A CHEMIST'S GUIDE TO VALENCE BOND THEORY
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1 A CHEMIST'S GUIDE TO VALENCE BOND THEORY Sason Shaik The Hebrew University Jerusalem, Israel Philippe C. Hiberty Universite de Paris-Sud Orsay, France BICENTENNIAL 3ICCNTENNIAL WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
2 CONTENTS PREFACE xiii 1 A Brief Story of Valence Bond Theory, Its Rivalry with Molecular Orbital Theory, Its Demise, and Resurgence RootsofVB Theory Origins of MO Theory and the Roots of VB-MO Rivalry One Theory is Up the Other is Down Mythical Failures of VB Theory: More Ground is Gained by MO Theory Are the Failures of VB Theory Real? The0 2 Failure The C 4 H 4 Failure The C 5 H + 5 Failure The Failure Associated with the Photoelectron Spectroscopy of CH Valence Bond is a Legitimate Theory Alongside Molecular Orbital Theory Modern VB Theory: Valence Bond Theory is Coming of Age 14 2 A Brief Tour Through Some Valence Bond Outputs and Terminology Valence Bond Output for the H 2 Molecule Valence Bond Mixing Diagrams Valence Bond Output for the HF Molecule 33 3 Basic Valence Bond Theory Writing and Representing Valence Bond Wave Functions VB Wave Functions with Localized Atomic Orbitals Valence Bond Wave Functions with Semilocalized AOs Valence Bond Wave Functions with Fragment Orbitals Writing Valence Bond Wave Functions Beyond the 2e/2c Case Pictorial Representation of Valence Bond Wave Functions by Bond Diagrams 45
3 viii CONTENTS 3.2 Overlaps between Determinants Valence Bond Formalism Using the Exact Hamiltonian Purely Covalent Singlet and Triplet Repulsive States Configuration Interaction Involving Ionic Terms Valence Bond Formalism Using an Effective Hamiltonian Some Simple Formulas for Elementary Interactions The Two-Electron Bond Repulsive Interactions in Valence Bond Theory Mixing of Degenerate Valence Bond Structures Nonbonding Interactions in Valence Bond Theory Structural Coefficients and Weights of Valence Bond Wave Functions Bridges between Molecular Orbital and Valence Bond Theories Comparison of Qualitative Valence Bond and Molecular Orbital Theories The Relationship between Molecular Orbital and Valence Bond Wave Functions 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 Mapping Molecular Orbital Configuration Interaction to Valence Bond Wave Functions Generating a Set of Valence Bond Structures Mapping a Molecular Orbital-Configuration Interaction Wave Function into a Valence Bond Wave Function Expansion of Molecular Orbital Determinants in Terms of Atomic Orbital Determinants Projecting the Molecular Orbital-Configuration Interaction Wave Function Onto the Rumer Basis of Valence Bond Structures An Example: The Hartree-Fock Wave Function ofbutadiene 86
4 CONTENTS ix 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? Introduction The Triplet Ground State of Dioxygen / Aromaticity-Antiaromaticity in Ionic Rings C n H n Aromaticity/Antiaromaticity in Neutral Rings The Valence Ionization Spectrum of CH The Valence Ionization Spectrum of H 2 0 and the "Rabbit-Ear" Lone Pairs A Summary 109 Exercises 111 Answers Valence Bond Diagrams for Chemical Reactivity Introduction Two Archetypal Valence Bond Diagrams The Valence Bond State Correlation Diagram Model and Its General Outlook on Reactivity Construction of Valence Bond State Correlation Diagrams for Elementary Processes Valence Bond State Correlation Diagrams for Radical Exchange Reactions Valence Bond State Correlation Diagrams for Reactions between Nucleophiles and Electrophiles Generalization of Valence Bond State Correlation Diagrams for Reactions Involving Reorganization of Covalent Bonds Barrier Expressions Based on the Valence Bond State Correlation Diagram Model Some Guidelines for Quantitative Applications of the Valence Bond State Correlation Diagram Model Making Qualitative Reactivity Predictions with the Valence Bond State Correlation Diagram Reactivity Trends in Radical Exchange Reactions Reactivity Trends in Allowed and Forbidden Reactions Reactivity Trends in Oxidative-Addition Reactions Reactivity Trends in Reactions between Nucleophiles and Electrophiles 136
5 x CONTENTS Chemical Significance of the f Factor Making Stereochemical Predictions with the VBSCD Model Predicting Transition State Structures with the Valence Bond State Correlation Diagram Model Trends in Transition State Resonance Energies Valence Bond Configuration Mixing Diagrams: General Features Valence Bond Configuration Mixing Diagram with Ionic Intermediate Curves Valence Bond Configuration Mixing Diagrams for Proton-Transfer Processes Insights from Valence Bond Configuration Mixing Diagrams: One Electron Less-One Electron More Nucleophilic Substitution on Silicon: Stable Hypercoordinated Species Valence Bond Configuration Mixing Diagram with Intermediates Nascent from "Foreign States" The Mechanism of Nucleophilic Substitution of Esters The SRN2 and SRN2 C Mechanisms Valence Bond State Correlation Diagram: A General Model for Electronic Delocalization in Clusters What is the Driving Force for the D 6h Geometry of Benzene,CTor TT? Valence Bond State Correlation Diagram: Application to Photochemical Reactivity Photoreactivity in 3e/3c Reactions Photoreactivity in 4e/3c Reactions A Summary 163 Exercises 171 Answers 176 Using Valence Bond Theory to Compute and Conceptualize Excited States Excited States of a Single Bond Excited States of Molecules with Conjugated Bonds Use of Molecular Symmetry to Generate Covalent Excited States Based on Valence Bond Theory Covalent Excited States of Polyenes A Summary 212 Exercises 215 Answers 216
6 CONTENTS xi Spin Hamiltonian Valence Bond Theory and its Applications to Organic Radicals, Diradicals, and Polyradicals A Topological Semiempirical Hamiltonian Applications Ground States of Polyenes and Hund's Rule Violations Spin Distribution in Alternant Radicals Relative Stabilities of Polyenes Extending Ovchinnikov's Rule to Search for Bistable Hydrocarbons ASummary 231 Exercises 232 Answers 234 Currently Available Ab Initio Valence Bond Computational Methods and their Principles Introduction Valence Bond Methods Based on Semilocalized Orbitals The Generalized Valence Bond Method The Spin-Coupled Valence Bond Method The CASVB Method The Generalized Resonating Valence Bond Method Multiconfiguration Valence Bond Methods with Optimized Orbitals Valence Bond Methods Based on Localized Orbitals Valence Bond Self-Consistent Field Method with Localized Orbitals The Breathing-Orbital Valence Bond Method The Valence Bond Configuration Interaction Method Methods for Getting Valence Bond Quantities from Molecular Orbital-Based Procedures Using Standard Molecular Orbital Software to Compute Single Valence Bond Structures or Determinants The Block-Localized Wave Function and Related Methods A Valence Bond Method with Polanzable Continuum Model 255 Appendix A. 1 Some Available Valence Bond Programs A. 1.1 The TURTLE Software A.1.2 The XMVB Program 257
7 xii CONTENTS 9.A.2 9.A.1.3 The CRUNCH Software A.1.4 The VB2000 Software 258 Implementations of Valence Bond Methods in Standard Ab Initio Packages Do Your Own Valence Bond Calculations A Practical Guide Introduction Wave Functions and Energies for the Ground State of F GVB, SC, and VBSCF Methods The BOVB Method The VBCI Method Valence Bond Calculations of Diabatic States and Resonance Energies Definition of Diabatic States Calculations of Meaningful Diabetic States Resonance Energies Comments on Calculations of VBSCDs and VBCMDs 287 Appendix 290 lo.a.l Calculating at the SD-BOVB Level in Low Symmetry Cases 290 Epilogue 304 Glossary 306 Index 311
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