coupling when the orbital topology is kept constant. For this purpose, calculations for a series of compounds in which only a terminal ligand is changed (10 with X = F, Cl, Br or I) were performed. The results (Fig. 6) indicate that, other things being equal, the less electronegative donors induce a stronger antiferromagnetic coupling. This is due to a greater hybridization of the dx 2 −y 2 -type SOMOs towards the bridge induced by better σ -donor terminal ligands, as predicted previously using the qualitative HTH model [30].

7.5.1.3

Carboxylato-bridged Cu(II) Compounds

Copper(II) carboxylates form a large family with many structurally characterized compounds for which magnetic properties have been measured. This wealth of information permits the detailed study of the influence of different factors on the exchange interaction between the two unpaired electrons. The different coordination modes of the carboxylato group (11–14) together with the choice of the bridging ligand substituent R, the terminal ligand L, and the number of bridging ligands, give rise to a large number of possibilities to obtain new compounds with tailored magnetic properties.


257

Although in most carboxylato-bridged dinuclear Cu(II) complexes the bridging ligands appear coordinated in a syn–syn fashion (11) [249, 250], some compounds with other bridging modes (12–14) have been prepared and their magnetic properties measured. In order to compare the exchange coupling mediated by a formiato bridge in syn–syn (11), syn–anti (12) [251–256], and anti–anti (13) [257, 258] coordination modes, the corresponding models were used, keeping the geometry of the formiato bridge and the copper sphere fixed. Water molecules were included in all cases as terminal ligands. The Cu · · · Cu distances in these model structures are 2.82, 5.15, and 5.77 Å for the syn–syn, syn–anti, and anti–anti compounds, respectively. The calculated coupling constants range from weakly ferromagnetic (+10.2 cm−1 ) for the syn-anti case to moderately antiferromagnetic (−61.3 cm−1 ) in the anti–anti case, in good agreement with the experimentally available data [257]. The known compounds with an anti–anti coordination mode have coupling constants of around −50 cm−1 , while that with a syn–anti coordination presents a weak ferromagnetic behavior (J = +14 cm−1 ) [257]. For the model with syn–syn coordination an intermediate behavior (J = −11.3 cm−1 ) was predicted. Changing the nature of R, the group bound to the carboxylato bridge, in compounds with four carboxylato bridges has a dramatic effect on the coupling constant. Calculated and experimental coupling constants for several compounds of this family are presented in Table 8 (experimental data are average values for compounds with slightly different geometries and/or terminal ligands) [51, 249, 250, 259, 260]. Exchange coupling between two paramagnetic centers that are not directly bound is frequently rationalized by adding the contributions of the different superexchange pathways mediated by the bridging ligands. Since dimers with four, three, two, and one carboxylato bridges have been structurally and magnetically characterized, this family of compounds offers an excellent opportunity to test the validity of such an approach. To this end, exchange coupling constants have been calculated for model compounds in which a varying number of carboxylato bridges have been Table 8. Calculated coupling constants (cm−1 ) for [L2 Cu2 (µ-RCOO)4 ]. [222]

a

L

R = -SiH3

−H

−CH3

−CF3

−CCl3

H2 O NH3 Exptl

−806 −749 −1000a

−417 −393 −550b

−299 −284 −300c

−254 −241 −300d

−158 −142 −200e

Ref. [259]; b Ref. [260]; c Ref. [51]; d Ref. [249]; e Ref. [250].

258


Fig. 7. Exchange coupling constants calculated for [(H2 O)5−n b Cu(µ-RCOO)n b Cu +

(H2 O)5−n b ](4−n b ) as a function of the number of bridging carboxylato ligands, n b [222].

replaced by two water molecules each. Fig. 7 shows that, regardless of the nature of the carboxylato bridge, the coupling constant exhibits a linear dependence on the number of bridges. The additive nature of the contribution of each bridge to J is also valid for hypothetical compounds with mixed bridges according to calculations. A compound with two formiato bridges and two trichloroacetato bridges, for example, should present a coupling constant of −301 cm−1 , which is in excellent agreement with the calculated values of −300 and −293 cm−1 for two model compounds in which the two formiato bridges are coordinated in a cis or trans disposition, respectively. Related questions, like the influence of the terminal ligands L on the coupling constant or the establishment of some magneto-structural correlations for these systems have also been tackled using the same computational methodology [222].

7.5.1.4

Azido-bridged Compounds

The azide ion is a versatile ligand that can bind to transition-metal atoms with different coordination modes, thus allowing for the assembly of dinuclear complexes with a wide range of magnetic behavior. When the N− 3 group acts as a bridging ligand with an end-on coordination mode (15), the resulting dinuclear complexes usually show ferromagnetic behavior. In contrast, when coordinated in an end-to-end fashion (16), antiferromagnetic coupling results. Although both situations have been computationally analyzed using the broken-symmetry approach, we will focus our discussion only on the ferromagnetically coupled dimers with azido bridges coordinated in an end-on fashion [218]. Details on magneto-structural correlations for compounds with N− 3 ligands with end-to-end coordination can be found in Ref. [219]. A large number of Cu(II) dinuclear complexes of such family have been reported, including end-on double-bridged compounds, all with ferromagnetic coupling. This behavior was formerly attributed by Kahn et al. to a spin polarization mechanism [261], a suggestion that has been ruled out more recently by the same authors in view of polarized neutron diffraction experiments [262] that indicate that the spin density at the bridging nitrogen atom has the same sign as that at the metal atoms. Calculation


259

Fig. 8. Magnetic coupling constants for a [Cu2 (µ-N3 )2 (C2 N2 H4 )2 ]2+ model complex as a function of the bridging angle θ with τ = 0◦ (empty circles) and 15◦ (empty squares). The black circles correspond to known experimental values [218].

of the coupling constant for the model compound [Cu2 (µ-N3 )2 (C2 N2 H4 )2 ]2+ with different Cu–N–Cu angles (Fig. 8) shows that the ferromagnetic behavior is only associated to the geometrical constraints that affect this angle in the experimentally known compounds. Antiferromagnetically coupled compounds can be expected in principle if one is able to force the Cu–N–Cu angle to adopt values larger than 104◦ , a prediction that had also been advanced by Thompson et al. based on the extrapolation of the experimental magneto-structural correlation [263]. The calculated spin densities at various atoms in [Cu2 (µ-N3 )2 (4-t Bu-py)4 ](ClO4 )2 (Table 9) are in good qualitative agreement with the experimental polarized neutron diffraction data [262]. It is interesting to note that the spin densities at the bridging (N1) and terminal (Nt ) nitrogen atoms have the same sign as in the copper atoms, indicating that the unpaired electron delocalization toward the donor atoms predominates over the spin polarization mechanism for this compound. There are some examples in the literature of end-on azido-bridged complexes with transition metals other than copper, the most common ones being those of Ni(II). From calculations [218] on a model compound (Fig. 9), J is seen to vary with the M–N–M angle in a different way than for the copper(II) model compound discussed above. The interaction is predicted to be ferromagnetic for all the range of angles

260


Table 9. Atomic spin densities obtained from experimental polarized neutron diffraction data [262] and calculated for [Cu2 (µ-N3 )2 (4-t Bupy)4 ](ClO4 )2 with the B3LYP functional using a Mulliken population analysis [218]. Atom

Experimental

Calculated

Cu N1 N2 N3 Nt

+0.78 +0.07 −0.02 +0.06 +0.07, +0.05

+0.60 +0.14 −0.04 +0.12 +0.09, +0.09

Fig. 9. Exchange coupling constant for the [Ni2 (µ-N3 )2 (NH3 )8 ]2+ model 15 as a function of the bridging angle θ (empty circles). The black circles correspond to known experimental values [218].

explored, with J increasing with the M–N–M angle, yielding a maximum at 104◦ . In this case, the strongest ferromagnetic coupling coincides with the most stable geometry and with the structures of the experimentally known compounds. For all of them a quintet ground state has been deduced from magnetic measurements, in good agreement with the calculations. A few compounds with transition metals other than copper or nickel have been also magnetically characterized. These compounds, with Co(II), Fe(III) or Mn(II) ions, show all ferromagnetic coupling. Calculations indicate that J increases with the M–N–M angle for a Mn(II) model, in a way analogous to that found for the nickel compound, although the maximum is now predicted at a larger M–N–M angle. Fig. 10 shows the calculated coupling constants as a function of the M–N–M angle for the three metals. A similar parabolic behavior is found in all cases, the main difference being the position of the maximum, which is found at 84◦ for Cu(II), 104◦ for Ni(II), and 114◦ for Mn(II). The range of low energy angles (outlined parts of the curves) is different for each metal, thus explaining why J decreases with the M–N–M angle for Cu(II), increases for Mn(II), and is practically constant for Ni(II).


261

Fig. 10. Total exchange constants (n 2 J , where n is the number of unpaired electrons per metal atom) for complexes of Cu(II), Ni(II) and Mn(II) with two end-on azido bridges as a function of the bridging angle θ. The outlined parts of the curves correspond to those geometries within 3 kcal mol−1 of the calculated minima [218].

7.5.2

Heterodinuclear Compounds

Among the dinuclear transition-metal complexes relevant to the field of molecular magnetism, those containing two different metal ions are especially interesting since it has been found that it is much easier to obtain ferromagnetic coupling in heterodimetallic compounds than in their homonuclear analogs [32]. Stabilization of high-spin states is much easier to achieve with two different paramagnetic centers because the unpaired electrons are more easily arranged in metal-centered orthogonal orbitals of such complexes. Although much progress has been made in recent years towards the accurate calculation of exchange coupling constants in homodinuclear transition-metal complexes, the field of heterodinuclear complexes remains relatively unexplored from the theoretical point of view. Only a few theoretical papers have been devoted to the quantitative evaluation of coupling constants for this type of complexes [264]. The influence of the exchange coupling on the electronic configuration has been investigated [223] for the series of bis(oximato)-bridged Cu(II)–M compounds (17) with M = Cu(II), Ni(II), Mn(II), Mn(III) or Cr(III). In all model compounds, ammonia molecules were used as terminal ligands. Due to the varying electronic configuration of the M atom, different coupling situations are expected in this family. Calculated exchange coupling constants for these model compounds (Table 10) are

262


Table 10. Exchange coupling constants (cm−1 ) for the series of model bis(oximato)-bridged Cu(II)–M compounds. Experimental values are provided for comparison [265]. M Cu(II) Ni(II) Mn(II) Mn(III) Cr(III)

Jcalc −648 −201 −67 127 43

Jexp −596 −198 −83 109 37

in excellent agreement with the experimental ones reported by Birkelbach et al. [265], showing that the broken-symmetry method combined with the B3LYP functional is also able to reproduce accurately the coupling constant for heterodinuclear compounds. As found for other compounds, the molecular structure is in this case important for the determination of the exchange coupling constant. The N–O distance at the bridge is one of the important geometrical parameters for oximato-bridged dimers in this respect. Fig. 11 shows the variation of J with such distance for the Cu(II)–Cu(II) compound. The antiferromagnetic coupling is significantly weakened when the N–O bonds are stretched, a finding that can be easily rationalized with the help of the HTH model. The in- and out-of-phase combinations of the metal x2 − y2 orbitals interact with a combination of N–O non-bonding and π ∗ orbitals of the ligand (18). When the bond is elongated, the π ∗ orbital is significantly stabilized, resulting in a poorer energy match with the metal x2 − y2 orbitals that effectively reduces the splitting of the SOMOs and, according to the HTH model, the antiferromagnetic contribution to J .

Fig. 11. Exchange coupling constants calculated for the model bis(oximato)-bridged Cu(II)–Cu(II) compound as a function of the N–O distance on the bridging ligand [223].


263

The influence of the terminal ligands, L, on the coupling constant or the analysis of some magneto-structural correlations for these systems have also been studied using the same computational methodology [223].

7.5.3

Polynuclear Compounds

Polynuclear transition metal compounds have attracted much attention during the last years due to their magnetic properties [266–268]. These complexes are particularly interesting because their intermediate size between the simplest binuclear complexes and bulk materials may result in completely new magnetic properties, being good candidates to behave as nanometer-sized magnetic particles. The presence of a larger number of metal atoms compared to binuclear complexes results in an increase of the complexity, since the polynuclear complexes have usually more than one J value, besides the intrinsic increase in computational resources required. Following the same strategy as for the binuclear complexes, we have chosen simple polynuclear systems in order to check the accuracy of the B3LYP method for such systems. One of the simplest and commonest cases of polynuclear complexes is that of the compounds containing a Cu4 O4 cubane core [269]. We have proposed to use the Cu · · · Cu distances as a classification criterion for the different structures adopted by these compounds [270]. We propose to divide this family of compounds in three classes: The first one contains complexes with two short and four long Cu · · · Cu distances, and we call them 2 + 4 (19). The second class presents four short and two long Cu · · · Cu distances, and will be labeled from here on as 4 + 2 (those with S4 symmetry, 20). Finally, for compounds in the third class all six Cu · · · Cu distances are similar, and they will be termed 6 + 0.

264


Two systems were selected for such a study: a complex with a 2 + 4 type structure and hydroxo bridging ligands [271] (21) and an alkoxo-bridged complex [272] that belongs to the 4 + 2 category (22).

The first molecule can be described as two binuclear complexes linked by weak interactions. In this case, due to the presence of two different exchange pathways, we have employed the following Hamiltonian to estimate the energy of the low-lying spin states, where the numbering of the paramagnetic centers and the definition of J and J are given in 23:

Hˆ = −J ( Sˆ1 Sˆ2 + Sˆ3 Sˆ4 ) − J ( Sˆ1 + Sˆ2 )( Sˆ3 + Sˆ4 )

(35)

In this model Cu1 and Cu2 are in the same binuclear unit and Cu3 and Cu4 in the other one. Using this expression, we can obtain the equations to calculate the two exchange coupling constants from the energies corresponding to three spin distributions (for more details of the procedure to calculate the J values, see Ref. [270]). The results indicate that the high spin state (S = 2) is the ground state and the two calculated coupling constants, corresponding to the intra-dimer (J ) and inter-dimer coupling (J ), are +68.0 and +0.6 cm−1 , respectively, to be compared with experimental values of +15.1 and +0.2 cm−1 . It is worth noting that this complex shows a relatively small experimental J value compared with other hydroxo-bridged binuclear complexes with similar Cu–O–Cu angles, [271] even if it shows a small roof-shape


265

distortion of the Cu2 O2 framework that was found to enhance the ferromagnetic behavior [217]. The second complex containing a Cu4 O4 core has alkoxo-bridging ligands and adopts a 4 + 2 structure with approximate S4 symmetry (22). This structure can be modeled by a square of copper atoms (24) with two exchange coupling constants:.

Hˆ = −J ( Sˆ1 + Sˆ2 ) · ( Sˆ3 + Sˆ4 ) − J ( Sˆ1 Sˆ2 + Sˆ3 Sˆ4 )

(36)

The calculated J and J values are +44.1 and +6.2 cm−1 , respectively. Comparison with the experimental values [272], +44.9 and −16.3 cm−1 , indicates a discrepancy in the sign of J . The analysis of the superexchange pathway for the J constant shows the presence of two long Cu · · · O distances of 2.5 Å at each side of the bridge. Equivalent dinuclear complexes with long bridging Cu · · · O distances present rather small exchange coupling constants, of ca. ±1 cm−1 [273, 274]. An alternative procedure to calculate the coupling constants for this complex is to transform the Cu4 O4 core in to a simple Cu(II) dinuclear complex by replacing two Cu(II) centers by diamagnetic Zn(II) ones. The new hypothetical systems generated in this way are equivalent to Cu(II) dinuclear complexes and, by using Eq. 30 we can obtain estimates for the two coupling constants depending on the sites occupied by the Cu(II) atoms (25). This approach gives values of J and J of +49.4 and +2.9 cm−1 , respectively, very close to those obtained from the calculation for the original Cu4 O4 core.

Let us point out that even if the two studied complexes with the Cu4 O4 core show ferromagnetic coupling between first neighbors, the origin of the ferromagnetism is different in each case. In the hydroxo-bridged complex, the nature of the hydroxo bridge combined with a Cu–O–Cu bond angle of 96.5◦ determines the ferromagnetism. For the alkoxo-bridged Cu4 O4 complex, on the other hand, the distortion

266


imposing long bridging Cu-O distances reduces the overlap between the dx 2 −y 2 orbitals of the Cu(II) atoms resulting in a weakening of the antiferromagnetic contribution compared to the undistorted alkoxo-bridged Cu(II) binuclear complexes. We have used a similar theoretical approach to study the magnetic behavior of hexanuclear Cu(II) and Ni(II) polysiloxanolato complexes [275, 276]. Our results confirm the crucial role of a guest chloride anion within the Ni(II) complex in the magnetic behavior resulting in a S = 0 ground state in contrast with the high spin state (S = 3) found for the Cu(II) complex [277]. For these two complexes, the agreement between the calculated and experimental exchange constants is really impressive. In summary, although little studies have been carried out so far for polynuclear complexes, the results found show promise that the DFT methods employing the B3LYP functional might be an excellent tool for the theoretical exploration of the magnetic behavior of complexes with high nuclearity.

7.5.4

Solid-state Compounds: The Case of Cu2 (OH)3 NO3

Given the wealth of theoretical results on hydroxo-bridged dinuclear Cu(II) molecular compounds presented in Section 5.1.1, it is worthwhile to focus on the behavior of solid copper hydroxonitrate Cu2 (OH)3 (NO3 ), which can be considered the solidstate counterpart of such dinuclear systems. The question arises on the applicability to periodic systems of the trends established for molecular ones. In certain situations, this approximation appears well founded and allows a considerable simplification of the theoretical treatment, combined with a reduction of the computational effort. For instance, in the case of CuGeO3 , the use of a binuclear molecular model was legitimated by invoking the covalent nature of the bonds and the local character of the exchange coupling [278] and the calculated coupling constants were found to be close to those obtained from experimental measurements. However, we shall see how the existence of several exchange pathways, the role played by interlayer interactions and the occurrence of frustration effects prevents magnetism in solid Cu2 (OH)3 NO3 from being investigated on the basis of isolated molecular entities. Copper hydroxonitrate provides an example of a layered solid featuring a planar array of transition-metal ions. In this system, the interlayer distance between stacked brucite-type Cu2 (OH)4 sheets is modulated via the replacement of one fourth of the OH− ions with NO− 3 molecular units. As revealed by an X-ray structural determination [279], the copper atoms in Cu2 (OH)3 NO3 are octahedrally coordinated to the neighboring OH− and NO− 3 groups in two non-equivalent sites. Cu1 atoms have four OH− and two oxygen atoms of the NO− 3 groups as nearest neighbors, while Cu2 atoms are coordinated by four OH− , an additional OH− at a longer distance, and one oxygen atom belonging to one NO− 3 group (see Fig. 12). Concerning its magnetic behavior, the dependence of magnetic susceptibility with the temperature has been measured until 350 K. Upon cooling, the susceptibility slightly increases, reaching a maximum at T = 12 K. An antiferromagnetic character within each plane is suggested by the concomitant decrease of the χ T product. The first attempt to gain insight into the exchange coupling in this system relied on extended Huckel ¨ (EH) calculations [280]. The effect of spin coupling between


267

Fig. 12. Top: a view of the unit cell of Cu2 (OH)3 NO3 as obtained according to the X-ray determination of Ref. [279]. The labeling is taken also from the same reference. Bottom: projection in the ab plane of Cu2 (OH)3 NO3 (including Cu and O atoms only). Cu and O atoms are labeled so as to indicate their different coordination [244].

268


the various pairs of Cu(II) ions (Cu2–Cu2, Cu1–Cu2 and Cu1–Cu1) on the magnetic behavior of Cu2 (OH)3 NO3 was analyzed by calculating spin multiplet energies and magnetic susceptibilities for a cluster of Cu(II) ions with S = 1/2 spin. This model consists of parallel Cu1 and Cu2 chains, taken to reproduce the crystal geometry along the b direction and corresponding to four exchange coupling constants. The temperature dependence of the susceptibility, investigated as a function of the sign and magnitude of the four exchange parameters, was interpreted as a clear evidence for antiferromagnetic interactions within one of the chains, coexisting with a much weaker antiferromagnetic coupling in the other chain. According to the EH calculations, it is the Cu2–Cu2 coupling which plays the dominant role, while Cu1–Cu1 and Cu1–Cu2 interactions are much weaker. This result was presented as a convincing argument in favor of a one-dimensional model, claimed to be more consistent with the experiments than a two-dimensional model. The most intriguing aspect of these results is the disregard of ferromagnetic coupling between Cu1–Cu1 and Cu2–Cu2 pairs. Interestingly, a recent NMR study devoted to this same compound [281], combined with a spin Heisenberg model, has been consistently interpreted in terms of both ferromagnetic and antiferromagnetic interactions among the Cu1 and Cu2 ions respectively. Furthermore, it should be recalled that ferromagnetic Cu–Cu site interactions play a major role in other Cu(II)-based layered compounds [282]. Two-dimensional models based on a planar triangular arrangement have also been proposed, providing a good description of the susceptibility in the paramagnetic regime. However, this amounts to neglecting the coupling between the layers, while ambiguities remain on the sign of the exchange interactions. Thus, it appears that neither the two-dimensional approach, nor the one-dimensional one, can satisfactorily describe the magnetism in Cu2 (OH)3 NO3 . Moreover, a priori assumptions on the model dimensionality appear unsuitable since they rule out variations in the spin distribution among different layers. To go beyond phenomenological models, calculations were performed on Cu2 (OH)3 NO3 within the Kohn-Sham density functional framework. A generalized gradient approximation due to Becke [89] and Perdew [283] for the exchange and correlation in the S = 0 spin polarized case (i. e. the equivalent of the brokensymmetry approach referred in the molecular compounds sections of this paper) was used. Only the valence electrons (including the 3d electrons of each Cu atom) were treated explicitly, while norm-conserving pseudopotentials were used to account for the core-valence interaction [284]. The system examined consisted of 96 atoms in a periodically repeated crystal made of four monoclinic unit cells (two in the a and c directions and one in the b direction) at the experimental lattice parameters. By taking as initial configuration the experimental geometry, [279] the electronic structure is relaxed to its ground state by minimization of the total energy with respect to the coefficients of the plane-wave expansion. Optimization of the structure is then carried out by means of the first-principle molecular dynamics scheme [243, 285]. The agreement found between theory and experiment was found quite satisfactory, as illustrated in Table 11 for the Cu-O distances and the Cu2–O–Cu2 angles, demonstrating the reliability of our structural model.


269

Table 11. Experimental (left column) and calculated (right column) Cu2 interatomic distances (given in Å) and Cu2–O–Cu2 angles in Cu2 (OH)3 NO3 . The unit cell is made of 24 atoms having positions defined with respect to the primitive coordinates x, y, z and −x, y + 1/2, −z [279]. Oh1, Oh21, Oh22 and O1 define the O atoms with respect to their coordination to Cu1 or Cu2 atoms.

Cu2–Oh1 Cu2–Oh21 Cu2–Oh22 Cu2–O1 Cu2–Oh21–Cu2 Cu2–Oh22–Cu2

Experimental

Calculated

2.30 (1) 1.99 (1) 2.00 (1) 2.36 (1) 99.8 (1) 99.7 (1)

2.31 1.99 2.00 2.39 99.5 99.2

Figure 13 shows the projections of the spin density distribution on the two (a, b) planes of our simulation cell. Our calculated distribution of spin densities yields an antiferromagnetic character on each (a, b) plane, but it differs from one (a, b) plane to the other. Focusing on the spin densities on the Cu2 sites, which were conjectured to be mostly antiferromagnetic on the basis of isolated chain models, one notes that both parallel and antiparallel alignments occur along the b direction. This feature is confirmed by the patterns observed for the four possible superexchange interactions among Cu centers, which are Cu2–Cu2 via two OH− groups (labeled “a” in Fig. 13), − Cu2–Cu1 via two OH− groups (labeled “b”), Cu1–Cu2 via a NO− 3 group and a OH − − group (labeled “c”) and Cu1–Cu1 via a NO3 group and a OH group (labeled “d”). All of these couplings exhibit either parallel or antiparallel spin alignments, as it can be deduced by moving along and across the b direction on the different rows of Cu sites forming the triangular lattice on the (a, b) planes. This suggests that the conjecture of a correlation existing between the nature of the bridging groups and the sign of the exchange interaction is likely not to hold. A delicate point concerns the role played by frustration effects in determining the topology of the spin densities. On the one hand, they may stabilize parallel or antiparallel alignments between neighboring spin moments, without systematic agreement with the actual signs of the competing interactions. On the other hand, the calculations were performed within the spin collinear framework and do not allow ascertaining the extent of non-collinearity in this system. The different topology of spin densities between the Cu planes provides compelling evidence on the fact that models for magnetism relying on only one single, isolated layer are insufficient for this compound. Moreover, the existence of a nonunique distribution of spin densities along the c direction has consequences on the dimensionality of magnetism in Cu2 (OH)3 NO3 . Indeed, it implies that the distribution of local magnetic moments on the (a, b) layers has a periodicity along the c direction which differs from that of the lattice. A precise assessment of this latter issue calls for simulations on even larger systems and on the possibility of assigning and controlling the distribution of spin densities on the different atoms.

270


Fig. 13. Spin density distribution on the two different (a, b) planes composing our model for Cu2 (OH)3 NO3 . Positive spin density is dark grey and negative spin density is in light grey. O atoms are black, Cu atoms are dark grey, N atoms are light grey and H atoms are white. Note that for sake of clarity the system of 96 atoms has been duplicated along the b direction. On the upper panel, the white lines and the black labels define the four different exchange pathways along which magnetic interactions occur in this compound. These are Cu2–Cu2 via two OH− groups (labeled by “a”), Cu1–Cu2 via two OH− groups (labeled by “b”), Cu1–Cu2 via a NO− 3 group and a OH− group (labeled by “c”) and Cu1–Cu1 via − a NO− 3 group and a OH group (labeled by “d”) [244].

Acknowledgments We are indebted to Dr. Coen de Graaf for performing the MOLCAS and DDCI calculations of the copper acetate. Our work was supported by DGES through project number PB98-1166-C02-01 Additional support came from CIRIT through grant 1997SGR-072. The computing resources were generously made available in the Center de Computacio´ de Catalunya (CESCA) with a grant provided by Fundacio´ Catalana per a la Recerca (FCR) and the Universitat def Barcelona. For the calculations on solid state compounds, we are grateful to the IDRIS computer center of CNRS (France). The collaboration between the Barcelona and Strasbourg groups has taken advantage of a PICASSO bilateral project between France and Spain. We also want to acknowledge in general to all the colleagues whose names appear in the references.

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8

Valence Tautomerism in Dioxolene Complexes of Cobalt David A. Shultz

8.1

8.1.1

Introduction – Bistability, Hysteresis, and Electronically Labile Materials Bistability and Hysteresis

There are several classes of molecules and materials whose electronic structures are a dramatic function of temperature, pressure, or other external stimuli. Such materials have been termed “electronically labile” [1] and are important in developing our understanding of electron transfer, conductivity, magnetism, light absorption, and related phenomena. Bistable molecules are those that can exist in two chemically distinct forms. Electronically labile molecules and materials are inherently bistable and therefore can serve as the basis for molecular electronic devices [2–10]. However, for such compounds to exhibit non-volatile memory, they must exhibit hysteresis, as illustrated in Fig. 1. Consider a bistable molecular material whose molecules can exist in two forms, A and B. Form A is stable at low temperatures and form B is stable at high temperatures. The temperature at which the mole fractions of A and B are equal (x(A) = x(B)) is called the critical temperature, T1/2 . If the interactions between molecules (λ) are very weak, then the transition from A to B is said to be non-cooperative, and the increase in x(B) as a function of increasing temperature is both single-valued and smooth as shown above. Thus, the non-cooperative transition can be viewed as a random distribution of B appearing as the temperature is increased. If however there is a moderate intermolecular interaction, λ, and if the interaction between molecules of A is different than the interaction between molecules of B, then the transition from A to B can be abrupt, and hysteresis can be observed [11]. Hysteresis is characterized by two T1/2 values: one observed upon cooling (T1/2 ↓), and one observed upon warming (T1/2 ↑). Between T1/2 ↓ and T1/2 ↑, A and B coexist. The coexistence of two chemically distinct species, and a mechanism for their interconversion is a recipe for molecular-level switching and information storage.

8.1.2

Electronically Labile Materials

Examples of electronically labile molecules are those that exhibit mixed-valence (MV) [12–17], valence tautomerism (VT) [18], or spin crossover (SC) [11, 19–27].

282

8 Valence Tautomerism in Dioxolene Complexes of Cobalt

Fig. 1. Bistability and hysteresis.

Mixed valence in inorganic complexes has been studied for over thirty years and can be described as a ligand-mediated interaction between two metal ions with different oxidation states, as shown in Fig. 2. Mixed-valent organic systems have also been described [28–41]. The study of MV complexes is interesting because of the opportunity to study electron transfer in well-characterized, single molecules. Depending on the degree of interaction between the metal centers, as mediated by bridging ligand(s), three classes of MV are possible [17]: Class I complexes are those in which no interaction

8.1 Introduction – Bistability, Hysteresis, and Electronically Labile Materials

283

Fig. 2. Mixed valence.

exists between metal ions; Class II complexes are those characterized by a weak interaction (β12 ); Class III complexes are delocalized. Class II is unique in that a particular valence state can be trapped if the thermal energy is less than the barrier to electron transfer, E TH . In addition, Class II complexes exhibit an electronic transition, E IT , called the intervalence transition [42]. Spin crossover, Fig. 3, refers to the change in spin multiplicity (high-spin = hs; low-spin = ls) of a transition metal ion (e. g., CrII , MnIII , FeIII , FeII , CoIII , or CoII ) as a function of temperature, pressure, light, or composition. Techniques used to study SC include Mossbauer ¨ spectroscopy, vibrational spectroscopy, electronic absorption spectroscopy, and magnetic susceptibility. SC compounds have a variety of interesting properties including photorefractivity and the propensity for bistability. Hauser has shown that an FeII SC complex when kept below 50 K can be trapped in its hs form by irradiating the ls form. The effect is called light induced excited state spin trapping (LIESST) [27, 43]. As indicated in Fig. 3, when two spin-states (e. g., 1 A and 5 T) have similar enthalpies but very different entropies, G ◦ can change sign within a readily attainable temperature range. Thus, depending on the temperature, either the hs form or ls form will predominate. We will call such equilibria “entropy driven.” In SC, the entropy driven equilibrium favors the hs-FeII form at high temperatures, and the ls-FeII form at low temperatures. Again, organic species with similar properties have been described [44–46]. The entropic driving force is primarily vibrational: occupied σ antibonding orbitals in the hs-FeII form result in longer Fe–L bond lengths and thus

Fig. 3. Spin crossover.

284


Fig. 4. Valence tautomerism.

a high density of vibrational states. Indeed, large differences in Fe–L stretching frequencies have been measured for FeII complexes in the hs and ls forms [47], and these frequency changes account for the large S ◦ reported from variable-temperature heat capacity measurements [48]. Valence tautomerism is presented graphically in Fig. 4. A combined intramolecular metal-ligand electron transfer and spin crossover characterizes VT. To date, VT involves quinone-type ligands in the dianion form (catecholate, Cat) and radical anion form (semiquinone, SQ). The quinone ligand orbitals generally lie close in energy to the metal orbitals and can donate electrons to or accept electrons from the metal. As in SC, VT complexes undergo changes in d-orbital occupation as a function of temperature. The ls-CoIII form has the metal electronic configuration (π )6 (σ ∗ )0 , and the hs-CoII form has the metal electronic configuration (π )5 (σ ∗ )2 . Occupation of the σ ∗ orbitals occurs only in the hs-CoII form and results in longer Co–ligand bond lengths. This transition to longer bond lengths is accompanied by a large entropy increase due to a higher density of vibrational levels in the hs-CoII form. Therefore VT equilibria, like SC equilibria, are entropy driven.

8.2 8.2.1

Valence Tautomerism in Dioxolene Complexes of Cobalt Valence Tautomerism – A General Chemical Description

Valence tautomerism (VT) has been reported for complexes containing a variety of metal ions (Mn [49–54], Rh and Ir [55, 56], and Co) ligated to dioxolene ligands [18]; however, the focus of this chapter is centered on cobalt-containing materials. VT can be thought of as a special case of SC – one that involves electroactive ligands. Redox-active ligands open the possibility for metal-ligand electron transfer to accompany SC. A generic VT equilibrium is shown in Fig. 5 (N–N is a chelating diamine ligand): a ls-CoIII (SQ)(Cat) complex at low temperature is transformed into a hs-CoII (SQ)2 complex at high temperatures. The spin crossover is defined by the low-spin (d6 CoIII ) to high-spin (d7 CoII ) multiplicity change at the metal ion, and

8.2 Valence Tautomerism in Dioxolene Complexes of Cobalt

285

Fig. 5. Generic VT equilibrium.

Fig. 6. Semiquinone and catecholate derivatives most commonly used in VT complexes.

the electron transfer involves either the reduction of CoIII by a Cat or the reduction of SQ to Cat by CoII . Most of the VT complexes reported to date are composed of two dioxolene ligands, a cobalt ion, and a diamine ligand. The most common dioxolene ligands are 3,5-dit-butylsemiquinone (3,5-DBSQ), 3,6-di-t-butylsemiquinone (3,6-DBSQ), and their corresponding catecholate forms (3,5-DBCat and 3,6-DBCat), Fig. 6. DBQ denotes di-t-butylquinone in either the SQ or Cat form. Semiquinones and catecholates are one- and two-electron reduction products of orthoquinones, and the coordination chemistry of these ligands has been reviewed [57–59]. As be discussed below, the important features of metal complexes of these dioxolene ligands include rather dramatic differences in bond lengths between metalSQ and metal-Cat forms. The magnetic properties of the two tautomeric forms are quite different, as shown in Fig. 7. Typical values of χ T , the paramagnetic susceptibility-temperature product, for the hs-CoII form range from ca. 2.4 to 3.8 emu K mol−1 (this corresponds to a spinonly effective magnetic moment between 4.4 and 5.5). The χ T value for the ls-CoIII tautomer is ca. 0.4 emu K mol−1 (this corresponds to a spin-only effective magnetic moment of ca. 1.8). Note that in the ls form the DBQ ligands are mixed-valent (one Cat and one SQ). In addition to magnetic differences, the optical properties of the VT tautomers differ substantially as shown in Fig. 8. The ls-CoIII tautomer is characterized by a band near 16 666 cm−1 (600 nm) and a ligand-based intervalence transition near 4000 cm−1 (2500 nm) [61]. The hs-CoII tautomer, on the other hand, shows a MLCT band near 13 000 cm−1 (770 nm) and no transition near 4000 cm−1 . There has been disagreement on the origin of the NIR band, but both computations [61] and analogy with ls-CoIII -monocatecholate complexes [62] point to a ligand-based intervalence transition rather than a LMCT band. The conversion of tautomeric forms can be followed quite easily using variabletemperature electronic absorption spectroscopy. The transformation is marked by several isosbestic points, consistent with two species only, i. e. no intermediates are involved.

286


Fig. 7. Magnetic moment for Co(3,5-DBQ)2 (bpy) as a function of temperature. Reprinted with permission from Ref. [60]. Copyright 1980 American Chemical Society.

Fig. 8. Electronic absorption spectra for Co(3,5-DBSQ)2 (phen).toluene as a function of temperature in a polystyrene matrix. Reprinted with permission from Ref. [61]. Copyright 1997 American Chemical Society.


8.2.2

287

Valence Tautomerism – A Simplified MO Description

Figure 9 shows the important frontier metal and dioxolene orbitals for the M(DBQ)2 (N–N) unit. For simplicity, the N–N orbitals have been ignored. The dioxolene π ∗ orbital is singly occupied for SQ and doubly occupied for Cat. A complete MO description of VT complexes has been presented by Hendrickson and Noodleman [61]. The metal t2g d-orbitals (dxy , dxz , dyz ) are of the correct symmetry to mix with the dioxolene π ∗ -MOs in a π-fashion, while the remaining eg metal d-orbitals mix with dioxolene oxygen lone pair orbitals in a σ -fashion. Because the dioxolene π ∗ MOs are slightly higher in energy than the t2g orbitals, the latter are transformed into metal-ligand π-bonding MOs. Conversely, the dioxolene oxygen lone pair orbitals are low-lying (oxygen is electronegative) and mix with the metal eg orbitals to produce σ ∗ MOs. Slightly higher in energy than these metal-based MOs are dioxolene-based MOs of metal-π ∗ -antibonding character. Since the ligand-metal orbital mixing is moderate, the resulting MOs retain metalbased and ligand-based character, while still allowing measurable interaction between metal and ligand. This fortuitous separation of metal and ligand orbital energies accounts for the possibility of simultaneous electron transfer and spin-crossover. If metal–ligand mixing were extensive, electron transfer would be impossible because the metal-based and ligand-based orbitals would loose their individuality – the electrons would be delocalized. If metal–ligand mixing were negligible, spin crossover would be impossible because the metal-centered orbitals would be neither bonding nor antibonding with respect to dioxolene orbitals. The net result, illustrated in Fig. 10, is a set of metal-based and ligand-based orbitals whose close energy spacings allow electron transfer, and the differential bonding character of the metal-based orbitals permits SC. Typical bond lengths are given in Table 1 for VT complexes with N–N ligands shown in Fig. 11. As can be, ls-CoIII –O and ls-CoIII –N bond lengths are 0.1–0.15 Å

Fig. 9. Dioxolene and metal frontier orbitals for M(DBQ)2 (N–N).

288


Fig. 10. Relative frontier orbital energies.

Fig. 11. N–N ligands for complexes in Table 1 [60, 63, 64]. Table 1. Bond lengths for VT complexes. N–N ligands shown in Fig. 11. Dioxolene ligand 3,5-DBSQ 3,5-DBCat 3,6-DBSQ 3,6-DBCat 3,6-DBSQ 3,6-DBSQ 3,6-DBSQ 3,6-DBSQ

Metal ion configuration

Ancillary ligand

Co–O (Å)

Co–N (Å)

Ref.

ls-CoIII

bpy

1.851–1.906

1.940–1.957

60

ls-CoIII

tmeda

1.852–1.899

2.021–2.031

63

hs-CoII

dafl

2.005–2.050

2.278–2.518

63

hs-CoII

NO2 phen

2.066

2.165

63, 77

shorter than the corresponding bond lengths for hs-CoII . This is because the ls-CoIII form has the metal electronic configuration (πyz )2 (πxz )2 (πxy )2 , and the hs-CoII form has the metal electronic configuration (πyz )2 (πxz )2 (πxy )1 (σx∗2 −y2 )1 (σz∗2 )1 , see Fig. 9. Occupation of the (σx∗2 −y2 and σz∗2 orbitals occurs only in the hs-CoII form and results in longer Co–N/Co–O bond lengths. As presented in the next section, the differences in metal–ligand bonding accounts for the large values of S ◦ .

8.2.3

VT Thermodynamics

Now that we have introduced a simple MO picture and pointed out salient bonding interactions within each MO, the stage is set for understanding the thermodynamics of the VT equilibrium and correlating thermodynamic parameters to features of our MO description.


289

Typically, H ◦ must be on the order of kT for both tautomers to be thermally accessible, and the equilibrium between ls-CoIII (SQ)(Cat)N–N and hs-CoII (SQ)2 is characterized by a positive H ◦ because the more Lewis acidic ls-CoIII has stronger metal-ligand bonds. Typical ls-CoIII –O (O = dioxolene oxygen) bond lengths are ∼1.85 Å, while those for hs-CoII –O are ∼2.05 Å. This is corroborated by the MO picture: metal electrons completely fill metal–ligand bonding orbitals in the ls-CoIII tautomer, while σ ∗ orbitals are occupied in the hs-CoII tautomer. The VT equilibrium is also characterized by a large, positive S ◦ . The origins of the positive S ◦ are primarily electronic and vibrational, as solvent reorganizational entropy is predicted to be very small [65]. Thus, S ◦ = Sel + Svib Before calculating the electronic term, a few comments on magnetic coupling of SQ and metal ion spins are in order. Exchange coupling between semiquinones and transition metal ions has been thoroughly studied [57, 58, 66–75]. Whether antiferromagnetic (low spin) or ferromagnetic (high spin) coupling is observed depends on metal orbital occupation and symmetry [11]. Basically, for octahedral metal complexes, a semiquinone spin is ferromagnetically coupled to unpaired electrons in the eg orbitals and antiferromagnetically coupled to unpaired electrons in the t2g orbitals. Recall that the SQ SOMO and eg orbitals are orthogonal, while the SQ SOMO and the t2g orbitals are of the same symmetry. The latter situation simultaneously gives rise to π-bonding and antiferromagnetic coupling since a bond is the quintessential example of antiferromagnetically-coupled electrons. The origin of ferromagnetic coupling between a SQ spin and unpaired metal electrons in the eg set can be traced back to Hund’s rule: electron-electron repulsion is reduced for spin-aligned electrons in orthogonal yet overlapping orbitals. For hs-CoII –SQ coupling, Hendrickson and Noodleman have calculated a rather substantial antiferromagnetic exchange parameter (J = −1700 cal mol−1 ), indicating that the SQ-π antiferromagnetic contribution is substantially greater than SQ-σ ∗ ferromagnetic contribution. This calculated J is much larger than that measured for the tetramer [Co4 (3,5-DBSQ)8 ], for which J = −86 cal mol−1 [72]. Increased entropy for the hs-CoII tautomer is expected due to (1) hs-metal ion configuration, and (2) spin–spin coupling between CoII and ligand spins. High-spin CoII has three unpaired electrons, and the two SQ ligands have one each. Interaction amongst the spins gives rise to 4 × 2 × 2 = 16 states: a sextet (S = 5/2), two quartets (2 × S = 3/2), and a doublet (S = 1/2). The doublet is the lowest-energy state due to antiferromagnetic coupling as described in the previous paragraph, and the electronic degeneracy (ghs ) for the CoII tautomer is 16. The CoIII tautomer on the other hand is a ground-state doublet with mixed-valent dioxolene ligands (SQ-Cat ↔ Cat-SQ). The electronic degeneracy (gls ) for this tautomer is therefore 2 × 2 = 4, and the electronic contribution to the entropy change can be calculated as, Sel = R ln(ghs /gls ) = R ln(16/4) ≈ 3 cal K−1 mol−1 As we will show below, estimated values for S ◦ are typically greater than 25 cal K−1 mol−1 , thus the electronic term makes only a small contribution to S ◦ .

290


Fig. 12. Cartoons of ls-CoIII and hs-CoII potential wells.

As in SC, the antibonding character of the σx∗2 −y2 and σz∗2 orbitals is critically important for VT, as they are the origin of the large positive S ◦ . Consider the energy diagrams shown in Fig. 12. The CoII tautomer, with its occupied antibonding orbitals has a much greater density of vibrational levels, owing to the weaker metal– ligand bonds. The vibrational contribution to the entropy change may be written as: (Svib = R ln (1 − exp(−νls /RT )/(1 − exp(−νhs /RT ) where [1 − exp(−νls /RT )] represents the product of the vibrational partition functions for ls-CoIII . Considering only the metal ion and the immediate coordination sphere, there are 3(7) − 6 = 15 normal modes to consider. For Svib = 22 cal K−1 mol−1 , the ratio of the products of the partition functions must be ca. 60 000! This corresponds to a striking decrease (ca. twofold) in vibrational frequencies in the hs-CoII tautomer. As noted in the Introduction, large decreases in metal– ligand stretching frequencies have been measured in hs-FeII SC complexes relative to ls forms. In VT complexes, additional low-frequency ligand modes might also contribute to Svib [1].

8.2.4

Experimental Determination of Thermodynamic Parameters

Quite often, magnetic or optical data can be transformed to illustrate the fraction of CoII as a function of temperature. Consider the generic VT equilibrium, ls-CoIII (SQ)(Cat)(N–N)

K VT

hs-CoII (SQ)2 (N–N)

If x is the fraction of CoII complexes, (1 − x) is the fraction of CoIII complexes, (χ T )exp is the measured paramagnetic susceptibility–temperature product, (χ T )Co(II) is the paramagnetic susceptibility–temperature product for hs-CoII , and (χ T )Co(III) is the paramagnetic susceptibility–temperature product for ls-CoIII , then:


291

(χ T )exp = x(χ T )Co(II) + (1 − x)(χ T )Co(III) = x(χ T )Co(II) + (χ T )Co(III) − x(χ T )Co(III) = x[(χ T )Co(II) − (χ T )Co(III) ] + (χ T )Co(III) so: x = [(χ T )exp − (χ T )Co(III) ]/[(χ T )Co(II) − (χ T )Co(III) ] Therefore, if the (χ T )exp is measured and if (χ T )Co(II) and (χ T )Co(III) are known (or estimated), a plot of x = f (T ) can be generated. Furthermore, since K VT = [hs-CoII ]/[ls-CoIII ] = exp(−G ◦ /RT ), then: K VT = x/(1 − x) = exp(−H ◦ /RT + S ◦ /R) and x = exp(−H ◦ /RT + S ◦ /R) − x[(−H ◦ /RT + S ◦ /R)] so: x[1 + exp(−H ◦ /RT + S ◦ /R)] = exp(−H ◦ /RT + S ◦ /R) and x = exp(−H ◦ /RT + S ◦ /R)/[1 + exp(−H ◦ /RT + S ◦ /R)] or x = 1/[exp(H ◦ /RT − S ◦ /R) + 1] Shown in Fig. 13 are plots of x = f (T ) for H ◦ = 5 kcal mol−1 and S ◦ = 15, 20, 25, and 30 e. u..

Fig. 13. Dependence of mole fraction of hs-CoII tautomer on S ◦ .

292


Fig. 14. N–N ligands for VT complexes in Table 2 [1, 76–80].

The critical temperature, T1/2 , is defined as the temperature where [CoII ] = [CoIII ], or x = 0.5. It is obvious that the equilibrium is entropy-driven. Experimentally, x = f (T ) plots can be generated from variable-temperature magnetic data, and the data fit to extract the thermodynamic parameters. Table 2 shows thermodynamic parameters for several CoIII /CoII VT complexes with different N–N ligands shown in Fig. 14.

8.2.5

Dependence of K VT Equilibrium on Ancillary Ligands

In 1980, Pierpont reported the structure and properties of Co(3,5-DBSQ)(3,5DBCat)(2,2 -bipyridine) · 0.5 toluene [60]. Since that time, a considerable amount of work has been reported on the mechanism and structure-property relationships for VT complexes. The majority of reports concern synthesis and characterization of CoII /CoIII VT compounds that differ in the chemical structure of the ancillary ligands. The thermodynamic parameters for KVT are intimately linked with the structure of the ancillary ligand.

8.2.5.1

Redox Potential

Hendrickson and coworkers found that the critical temperature of a series of complexes depends on the electronic structure of ancillary, aromatic N–N ligands [78, 81]. As estimated from variable-temperature electronic absorption spectra, the T1/2 values decrease in the order ∼348 K (dpbpy, Entry 7, Table 2), ∼298 K (dmbpy, Entry 6, Table 2), ∼273 K (bpy, Entry 5, Table 2), ∼230 K (phen, Entry 4, Table 2), ∼190 K (bpym, Entry 12, Table 2), and 400b 310 >400b ca. 110 178b 226.6 240b,e 277.0 327b 286.6 350.0 270f 110 (T1/2 ↓)b,c 330 (T1/2 ↑)b,d 255f 370b 225f 290b

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