# A Chemist's Guide to Valence Bond Theory

# A Chemist's Guide to Valence Bond Theory

ISBN: 978-0-470-19259-7

Apr 2007

332 pages

## Description

This reference on current VB theory and applications presents a practical system that can be applied to a variety of chemical problems in a uniform manner. After explaining basic VB theory, it discusses VB applications to bonding problems, aromaticity and antiaromaticity, the dioxygen molecule, polyradicals, excited states, organic reactions, inorganic/organometallic reactions, photochemical reactions, and catalytic reactions. With a guide for performing VB calculations, exercises and answers, and numerous solved problems, this is the premier reference for practitioners and upper-level students.PREFACE xiii

**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 C4H4 Failure 13

1.5.3 The C5H5þ Failure 13

1.5.4 The Failure Associated with the Photoelectron Spectroscopy of CH4 13

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 14

**2 A Brief Tour Through Some Valence Bond Outputs and Terminology 26**

2.1 Valence Bond Output for the H2 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 41

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 45

3.2 Overlaps between Determinants 45

3.3 Valence Bond Formalism Using the Exact Hamiltonian 46

3.3.1 Purely Covalent Singlet and Triplet Repulsive States 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 51

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 54

3.6 Structural Coefficients and Weights of Valence Bond Wave Functions 56

3.7 Bridges between Molecular Orbital and Valence Bond Theories 56

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 60

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 Determinant 66

3.A.1.2 Hamiltonian Matrix Elements and Overlaps between Atomic Orbital-Based Determinants 68

3.A.2 Simple Guidelines for Valence Bond Mixing 68

Exercises 70

Answers 74

**4 Mapping Molecular Orbital—Configuration Interaction to Valence Bond Wave Functions 81**

4.1 Generating a Set of Valence Bond Structures 81

4.2 Mapping a Molecular Orbital–Configuration Interaction Wave Function into a Valence Bond Wave Function 83

4.2.1 Expansion of Molecular Orbital Determinants in Terms of Atomic Orbital Determinants 83

4.2.2 Projecting the Molecular Orbital–Configuration Interaction Wave Function Onto the Rumer Basis of Valence Bond Structures 85

4.2.3 An Example: The Hartree–Fock Wave Function of Butadiene 86

4.3 Using Half-Determinants to Calculate Overlaps between Valence Bond Structures 88

Exercises 89

Answers 90

**5 Are the ‘‘Failures’’ of Valence Bond Theory Real? 94**

5.1 Introduction 94

5.2 The Triplet Ground State of Dioxygen 94

5.3 Aromaticity–Antiaromaticity in Ionic Rings CnHnþ/_ 97

5.4 Aromaticity/Antiaromaticity in Neutral Rings 100

5.5 The Valence Ionization Spectrum of CH4 104

5.6 The Valence Ionization Spectrum of H2O and the ‘‘Rabbit-Ear’’ Lone Pairs 106

5.7 A Summary 109

Exercises 111

Answers 112

**6 Valence Bond Diagrams for Chemical Reactivity 116**

6.1 Introduction 116

6.2 Two Archetypal Valence Bond Diagrams 116

6.3 The Valence Bond State Correlation Diagram Model and Its General Outlook on Reactivity 117

6.4 Construction of Valence Bond State Correlation Diagrams for Elementary Processes 119

6.4.1 Valence Bond State Correlation Diagrams for Radical Exchange Reactions 119

6.4.2 Valence Bond State Correlation Diagrams for Reactions between Nucleophiles and Electrophiles 122

6.4.3 Generalization of Valence Bond State Correlation Diagrams for Reactions Involving Reorganization of

Covalent Bonds 124

6.5 Barrier Expressions Based on the Valence Bond State Correlation Diagram Model 126

6.5.1 Some Guidelines for Quantitative Applications of the Valence Bond State Correlation Diagram Model 128

6.6 Making Qualitative Reactivity Predictions with the Valence Bond State Correlation Diagram 128

6.6.1 Reactivity Trends in Radical Exchange Reactions 130

6.6.2 Reactivity Trends in Allowed and Forbidden Reactions 132

6.6.3 Reactivity Trends in Oxidative–Addition Reactions 133

6.6.4 Reactivity Trends in Reactions between Nucleophiles and Electrophiles 136

6.6.5 Chemical Significance of the f Factor 138

6.6.6 Making Stereochemical Predictions with the VBSCD Model 138

6.6.7 Predicting Transition State Structures with the Valence Bond State Correlation Diagram Model 140

6.6.8 Trends in Transition State Resonance Energies 141

6.7 Valence Bond Configuration Mixing Diagrams: General Features 144

6.8 Valence Bond Configuration Mixing Diagram with Ionic Intermediate Curves 144

6.8.1 Valence Bond Configuration Mixing Diagrams for Proton-Transfer Processes 145

6.8.2 Insights from Valence Bond Configuration Mixing Diagrams: One Electron Less–One Electron More 146

6.8.3 Nucleophilic Substitution on Silicon: Stable Hypercoordinated Species 147

6.9 Valence Bond Configuration Mixing Diagram with Intermediates Nascent from ‘‘Foreign States’’ 149

6.9.1 The Mechanism of Nucleophilic Substitution of Esters 149

6.9.2 The SRN2 and SRN2c Mechanisms 150

6.10 Valence Bond State Correlation Diagram: A General Model for Electronic Delocalization in Clusters 153

6.10.1 What is the Driving Force for the D6h Geometry of Benzene, s or p? 154

6.11 Valence Bond State Correlation Diagram: Application to Photochemical Reactivity 157

6.11.1 Photoreactivity in 3e/3c Reactions 158

6.11.2 Photoreactivity in 4e/3c Reactions 159

6.12 A Summary 163

Exercises 171

Answers 176

**7 Using Valence Bond Theory to Compute and Conceptualize Excited States 193**

7.1 Excited States of a Single Bond 194

7.2 Excited States of Molecules with Conjugated Bonds 196

7.2.1 Use of Molecular Symmetry to Generate Covalent Excited States Based on Valence Bond Theory 197

7.2.2 Covalent Excited States of Polyenes 209

7.3 A Summary 212

Exercises 215

Answers 216

**8 Spin Hamiltonian Valence Bond Theory and its Applications to Organic Radicals, Diradicals, and Polyradicals 222**

8.1 ATopological Semiempirical Hamiltonian 223

8.2 Applications 225

8.2.1 Ground States of Polyenes and Hund’s Rule Violations 225

8.2.2 Spin Distribution in Alternant Radicals 227

8.2.3 Relative Stabilities of Polyenes 228

8.2.4 Extending Ovchinnikov’s Rule to Search for Bistable Hydrocarbons 230

8.3 A Summary 231

Exercises 232

Answers 234

**9 Currently Available Ab Initio Valence Bond Computational Methods and their Principles 238**

9.1 Introduction 238

9.2 Valence Bond Methods Based on Semilocalized Orbitals 239

9.2.1 The Generalized Valence Bond Method 240

9.2.2 The Spin-Coupled Valence Bond Method 242

9.2.3 The CASVB Method 243

9.2.4 The Generalized Resonating Valence Bond Method 245

9.2.5 Multiconfiguration Valence Bond Methods with Optimized Orbitals 246

9.3 Valence Bond Methods Based on Localized Orbitals 247

9.3.1 Valence Bond Self-Consistent Field Method with Localized Orbitals 247

9.3.2 The Breathing-Orbital Valence Bond Method 249

9.3.3 The Valence Bond Configuration Interaction Method 252

9.4 Methods for Getting Valence Bond Quantities from Molecular Orbital-Based Procedures 253

9.4.1 Using Standard Molecular Orbital Software to Compute Single Valence Bond Structures or Determinants 253

9.4.2 The Block-Localized Wave Function and Related Methods 254

9.5 AValence Bond Method with Polarizable Continuum Model 255

Appendix 257

9.A.1 Some Available Valence Bond Programs 257

9.A.1.1 The TURTLE Software 257

9.A.1.2 The XMVB Program 257

9.A.1.3 The CRUNCH Software 257

9.A.1.4 The VB2000 Software 258

9.A.2 Implementations of Valence Bond Methods in Standard Ab Initio Packages 258

**10 Do Your Own Valence Bond Calculations—A Practical Guide 271**

10.1 Introduction 271

10.2 Wave Functions and Energies for the Ground State of F2 271

10.2.1 GVB, SC, and VBSCF Methods 272

10.2.2 The BOVB Method 276

10.2.3 The VBCI Method 280

10.3 Valence Bond Calculations of Diabatic States and Resonance Energies 281

10.3.1 Definition of Diabatic States 282

10.3.2 Calculations of Meaningful Diabetic States 282

10.3.3 Resonance Energies 284

10.4 Comments on Calculations of VBSCDs and VBCMDs 287

Appendix 290

10.A.1 Calculating at the SD–BOVB Level in Low Symmetry Cases 290

*Epilogue 304*

*Glossary 306*

*Index 311*

*Angewandte Chemie International Edition*, December 8, 2008)