Preface to the First Edition xv
Preface to the Second Edition xix
Acknowledgments xxi

1 What are Theory, Computation, and Modeling? 1

1.1 Definition of Terms 1

1.2 Quantum Mechanics 4

1.3 Computable Quantities 5

1.4 Cost and Efficiency 11

1.5 Note on Units 15

2 Molecular Mechanics 17

2.1 History and Fundamental Assumptions 17

2.2 Potential Energy Functional Forms 19

2.3 Force-field Energies and Thermodynamics 39

2.4 Geometry Optimization 40

2.5 Menagerie of Modern Force Fields 50

2.6 Force Fields and Docking 62

2.7 Case Study: (2R,4S)-1-Hydroxy-2,4-dimethylhex-5-ene 64

3 Simulations of Molecular Ensembles 69

3.1 Relationship Between MM Optima and Real Systems 69

3.2 Phase Space and Trajectories 70

3.3 Molecular Dynamics 72

3.4 Monte Carlo 80

3.5 Ensemble and Dynamical Property Examples 82

3.6 Key Details in Formalism 88

3.7 Force Field Performance in Simulations 98

3.8 Case Study: Silica Sodalite 99

4 Foundations of Molecular Orbital Theory 105

4.1 Quantum Mechanics and the Wave Function 105

4.2 The Hamiltonian Operator 106

4.3 Construction of Trial Wave Functions 111

4.4 Huckel Theory 115

4.5 Many-electron Wave Functions 119

5 Semiempirical Implementations of Molecular Orbital Theory 131

5.1 Semiempirical Philosophy 131

5.2 Extended Huckel Theory 134

5.3 CNDO Formalism 136

5.4 INDO Formalism 139

5.5 Basic NDDO Formalism 143

5.6 General Performance Overview of Basic NDDO Models 147

5.7 Ongoing Developments in Semiempirical MO Theory 152

5.8 Case Study: Asymmetric Alkylation of Benzaldehyde 159

6 Ab Initio Implementations of Hartree-Fock Molecular Orbital Theory 165

6.1 Ab Initio Philosophy 165

6.2 Basis Sets 166

6.3 Key Technical and Practical Points of Hartree-Fock Theory 180

6.4 General Performance Overview of Ab Initio HF Theory 192

6.5 Case Study: Polymerization of 4-Substituted Aromatic Enynes 199

7 Including Electron Correlation in Molecular Orbital Theory 203

7.1 Dynamical vs. Non-dynamical Electron Correlation 203

7.2 Multiconfiguration Self-Consistent Field Theory 205

7.3 Configuration Interaction 211

7.4 Perturbation Theory 216

7.5 Coupled-cluster Theory 224

7.6 Practical Issues in Application 227

7.7 Parameterized Methods 237

7.8 Case Study: Ethylenedione Radical Anion 244

8 Density Functional Theory 249

8.1 Theoretical Motivation 249

8.2 Rigorous Foundation 252

8.2.1 The Hohenberg-Kohn Existence Theorem 252

8.3 Kohn-Sham Self-consistent Field Methodology 255

8.4 Exchange-correlation Functionals 257

8.5 Advantages and Disadvantages of DFT Compared to MO Theory 271

8.6 General Performance Overview of DFT 280

8.7 Case Study: Transition-Metal Catalyzed Carbonylation of Methanol 299

9 Charge Distribution and Spectroscopic Properties 305

9.1 Properties Related to Charge Distribution 305

9.2 Ionization Potentials and Electron Affinities 330

9.3 Spectroscopy of Nuclear Motion 331

9.4 NMR Spectral Properties 344

9.5 Case Study: Matrix Isolation of Perfluorinated p-Benzyne 349

10 Thermodynamic Properties 355

10.1 Microscopic-macroscopic Connection 355

10.2 Zero-point Vibrational Energy 356

10.3 Ensemble Properties and Basic Statistical Mechanics 357

10.4 Standard-state Heats and Free Energies of Formation and Reaction 366

10.5 Technical Caveats 375

10.6 Case Study: Heat of Formation of H2NOH 381

11 Implicit Models for Condensed Phases 385

11.1 Condensed-phase Effects on Structure and Reactivity 385

11.2 Electrostatic Interactions with a Continuum 393

11.3 Continuum Models for Non-electrostatic Interactions 406

11.4 Strengths and Weaknesses of Continuum Solvation Models 410

11.5 Case Study: Aqueous Reductive Dechlorination of Hexachloroethane 422

12 Explicit Models for Condensed Phases 429

12.1 Motivation 429

12.2 Computing Free-energy Differences 429

12.3 Other Thermodynamic Properties 444

12.4 Solvent Models 445

12.5 Relative Merits of Explicit and Implicit Solvent Models 448

12.6 Case Study: Binding of Biotin Analogs to Avidin 452

13 Hybrid Quantal/Classical Models 457

13.1 Motivation 457

13.2 Boundaries Through Space 458

13.3 Boundaries Through Bonds 467

13.4 Empirical Valence Bond Methods 477

13.5 Case Study: Catalytic Mechanism of Yeast Enolase 482

14 Excited Electronic States 487

14.1 Determinantal/Configurational Representation of Excited States 487

14.2 Singly Excited States 492

14.3 General Excited State Methods 499

14.4 Sum and Projection Methods 504

14.5 Transition Probabilities 507

14.6 Solvatochromism 511

14.7 Case Study: Organic Light Emitting Diode Alq3 513

15 Adiabatic Reaction Dynamics 519

15.1 Reaction Kinetics and Rate Constants 519

15.2 Reaction Paths and Transition States 522

15.3 Transition-state Theory 524

15.4 Condensed-phase Dynamics 538

15.5 Non-adiabatic Dynamics 539

15.6 Case Study: Isomerization of Propylene Oxide 544

Bibliography and Suggested Additional Reading 546

References 546

Appendix A Acronym Glossary 549

Appendix B Symmetry and Group Theory 557

B.1 Symmetry Elements 557

B.2 Molecular Point Groups and Irreducible Representations 559

B.3 Assigning Electronic State Symmetries 561

B.4 Symmetry in the Evaluation of Integrals and Partition Functions 562

Appendix C Spin Algebra 565

C.1 Spin Operators 565

C.2 Pure- and Mixed-spin Wave Functions 566

C.3 UHF Wave Functions 571

C.4 Spin Projection/Annihilation 571

Appendix D Orbital Localization 575

D.1 Orbitals as Empirical Constructs 575

D.2 Natural Bond Orbital Analysis 578

References 579

Index 581