Chemist's Guide to Valence Bond Theory

Sason Shaik is a Saerree K. and Louis P. Fiedler Emeritus Professor of Chemistry at the Hebrew University. He has developed a number of new paradigms and concepts using valence bond theory and participated in the initiation of various valence bond methods. David Danovich is a senior computational chemist at the Institute of Chemistry in the Hebrew University, and an expert on VB calculations Philippe C. Hiberty is an Emeritus Director of Research at the Centre National de la Recherche Scientifique in the Université Paris-Saclay. He has developed the Breathing-Orbital VB method.

• Preface xv1 A Brief Story of Valence Bond Theory, its Rivalry with Molecular Orbital Theory, its Demise, and Resurgence 11.1 Roots of VB Theory 21.2 Origins of MO Theory and the Roots of VB–MO Rivalry 51.3 One Theory is Up, The Other is Down 71.4 Mythical Failures of VB Theory: More Ground is Gained by MO Theory 81.5 Are the Failures of VB Theory Real? 121.5.1 The O2 Failure 121.5.2 The C 4 H 4 Failure 131.5.3 The C 5 H 5 + Failure 131.5.4 The Failure Associated with the Photoelectron Spectroscopy of CH 4 141.6 Valence Bond is a Legitimate Theory Alongside Molecular Orbital Theory 141.7 Modern VB Theory: Valence Bond Theory is Coming of Age 152 A Brief Tour Through Some Valence Bond Outputs and Terminology 262.1 Valence Bond Output for the H 2 Molecule 262.2 Valence Bond Mixing Diagrams 322.3 Valence Bond Output for the HF Molecule 333 Basic Valence Bond Theory 403.1 Writing and Representing Valence Bond Wave Functions 403.1.1 VB Wave Functions with Localized Atomic Orbitals 403.1.2 Valence Bond Wave Functions with Semilocalized AOs 423.1.3 Valence Bond Wave Functions with Fragment Orbitals 423.1.4 Writing Valence Bond Wave Functions Beyond the 2e/2c Case 433.1.5 Pictorial Representation of Valence Bond Wave Functions by Bond Diagrams 443.2 Overlaps Between Determinants 453.3 Valence Bond Formalism Using the Exact Hamiltonian 473.3.1 Purely Covalent Singlet State and a Triplet Repulsive State 473.3.2 Configuration Interaction Involving Ionic Terms 493.4 Valence Bond Formalism Using an Effective Hamiltonian 493.5 Some Simple Formulas for Elementary Interactions 513.5.1 The Two-Electron Bond 523.5.2 Repulsive Interactions in Valence Bond Theory 523.5.3 Mixing of Degenerate Valence Bond Structures 533.5.4 Nonbonding Interactions in Valence Bond Theory 553.6 Structural Coefficients and Weights of Valence Bond Wave Functions 563.7 Bridges Between Molecular Orbital and Valence Bond Theories 573.7.1 Comparison of Qualitative Valence Bond and Molecular Orbital Theories 573.7.2 The Relationship Between Molecular Orbital and Valence Bond Wave Functions 583.7.3 Localized Bond Orbitals: A Pictorial Bridge Between Molecular Orbital and Valence Bond Wave Functions 61Appendix 653.a.1 Normalization Constants, Energies, Overlaps, and Matrix Elements of Valence Bond Wave Functions 653.a.1.1 Energy and Self-Overlap of an Atomic Orbital-Based Determinants 673.a.1.2 Hamiltonian Matrix Elements and Overlaps Between Atomic Orbital-Based Determinants 693.a.2 Guidelines for Valence Bond Mixing 69Exercises 71Answers 764 Mapping Molecular Orbital–Configuration Interaction to Valence Bond Wave Functions 834.1 Generating a Set of Valence Bond Structures 834.2 Mapping a Molecular Orbital–Configuration Interaction Wave Function into a Valence Bond Wave Function 854.2.1 Expansion of Molecular Orbital Determinants in Terms of Atomic Orbital Determinants 854.2.2 Projecting the Molecular Orbital–Configuration Interaction Wave Function to the Rumer Basis of Valence Bond Structures 884.2.3 An Example: The Hartree–Fock Wave Function of Butadiene 884.3 Using Half-Determinants to Calculate Overlaps between Valence Bond Structures 90Exercises 92Answers 935 Are The “Failures” of Valence Bond Theory Real? 965.1 Introduction 965.2 The Triplet Ground State of Dioxygen 965.3 Aromaticity–Antiaromaticity in Ionic Rings C n H n ± 1005.4 Aromaticity/Antiaromaticity in Neutral Rings 1035.5 The Valence Ionization Spectrum of CH 4 1085.6 The Valence Ionization Spectrum of H 2 O and the “Rabbit-Ear” Lone Pairs 1105.7 A Summary 113Exercises 115Answers 1166 Valence Bond Diagrams for Chemical Reactivity 1206.1 Introduction 1206.2 Two Archetypal Valence Bond Diagrams 1216.3 The Valence Bond State Correlation Diagram Model and its General Outlook on Reactivity 1226.4 Construction of Valence Bond State Correlation Diagrams for Elementary Processes 1236.4.1 Valence Bond State Correlation Diagrams for Radical Exchange Reactions 1236.4.2 Valence Bond State Correlation Diagrams for Reactions Between Nucleophiles and Electrophiles 1276.4.3 Generalization of Valence Bond State Correlation Diagrams for Reactions Involving Reorganization of Covalent Bonds 1296.5 Barrier Expressions Based on the Valence Bond State Correlation Diagram Model 1316.5.1 Some Guidelines for Quantitative Applications of the Valence Bond State Correlation Diagram Model 1336.6 Making Qualitative Reactivity Predictions with the Valence Bond State Correlation Diagram 1336.6.1 Reactivity Trends in Radical Exchange Reactions 1356.6.2 Reactivity Trends in Allowed and Forbidden Reactions 1376.6.3 Reactivity Trends in Oxidative–Addition Reactions 1386.6.4 Reactivity Trends in Reactions Between Nucleophiles and Electrophiles 1416.6.5 Chemical Significance of the f Factor 1426.6.6 Making Stereochemical Predictions with the VBSCD Model 1436.6.7 Predicting Transition-State Structures with the Valence Bond State Correlation Diagram Model 1456.6.8 Trends in Transition-State Resonance Energies 1466.7 Valence Bond Configuration Mixing Diagrams: General Features 1496.8 Valence Bond Configuration Mixing Diagram with Ionic Intermediate Curves 1496.8.1 Valence Bond Configuration Mixing Diagram for Proton-Transfer Processes 1496.8.2 Insights from Valence Bond Configuration Mixing Diagrams: One Electron Less–One Electron More 1516.8.3 Nucleophilic Substitution on Silicon: Stable Hypercoordinated Species 1526.9 Valence Bond Configuration Mixing Diagram with Intermediates Nascent from “Foreign States” 1546.9.1 The Mechanism of Nucleophilic Substitution of Esters 1546.9.2 The S RN 2 and SRN2c Mechanisms 1556.10 Valence Bond State Correlation Diagram: A General Model for Electronic Delocalization in Clusters 1576.10.1 What is the Driving Force for the D 6h Geometry of Benzene, σ or π? 1606.11 Valence Bond State Correlation Diagram: Application to Photochemical Reactivity 1636.11.1 Photoreactivity in 3e/3c Reactions 1646.11.2 Photoreactivity in 4e/3c Reactions 1656.12 A Summary 169Exercises 179Answers 1857 Using Valence Bond Theory to Compute and Conceptualize Excited States 2037.1 Excited States of a Single Bond 2057.2 Excited States of Molecules with Conjugated Bonds 2077.2.1 Use of Molecular Symmetry to Generate Covalent Excited States Based on Valence Bond Theory 2077.2.2 Covalent Excited States of Polyenes 2197.3 A Summary 223Exercises 225Answers 2268 Spin Hamiltonian Valence Bond Theory and its Applications to Organic Radicals, Diradicals, and Polyradicals 2328.1 A Topological Semiempirical Hamiltonian 2338.2 Applications 2358.2.1 Ground States of Polyenes and Hund’s Rule Violations 2358.2.2 Spin Distribution in Alternant Radicals 2378.2.3 Relative Stabilities of Polyenes 2388.2.4 Extending Ovchinnikov’s Rule to Search for Bistable Hydrocarbons 2408.3 A Summary 241Exercises 243Answers 2459 Currently Available Ab Initio Valence Bond Computational Methods and Their Principles 2499.1 Introduction 2499.2 Valence Bond Methods Based on Semi-Localized Orbitals 2509.2.1 The Generalized Valence Bond Method 2519.2.2 The Spin-Coupled Generalized Valence Bond Method 2539.2.3 The CASVB Method 2549.2.4 The Generalized Resonating Valence Bond Method 2569.2.5 Multiconfiguration Valence Bond Methods with Optimized Orbitals 2579.3 Valence Bond Methods Based on Localized Orbitals 2589.3.1 Valence Bond Self-Consistent Field Method with Localized Orbitals 2599.3.2 The Breathing-Orbital Valence Bond Method 2609.3.3 The Valence Bond Configuration Interaction Method 2639.3.4 The Valence Bond Quantum Monte Carlo Method 2659.4 Methods for Getting Valence Bond Quantities from Molecular Orbital-Based Procedures 2669.4.1 Using Standard Molecular Orbital Software to Compute Single Valence Bond Structures or Determinants 2669.4.2 The Block-Localized Wave Function and Related Methods 2679.5 A Valence Bond Method with Polarizable Continuum Model 2689.6 Perspective 269Appendix 2699.a.1 Some Available Valence Bond Programs 2699.a.1.1 The TURTLE Software 2709.a.1.2 The XMVB Program 2709.a.1.3 The CRUNCH Software 2709.a.1.4 The VB2000 Software 2709.a.1.5 The CHAMP Program for the VB-QMC Method 2719.a.2 Implementations of Valence Bond Methods in Standard Ab Initio Packages 27110 Do Your Own Valence Bond Calculation—A Practical Guide 28210.1 Introduction 28210.2 Wave Functions and Energies for the Ground State of F 2 28210.2.1 GVB, SC, and VBSCF Methods 28310.2.2 The BOVB Method 28710.2.3 The VBCI Method 29210.3 Valence Bond Calculations of Diabatic States and Resonance Energies 29310.3.1 Definition of Diabatic States 29310.3.2 Calculations of Meaningful Diabatic States 29410.3.3 Resonance Energies 29510.4 Comments on Calculations of VBSCDS and VBCMDS 29810.4.1 VBSCD Calculations 29910.4.2 VBCMD Calculations 300Appendix 30110.A.1 Calculating at the SD-BOVB Level in Low Symmetry Cases 30111 The Chemical Bonds in Valence Bond Theory: Review Chapters on Specific Topics in Valence Bond Theory 31811.1 Introduction 31811.2 VB Approaches: Their Bond Descriptions and Representations 31911.2.1 Single Two-Electron Bonds 31911.2.2 Multiple Two-Electron Bonds 32111.2.3 Classical VB Methods for Single Bonds 32111.2.4 VB Methods for Multiple Bonds 32311.3 Applications of VB Theory to Chemical Bonding 32511.3.1 Electron-Pair Bonds 32511.3.2 Pauli Repulsion: The Major Driver of CSB Bonds Between Main Elements 33411.3.3 Experimental Manifestations of CSB 33811.3.4 Deducing Bonding Features from Energy Barriers 34011.3.5 Unique Features of Charge-Shift Bonds 34111.4 Why and When Will Atoms Form Hypervalent Molecules? 34311.5 Features of Orbital Hybridization in Modern VB Theory 34611.5.1 Overlaps of Optimized Hybrid Orbitals 34711.5.2 Typical Molecules and Their Variationally Optimized Hybrid Orbitals 34811.5.3 An Overview of Hybridization Results 35211.6 Description of Multiple Bonding 35311.6.1 The Bond Multiplicity of C 2 35411.6.2 Multi-Structure VBSCF Calculations of C 2 35511.6.3 Properties of Quadruply Bonded Species 36111.6.4 Some Lessons from the C 2 Study 36411.6.5 The Kinetic Stability of Dioxygen Originates in the Cooperative π-Three-Electron Bonding 36511.6.6 Outcomes of π–σ Interplay in Multiple Bonds 36711.7 Triplet-Pair Bonds (TPB) in Ferromagnetic Metal Clusters 37511.7.1 VB Modeling of Bonding in Triplet-Pair Bonds 37711.7.2 VB Modeling of n+1Mn Clusters 38011.7.3 Bond Energies of Triplet-Pair Bonds 38511.7.4 A Summary of No-Pair Bonding 38711.8 Concluding Remarks 38811.9 Supporting Information 39111.9.1 Supplementary Issues 39111.9.2 VB Structures for C 2 39311.9.3 Pauli Repulsion and VB Structure Counts for Triplet-Pair Bond (TPB) in No-Pair Clusters 40212 Breathing-Orbital Valence Bond: Methods and Applications 41712.1 Introduction 41712.2 Methodology 41812.2.1 From VBSCF to BOVB 41812.2.2 Static and Dynamic Correlations in Electron-Pair Bonds 42012.2.3 Odd-Electron Bonds 42212.2.4 Spin-Unrestricted VBSCF and BOVB Methods 42512.3 Some Applications of the BOVB Method 42612.3.1 A Quantitative Definition of Diradical Character 42612.3.2 When the Diradical Character Rules the Reaction Barriers 42912.3.3 Fast, Accurate, and Insightful Calculations of Challenging Excited States 43112.4 Concluding Remarks 44112.4.1 The Specific Insight Provided by VB Ab Initio Computations 44112.4.2 Nonorthogonality: A Handicap or an Opportunity? 442Epilogue 447Glossary 450Index 455