Buch, Englisch, 496 Seiten
Insights Into Chemical Bonding, Reactivity, and Excited States
Buch, Englisch, 496 Seiten
ISBN: 978-1-394-23879-8
Verlag: Wiley
Updated resource on theoretical aspects and applications of valence bond methods to chemical calculations
A Chemist's Guide to Valence Bond Theory explains how to use valence bond theory to think concisely and rigorously and how to use VB computations. It familiarizes the reader with the various VB-based computational tools and methods available today and their use for a given chemical problem and provides samples of inputs/outputs that instruct the reader on how to interpret the results. The book also covers the theoretical basis of Valence Bond (VB) theory and its applications to chemistry in the ground- and excited-states. Applications discussed in the book include sets of exercises and corresponding answers on bonding problems, organic reactions, inorganic/organometallic reactions, and bioinorganic/biochemical reactions.
This Second Edition contains a new chapter on chemical bonds which includes sections on covalent, ionic, and charge-shift bonds as well as triplet bond pairs, a new chapter on the Breathing-Orbital VB method with its application to molecular excited states, and several new sections discussing recent developments such as DFT-based methods and solvent effects via the Polarizable Continuum Model (PCM).
A Chemist's Guide to Valence Bond Theory includes information on: - Writing and representing valence bond wave functions, overlaps between determinants, and valence bond formalism using the exact Hamiltonian
- Generating a set of valence bond structures and mapping a molecular orbital-configuration interaction wave function into a valence bond wave function
- The “failures” of valence bond theory, such as the triplet ground state of dioxygen, and whether or not these failures are “real”
- Spin Hamiltonian valence bond theory and its applications to organic radicals, diradicals, and polyradicals
A Chemist's Guide to Valence Bond Theory is an essential reference on the subject for chemists who are not necessarily experts on theory but have some background in quantum chemistry. The text is also appropriate for upper undergraduate and graduate students in advanced courses on valence bond theory.
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PREFACE
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 C5H5+ 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 CnHn+/- 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 A Topological 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 A Valence 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 Diabatic 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
11 The Chemical Bonds in Valence Bond Theory 304
11.1 Introduction 304
11.2 VB Approaches: Their Bond Descriptions and Representations 304
11.2.1 Single Two-Electron Bonds 304
11.2.2 Multiple Two-Electron Bonds 306
11.2.3 Classical VB Methods for Single Bonds 306
11.2.4 VB Methods for Multiple Bonds 307
11.3 Applications of VB Theory to Chemical Bonding 309
11.3.1 Electron-Pair Bonds 309 11.3.1.1 The Logic Behind the Existence of Three Bond Families 314 11.3.1.2 Do Other Computational Methods Reveal the CSB Family? 315
11.3.2 Pauli Repulsion: The Major Driver of CSB 317 11.3.2.1 Bonds Between Main Elements 318 11.3.2.2 Bonds Between Transition Metals (TMs) 320 11.3.2.3 Post Transition Metals, Groups 11 and 12 321 11.3.2.4 Other CSB Factors 321
11.3.3 Experimental Manifestations of CSB 322
11.3.4 Deducing Bonding Features from Energy Barriers 323
11.3.5 Unique Features of Charge-Shift Bonds 324
11.4 Why and When will Atoms Form Hypervalent Molecules? 325
11.5 Features of Orbital Hybridization in Modern VB Theory 328
11.5.1 Overlaps of Optimized Hybrid Orbitals 329
11.5.2 Typical Molecules and Their Variationally Optimized Hybrid Orbitals 330 11.5.2.1 Tetrahedral Hybrids in CH4, B and N 330 11.5.2.2 Tetrahedral Hybrids 332 11.5.2.3 Linear Hybrids 333
11.5.3 An Overview of Hybridization Results 333 11.5.3.1 Summary of Hybridization Trends in Classical VB Theory 334 11.6 Description of Multipole Bonding 334 11.6.1 The Bond Multiplicity of C2 335 11.6.2 Multi-Structure VBSCF Calculations of C2 335 11.6.2.1 The Covalent VB-Structure Set 336 11.6.2.2 Adding the Ionic Structures 337
11.6.3 Properties of Quadruply-Bonded Species 342 11.6.3.1 The Resonance-Energy Effect of Doubly-Bonded Structures on Quadruple Bonds 343 11.6.3.2 The Nature of the s-Bonds in C2 343 11.6.3.3 The Exo s-Bonds in C2 344
11.6.4 Some Lessons from the C2 Study 344
11.6.5 The Kinetic Stability of Dioxygen Originates in the Cooperative p-Three- Electron Bonding 345
11.6.6 Outcomes of p-s Interplay in Multiple Bonding 347 11.6.6.1 The p-s Interplay in Benzene: What Factor Determines the D6h Structure? 348 11.6.6.2 The p-s Interplay in Triply-Bonded Molecules 352 11.6.6.2.1 Conclusions and Extensions of the p-s Interplay 353 11.7 Triplet-Pair Bonds (TPB) in Ferromagnetic Metal-Clusters 354
11.7.1 VB Modelling of Bonding in Triplet-Pair Bonds 357
11.7.2 VB Modelling of n+1Mn Clusters 360
11.7.3 Bond Energies of Triplet-Pair Bonds 364
11.7.4 A Summary of No-Pair Bonding 365 11.8 Concluding Remarks 368 11.9 Supporting Information 368 11.9.1 Supplementary Issues 368 11.9.2 VB Structures for C2 370 11.9.3 Pauli Repulsion and VB Structure Counts For Triplet-Pair Bond (TPB) in No-Pair Clusters 377 11.9.3.1 Coinage Metal Clusters 377 11.9.3.2 Alkali Metal Clusters 379
12 Breathing-Orbital Valence Bond: Methods and Applications 391
12.1 Introduction 391
12.2 Methodology 391 12.2.1 From VBSCF to BOVB 392 12.2.2 Static and Dynamic Correlations in Electron-Pair Bonds 393 12.2.3 Odd-Electron Bonds 395 12.2.4 Spin-Unrestricted VBSCF and BOVB Methods 398
12.3 Some Applications of the BOVB Method 398 12.3.1 A Quantitative Definition of Diradical Character 398 12.3.2 When the Diradical Character Rules the Reaction Barriers 400 12.3.3 Fast, Accurate and Insightful Calculations of Challenging Excited States 403 12.3.3.1 The V State of Ethylene 403 12.3.3.2 The Low-Lying Excited States of Ozone and Sulfur Dioxide 406
12.4 Concluding Remarks 410 12.4.1 The Specific Insight Provided by VB Ab Initio Computations 410 12.4.2 Non-Orthogonality: A Handicap or an Opportunity? 411
Epilogue 416
Glossary 418
Index 423
