Orbital Interactions in Chemistry

THOMAS A. ALBRIGHT, PhD, is Professor Emeritus in theDepartment of Chemistry at the University of Houston. He was aCamille and Henry Dreyfus Teacher-Scholar and an Alfred P. SloanResearch Fellow. He has been interested in exploring reactiondynamics in organometallic chemistry. The late JEREMY K. BURDETT, PhD, was Professor and Chairof the Chemistry Department at the University of Chicago. Dr.Burdett was awarded the Tilden Prize and Meldola Medal by the RoyalSociety of Chemistry. He was also a Camille and Henry DreyfusTeacher-Scholar and a Fellow of the John Guggenheim MemorialFoundation and Alfred P. Sloan Foundation. MYUNG-HWAN WHANGBO, PhD, is Distinguished Professor inthe Chemistry Department of North Carolina State University. He hasbeen awarded the Camille and Henry Dreyfus Fellowship, theAlexander von Humboldt Research Award to Senior Scientists, theHo-Am Prize in Science, and Docteur Honoris Causa from Universit deNantes.

"This book can be viewed as a unique and rather complete'encyclopaedia' of the chemical applications ofmolecular orbital theory." (Applied OrganometallicChemistry,1 November 2014)

• Preface xiAbout the Authors xiiiChapter 1 Atomic and Molecular Orbitals 11.1 Introduction 11.2 Atomic Orbitals 11.3 Molecular Orbitals 7Problems 13References 14Chapter 2 Concepts of Bonding and Orbital Interaction 152.1 Orbital Interaction Energy 152.1.1 Degenerate Interaction 162.1.2 Nondegenerate Interaction 182.2 Molecular Orbital Coefficients 202.2.1 Degenerate Interaction 212.2.2 Nondegenerate Interaction 222.3 The Two-Orbital Problem—Summary 242.4 Electron Density Distribution 26Problems 31References 31Chapter 3 Perturbational Molecular Orbital Theory 323.1 Introduction 323.2 Intermolecular Perturbation 353.3 Linear H3, HF, and the Three-Orbital Problem 383.4 Degenerate Perturbation 43Problems 45References 46Chapter 4 Symmetry 474.1 Introduction 474.2 Symmetry of Molecules 474.3 Representations of Groups 534.4 Symmetry Properties of Orbitals 594.5 Symmetry-Adapted Wavefunctions 624.6 Direct Products 654.7 Symmetry Properties, Integrals, and the Noncrossing Rule 674.8 Principles of Orbital Construction Using Symmetry Principles 694.9 Symmetry Properties of Molecular Vibrations 73Problems 75References 77Chapter 5 Molecular Orbital Construction from Fragment Orbitals 785.1 Introduction 785.2 Triangular H3 785.3 Rectangular and Square Planar H4 825.4 Tetrahedral H4 845.5 Linear H4 865.6 Pentagonal H5 and Hexagonal H6 885.7 Orbitals of Cyclic Systems 91Problems 94References 96Chapter 6 Molecular Orbitals of Diatomic Molecules and Electronegativity Perturbation 976.1 Introduction 976.2 Orbital Hybridization 986.3 Molecular Orbitals of Diatomic Molecules 996.4 Electronegativity Perturbation 1056.5 Photoelectron Spectroscopy and Through-Bond Conjugation 112Problems 118References 122Chapter 7 Molecular Orbitals and Geometrical Perturbation 1237.1 Molecular Orbitals of AH2 1237.2 Geometrical Perturbation 1287.3 Walsh Diagrams 1317.4 Jahn–Teller Distortions 1347.4.1 First-Order Jahn–Teller Distortion 1357.4.2 Second-Order Jahn–Teller Distortion 1367.4.3 Three-Center Bonding 1397.5 Bond Orbitals and Photoelectron Spectra Of AH2 Molecules 141Problems 147References 150Chapter 8 State Wavefunctions and State Energies 1518.1 Introduction 1518.2 The Molecular Hamiltonian and State Wavefunctions 1528.3 Fock Operator 1548.4 State Energy 1568.5 Excitation Energy 1578.6 Ionization Potential and Electron Affinity 1608.7 Electron Density Distribution and Magnitudes of Coulomb and Exchange Repulsions 1608.8 Low versus High Spin States 1628.9 Electron–Electron Repulsion and Charged Species 1648.10 Configuration Interaction 1658.11 Toward More Quantitative Treatments 1708.12 The Density Functional Method 174Problems 176References 177Chapter 9 Molecular Orbitals of Small Building Blocks 1799.1 Introduction 1799.2 The AH System 1799.3 Shapes of AH3 Systems 1829.4 π-Bonding Effects of Ligands 1909.5 The AH4 System 1939.6 The AHn Series—Some Generalizations 198Problems 201References 202Chapter 10 Molecules with Two Heavy Atoms 20410.1 Introduction 20410.2 A2 H6 Systems 20410.3 12-Electron A2 H4 Systems 20810.3.1 Sudden Polarization 21110.3.2 Substituent Effects 21410.3.3 Dimerization and Pyramidalization of AH 2 21810.4 14-Electron AH2 BH2 Systems 22010.5 AH3 BH2 Systems 22310.6 AH3 BH Systems 232Problems 234References 238Chapter 11 Orbital Interactions through Space and through Bonds 24111.1 Introduction 24111.2 In-Plane σ orbitals of Small Rings 24111.2.1 Cyclopropane 24111.2.2 Cyclobutane 24611.3 Through-Bond Interaction 25311.3.1 The Nature of Through-Bond Coupling 25311.3.2 Other Through-Bond Coupling Units 25611.4 Breaking a C–C Bond 258Problems 265References 269Chapter 12 Polyenes and Conjugated Systems 27212.1 Acyclic Polyenes 27212.2 Hückel Theory 27412.3 Cyclic Systems 27712.4 Spin Polarization 28512.5 Low- versus High-Spin States in Polyenes 28912.6 Cross-Conjugated Polyenes 29112.7 Perturbations of Cyclic Systems 29412.8 Conjugation in Three Dimensions 303Problems 306References 310Chapter 13 Solids 31313.1 Energy Bands 31313.2 Distortions in One-Dimensional Systems 32813.3 Other One-Dimensional Systems 33413.4 Two- and Three-Dimensional Systems 33913.5 Electron Counting and Structure 35013.6 High-Spin and Low-Spin Considerations 353Problems 353References 357Chapter 14 Hypervalent Molecules 35914.1 Orbitals of Octahedrally Based Molecules 35914.2 Solid-State Hypervalent Compounds 37314.3 Geometries of Hypervalent Molecules 383Problems 392References 399Chapter 15 Transition Metal Complexes: A Starting Point at the Octahedron 40115.1 Introduction 40115.2 Octahedral ML6 40215.3 π-Effects in an Octahedron 40615.4 Distortions from an Octahedral Geometry 41615.5 The Octahedron in the Solid State 423Problems 431References 434Chapter 16 Square Planar, Tetrahedral ML 4 Complexes, and Electron Counting 43616.1 Introduction 43616.2 The Square Planar ML4 Molecule 43616.3 Electron Counting 43816.4 The Square Planar-Tetrahedral ML4 Interconversion 44816.5 The Solid State 453Problems 460References 463Chapter 17 Five Coordination 46517.1 Introduction 46517.2 The C4v M5 Fragment 46617.3 Five Coordination 46817.4 Molecules Built Up from ML5 Fragments 48017.5 Pentacoordinate Nitrosyls 48917.6 Square Pyramids in The Solid State 492Problems 498References 500Chapter 18 The C2v ML3 Fragment 50318.1 Introduction 50318.2 The Orbitals of A C2v ML3 Fragment 50318.3 ML3-Containing Metallacycles 51118.4 Comparison of C2v ML3 and C4v ML5 Fragments 518Problems 523References 525Chapter 19 The ML2 and ML4 Fragments 52719.1 Development of the C2v ML4 Fragment Orbitals 52719.2 The Fe(CO)4 Story 52919.3 Olefin–ML 4 Complexes and M2 L8 Dimers 53319.4 The C2v ML2 Fragment 53719.5 Polyene–ML2 Complexes 53919.6 Reductive Elimination and Oxidative Addition 552Problems 561References 566Chapter 20 Complexes of ML3 , MCp and Cp2 M57020.1 Derivation of Orbitals for a C3v ML3 Fragment 57020.2 The CpM Fragment Orbitals 58220.3 Cp2 M and Metallocenes 59220.4 Cp2 MLn Complexes 595Problems 607References 613Chapter 21 The Isolobal Analogy 61621.1 Introduction 61621.2 Generation of Isolobal Fragments 61721.3 Caveats 62121.4 Illustrations of the Isolobal Analogy 62321.5 Reactions 63421.6 Extensions 639Problems 646References 649Chapter 22 Cluster Compounds 65322.1 Types of Cluster Compounds 65322.2 Cluster Orbitals 65722.3 Wade’s Rules 66022.4 Violations 67122.5 Extensions 677Problems 681References 687Chapter 23 Chemistry on the Surface 69123.1 Introduction 69123.2 General Structural Considerations 69323.3 General Considerations of Adsorption on Surfaces 69623.4 Diatomics on a Surface 69923.5 The Surface of Semiconductors 721Problems 728References 731Chapter 24 Magnetic Properties 73524.1 Introduction 73524.2 The Magnetic Insulating State 73624.2.1 Electronic Structures 73624.2.2 Factors Affecting the Effective On-Site Repulsion 73824.2.3 Effect of Spin Arrangement on the Band Gap 74024.3 Properties Associated with the Magnetic Moment 74124.3.1 The Magnetic Moment 74124.3.2 Magnetization 74324.3.3 Magnetic Susceptibility 74324.3.4 Experimental Investigation of Magnetic Energy Levels 74524.4 Symmetric Spin Exchange 74524.4.1 Mapping Analysis for a Spin Dimer 74524.4.2 Through-Space and Through-Bond Orbital Interactions Leading to Spin Exchange 74824.4.3 Mapping Analysis Based on Broken-Symmetry States 75124.5 Magnetic Structure 75424.5.1 Spin Frustration and Noncollinear Spin Arrangement 75424.5.2 Long-Range Antiferromagnetic Order 75524.5.3 Ferromagnetic and Ferromagnetic-Like Transitions 75924.5.4 Typical Cases Leading to Ferromagnetic Interaction 76024.5.5 Short-Range Order 76324.6 The Energy Gap in the Magnetic Energy Spectrum 76324.6.1 Spin Gap and Field-Induced Magnetic Order 76324.6.2 Magnetization Plateaus 76524.7 Spin–Orbit Coupling 76624.7.1 Spin Orientation 76624.7.2 Single-Ion Anisotropy 77024.7.3 Uniaxial Magnetism versus Jahn–Teller Instability 77124.7.4 The Dzyaloshinskii–Moriya Interaction 77424.7.5 Singlet–Triplet Mixing Under Spin–Orbit Coupling 77724.8 What Appears versus What Is 77824.8.1 Idle Spin in Cu3(OH)4SO4 77824.8.2 The FM–AFM versus AFM–AFM Chain 77924.8.3 Diamond Chains 78024.8.4 Spin Gap Behavior of a Two-Dimensional Square Net 78224.9 Model Hamiltonians Beyond the Level of Spin Exchange 78524.10 Summary Remarks 785Problems 786References 789Appendix I Perturbational Molecular Orbital Theory 793Appendix II Some Common Group Tables 803Appendix III Normal Modes for Some Common Structural Types 808Index 813