Orbital Interactions in Chemistry
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Orbital Interactions in Chemistry
Albright, Thomas A.; Burdett, Jeremy K.; Whangbo, Myung-Hwan
John Wiley & Sons Inc
05/2013
848
Dura
Inglês
9780471080398
15 a 20 dias
2154
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Preface xi
About the Authors xiii
Chapter 1 Atomic and Molecular Orbitals 1
1.1 Introduction 1
1.2 Atomic Orbitals 1
1.3 Molecular Orbitals 7
Problems 13
References 14
Chapter 2 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 3 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 4 Symmetry 47
4.1 Introduction 47
4.2 Symmetry of Molecules 47
4.3 Representations of Groups 53
4.4 Symmetry Properties of Orbitals 59
4.5 Symmetry-Adapted Wavefunctions 62
4.6 Direct Products 65
4.7 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
Chapter 5 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 6 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 7 Molecular Orbitals and Geometrical Perturbation 123
7.1 Molecular Orbitals of AH2 123
7.2 Geometrical Perturbation 128
7.3 Walsh Diagrams 131
7.4 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 8 State Wavefunctions and State Energies 151
8.1 Introduction 151
8.2 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
Chapter 9 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 ?-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 A2 H6 Systems 204
10.3 12-Electron A2 H4 Systems 208
10.3.1 Sudden Polarization 211
10.3.2 Substituent Effects 214
10.3.3 Dimerization and Pyramidalization of AH 2 218
10.4 14-Electron AH2 BH2 Systems 220
10.5 AH3 BH2 Systems 223
10.6 AH3 BH Systems 232
Problems 234
References 238
Chapter 11 Orbital Interactions through Space and through Bonds 241
11.1 Introduction 241
11.2 In-Plane ? 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 C-C Bond 258
Problems 265
References 269
Chapter 12 Polyenes and Conjugated Systems 272
12.1 Acyclic Polyenes 272
12.2 Hueckel 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 313
13.1 Energy Bands 313
13.2 Distortions in One-Dimensional Systems 328
13.3 Other One-Dimensional Systems 334
13.4 Two- and Three-Dimensional Systems 339
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 ?-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 ML 4 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 M5 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 527
19.1 Development of the C2v ML4 Fragment Orbitals 527
19.2 The Fe(CO)4 Story 529
19.3 Olefin-ML 4 Complexes and M2 L8 Dimers 533
19.4 The C2v ML2 Fragment 537
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 Cp2 M570
20.1 Derivation of Orbitals for a C3v ML3 Fragment 570
20.2 The CpM Fragment Orbitals 582
20.3 Cp2 M and Metallocenes 592
20.4 Cp2 MLn Complexes 595
Problems 607
References 613
Chapter 21 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 735
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
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
About the Authors xiii
Chapter 1 Atomic and Molecular Orbitals 1
1.1 Introduction 1
1.2 Atomic Orbitals 1
1.3 Molecular Orbitals 7
Problems 13
References 14
Chapter 2 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 3 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 4 Symmetry 47
4.1 Introduction 47
4.2 Symmetry of Molecules 47
4.3 Representations of Groups 53
4.4 Symmetry Properties of Orbitals 59
4.5 Symmetry-Adapted Wavefunctions 62
4.6 Direct Products 65
4.7 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
Chapter 5 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 6 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 7 Molecular Orbitals and Geometrical Perturbation 123
7.1 Molecular Orbitals of AH2 123
7.2 Geometrical Perturbation 128
7.3 Walsh Diagrams 131
7.4 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 8 State Wavefunctions and State Energies 151
8.1 Introduction 151
8.2 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
Chapter 9 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 ?-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 A2 H6 Systems 204
10.3 12-Electron A2 H4 Systems 208
10.3.1 Sudden Polarization 211
10.3.2 Substituent Effects 214
10.3.3 Dimerization and Pyramidalization of AH 2 218
10.4 14-Electron AH2 BH2 Systems 220
10.5 AH3 BH2 Systems 223
10.6 AH3 BH Systems 232
Problems 234
References 238
Chapter 11 Orbital Interactions through Space and through Bonds 241
11.1 Introduction 241
11.2 In-Plane ? 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 C-C Bond 258
Problems 265
References 269
Chapter 12 Polyenes and Conjugated Systems 272
12.1 Acyclic Polyenes 272
12.2 Hueckel 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 313
13.1 Energy Bands 313
13.2 Distortions in One-Dimensional Systems 328
13.3 Other One-Dimensional Systems 334
13.4 Two- and Three-Dimensional Systems 339
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 ?-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 ML 4 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 M5 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 527
19.1 Development of the C2v ML4 Fragment Orbitals 527
19.2 The Fe(CO)4 Story 529
19.3 Olefin-ML 4 Complexes and M2 L8 Dimers 533
19.4 The C2v ML2 Fragment 537
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 Cp2 M570
20.1 Derivation of Orbitals for a C3v ML3 Fragment 570
20.2 The CpM Fragment Orbitals 582
20.3 Cp2 M and Metallocenes 592
20.4 Cp2 MLn Complexes 595
Problems 607
References 613
Chapter 21 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 735
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
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
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solid state chemistry, chemical spectrum, applied molecular orbital theory, organometallic chemistry, organic chemistry, common orbital situations, inorganic chemistry, computational chemistry
Preface xi
About the Authors xiii
Chapter 1 Atomic and Molecular Orbitals 1
1.1 Introduction 1
1.2 Atomic Orbitals 1
1.3 Molecular Orbitals 7
Problems 13
References 14
Chapter 2 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 3 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 4 Symmetry 47
4.1 Introduction 47
4.2 Symmetry of Molecules 47
4.3 Representations of Groups 53
4.4 Symmetry Properties of Orbitals 59
4.5 Symmetry-Adapted Wavefunctions 62
4.6 Direct Products 65
4.7 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
Chapter 5 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 6 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 7 Molecular Orbitals and Geometrical Perturbation 123
7.1 Molecular Orbitals of AH2 123
7.2 Geometrical Perturbation 128
7.3 Walsh Diagrams 131
7.4 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 8 State Wavefunctions and State Energies 151
8.1 Introduction 151
8.2 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
Chapter 9 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 ?-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 A2 H6 Systems 204
10.3 12-Electron A2 H4 Systems 208
10.3.1 Sudden Polarization 211
10.3.2 Substituent Effects 214
10.3.3 Dimerization and Pyramidalization of AH 2 218
10.4 14-Electron AH2 BH2 Systems 220
10.5 AH3 BH2 Systems 223
10.6 AH3 BH Systems 232
Problems 234
References 238
Chapter 11 Orbital Interactions through Space and through Bonds 241
11.1 Introduction 241
11.2 In-Plane ? 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 C-C Bond 258
Problems 265
References 269
Chapter 12 Polyenes and Conjugated Systems 272
12.1 Acyclic Polyenes 272
12.2 Hueckel 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 313
13.1 Energy Bands 313
13.2 Distortions in One-Dimensional Systems 328
13.3 Other One-Dimensional Systems 334
13.4 Two- and Three-Dimensional Systems 339
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 ?-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 ML 4 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 M5 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 527
19.1 Development of the C2v ML4 Fragment Orbitals 527
19.2 The Fe(CO)4 Story 529
19.3 Olefin-ML 4 Complexes and M2 L8 Dimers 533
19.4 The C2v ML2 Fragment 537
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 Cp2 M570
20.1 Derivation of Orbitals for a C3v ML3 Fragment 570
20.2 The CpM Fragment Orbitals 582
20.3 Cp2 M and Metallocenes 592
20.4 Cp2 MLn Complexes 595
Problems 607
References 613
Chapter 21 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 735
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
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
About the Authors xiii
Chapter 1 Atomic and Molecular Orbitals 1
1.1 Introduction 1
1.2 Atomic Orbitals 1
1.3 Molecular Orbitals 7
Problems 13
References 14
Chapter 2 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 3 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 4 Symmetry 47
4.1 Introduction 47
4.2 Symmetry of Molecules 47
4.3 Representations of Groups 53
4.4 Symmetry Properties of Orbitals 59
4.5 Symmetry-Adapted Wavefunctions 62
4.6 Direct Products 65
4.7 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
Chapter 5 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 6 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 7 Molecular Orbitals and Geometrical Perturbation 123
7.1 Molecular Orbitals of AH2 123
7.2 Geometrical Perturbation 128
7.3 Walsh Diagrams 131
7.4 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 8 State Wavefunctions and State Energies 151
8.1 Introduction 151
8.2 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
Chapter 9 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 ?-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 A2 H6 Systems 204
10.3 12-Electron A2 H4 Systems 208
10.3.1 Sudden Polarization 211
10.3.2 Substituent Effects 214
10.3.3 Dimerization and Pyramidalization of AH 2 218
10.4 14-Electron AH2 BH2 Systems 220
10.5 AH3 BH2 Systems 223
10.6 AH3 BH Systems 232
Problems 234
References 238
Chapter 11 Orbital Interactions through Space and through Bonds 241
11.1 Introduction 241
11.2 In-Plane ? 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 C-C Bond 258
Problems 265
References 269
Chapter 12 Polyenes and Conjugated Systems 272
12.1 Acyclic Polyenes 272
12.2 Hueckel 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 313
13.1 Energy Bands 313
13.2 Distortions in One-Dimensional Systems 328
13.3 Other One-Dimensional Systems 334
13.4 Two- and Three-Dimensional Systems 339
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 ?-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 ML 4 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 M5 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 527
19.1 Development of the C2v ML4 Fragment Orbitals 527
19.2 The Fe(CO)4 Story 529
19.3 Olefin-ML 4 Complexes and M2 L8 Dimers 533
19.4 The C2v ML2 Fragment 537
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 Cp2 M570
20.1 Derivation of Orbitals for a C3v ML3 Fragment 570
20.2 The CpM Fragment Orbitals 582
20.3 Cp2 M and Metallocenes 592
20.4 Cp2 MLn Complexes 595
Problems 607
References 613
Chapter 21 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 735
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
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
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