Preface xv
1 A Brief Story of Valence Bond Theory, its Rivalry with Molecular Orbital Theory, its Demise, and Resurgence 1
1.1 Roots of VB Theory 2
1.2 Origins of MO Theory and the Roots of VB-MO Rivalry 5
1.3 One Theory is Up, The Other is Down 7
1.4 Mythical Failures of VB Theory: More Ground is Gained by MO Theory 8
1.5 Are the Failures of VB Theory Real? 12
1.5.1 The O2 Failure 12
1.5.2 The C 4 H 4 Failure 13
1.5.3 The C 5 H 5 + Failure 13
1.5.4 The Failure Associated with the Photoelectron Spectroscopy of CH 4 14
1.6 Valence Bond is a Legitimate Theory Alongside Molecular Orbital Theory 14
1.7 Modern VB Theory: Valence Bond Theory is Coming of Age 15
2 A Brief Tour Through Some Valence Bond Outputs and Terminology 26
2.1 Valence Bond Output for the H 2 Molecule 26
2.2 Valence Bond Mixing Diagrams 32
2.3 Valence Bond Output for the HF Molecule 33
3 Basic Valence Bond Theory 40
3.1 Writing and Representing Valence Bond Wave Functions 40
3.1.1 VB Wave Functions with Localized Atomic Orbitals 40
3.1.2 Valence Bond Wave Functions with Semilocalized AOs 42
3.1.3 Valence Bond Wave Functions with Fragment Orbitals 42
3.1.4 Writing Valence Bond Wave Functions Beyond the 2e/2c Case 43
3.1.5 Pictorial Representation of Valence Bond Wave Functions by Bond Diagrams 44
3.2 Overlaps Between Determinants 45
3.3 Valence Bond Formalism Using the Exact Hamiltonian 47
3.3.1 Purely Covalent Singlet State and a Triplet Repulsive State 47
3.3.2 Configuration Interaction Involving Ionic Terms 49
3.4 Valence Bond Formalism Using an Effective Hamiltonian 49
3.5 Some Simple Formulas for Elementary Interactions 51
3.5.1 The Two-Electron Bond 52
3.5.2 Repulsive Interactions in Valence Bond Theory 52
3.5.3 Mixing of Degenerate Valence Bond Structures 53
3.5.4 Nonbonding Interactions in Valence Bond Theory 55
3.6 Structural Coefficients and Weights of Valence Bond Wave Functions 56
3.7 Bridges Between Molecular Orbital and Valence Bond Theories 57
3.7.1 Comparison of Qualitative Valence Bond and Molecular Orbital Theories 57
3.7.2 The Relationship Between Molecular Orbital and Valence Bond Wave Functions 58
3.7.3 Localized Bond Orbitals: A Pictorial Bridge Between Molecular Orbital and Valence Bond Wave Functions 61
Appendix 65
3.a.1 Normalization Constants, Energies, Overlaps, and Matrix Elements of Valence Bond Wave Functions 65
3.a.1.1 Energy and Self-Overlap of an Atomic Orbital-Based Determinants 67
3.a.1.2 Hamiltonian Matrix Elements and Overlaps Between Atomic Orbital-Based Determinants 69
3.a.2 Guidelines for Valence Bond Mixing 69
Exercises 71
Answers 76
4 Mapping Molecular Orbital-Configuration Interaction to Valence Bond Wave Functions 83
4.1 Generating a Set of Valence Bond Structures 83
4.2 Mapping a Molecular Orbital-Configuration Interaction Wave Function into a Valence Bond Wave Function 85
4.2.1 Expansion of Molecular Orbital Determinants in Terms of Atomic Orbital Determinants 85
4.2.2 Projecting the Molecular Orbital-Configuration Interaction Wave Function to the Rumer Basis of Valence Bond Structures 88
4.2.3 An Example: The Hartree-Fock Wave Function of Butadiene 88
4.3 Using Half-Determinants to Calculate Overlaps between Valence Bond Structures 90
Exercises 92
Answers 93
5 Are The "Failures" of Valence Bond Theory Real? 96
5.1 Introduction 96
5.2 The Triplet Ground State of Dioxygen 96
5.3 Aromaticity-Antiaromaticity in Ionic Rings C n H n ± 100
5.4 Aromaticity/Antiaromaticity in Neutral Rings 103
5.5 The Valence Ionization Spectrum of CH 4 108
5.6 The Valence Ionization Spectrum of H 2 O and the "Rabbit-Ear" Lone Pairs 110
5.7 A Summary 113
Exercises 115
Answers 116
6 Valence Bond Diagrams for Chemical Reactivity 120
6.1 Introduction 120
6.2 Two Archetypal Valence Bond Diagrams 121
6.3 The Valence Bond State Correlation Diagram Model and its General Outlook on Reactivity 122
6.4 Construction of Valence Bond State Correlation Diagrams for Elementary Processes 123
6.4.1 Valence Bond State Correlation Diagrams for Radical Exchange Reactions 123
6.4.2 Valence Bond State Correlation Diagrams for Reactions Between Nucleophiles and Electrophiles 127
6.4.3 Generalization of Valence Bond State Correlation Diagrams for Reactions Involving Reorganization of Covalent Bonds 129
6.5 Barrier Expressions Based on the Valence Bond State Correlation Diagram Model 131
6.5.1 Some Guidelines for Quantitative Applications of the Valence Bond State Correlation Diagram Model 133
6.6 Making Qualitative Reactivity Predictions with the Valence Bond State Correlation Diagram 133
6.6.1 Reactivity Trends in Radical Exchange Reactions 135
6.6.2 Reactivity Trends in Allowed and Forbidden Reactions 137
6.6.3 Reactivity Trends in Oxidative-Addition Reactions 138
6.6.4 Reactivity Trends in Reactions Between Nucleophiles and Electrophiles 141
6.6.5 Chemical Significance of the f Factor 142
6.6.6 Making Stereochemical Predictions with the VBSCD Model 143
6.6.7 Predicting Transition-State Structures with the Valence Bond State Correlation Diagram Model 145
6.6.8 Trends in Transition-State Resonance Energies 146
6.7 Valence Bond Configuration Mixing Diagrams: General Features 149
6.8 Valence Bond Configuration Mixing Diagram with Ionic Intermediate Curves 149
6.8.1 Valence Bond Configuration Mixing Diagram for Proton-Transfer Processes 149
6.8.2 Insights from Valence Bond Configuration Mixing Diagrams: One Electron Less-One Electron More 151
6.8.3 Nucleophilic Substitution on Silicon: Stable Hypercoordinated Species 152
6.9 Valence Bond Configuration Mixing Diagram with Intermediates Nascent from "Foreign States" 154
6.9.1 The Mechanism of Nucleophilic Substitution of Esters 154
6.9.2 The S RN 2 and SRN2c Mechanisms 155
6.10 Valence Bond State Correlation Diagram: A General Model for Electronic Delocalization in Clusters 157
6.10.1 What is the Driving Force for the D 6h Geometry of Benzene, ¿ or ¿? 160
6.11 Valence Bond State Correlation Diagram: Application to Photochemical Reactivity 163
6.11.1 Photoreactivity in 3e/3c Reactions 164
6.11.2 Photoreactivity in 4e/3c Reactions 165
6.12 A Summary 169
Exercises 179
Answers 185
7 Using Valence Bond Theory to Compute and Conceptualize Excited States 203
7.1 Excited States of a Single Bond 205
7.2 Excited States of Molecules with Conjugated Bonds 207
7.2.1 Use of Molecular Symmetry to Generate Covalent Excited States Based on Valence Bond Theory 207
7.2.2 Covalent Excited States of Polyenes 219
7.3 A Summary 223
Exercises 225
Answers 226
8 Spin Hamiltonian Valence Bond Theory and its Applications to Organic Radicals, Diradicals, and Polyradicals 232
8.1 A Topological Semiempirical Hamiltonian 233
8.2 Applications 235
8.2.1 Ground States of Polyenes and Hund's Rule Violations 235
8.2.2 Spin Distribution in Alternant Radicals 237
8.2.3 Relative Stabilities of Polyenes 238
8.2.4 Extending Ovchinnikov's Rule to Search for Bistable Hydrocarbons 240
8.3 A Summary 241
Exercises 243
Answers 245
9 Currently Available Ab Initio Valence Bond Computational Methods and Their Principles 249
9.1 Introduction 249
9.2 Valence Bond Methods Based on Semi-Localized Orbitals 250
9.2.1 The Generalized Valence Bond Method 251
9.2.2 The Spin-Coupled Generalized Valence Bond Method 253
9.2.3 The CASVB Method 254
9.2.4 The Generalized Resonating Valence Bond Method 256
9.2.5 Multiconfiguration Valence Bond Methods with Optimized Orbitals 257
9.3 Valence Bond Methods Based on Localized Orbitals 258
9.3.1 Valence Bond Self-Consistent Field Method with Localized Orbitals 259
9.3.2 The Breathing-Orbital Valence Bond Method 260
9.3.3 The Valence Bond Configuration Interaction Method 263
9.3.4 The Valence Bond Quantum Monte Carlo Method 265
9.4 Methods for Getting Valence Bond Quantities from Molecular Orbital-Based Procedures 266
9.4.1 Using Standard Molecular Orbital Software to Compute Single Valence Bond Structures or Determinants 266
9.4.2 The Block-Localized Wave Function and Related Methods 267
9.5 A Valence Bond Method with Polarizable Continuum Model 268
9.6 Perspective 269
Appendix 269
9.a.1 Some Available Valence Bond Programs 269
9.a.1.1 The TURTLE Software 270
9.a.1.2 The XMVB Program 270
9.a.1.3 The CRUNCH Software 270
9.a.1.4 The VB2000 Software 270
9.a.1.5 The CHAMP Program for the VB-QMC Method 271
9.a.2 Implementations of Valence Bond Methods in Standard Ab Initio Packages 271
10 Do Your Own Valence Bond Calculation-A Practical Guide 282
10.1 Introduction 282
10.2 Wave Functions and Energies for the Ground State of F 2 282
10.2.1 GVB, SC, and VBSCF Methods 283
10.2.2 The BOVB Method 287
10.2.3 The VBCI Method 292
10.3 Valence Bond Calculations of Diabatic States and Resonance Energies 293
10.3.1 Definition of Diabatic States 293
10.3.2 Calculations of Meaningful Diabatic States 294
10.3.3 Resonance Energies 295
10.4 Comments on Calculations of VBSCDS and VBCMDS 298
10.4.1 VBSCD Calculations 299
10.4.2 VBCMD Calculations 300
Appendix 301
10.A.1 Calculating at the SD-BOVB Level in Low Symmetry Cases 301
11 The Chemical Bonds in Valence Bond Theory: Review Chapters on Specific Topics in Valence Bond Theory 318
11.1 Introduction 318
11.2 VB Approaches: Their Bond Descriptions and Representations 319
11.2.1 Single Two-Electron Bonds 319
11.2.2 Multiple Two-Electron Bonds 321
11.2.3 Classical VB Methods for Single Bonds 321
11.2.4 VB Methods for Multiple Bonds 323
11.3 Applications of VB Theory to Chemical Bonding 325
11.3.1 Electron-Pair Bonds 325
11.3.2 Pauli Repulsion: The Major Driver of CSB Bonds Between Main Elements 334
11.3.3 Experimental Manifestations of CSB 338
11.3.4 Deducing Bonding Features from Energy Barriers 340
11.3.5 Unique Features of Charge-Shift Bonds 341
11.4 Why and When Will Atoms Form Hypervalent Molecules? 343
11.5 Features of Orbital Hybridization in Modern VB Theory 346
11.5.1 Overlaps of Optimized Hybrid Orbitals 347
11.5.2 Typical Molecules and Their Variationally Optimized Hybrid Orbitals 348
11.5.3 An Overview of Hybridization Results 352
11.6 Description of Multiple Bonding 353
11.6.1 The Bond Multiplicity of C 2 354
11.6.2 Multi-Structure VBSCF Calculations of C 2 355
11.6.3 Properties of Quadruply Bonded Species 361
11.6.4 Some Lessons from the C 2 Study 364
11.6.5 The Kinetic Stability of Dioxygen Originates in the Cooperative ¿-Three-Electron Bonding 365
11.6.6 Outcomes of ¿-¿ Interplay in Multiple Bonds 367
11.7 Triplet-Pair Bonds (TPB) in Ferromagnetic Metal Clusters 375
11.7.1 VB Modeling of Bonding in Triplet-Pair Bonds 377
11.7.2 VB Modeling of n+1Mn Clusters 380
11.7.3 Bond Energies of Triplet-Pair Bonds 385
11.7.4 A Summary of No-Pair Bonding 387
11.8 Concluding Remarks 388
11.9 Supporting Information 391
11.9.1 Supplementary Issues 391
11.9.2 VB Structures for C 2 393
11.9.3 Pauli Repulsion and VB Structure Counts for Triplet-Pair Bond (TPB) in No-Pair Clusters 402
12 Breathing-Orbital Valence Bond: Methods and Applications 417
12.1 Introduction 417
12.2 Methodology 418
12.2.1 From VBSCF to BOVB 418
12.2.2 Static and Dynamic Correlations in Electron-Pair Bonds 420
12.2.3 Odd-Electron Bonds 422
12.2.4 Spin-Unrestricted VBSCF and BOVB Methods 425
12.3 Some Applications of the BOVB Method 426
12.3.1 A Quantitative Definition of Diradical Character 426
12.3.2 When the Diradical Character Rules the Reaction Barriers 429
12.3.3 Fast, Accurate, and Insightful Calculations of Challenging Excited States 431
12.4 Concluding Remarks 441
12.4.1 The Specific Insight Provided by VB Ab Initio Computations 441
12.4.2 Nonorthogonality: A Handicap or an Opportunity? 442
Epilogue 447
Glossary 450
Index 455
