Essentials of Computational Chemistry

Christopher Cramer, Professor of Computational Chemistry Department of Chemistry, University of Minnesota,Minneapolis, USA

• Preface to the First Edition xvPreface to the Second Edition xixAcknowledgments xxi1 What are Theory, Computation, and Modeling? 11.1 Definition of Terms 11.2 Quantum Mechanics 41.3 Computable Quantities 51.4 Cost and Efficiency 111.5 Note on Units 152 Molecular Mechanics 172.1 History and Fundamental Assumptions 172.2 Potential Energy Functional Forms 192.3 Force-field Energies and Thermodynamics 392.4 Geometry Optimization 402.5 Menagerie of Modern Force Fields 502.6 Force Fields and Docking 622.7 Case Study: (2R∗,4S∗)-1-Hydroxy-2,4-dimethylhex-5-ene 643 Simulations of Molecular Ensembles 693.1 Relationship Between MM Optima and Real Systems 693.2 Phase Space and Trajectories 703.3 Molecular Dynamics 723.4 Monte Carlo 803.5 Ensemble and Dynamical Property Examples 823.6 Key Details in Formalism 883.7 Force Field Performance in Simulations 983.8 Case Study: Silica Sodalite 994 Foundations of Molecular Orbital Theory 1054.1 Quantum Mechanics and the Wave Function 1054.2 The Hamiltonian Operator 1064.3 Construction of Trial Wave Functions 1114.4 H¨uckel Theory 1154.5 Many-electron Wave Functions 1195 Semiempirical Implementations of Molecular Orbital Theory 1315.1 Semiempirical Philosophy 1315.2 Extended H¨uckel Theory 1345.3 CNDO Formalism 1365.4 INDO Formalism 1395.5 Basic NDDO Formalism 1435.6 General Performance Overview of Basic NDDO Models 1475.7 Ongoing Developments in Semiempirical MO Theory 1525.8 Case Study: Asymmetric Alkylation of Benzaldehyde 1596 Ab Initio Implementations of Hartree–Fock Molecular Orbital Theory 1656.1 Ab Initio Philosophy 1656.2 Basis Sets 1666.3 Key Technical and Practical Points of Hartree–Fock Theory 1806.4 General Performance Overview of Ab Initio HF Theory 1926.5 Case Study: Polymerization of 4-Substituted Aromatic Enynes 1997 Including Electron Correlation in Molecular Orbital Theory 2037.1 Dynamical vs. Non-dynamical Electron Correlation 2037.2 Multiconfiguration Self-Consistent Field Theory 2057.3 Configuration Interaction 2117.4 Perturbation Theory 2167.5 Coupled-cluster Theory 2247.6 Practical Issues in Application 2277.7 Parameterized Methods 2377.8 Case Study: Ethylenedione Radical Anion 2448 Density Functional Theory 2498.1 Theoretical Motivation 2498.2 Rigorous Foundation 2528.2.1 The Hohenberg–Kohn Existence Theorem 2528.3 Kohn–Sham Self-consistent Field Methodology 2558.4 Exchange-correlation Functionals 2578.5 Advantages and Disadvantages of DFT Compared to MO Theory 2718.6 General Performance Overview of DFT 2808.7 Case Study: Transition-Metal Catalyzed Carbonylation of Methanol 2999 Charge Distribution and Spectroscopic Properties 3059.1 Properties Related to Charge Distribution 3059.2 Ionization Potentials and Electron Affinities 3309.3 Spectroscopy of Nuclear Motion 3319.4 NMR Spectral Properties 3449.5 Case Study: Matrix Isolation of Perfluorinated p-Benzyne 34910 Thermodynamic Properties 35510.1 Microscopic–macroscopic Connection 35510.2 Zero-point Vibrational Energy 35610.3 Ensemble Properties and Basic Statistical Mechanics 35710.4 Standard-state Heats and Free Energies of Formation and Reaction 36610.5 Technical Caveats 37510.6 Case Study: Heat of Formation of H2NOH 38111 Implicit Models for Condensed Phases 38511.1 Condensed-phase Effects on Structure and Reactivity 38511.2 Electrostatic Interactions with a Continuum 39311.3 Continuum Models for Non-electrostatic Interactions 40611.4 Strengths and Weaknesses of Continuum Solvation Models 41011.5 Case Study: Aqueous Reductive Dechlorination of Hexachloroethane 42212 Explicit Models for Condensed Phases 42912.1 Motivation 42912.2 Computing Free-energy Differences 42912.3 Other Thermodynamic Properties 44412.4 Solvent Models 44512.5 Relative Merits of Explicit and Implicit Solvent Models 44812.6 Case Study: Binding of Biotin Analogs to Avidin 45213 Hybrid Quantal/Classical Models 45713.1 Motivation 45713.2 Boundaries Through Space 45813.3 Boundaries Through Bonds 46713.4 Empirical Valence Bond Methods 47713.5 Case Study: Catalytic Mechanism of Yeast Enolase 48214 Excited Electronic States 48714.1 Determinantal/Configurational Representation of Excited States 48714.2 Singly Excited States 49214.3 General Excited State Methods 49914.4 Sum and Projection Methods 50414.5 Transition Probabilities 50714.6 Solvatochromism 51114.7 Case Study: Organic Light Emitting Diode Alq3 51315 Adiabatic Reaction Dynamics 51915.1 Reaction Kinetics and Rate Constants 51915.2 Reaction Paths and Transition States 52215.3 Transition-state Theory 52415.4 Condensed-phase Dynamics 53815.5 Non-adiabatic Dynamics 53915.6 Case Study: Isomerization of Propylene Oxide 544Bibliography and Suggested Additional Reading 546References 546Appendix A Acronym Glossary 549Appendix B Symmetry and Group Theory 557B.1 Symmetry Elements 557B.2 Molecular Point Groups and Irreducible Representations 559B.3 Assigning Electronic State Symmetries 561B.4 Symmetry in the Evaluation of Integrals and Partition Functions 562Appendix C Spin Algebra 565C.1 Spin Operators 565C.2 Pure- and Mixed-spin Wave Functions 566C.3 UHF Wave Functions 571C.4 Spin Projection/Annihilation 571Appendix D Orbital Localization 575D.1 Orbitals as Empirical Constructs 575D.2 Natural Bond Orbital Analysis 578References 579Index 581