Orbital interactions in chemistry second edition

ORBITAL INTERACTIONS IN CHEMISTRY ORBITAL INTERACTIONS IN CHEMISTRY Second Edition By Thomas A Albright Jeremy K Burdett Myung-Hwan Whangbo Copyright # 2013 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 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United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Albright, Thomas A Orbital interactions in chemistry / Thomas A Albright, Jeremy K Burdett, Myung-Hwan Whangbo – 2nd edition pages cm Includes index ISBN 978-0-471-08039-8 (hardback) Molecular orbitals I Burdett, Jeremy K., 1947- II Whangbo, Myung-Hwan III Title QD461.A384 2013 5410 28–dc23 2012040257 Printed in the United States of America ISBN: 9780471080398 10 Contents Preface xi About the Authors xiii Chapter | Atomic and Molecular Orbitals 1.1 Introduction 1.2 Atomic Orbitals 1.3 Molecular Orbitals Problems 13 References 14 Chapter | Concepts of Bonding and Orbital Interaction 15 2.1 Orbital Interaction Energy 15 2.1.1 Degenerate Interaction 16 2.1.2 Nondegenerate Interaction 18 2.2 Molecular Orbital Coefficients 20 2.2.1 Degenerate Interaction 21 2.2.2 Nondegenerate Interaction 22 2.3 The Two-Orbital Problem—Summary 24 2.4 Electron Density Distribution 26 Problems 31 References 31 Chapter | Perturbational Molecular Orbital Theory 32 3.1 Introduction 32 3.2 Intermolecular Perturbation 35 3.3 Linear H3, HF, and the Three-Orbital Problem 38 3.4 Degenerate Perturbation 43 Problems 45 References 46 Chapter | Symmetry 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Introduction 47 Symmetry of Molecules 47 Representations of Groups 53 Symmetry Properties of Orbitals 59 Symmetry-Adapted Wavefunctions 62 Direct Products 65 Symmetry Properties, Integrals, and the Noncrossing Rule 67 4.8 Principles of Orbital Construction Using Symmetry Principles 69 4.9 Symmetry Properties of Molecular Vibrations 73 Problems 75 References 77 47 vi CONTENTS Chapter | Molecular Orbital Construction from Fragment Orbitals 78 5.1 Introduction 78 5.2 Triangular H3 78 5.3 Rectangular and Square Planar H4 82 5.4 Tetrahedral H4 84 5.5 Linear H4 86 5.6 Pentagonal H5 and Hexagonal H6 88 5.7 Orbitals of Cyclic Systems 91 Problems 94 References 96 Chapter | Molecular Orbitals of Diatomic Molecules and Electronegativity Perturbation 97 6.1 Introduction 97 6.2 Orbital Hybridization 98 6.3 Molecular Orbitals of Diatomic Molecules 99 6.4 Electronegativity Perturbation 105 6.5 Photoelectron Spectroscopy and Through-Bond Conjugation 112 Problems 118 References 122 Chapter | Molecular Orbitals and Geometrical Perturbation 123 7.1 7.2 7.3 7.4 Molecular Orbitals of AH2 123 Geometrical Perturbation 128 Walsh Diagrams 131 Jahn–Teller Distortions 134 7.4.1 First-Order Jahn–Teller Distortion 135 7.4.2 Second-Order Jahn–Teller Distortion 136 7.4.3 Three-Center Bonding 139 7.5 Bond Orbitals and Photoelectron Spectra Of AH2 Molecules 141 Problems 147 References 150 Chapter | State Wavefunctions and State Energies 8.1 8.2 Introduction 151 The Molecular Hamiltonian and State Wavefunctions 152 8.3 Fock Operator 154 8.4 State Energy 156 8.5 Excitation Energy 157 8.6 Ionization Potential and Electron Affinity 160 8.7 Electron Density Distribution and Magnitudes of Coulomb and Exchange Repulsions 160 8.8 Low versus High Spin States 162 8.9 Electron–Electron Repulsion and Charged Species 164 8.10 Configuration Interaction 165 8.11 Toward More Quantitative Treatments 170 8.12 The Density Functional Method 174 Problems 176 References 177 151 vii CONTENTS Chapter | Molecular Orbitals of Small Building Blocks 179 9.1 Introduction 179 9.2 The AH System 179 9.3 Shapes of AH3 Systems 182 9.4 p-Bonding Effects of Ligands 190 9.5 The AH4 System 193 9.6 The AHn Series—Some Generalizations 198 Problems 201 References 202 Chapter 10 | Molecules with Two Heavy Atoms 204 10.1 Introduction 204 10.2 A2H6 Systems 204 10.3 12-Electron A2H4 Systems 208 10.3.1 Sudden Polarization 211 10.3.2 Substituent Effects 214 10.3.3 Dimerization and Pyramidalization of AH2 218 10.4 14-Electron AH2BH2 Systems 220 10.5 AH3BH2 Systems 223 10.6 AH3BH Systems 232 Problems 234 References 238 Chapter 11 | Orbital Interactions through Space and through Bonds 241 11.1 Introduction 241 11.2 In-Plane s orbitals of Small Rings 241 11.2.1 Cyclopropane 241 11.2.2 Cyclobutane 246 11.3 Through-Bond Interaction 253 11.3.1 The Nature of Through-Bond Coupling 253 11.3.2 Other Through-Bond Coupling Units 256 11.4 Breaking a CÀÀC Bond 258 Problems 265 References 269 Chapter 12 | Polyenes and Conjugated Systems 272 12.1 Acyclic Polyenes 272 12.2 H€ uckel Theory 274 12.3 Cyclic Systems 277 12.4 Spin Polarization 285 12.5 Low- versus High-Spin States in Polyenes 289 12.6 Cross-Conjugated Polyenes 291 12.7 Perturbations of Cyclic Systems 294 12.8 Conjugation in Three Dimensions 303 Problems 306 References 310 Chapter 13 | Solids 13.1 13.2 13.3 13.4 Energy Bands 313 Distortions in One-Dimensional Systems 328 Other One-Dimensional Systems 334 Two- and Three-Dimensional Systems 339 313 viii CONTENTS 13.5 Electron Counting and Structure 350 13.6 High-Spin and Low-Spin Considerations 353 Problems 353 References 357 Chapter 14 | Hypervalent Molecules 359 14.1 Orbitals of Octahedrally Based Molecules 359 14.2 Solid-State Hypervalent Compounds 373 14.3 Geometries of Hypervalent Molecules 383 Problems 392 References 399 Chapter 15 | Transition Metal Complexes: A Starting Point at the Octahedron 401 15.1 Introduction 401 15.2 Octahedral ML6 402 15.3 p-Effects in an Octahedron 406 15.4 Distortions from an Octahedral Geometry 416 15.5 The Octahedron in the Solid State 423 Problems 431 References 434 Chapter 16 | Square Planar, Tetrahedral ML4 Complexes, and Electron Counting 436 16.1 Introduction 436 16.2 The Square Planar ML4 Molecule 436 16.3 Electron Counting 438 16.4 The Square Planar-Tetrahedral ML4 Interconversion 448 16.5 The Solid State 453 Problems 460 References 463 Chapter 17 | Five Coordination 465 17.1 Introduction 465 17.2 The C4v ML5 Fragment 466 17.3 Five Coordination 468 17.4 Molecules Built Up from ML5 Fragments 480 17.5 Pentacoordinate Nitrosyls 489 17.6 Square Pyramids in The Solid State 492 Problems 498 References 500 Chapter 18 | The C2v ML3 Fragment 503 18.1 Introduction 503 18.2 The Orbitals of A C2v ML3 Fragment 503 18.3 ML3-Containing Metallacycles 511 18.4 Comparison of C2v ML3 and C4v ML5 Fragments 518 Problems 523 References 525 Chapter 19 | The ML2 and ML4 Fragments 19.1 19.2 19.3 19.4 Development of the C2v ML4 Fragment Orbitals 527 The Fe(CO)4 Story 529 Olefin–ML4 Complexes and M2L8 Dimers 533 The C2v ML2 Fragment 537 527 ix CONTENTS 19.5 Polyene–ML2 Complexes 539 19.6 Reductive Elimination and Oxidative Addition 552 Problems 561 References 566 Chapter 20 | Complexes of ML3, MCp and Cp2M 20.1 Derivation of Orbitals for a C3v ML3 Fragment 20.2 The CpM Fragment Orbitals 582 20.3 Cp2M and Metallocenes 592 20.4 Cp2MLn Complexes 595 Problems 607 References 613 Chapter 21 570 570 | The Isolobal Analogy 616 21.1 Introduction 616 21.2 Generation of Isolobal Fragments 617 21.3 Caveats 621 21.4 Illustrations of the Isolobal Analogy 623 21.5 Reactions 634 21.6 Extensions 639 Problems 646 References 649 Chapter 22 | Cluster Compounds 653 22.1 Types of Cluster Compounds 653 22.2 Cluster Orbitals 657 22.3 Wade’s Rules 660 22.4 Violations 671 22.5 Extensions 677 Problems 681 References 687 Chapter 23 | Chemistry on the Surface 691 23.1 Introduction 691 23.2 General Structural Considerations 693 23.3 General Considerations of Adsorption on Surfaces 696 23.4 Diatomics on a Surface 699 23.5 The Surface of Semiconductors 721 Problems 728 References 731 Chapter 24 | Magnetic Properties 24.1 Introduction 735 24.2 The Magnetic Insulating State 736 24.2.1 Electronic Structures 736 24.2.2 Factors Affecting the Effective On-Site Repulsion 738 24.2.3 Effect of Spin Arrangement on the Band Gap 740 24.3 Properties Associated with the Magnetic Moment 741 24.3.1 The Magnetic Moment 741 24.3.2 Magnetization 743 24.3.3 Magnetic Susceptibility 743 24.3.4 Experimental Investigation of Magnetic Energy Levels 745 735 x CONTENTS 24.4 Symmetric Spin Exchange 745 24.4.1 Mapping Analysis for a Spin Dimer 745 24.4.2 Through-Space and Through-Bond Orbital Interactions Leading to Spin Exchange 748 24.4.3 Mapping Analysis Based on Broken-Symmetry States 751 24.5 Magnetic Structure 754 24.5.1 Spin Frustration and Noncollinear Spin Arrangement 754 24.5.2 Long-Range Antiferromagnetic Order 755 24.5.3 Ferromagnetic and Ferromagnetic-Like Transitions 759 24.5.4 Typical Cases Leading to Ferromagnetic Interaction 760 24.5.5 Short-Range Order 763 24.6 The Energy Gap in the Magnetic Energy Spectrum 763 24.6.1 Spin Gap and Field-Induced Magnetic Order 763 24.6.2 Magnetization Plateaus 765 24.7 Spin–Orbit Coupling 766 24.7.1 Spin Orientation 766 24.7.2 Single-Ion Anisotropy 770 24.7.3 Uniaxial Magnetism versus Jahn–Teller Instability 771 24.7.4 The Dzyaloshinskii–Moriya Interaction 774 24.7.5 Singlet–Triplet Mixing Under Spin–Orbit Coupling 777 24.8 What Appears versus What Is 778 24.8.1 Idle Spin in Cu3(OH)4SO4 778 24.8.2 The FM–AFM versus AFM–AFM Chain 779 24.8.3 Diamond Chains 780 24.8.4 Spin Gap Behavior of a Two-Dimensional Square Net 782 24.9 Model Hamiltonians Beyond the Level of Spin Exchange 785 24.10 Summary Remarks 785 Problems 786 References 789 Appendix I Perturbational Molecular Orbital Theory 793 Appendix II Some Common Group Tables 803 Appendix III Normal Modes for Some Common Structural Types 808 Index 813 Preface Use of molecular orbital theory facilitates an understanding of physical properties associated with molecules and the pathways taken by chemical reactions The gigantic strides in computational resources as well as a plethora of standardized quantum chemistry packages have created a working environment for theoreticians and experimentalists to explore the structures and energy relationships associated with virtually any molecule or solid There are many books that cover the fundamentals of quantum mechanics and offer summaries of how to tackle computational problems It is normally a straightforward procedure to “validate” a computational procedure for a specific problem and then compute geometries and associated energies There are also prescriptions for handling solvation So, does it mean that all a chemist needs to is to plug the problem into the “black-box” and he or she will receive understanding in terms of a pile of numbers? We certainly think not This book takes the problem one step further We shall study in some detail the mechanics behind the molecular orbital level structures of molecules We shall ask why these orbitals have a particular form and are energetically ordered in the way that they are, and whether they are generated by a Hartree–Fock (HF), density functional, or semiempirical technique Furthermore, we want to understand in a qualitative or semiquantitative sense what happens to the shape and energy of orbitals when the molecule distorts or undergoes a chemical reaction These models are useful to the chemical community They collect data to generate patterns and ideally offer predictions about the directions of future research An experimentalist must have an understanding of why molecules of concern react the way they do, as well as what determines their molecular structure and how this influences reactivity So too, it is the duty and obligation of a theorist (or an experimentalist doing calculations on the side) to understand why the numbers from a calculation come out the way they Models in this vein must be simple The ones we use here are based on concepts such as symmetry, overlap, and electronegativity The numerical and computational aspects of the subject in this book are deliberately de-emphasized In fact there were only a couple of computational numbers cited in the first edition People sometimes expressed the opinion that the book was based on extended H€ uckel theory It, in fact, was and is not An even more parochial attitude (and unfortunately common one) was expressed recently “I imagine that there are still people that HF calculations too But these days they cannot be taken too seriously.” In this edition, computational results from a wide variety of levels have been cited This is certainly not to say that computations at a specific level of theory will accurately reproduce experimental data It is reassuring to chemists that, say, a geometry optimization replicates the experimental structure for a molecule But that does not mean that the calculation tells the user why the molecule does have the geometry that it does or what other molecules have a similar bonding scheme The goal of our approach is the generation of global ideas that will lead to a qualitative understanding of electronic structure no matter what computational levels have been used An important aim of this book is then to show how common orbital situations arise throughout the whole chemical spectrum For example, there are isomorphisms between the electronic structure of CH2, Fe(CO)4, and Ni(PR3)2 and between the Jahn–Teller instability in cyclobutadiene and the Peierls distortion in solids These relationships will be highlighted, and to a certain extent, we have 805 APPENDIX II D2h E C2(z) C2(y) Ag B1g B2g B3g Au B1u B2u B3u 1 1 1 1 1 À1 À1 1 À1 À1 À1 À1 À1 À1 C2(x) À1 À1 1 À1 À1 i s(xy) s(xz) s(yz) 1 1 À1 À1 À1 À1 1 À1 À1 À1 À1 1 À1 À1 À1 À1 1 À1 À1 À1 1 À1 D3h E 2C3 3C2 sh 2S3 3s v A01 A02 1 1 1 À1 1 À1 À1 À1 1 À1 À1 À2 1 À1 À1 À1 1 À1 À1 E A001 A002 E00 D4h E 2C4 C2 2C02 2C002 i 2S4 sh 2s v 2s d A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu 1 1 1 1 1 À1 À1 1 À1 À1 1 1 À2 1 1 À2 À1 À1 À1 À1 À1 À1 1 À1 À1 1 1 À1 À1 À1 À1 À2 1 À1 À1 À1 À1 1 1 1 À2 À1 À1 À1 À1 À1 –1 À1 À1 1 À1 À1 À1 1 À1 D5h E 2C5 2C25 5C2 sh 2S5 2S35 5s v A01 A02 E01 E02 A001 A002 E001 E002 1 2 1 2 1 cos 72 cos 144 1 cos 72 cos 144 1 cos 144 cos 72 1 cos 144 cos 72 À1 0 À1 0 1 2 À1 À1 À2 À2 1 cos 72 cos 144 À1 À1 À2 cos 72 À2 cos 144 1 cos 144 cos 72 À1 À1 À2 cos 144 À2 cos 72 À1 0 À1 0 806 APPENDIX II D6h E 2C6 2C3 C2 3C02 3C002 i 2S3 2S6 sh 3s d 3s v A1g A2g B1g B2g E1g E2g A1u A2u B1u B2u E1u E2u 1 1 2 1 1 2 1 À1 À1 À1 1 À1 À1 À1 1 1 À1 À1 1 1 À1 À1 1 À1 À1 À2 1 À1 À1 À2 À1 À1 0 À1 À1 0 À1 À1 0 À1 À1 0 1 1 2 À1 À1 À1 À1 À2 À2 1 À1 À1 À1 À1 À1 1 À1 1 1 À1 À1 À1 À1 À1 À1 1 1 À1 À1 À2 À1 À1 1 À2 À1 À1 0 À1 À1 0 À1 À1 0 À1 1 À1 0 D2d E 2S4 C2 2C02 2s d A1 A2 B1 B2 E 1 1 1 À1 À1 1 1 À2 À1 À1 À1 À1 D3d E 2C3 3C2 i 2S6 3s d A1g A2g Eg A1u A2u Eu 1 1 1 À1 1 À1 À1 À1 1 À1 À1 À2 1 À1 À1 À1 1 À1 À1 D4d E 2S8 2C4 2S38 C2 4C02 4s d A1 A2 B1 B2 E1 E2 E3 1 1 2 1 À1 À1 p À2 1 1 À2 1 À1 À1 p À p 1 1 À2 À2 À1 À1 0 À1 À1 0 2S310 2S10 2s d 1 cos 72 cos 144 À1 À1 À2 cos 72 À2 cos 144 1 cos 144 cos 72 À1 À1 À2 cos 144 À2 cos 72 À1 0 À1 0 D5d E 2C5 2C25 5C2 i A1g A2g E1g E2g A1u A2u E1u E2u 1 2 1 2 1 cos 72 cos 144 1 cos 72 cos 144 1 cos 144 cos 72 1 cos 144 cos 72 À1 0 À1 0 1 2 À1 À1 À2 À2 807 APPENDIX II D6d E 2S12 2C6 2S4 2C3 2S512 C2 6C02 6s d A1 A2 B1 B2 E1 E2 E3 E4 E5 1 1 2 2 1 À1 À1 p À1 p 1 1 À1 À2 À1 1 À1 À1 À2 1 1 À1 À1 À1 À1 1 À1 À1 p À À1 p 1 1 À2 À2 À2 À2 À1 À1 0 0 À1 À1 0 0 Td E 8C3 3C2 6S4 6s d A1 A2 E T1 T2 1 3 1 À1 0 1 À1 À1 À1 À0 À1 À1 À1 Oh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3s h 6s d A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u 1 3 1 3 1 À1 0 1 À1 0 À1 À1 1 À1 À1 1 À1 À1 À1 À1 1 À1 À1 1 À1 À1 1 3 À1 À1 À2 À3 À3 À1 À1 À1 À1 1 À1 0 À1 À1 0 1 À1 À1 À1 À1 À2 1 À1 À1 1 1 C1v ỵ S (ẳ A1) SÀ (¼ A2) P (¼ E1) D (¼ E2) D1h E Sỵ g S g E 2C1f 2C12f 1 2 1 2cos f 2cos 2f 1 2cos 2f 2cos 4f sv À1 0 1sv i 1 1 À1 1 À1 2C1f 2S1f sv Pg 2 cos f À2 cos f Dg 2 cos 2f 2 cos f Sỵ u S u 1 À1 À1 À1 1 À1 À1 À1 Pu 2 cos f À2 cos f Du 2 cos 2f À2 À2 cos f A P P E N D I X I I I Normal Modes for Some Common Structural Types For the molecules in this appendix, the symbols (ỵ) and () are used for displacement vectors above and behind the plane of the paper, respectively The length of the displacement vectors has been drawn in an arbitrary manner and will depend on the relative masses of the A and B atoms Orbital Interactions in Chemistry, Second Edition Thomas A Albright, Jeremy K Burdett, and Myung-Hwan Whangbo Ó 2013 John Wiley & Sons, Inc Published 2013 by John Wiley & Sons, Inc APPENDIX III 809 810 APPENDIX III APPENDIX III 811 812 APPENDIX III Index acetylene on metal surfaces 718, 719 adamantyl cation 224 adsorption on surfaces general 694, 696–699 AFM-AFM chain 779 A-frame complexes 524, 525 Ag2MnO2 769 AH 179 AH2 123–125, 127 AH2AH2 221 AH2BH2 220 AH3 70, 71, 80, 182–184, 201 C2v 370, 383, 384 AH3BH 232 AH3BH2 223 AH4 72 C2v 372 D4h 363 AH5, C4v 367–369 D3h 387, 388 AH6, octahedral 360 AHn 198 A2, homonuclear diatomic 99 A2H4 208 A2H6 204, 210 AlH2 133 AMO3 429, 430 Al2 102, 104 Al42À 266 allyl 273 angular node 10-annulene 294 anomeric effect 233 Antiferromagnetic ordering 459, 460 Ar 199, 200 aromatic systems 281 cyclobutadiene2À 281 cyclopentadienylÀ 281 benzene 281 cycloheptatrieneỵ 281 Ar2 102 As(CH3)3 188 AsF3 188 AsH3 188, 189 As2 104, 117 As4S4 301, 302 As4Se4 301 Au(PR3) 639, 640 (Au-PR3)42ỵ 85 azulene 161 ionization potential 162 electron afficnity 162 excitation energy 162 Azurite 781, 782 BaBiO3 373–375 Ba2Bi2Sb 379 BaCrS2 496, 497 Ba2Cu(PO4)2 788 BaCuSi2O6 764, 765 BaCu2V2O8 750, 751 BaGe2 378 Ba2Ge4 355 Ba2GeP2 356 BaHgO4 355 Ba1-xKxBiO3 superconductivity in 375 BaLiSi2 338 BaMg0.1Li0.9Si2 337 Ba2NaOsO6 738, 739, 740 band dispersion 318 band folding 326 effect of overlap 323 sulfur chain 335, 336 band gap 315 band gap, effect of spin arrangement on 740 band orbital 321 BaNiS2 496, 497 BaPdAs2 497, 498 Ba2Si3Ni 591 barralene 305 BaSi 351 Ba3Si4 351 BaTiO3 426–428 BCS theory 349 Be2 102, 103 BeH2 133 BeH3ỵ 385 benzene 109, 110, 278–280 D6h versus D3h 284 Orbital Interactions in Chemistry, Second Edition Thomas A Albright, Jeremy K Burdett, and Myung-Hwan Whangbo Ó 2013 John Wiley & Sons, Inc Published 2013 by John Wiley & Sons, Inc inorganic 295, 296 Second-order Jahn-Teller distortion 285 benzene-Cr(CO)3 607 (benzene)2Geỵ 397 BH2 133, 145 BH3 185, 187, 189 BH42ỵ 149, 197 B2 102, 104, 120 B2C 235 B2H6 187, 206, 208 bicapped pentagonal antiprism 75 bicapped tetrahedron distortions 418–420, 433 Bi(CH3)3 188 Bi2CuO4 769, 770, 771 Bi4Cu3V2O14 780, 781 bicyclobutane 261 bicyclo[1.1.0]butane 214 bicyclo[3.1.0]hexane 214 bicyclodienes 257, 258 bicyclo[2.1.1]hexene 251 bicyclo[3.1.0]hexyl tosylate 245 bicyclo[2.2.0]cyclohexane 266 BiF3 188 Bi2Se3 349 bismethylenecyclobutane 269 Bi2Te3 349 biquadratic spin exchange 785 Blyholder model 700 Bloch function 318, 321 BN 355 B2N 111 B3N3H3 295, 296 B4N5H6 302 B2N2R4 300, 307 B(OH)3 75 B2O 111 Bohlman band 226 Boltzmann distribution 745 bond order 103 bond stretch isomerization 260 bond valence 738, 739 borazine 295, 296 Bose-Einstein system 764 814 boundary surface BrF5 75 bridging carbonyls 446, 447 Brillouin’s theorem 166 Brillouin zone 339, 340 bromonium ion 265, 266 1,3-butadiene 177, 213 butadiene-Fe(CO)3 608 BrF3 370, 371 BrF5 369 C2 102, 104, 118 C22À 106, 107 C60 282 C78 282 CaBe2Ge2 378 Ca3Co2O6 772, 773, 774 Ca3CoIrO6 772 Ca3CoRhO6 772 CaCuGe2O6 788 Ca3LiOsO6 738, 739 Ca3Mn7O12 761, 762, 766–767 strong Dzyaloshinskii-Moriya interaction 762 carbene complexes 410, 411, 413–415 carbon nanotube 282 CaSi2 351 Ca2Si 350 Cd2 104 Cd2Os2O7 741 CH 46 CH2 133, 138, 145, 163, 170 CH2, dimerization of 218 CH22ỵ 198 CH3 201 CH3ỵ 185, 186 CH4 49,193, 199, 200 CH42ỵ 149, 197, 198, 201 CH5ỵ 390, 391 C2H2 209, 210 C2H4 75, 209, 210, 219, 228 C2H5ỵ 223, 225 C2H5 225227 C2H6 204207 C2H6ỵ 207 C3H4 149 C3H4D2 75 C5H5ỵ 261, 262, 263 C6H62ỵ isolobal analogs 628, 629 C6H62ỵ 265 C6H62ỵ 265 C7H7ỵ 75 C18H18 284 charge density wave 344 charge polarization 216 open versus closed bond-stretch isomer 262, 263 CH2CH¼O 192 (CH2)2ML4 564 INDEX CH2ML5 498 CH2NO2 192 CH2¼O 227, 228 CH3Mn(CO)5 519 CH3OH 232 CH3PtCl32 519 (C2H4)Agỵ 542, 543 (C2H4)M2L2n 545547 (C2H4)Os(CO)4 542, 543 (C2H4)3Ni 540, 541 (C2H4)Pt(PH3)2 542, 543 C5H5X heterocycles 298, 299 (C2R4)Pt(PH3)2 543, 544 ClF3 370, 371 Cl2 102, 104 ClH 199, 200 closed-shell 153–158 Fock operator 154, 155 Coulomb operator 155 exchange operator 155 total electron-electron repulsion 156 total energy 156 SCF iteration 157 effective potential, occupied 158 unoccupied 158 singlet state 158 cluster electrons for inorganic fragments 666–669 cluster orbitals 657 Cl3WC3H3 515518 (C5Me5)B-Brỵ 264 C5Me5-M 264 C5Me5Siỵ 269 C6Me62ỵ 264 CN2 235 C4(NR2)2(CO2R)2 300 CO 46, 106, 107, 109 CO2 235 Co2(h5-C5Me5)2(m-CO)2 164 conduction band 315 configuration interaction 165 symmetry-forbidden reaction 167 CH2 168, 169 conjugation in three dimensions 303 conrotatory electrocyclization 177 CO on Ni(100), cluster model 704, 705 X-ray emission spectroscopy 710, 711 c(2 x 2) CO on Ni(100), DOS 700–704 X-ray emission spectroscopy 705, 706 COOP curve 324 Cooper pair 350 cooperative Jahn-Teller distortion 760 Co(PMe3)4ỵ 532 copper oxide superconductors 454 Coulomb repulsion 154, 155 CpAl 642, 643 CpCo(CO)2 549–552 Cp2Co2(tetramethylene) 612 CpFe chains 588–591 CpFe(CO)2ỵ 551, 552 CpIr(NH) 608 CpM 581584 CpMn(CO)2 551, 552 CpMn(CO)3 578–580 Cp2M(ethylene)2 coupling 605–607 Cp2MLn 595–597 Cp2Mo(CO) 610 Cp2Mo(ethylene) 610 Cp2MR2 reductive elimination 599, 600 CpMn(CO)3 579, 580 Cp3NbH3 598, 599 CpNi(NO) 608, 609 Cp2ReH 597, 598 Cp2V2(C6H6) 586–588 CpV(CO)4 561 Cp2WH2 598 Cp2WO 600–603 Cr(CH3)4 451 Cr(CO)5 170, 468, 475–477 Cr(CO)6 164 Cr(CO)6 PE spectrum 408, 409 CrH6 421, 422 cross-conjugated polyene 291 crystal orbital overlap population 324 Cs2CuCl4 751 Cs2O 196 cubic lattice 345 CuBr2 417, 770, 771 CuCl2 769, 770, 771 (CuCl)LaNb2O7 782–784 Cu3(CO2)2(OH)2 766, 781, 782 CuO22À 455, 456 CuO2 ribbon chain 748, 754 Cu3(OH)4SO4 778, 779 Cu3(P2O6OH)2 766 Cu2Te2O5Br2 789 Cu2Te2O5Cl2 789 cyclic polyenes 277, 278 cycloalkane isolobal analogs 623, 624 cyclobutane 77 in-plane s orbitals 246–248 in caged structure 250 cyclobutadiene 92, 94 singlet versus triplet 285 cyclobutadiene-Fe(CO)3 580, 581 cyclobutene 177 cycloheptatriene 75 cyclohexane, monosubstituted 233 cyclohexane, 1,3,5-trimethyl 75 cyclooctatetraene 75 cyclopropane 241 in-plane s orbitals of 242, 243 protonation of 245 cyclopropenium 93 cyclopropenium radical 266 cyclopropenyl 92 815 INDEX cyclopentadienyl anion 120, 121 cyclotriplumbane 242 1,4-dehydrobenzene 307 deltahedra 654 density functional method 174 density of states 320 DFTỵU method 737 diamond 347 diamond chain 780 diazabicyclooctane 253 diazanaphethalene 269 diazene-Cr(CO)5 523 1,1-dicarboxycyclopropane 245 2,3-dichloro-1,4-dioxane 233 Diels-Alder reaction 250 dimethylcyclopropyl carbocation 244 Dirac cones 349 Dirac point 349 direct product 65 disjoint degenerate orbital 290 disrotatory electrocyclization 177 double exchange 761 double zeta basis set DOS plot 320 dynamic spin polarization 290, 291 Dzyaloshinskii-Moriya interaction 774energy-mapping analysis 775 effective nuclear charge effective potential electron correlation 165 main group atoms 27 electron affinity 160 ethylene 276 1,3-butadiene 276 1,3,5-hexatrene 276 electronegativity perturbation 97 electronegativity, scale 26 electron correlation 738 electron counting, in hypervalent solid state compounds 376–380 in transition metal complexes 438–440 electron transmission spectroscopy 217 electron transfer, inner sphere 487, 488 elemental As 352 elemental black phosphorus 347 encapsulated atoms 670, 671 energy band 313 energy scale, magnetic field 743 ethylene, addition of singlet carbine on 246 ethylene, concerted dimerization of 249 ethylene-Fe(CO)4 533–535 (ethylene)2Fe(CO)3, C–C coupling reaction 511–515 ethylene, isolobal analogs 624, 625 ethylene-ML2 539, 540 ethylene on metal surfaces 717, 718 (ethylene)PtCl3À 520, 521 ethylene, trans-1,2-difluoro 75 exchange repulsion 154, 155 overlap density 161 excited state, singlet 159 triplet 159 F2 101, 102, 104 F3À 235 FCH2CH2À 230 Fe(CO)4 170 Fe(CH3)4 451 Fe(CO)5 473, 474 Fe(CO)4 529–531 Fe2(CO)8 536, 537 Fe[C(SiMe3)3]2 771 Fermi surface 343, 344 Fermi surface nesting 344, 345 Fermi vector 319 ferrimagnetic-like transition 759 spin canting 759 Dzyaloshinskii-Moriya interaction 759 ferrocene 592–594 ferrocene isolobal analogs 629, 630 ferromagnetic ordering 459, 460 ferromagnetic transition 759 ferromagnetic domain 759 typical cases 760FH 199, 200 FH2ỵ 138, 139 field-induced three-dimensional ordering 764 first-order mixing 37, 39 Fischer-Tropisch process 728–730 fitting analysis, nonuniqueness of 753 FM-AFM chain 779 4n p electron system cyclooctatetraene 282, 283 cyclobutadiene 283, 284 Jahn-Teller distortion 283 C4H42 284 4nỵ2 p electron rule 281 fragment orbital 204 F4SCH2 393 F5SCH2À 393 Ga2 104 GaIn2 355 GaS 352 Gaussian type orbital 5–7 Ge2 104 GeH2 138, 170 GeH3 189 Ge2H4 219 GdSi 350 gold clusters 676 graphite 347, 348, 352 group theory 47 H2 21, 22, 33, 38, 79, 171 solid 96 photoelectron spectrum 115 H3, linear 13, 38, 43, 69, 81, 109, 135 equilateral 79, 81,135, 139, 140 isosceles 80, 135, 139, 140 H3ỵ 81, 82, 111, 225 H3 81, 82, 111, 227 H4, rectangular 82, 83 square planar 44, 82, 83, 85 tetrahedral 73, 84, 85 linear 85 D3h 121 H42ỵ 85 H42À 85 H5, pentagonal 88, 90 square pyramid 94 trigonalbipyramid 95 H5ỵ 95 H6, hexagonal 88, 89, 95 octahedral 95, 121, 122 Hn, cyclic 92 H€ uckel 93 M€ obius 93 H4A3 148 Hartree-Fock method 165, 174 HC 181, 182 HCLi3 196 (H3C)3P 236 H3C-S-CH3 236 HCr2(CO)10À 482, 483 He2 24 HF 38, 42, 43, 181, 182 Hg2 104 H-Heỵ 33, 34 high-spin versus low-spin 353 H2N-BH2 214 H2NCH¼O 91, 196 H2N-OH 201, 202 HOÀ 165 H2O 48, 70,127, 128, 133, 137139, 141144 H2O2 75 H3Pỵ-CH2 231 H2PCHẳO 191, 196 H2S 131 H2Se 137, 138, 144 H3Si-O-SiH3 231 H3Si-S-SiH3 236 (H3Si)3P 236 H2SiSiH2 234, 235 H2Te 137, 138, 144 H€ uckel theory 274, 275, 276 valence ionization potential 146 Hund’s rule 18 816 H2Fe(CO)4 559–561 H2ML5 499 H2 on Cu surfaces 719721 H2Sỵ-CH2 222 hopping integral 11 cis,trans-1,3,5-hexatriene 214 hybrid functional method 738 I2 104 idle spin 778, 779 In2 104 inelastic neutron scattering 745 insulator 315 ionization potentials C5H5X heterocycles 298, 299 donor substituted arenes 297 ethylene 276 1,3-butadiene 276 1,3,5-hexatrene 276 H3Si(SiH2)nSiH3 276 ionization potential 160 Ionization potential, vertical 114 adiabatic 114 isolobal caveats 621–623 isolobal definition of 616 isolobal fragments generation of 617, 618 isolobal reactions 634–639 7-isopropylidenenorbonadiene 304, 305 Jahn-Teller distortion first order 134, 135 pseudo Jahn-Teller 136 square H4 136 cyclobutadiene 136 second-order 136, 137, 238 K2 104 KCuF3 760 K3In2As3 356 Koopmans’ theorem 113, 114, 161 K4P2Be 355 K2PdP2 547–549 Kramers degeneracy theorem 787 KrF6 362 K4Si4 351 K5TiO4 355 La2CdGe2 380–383 LaCuO4 453 ladder operators, spin 746 orbital 767 LaGaBi2 379 laticyclic 306 Li2 102, 103, 104 LiCuVO4 748, 754, 769–771 Lifshitz salts 453 LiH 31 LiH3 201 INDEX linear chain polyene 273 Li2O 196 Li2Sb 377 LiSn 380 Li3Al2 356 Li9Ge4 356 longicyclic 304 long-range antiferromagnetic ordering 755, 756 magnetic entropy 756 magnetic susceptibility 756 low versus high spin state 162 magnetic bonds 735 magnetic d-block levels 736 magnetic dipole-dipole interaction 754, 758 Ewald summation method 758 ferromagnetic domains 759 Dy2Ti2O7 758 Ho2Ti2O7 758 spin ice 758 Sr3Fe2O5 758 magnetic insulating 736, 737 magnetic metallic 737 magnetic moment, isotropic 741 uniaxial 741 magnetization, magnetic bonding 743 magnetic antibonding 743 magnetization plateau 765 energy gap 765 finite magnetization plateau 765 zero magnetization plateau 765 magnetic specific heat 745 magnetic susceptibility 743, 744 Curie-Weiss temperature 744 effective moment 744 mean-field approximation 744 mapping analysis 745–748 based on broken-symmetry states 751–754 MCl3 chains 611, 612 M2Cl93À 610, 611 M(CO)6 bonding in 409, 410 MCSCF 172 metal 315 metallabenzene 432 metallacyclobutadiene 432, 515–518 metallacyclopropanes versus metalolefins 541–544, 620–621 metallocenes 592–595 metal-metal bonds electron counting in 445, 446 Mg2 102, 103 MgB2 350 MgH2 133 M(H2O)62ỵ 431 Miller indices 694 ML2 C2v 537–539 ML3 C2v 503 C3v 570–574 ML4 C2v 527–529 D4h 436–438 square planar to tetrahedral 448–452 ML4X chains 423, 424 ML5 C4v 466–468 ML5,L-M-L bending 469–471 ML5,C4v to D3h 471–473 ML5, alternate geometries 474, 475 ML5, p effects 478–480 ML7 D5h 500 M2L10X distortions 484–489 MLn, generalized interaction diagram 439 ML6, octahedral 403, 404 mno rule 677, 678 Mo(CO)6 PE spectra 408, 409 Mn(CO)6ỵ 164 Mfller–Plesset perturbation theory 172, 173 molecular Hamiltonian 152 molecular vibration 73 of H2O 74, 75 multiconfiguration wavefunction 165 N2 102, 103, 109, 112, 113, 117 photoelectron spectrum 116 Na2 102, 104 Na3Cu2SbO6 779 Na3Cu2TeO6 779 Na2Fe(CO)4 531 NaMnP 457, 458 NaOsO3 738, 739, 741 Na2OsO4 738, 739 naphthalene 161, 294 ionization potential 162 electronafficnity 162 excitation energy 162 Nb2 119 NbCl4 chains 424, 425 NbCl5O2À 431 NbO 197, 462, 463 N(CH3)3 188, 190 Ne 199 Ne2 24, 102 NF3 188, 190 NH2 133, 145 NH2À 138, 139 NH2NH2 222 NH3 48, 184, 188, 190, 199, 200, 201 NH3ỵ 189 NH4ỵ 193 Ni(100), surface band structure 692, 693 Ni(CO)4 450 NiF42À 452 NiH3À bending 505, 506 817 INDEX Ni(PF3)4 450 Ni(PPh3)3 506 Ni(PPh3)3ỵ 506 nitrosyl bending in ML5 complexes 489492 N-R fragments 642–644 N2 on Ni(110) 712 NO on Ni(111) 713, 714 N2O 111 norbornadiene 305 nodal plane 3, noncrossing rule 67, 68 reaction coordinate 68 avoided crossing 68 HOMO-LUMO crossing 68 symmetry-forbidden 68 noncollinear spin arrangement 754 non-magnetic metallic 737 nondisjoint orbital 292 N(SiMe3)3 231 N(SiH3)3 192 nucleophillic attack on metalolefins 544, 545 O2 101, 102, 104 octahedron orbitals 658–660 octahedron - p effects 406–412 OF2 61, 235 OH2 199, 200 OH3ỵ 201 Os(CO)4 531 Os(N-Ar)3 511 olefin insertion 521–523, 603–605 olefin-ML4 533–535 on-site repulsion 738 O2ML5 M-O-O bending 499, 500 O2 on metal surfaces 714–717 operator, projection 63 orbital correlation diagram 81 orbital hybridization 97, 98 orbital moment quenching 742 orbital ordering 760 orbital interaction, 16–24 degenerate 16, 21 high-spin 18 low-spin 18 nondegenerate 18, 22, 23 two-orbital four-electron 17, 18, 20, 24 two-orbital two-electron 17, 18, 20, 24 overlap integral 8–11 angular dependence 10, 11 molecular basis 35 type overlap density 287 exchange integral 287 oxidative addition oxyallyl 307 552–560 P2 102, 103, 104, 117 P4 75 P64À 297 Pauli exclusion principle 153 Pauli repulsion PbO 395, 396 PbTiO3 428, 429 P(CH3)3 188 Pd3Cl93À 525 pentalene, inorganic 302 pentalene-TaCl3 612 perovskites 429 perturbation degenerate 43, 44 electronegativity 32, 34 geometry 32, 34, 129 interrmolecular 32, 34, 35, 43 nondegenerate 44 PF3 188 PF5 75, 388 -390 PH2 133 PH3 186, 188, 189, 199 (Ph3P)3RhCl 532 PH5 392 PH2NH2 223 photoelectron spectroscopy 113, 114 photoelectron spectrum acrylonitrile 215 allene 237 barralene 305 benzene 281, 308 B2H6 211 bicyclo[2.2.0]octane 305 bicyclo[2.2.0]octadiene 305 1,3-butadiene 306 1,3-butadiyne 306 C60 281 C2H2 210 C2H4 210, 211 C2H6 210 CO on Ni(100) 699, 700 CO2 235 CpMn(CO)3 579, 580 CpCo(CO)2 551 Cp2V2(C6H6) 586–588 cyclopropene 268 cyclopropane 268 diazabicyclooctane 254 ethylene 308 Fe(CO)5 473, 474 H2C¼NH 235 H2C¼PH 235 7-isopropylidenenorbonadiene 305 methylenecyclopropane 268 methylenecyclopropene 268 N2O 235 hexafluorobenzene 308 N2 on Ni(110) 712 naphthalene 309 Ni(CO)4 450 Ni(PF3)4 450 octafluoronaphthalene 309 pentafluoropyridine 309 poly-ynes 310 pyridine 309 Re2Cl82À 535, 536 Re2(CO)10 481, 482 phosphorescence 777 PH2PH2 222 p-bonding effect 190, 191 pointgroup 51 Abelian 53, 57 conjugy class 52 linear 58 order 51 product 58 Schoenflies symbol 52 polarization function polyacene 356 polyacetylene 329 electronegativity perturbation 332 Peierls distortion 330 soliton 332 polydiazacene 357 polyene 78 polyorganonitrile 333 population, 29–31 gross 29 Mulliken 29 net 28 overlap 28 two-orbital two electron 30 two-orbital four electron 30 preferred spin orientation 767 DFTỵUỵSOC calculations 768 SOC Hamiltonian as perturbation 768–769 propellane 259 PtCl3À 504, 505 PtCl42À 75 PtCl62À 75 Pt3(CNR)6 563, 564 PtH42À 48, 51 PtF42 452 Pt(PPh3)3 506 Pt2ỵ/Pt4ỵ mixed valence chains 488, 489 pyridine 109, 110, 308 pyrrole 120, 121 radial function 2, radial node 3, 4, Rb2 104 Rb4P6 297 Re2Cl82À 535, 536 Re3Cl9 564–566 818 Re2Cl104À 480–482 Re2(CO)10 480–482 Re2(CO)10 481, 482 reductive elimination 552–560 ReO3 433 representation 53 basis of 54, 55 character of 55 character table 57,62 dimension 56, 58 irreducible 56,59 order of 57 reducible 56, 59 totally symmetric 57, 66 resonance integral 11 molecular basis 35 Wolfsberg–Helmholtz formula 11, 34, 105 retinal 214 Rh(PMe3)4ỵ 532 Rh(PPh3)3ỵ 507 ring whizzing 634636 (RO)3Ta(BH3) 609 R3P-Au 201 (R3P)6Ru2H32ỵ 610 Ru(C6F5S)2(PPh3)2 532 Ru(CO)4 531 Ru3(CO)12 562 RundlePimentel bonding scheme 361 Ruddlesden-Popper phases 425, 426 Ru(NMe2)2(CO)4 432 S2 102, 103, 104 Sb2 104 Sb(CH3)3 188 SbF3 188 SbH3 188, 189 Sb2Te3 349 S(t-Bu)2 147 S(CH3)2 147 Schlenk’s hydrocarbon 293 Schmidt orthogonalization 64 Se2 104 Se3Br82À 75 Se4Br142À 394 second-order energy correction 38 second-order mixing 37, 38, 39 secular equation 12, 13 secular determinant 13 self-consistent-field 36 semibullvalene 251 SF4 62, 373, 386, 387 SF6 d orbitals in 361, 362 SH2 133, 137, 138, 141, 144, 170 photoelectron spectrum 145, 147 valence ionization potential 146 SH2 199, 200 SH4 148 INDEX SH6 360 short-range order 763 susceptibility maximum 763 Si2 102, 104 Si46À chain 338 SiH3 189 SiH4 199, 200 Si2H4 219 Si (100) surface reaction with acetylene 725, 726 Si (100) surface reaction with H2O, H3N and H2 726, 727 Si (100) surface symmetric dimer model 721, 723–725 Si (100) surface unsymmetric dimer model 721–723 sigmatropic rearrangements 634–636 single-ion anisotropy 770 zero-field spin Hamiltonian 770 effective spin approximation 770 easy-axis anisotropy 769 easy-plane anisotropy 771 Slater determinant 153 Slater transition 741 Slater type orbitals 5–7 Sn2 104 SnH3 189 Sn2H4 219 S2N2 295, 297, 300 S3N3À 296, 297 S4N4 300, 301 S4N42ỵ 301 (SN)x 333 SO2 PE spectrum 393 spin exchange parameter 290 spin dimer 745 spin exchange, symmetric 745 Heisenberg 745 through-space interaction 748–749, 751 through-bond interaction 748–751 spin frustration 754 equilateral triangle 755 frustration index 755 Kagome lattice 755 pyrochlore lattice 755 triangular lattice 755 spin gap 763 magnetic field-induced magnetic order 763 Haldane conjecture 763 Ni(C2H8N2)2NO2(ClO4) 763 spin dimer 764 alternating chain 764 two-leg ladder 764 spin Hamiltonian 735, 736 spin lattice 735 spin-orbit coupling 736, 766 spin-conserving term 768 spin-nonconserving term 768 singlet-triplet mixing 777 spin polarization in a p radical 285, 286 allyl radical 288 spin-wave dispersion 745 spiral spin arrangement 754 cycloidal 754 helical 754 spiro-antiaromatic 303 spiro-aromatic 303 spiro-nonatetraene 304 spiro-octatrienylcation 304 square cyclobutadiene singlet versus triplet state 289 square hydrogen net 340, 341–343 square lattice 340 SrCa2In2Ge 351, 354 Sr2CuOsO6 738, 739 SrFeO2 460, 757,769 Sr3Fe2O5 756–758, 769 Sr3In5 398 Sr2NiOsO6 738, 739 state averaged ionization potential, charging effect 26 relativistic effect 26 screening 25 s-p energy gap 25, 26 substituent effect 214 methyl substituted olefin 217 substituted olefin 216 sudden polarization 211, 213 superconductivity 349 superexchange 749 Goodenough-Kanamori rule 751 super-superexchange 749 surface reconstructions transition metals 695 symmetry operations 48 rotation 48 improper rotation 48 horizontal mirror plane 48 vertical mirror plane 48 inverse 50 symmetry of spin inversion 786 mirror plane of symmetry 786, 787 time reversal 787 Te42ỵ 397 tetracyanoethylene 217 tetragonal distortions 416, 417 tetrahedrane isolobal analogs 626, 627 tetramethyleneethane 293 tetrasilabicyclobutane, Si4H6 260 tetrathiafulvalene 217 819 INDEX TCNQ 337 Te2 104 three-center bonding 139 two-electron 140 four-electron 139, 140, 141 three-orbital problem 38 through-bond coupling units 256 through-bond conjugation 112, 113, 116 through-bond interaction 241, 253 through-space conjugation 304 through-space interaction 241 TiCl4 451 TiO 197 TiO2 430, 431 TMTSF 337 TMTTF 337 topological charge stabilization 302 topological insulator 349 transition metals kink 695 transition metals step 695 transition metals structure 693, 694 transition metals terrace 695 tricyclooctadiene 251 ethylene and cyclobutane units of 251 butadiene and cyclobutane units of 252 tricyclo-3,7-octadiene 255 trigonal pyramid orbitals 658–660 2,4,6-trimethyl-1,3-dioxane 233 trimethylenemethane 291, 307 trimethylenemethane-Fe(CO)3 607 triple-decker sandwiches 585–588 tris(acetylene)W(PMe3) 444 TTF 337 W2(carboxylate)4 PE spectrum 536 W2Cl6 75, 574 W(CH3)6 421 W(CO)6 PE spectra 408, 409 WF6 421 WH6 421 WS2 433 uniaxial magnetism 771 versus Jahn-Teller instability 771, 774 g-factor 772 XCH2CH2À 229 XCH2OH 232, 233 XeF3 385 XeF3ỵ 385 XeF5 366, 367 XeF6 364 valence band 315 valence shell electron pair repulsion model 141, 365, 366 van Hove singularity 320 variational theorem 5, 12, 13 V2O5 492–494 V(CO)6À 164 Wade’s rules 660–663 Wade’s rules violations 671–676 Walsh diagram 131, 135 wavevector 317 William’s rules 663–666 Wolsberg-Helmholz approximation Wood’s notation 696, 697 Wurtzite surface 730, 731 WC3 575–577 YBa2Cu3O7 131 494–496 Zeeman interaction 742 zero-field splitting Hamiltonian Ziegler–Natta polymerization 603–605 Zintl-Klemm concept 350 z value, electronegativity z value, energy optimized Zn2 104 ZnS 352 ZrS2 433 zwitterionic 212, 213 787 ... u cos f sin u sin f cos u sin2 u cos 2f 3cos2u À sin2 u sin 2f sin u cos u cos f sin u cos u sin f Section 1.3 These atomic orbitals (AOs) using polar coordinates have the form shown in equation... atomic orbital and the second to the molecular orbital The overlap and interaction integrals to consider are as follows: hx1 jx1 i ¼ hx2 jx2 i ¼ hx1 jx2 i ¼ S12 Orbital Interactions in Chemistry, Second. .. discussed in Orbital Interactions in Chemistry, Second Edition Thomas A Albright, Jeremy K Burdett, and Myung-Hwan Whangbo Ó 2013 John Wiley & Sons, Inc Published 2013 by John Wiley & Sons, Inc 2