Chemist's Guide to Valence Bond Theory

Sason S. Shaik, PhD, is a Professor and the Director of the Lise Meitner-Minerva Center for Computational Quantum Chemistry in the Hebrew University in Jerusalem. He has been a Fulbright Fellow (1974-1979) and became a Fellow of the AAAS in 2005. Among his awards are the Israel Chemical Society Medal for the Outstanding Young Chemist (1987), the Alexander von Humboldt Senior Award in 1996-1999, the 2001 Kolthoff Award, the 2001 Israel Chemical Society Prize, and the 2007 Schrödinger Medal of WATOC. His research interests are in the use of quantum chemistry to develop paradigms that can pattern data and lead to the generation and solution of new problems. From 1981-1992, the main focus of his research was on valence bond theory and its relationship to MO theory, and during that time, he developed a general model of reactivity based on a blend of VB and MO elements. In 1994, he entered the field of oxidation and bond activation by metal oxo catalysts and enzymes, an area where he has contributed several seminal ideas (e.g., two-state reactivity) that led to resolution of major controversies and new predictions. Philippe C. Hiberty is Director of Research at the Centre National de la Recherche Scientifique (CNRS) and a member of the Theoretical Chemistry Group in the Laboratoire de Chimie Physique at the?University of Paris-Sud. He taught quantum chemistry for years at the Ecole Polytechique in Palaiseau. He received the Grand Prix Philippe A. Guye from the French Academy of Sciences in 2002. Under the supervision of Professor Lionel Salem, he devoted his PhD to building a bridge between MO and VB theories by devising a method for mapping MO wave functions to VB ones. In collaboration with Professor Sason Shaik, he applied VB theory to fundamental concepts of organic chemistry such as aromaticity, hypervalence, odd-electron bonds, prediction of reaction barriers from properties of reactants and products, and so on. He is the originator of the Breathing-Orbital Valence Bond method, which is aimed at combining the lucidity of compact VB wave functions with a good accuracy of the energetics.

"The textbook provides a qualitative overview of the possibilities within the VB approach. As such, we strongly recommend it, both to interested chemists and to university libraries." (Angewandte Chemie International Edition, December 8, 2008)

• Preface xiii1 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 C4H4 Failure 131.5.3 The C5H5+ Failure 131.5.4 The Failure Associated with the Photoelectron Spectroscopy of CH4 131.6 Valence Bond is a Legitimate Theory Alongside Molecular Orbital Theory 141.7 Modern VB Theory: Valence Bond Theory is Coming of Age 142 A Brief Tour Through Some Valence Bond Outputs and Terminology 262.1 Valence Bond Output for the H2 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 413.1.3 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 453.2 Overlaps between Determinants 453.3 Valence Bond Formalism Using the Exact Hamiltonian 463.3.1 Purely Covalent Singlet and Triplet Repulsive States 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 513.5.2 Repulsive Interactions in Valence Bond Theory 523.5.3 Mixing of Degenerate Valence Bond Structures 533.5.4 Nonbonding Interactions in Valence Bond Theory 543.6 Structural Coefficients and Weights of Valence Bond Wave Functions 563.7 Bridges between Molecular Orbital and Valence Bond Theories 563.7.1 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 60Appendix 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 Determinant 663.A.1.2 Hamiltonian Matrix Elements and Overlaps between Atomic Orbital-Based Determinants 683.A.2 Simple Guidelines for Valence Bond Mixing 68Exercises 70Answers 744 Mapping Molecular Orbital—Configuration Interaction to Valence Bond Wave Functions 814.1 Generating a Set of Valence Bond Structures 814.2 Mapping a Molecular Orbital–Configuration Interaction Wave Function into a Valence Bond Wave Function 834.2.1 Expansion of Molecular Orbital Determinants in Terms of Atomic Orbital Determinants 834.2.2 Projecting the Molecular Orbital–Configuration Interaction Wave Function Onto the Rumer Basis of Valence Bond Structures 854.2.3 An Example: The Hartree–Fock Wave Function of Butadiene 864.3 Using Half-Determinants to Calculate Overlaps between Valence Bond Structures 88Exercises 89Answers 905 Are the ‘‘Failures’’ of Valence Bond Theory Real? 945.1 Introduction 945.2 The Triplet Ground State of Dioxygen 945.3 Aromaticity–Antiaromaticity in Ionic Rings CnHn+/- 975.4 Aromaticity/Antiaromaticity in Neutral Rings 1005.5 The Valence Ionization Spectrum of CH4 1045.6 The Valence Ionization Spectrum of H2O and the ‘‘Rabbit-Ear’’ Lone Pairs 1065.7 A Summary 109Exercises 111Answers 1126 Valence Bond Diagrams for Chemical Reactivity 1166.1 Introduction 1166.2 Two Archetypal Valence Bond Diagrams 1166.3 The Valence Bond State Correlation Diagram Model and Its General Outlook on Reactivity 1176.4 Construction of Valence Bond State Correlation Diagrams for Elementary Processes 1196.4.1 Valence Bond State Correlation Diagrams for Radical Exchange Reactions 1196.4.2 Valence Bond State Correlation Diagrams for Reactions between Nucleophiles and Electrophiles 1226.4.3 Generalization of Valence Bond State Correlation Diagrams for Reactions Involving Reorganization of Covalent Bonds 1246.5 Barrier Expressions Based on the Valence Bond State Correlation Diagram Model 1266.5.1 Some Guidelines for Quantitative Applications of the Valence Bond State Correlation Diagram Model 1286.6 Making Qualitative Reactivity Predictions with the Valence Bond State Correlation Diagram 1286.6.1 Reactivity Trends in Radical Exchange Reactions 1306.6.2 Reactivity Trends in Allowed and Forbidden Reactions 1326.6.3 Reactivity Trends in Oxidative–Addition Reactions 1336.6.4 Reactivity Trends in Reactions between Nucleophiles and Electrophiles 1366.6.5 Chemical Significance of the f Factor 1386.6.6 Making Stereochemical Predictions with the VBSCD Model 1386.6.7 Predicting Transition State Structures with the Valence Bond State Correlation Diagram Model 1406.6.8 Trends in Transition State Resonance Energies 1416.7 Valence Bond Configuration Mixing Diagrams: General Features 1446.8 Valence Bond Configuration Mixing Diagram with Ionic Intermediate Curves 1446.8.1 Valence Bond Configuration Mixing Diagrams for Proton-Transfer Processes 1456.8.2 Insights from Valence Bond Configuration Mixing Diagrams: One Electron Less–One Electron More 1466.8.3 Nucleophilic Substitution on Silicon: Stable Hypercoordinated Species 1476.9 Valence Bond Configuration Mixing Diagram with Intermediates Nascent from ‘‘Foreign States’’ 1496.9.1 The Mechanism of Nucleophilic Substitution of Esters 1496.9.2 The SRN2 and SRN2c Mechanisms 1506.10 Valence Bond State Correlation Diagram: A General Model for Electronic Delocalization in Clusters 1536.10.1 What is the Driving Force for the D6h Geometry of Benzene, σ or π? 1546.11 Valence Bond State Correlation Diagram: Application to Photochemical Reactivity 1576.11.1 Photoreactivity in 3e/3c Reactions 1586.11.2 Photoreactivity in 4e/3c Reactions 1596.12 A Summary 163Exercises 171Answers 1767 Using Valence Bond Theory to Compute and Conceptualize Excited States 1937.1 Excited States of a Single Bond 1947.2 Excited States of Molecules with Conjugated Bonds 1967.2.1 Use of Molecular Symmetry to Generate Covalent Excited States Based on Valence Bond Theory 1977.2.2 Covalent Excited States of Polyenes 2097.3 A Summary 212Exercises 215Answers 2168 Spin Hamiltonian Valence Bond Theory and its Applications to Organic Radicals, Diradicals, and Polyradicals 2228.1 A Topological Semiempirical Hamiltonian 2238.2 Applications 2258.2.1 Ground States of Polyenes and Hund’s Rule Violations 2258.2.2 Spin Distribution in Alternant Radicals 2278.2.3 Relative Stabilities of Polyenes 2288.2.4 Extending Ovchinnikov’s Rule to Search for Bistable Hydrocarbons 2308.3 A Summary 231Exercises 232Answers 2349 Currently Available Ab Initio Valence Bond Computational Methods and their Principles 2389.1 Introduction 2389.2 Valence Bond Methods Based on Semilocalized Orbitals 2399.2.1 The Generalized Valence Bond Method 2409.2.2 The Spin-Coupled Valence Bond Method 2429.2.3 The CASVB Method 2439.2.4 The Generalized Resonating Valence Bond Method 2459.2.5 Multiconfiguration Valence Bond Methods with Optimized Orbitals 2469.3 Valence Bond Methods Based on Localized Orbitals 2479.3.1 Valence Bond Self-Consistent Field Method with Localized Orbitals 2479.3.2 The Breathing-Orbital Valence Bond Method 2499.3.3 The Valence Bond Configuration Interaction Method 2529.4 Methods for Getting Valence Bond Quantities from Molecular Orbital-Based Procedures 2539.4.1 Using Standard Molecular Orbital Software to Compute Single Valence Bond Structures or Determinants 2539.4.2 The Block-Localized Wave Function and Related Methods 2549.5 A Valence Bond Method with Polarizable Continuum Model 255Appendix 2579.A.1 Some Available Valence Bond Programs 2579.A.1.1 The TURTLE Software 2579.A.1.2 The XMVB Program 2579.A.1.3 The CRUNCH Software 2579.A.1.4 The VB2000 Software 2589.A.2 Implementations of Valence Bond Methods in Standard Ab Initio Packages 25810 Do Your Own Valence Bond Calculations—A Practical Guide 27110.1 Introduction 27110.2 Wave Functions and Energies for the Ground State of F2 27110.2.1 GVB, SC, and VBSCF Methods 27210.2.2 The BOVB Method 27610.2.3 The VBCI Method 28010.3 Valence Bond Calculations of Diabatic States and Resonance Energies 28110.3.1 Definition of Diabatic States 28210.3.2 Calculations of Meaningful Diabetic States 28210.3.3 Resonance Energies 28410.4 Comments on Calculations of VBSCDs and VBCMDs 287Appendix 29010.A.1 Calculating at the SD–BOVB Level in Low Symmetry Cases 290Epilogue 304Glossary 306Index 311