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 51.3.1 Structure 51.3.2 Potential Energy Surfaces 61.3.3 Chemical Properties 101.4 Cost and Efficiency 111.4.1 Intrinsic Value 111.4.2 Hardware and Software 121.4.3 Algorithms 141.5 Note on Units 15Bibliography and Suggested Additional Reading 15References 162 Molecular Mechanics 172.1 History and Fundamental Assumptions 172.2 Potential Energy Functional Forms 192.2.1 Bond Stretching 192.2.2 Valence Angle Bending 212.2.3 Torsions 222.2.4 van der Waals Interactions 272.2.5 Electrostatic Interactions 302.2.6 Cross Terms and Additional Non-bonded Terms 342.2.7 Parameterization Strategies 362.3 Force-field Energies and Thermodynamics 392.4 Geometry Optimization 402.4.1 Optimization Algorithms 412.4.2 Optimization Aspects Specific to Force Fields 462.5 Menagerie of Modern Force Fields 502.5.1 Available Force Fields 502.5.2 Validation 592.6 Force Fields and Docking 622.7 Case Study: (2R∗,4S∗)-1-Hydroxy-2,4-dimethylhex-5-ene 64Bibliography and Suggested Additional Reading 66References 673 Simulations of Molecular Ensembles 693.1 Relationship Between MM Optima and Real Systems 693.2 Phase Space and Trajectories 703.2.1 Properties as Ensemble Averages 703.2.2 Properties as Time Averages of Trajectories 713.3 Molecular Dynamics 723.3.1 Harmonic Oscillator Trajectories 723.3.2 Non-analytical Systems 743.3.3 Practical Issues in Propagation 773.3.4 Stochastic Dynamics 793.4 Monte Carlo 803.4.1 Manipulation of Phase-space Integrals 803.4.2 Metropolis Sampling 813.5 Ensemble and Dynamical Property Examples 823.6 Key Details in Formalism 883.6.1 Cutoffs and Boundary Conditions 883.6.2 Polarization 903.6.3 Control of System Variables 913.6.4 Simulation Convergence 933.6.5 The Multiple Minima Problem 963.7 Force Field Performance in Simulations 983.8 Case Study: Silica Sodalite 99Bibliography and Suggested Additional Reading 101References 1024 Foundations of Molecular Orbital Theory 1054.1 Quantum Mechanics and the Wave Function 1054.2 The Hamiltonian Operator 1064.2.1 General Features 1064.2.2 The Variational Principle 1084.2.3 The Born–Oppenheimer Approximation 1104.3 Construction of Trial Wave Functions 1114.3.1 The LCAO Basis Set Approach 1114.3.2 The Secular Equation 1134.4 H¨uckel Theory 1154.4.1 Fundamental Principles 1154.4.2 Application to the Allyl System 1164.5 Many-electron Wave Functions 1194.5.1 Hartree-product Wave Functions 1204.5.2 The Hartree Hamiltonian 1214.5.3 Electron Spin and Antisymmetry 1224.5.4 Slater Determinants 1244.5.5 The Hartree-Fock Self-consistent Field Method 126Bibliography and Suggested Additional Reading 129References 1305 Semiempirical Implementations of Molecular Orbital Theory 1315.1 Semiempirical Philosophy 1315.1.1 Chemically Virtuous Approximations 1315.1.2 Analytic Derivatives 1335.2 Extended H¨uckel Theory 1345.3 CNDO Formalism 1365.4 INDO Formalism 1395.4.1 INDO and INDO/S 1395.4.2 MINDO/3 and SINDO1 1415.5 Basic NDDO Formalism 1435.5.1 MNDO 1435.5.2 AM1 1455.5.3 PM3 1465.6 General Performance Overview of Basic NDDO Models 1475.6.1 Energetics 1475.6.2 Geometries 1505.6.3 Charge Distributions 1515.7 Ongoing Developments in Semiempirical MO Theory 1525.7.1 Use of Semiempirical Properties in SAR 1525.7.2 d Orbitals in NDDO Models 1535.7.3 SRP Models 1555.7.4 Linear Scaling 1575.7.5 Other Changes in Functional Form 1575.8 Case Study: Asymmetric Alkylation of Benzaldehyde 159Bibliography and Suggested Additional Reading 162References 1636 Ab Initio Implementations of Hartree–Fock Molecular Orbital Theory 1656.1 Ab Initio Philosophy 1656.2 Basis Sets 1666.2.1 Functional Forms 1676.2.2 Contracted Gaussian Functions 1686.2.3 Single-ζ , Multiple-ζ , and Split-Valence 1706.2.4 Polarization Functions 1736.2.5 Diffuse Functions 1766.2.6 The HF Limit 1766.2.7 Effective Core Potentials 1786.2.8 Sources 1806.3 Key Technical and Practical Points of Hartree–Fock Theory 1806.3.1 SCF Convergence 1816.3.2 Symmetry 1826.3.3 Open-shell Systems 1886.3.4 Efficiency of Implementation and Use 1906.4 General Performance Overview of Ab Initio HF Theory 1926.4.1 Energetics 1926.4.2 Geometries 1966.4.3 Charge Distributions 1986.5 Case Study: Polymerization of 4-Substituted Aromatic Enynes 199Bibliography and Suggested Additional Reading 201References 2017 Including Electron Correlation in Molecular Orbital Theory 2037.1 Dynamical vs. Non-dynamical Electron Correlation 2037.2 Multiconfiguration Self-Consistent Field Theory 2057.2.1 Conceptual Basis 2057.2.2 Active Space Specification 2077.2.3 Full Configuration Interaction 2117.3 Configuration Interaction 2117.3.1 Single-determinant Reference 2117.3.2 Multireference 2167.4 Perturbation Theory 2167.4.1 General Principles 2167.4.2 Single-reference 2197.4.3 Multireference 2237.4.4 First-order Perturbation Theory for Some Relativistic Effects 2237.5 Coupled-cluster Theory 2247.6 Practical Issues in Application 2277.6.1 Basis Set Convergence 2277.6.2 Sensitivity to Reference Wave Function 2307.6.3 Price/Performance Summary 2357.7 Parameterized Methods 2377.7.1 Scaling Correlation Energies 2387.7.2 Extrapolation 2397.7.3 Multilevel Methods 2397.8 Case Study: Ethylenedione Radical Anion 244Bibliography and Suggested Additional Reading 246References 2478 Density Functional Theory 2498.1 Theoretical Motivation 2498.1.1 Philosophy 2498.1.2 Early Approximations 2508.2 Rigorous Foundation 2528.2.1 The Hohenberg–Kohn Existence Theorem 2528.2.2 The Hohenberg–Kohn Variational Theorem 2548.3 Kohn–Sham Self-consistent Field Methodology 2558.4 Exchange-correlation Functionals 2578.4.1 Local Density Approximation 2588.4.2 Density Gradient and Kinetic Energy Density Corrections 2638.4.3 Adiabatic Connection Methods 2648.4.4 Semiempirical DFT 2688.5 Advantages and Disadvantages of DFT Compared to MO Theory 2718.5.1 Densities vs. Wave Functions 2718.5.2 Computational Efficiency 2738.5.3 Limitations of the KS Formalism 2748.5.4 Systematic Improvability 2788.5.5 Worst-case Scenarios 2788.6 General Performance Overview of DFT 2808.6.1 Energetics 2808.6.2 Geometries 2918.6.3 Charge Distributions 2948.7 Case Study: Transition-Metal Catalyzed Carbonylation of Methanol 299Bibliography and Suggested Additional Reading 300References 3019 Charge Distribution and Spectroscopic Properties 3059.1 Properties Related to Charge Distribution 3059.1.1 Electric Multipole Moments 3059.1.2 Molecular Electrostatic Potential 3089.1.3 Partial Atomic Charges 3099.1.4 Total Spin 3249.1.5 Polarizability and Hyperpolarizability 3259.1.6 ESR Hyperfine Coupling Constants 3279.2 Ionization Potentials and Electron Affinities 3309.3 Spectroscopy of Nuclear Motion 3319.3.1 Rotational 3329.3.2 Vibrational 3349.4 NMR Spectral Properties 3449.4.1 Technical Issues 3449.4.2 Chemical Shifts and Spin–spin Coupling Constants 3459.5 Case Study: Matrix Isolation of Perfluorinated p-Benzyne 349Bibliography and Suggested Additional Reading 351References 35110 Thermodynamic Properties 35510.1 Microscopic–macroscopic Connection 35510.2 Zero-point Vibrational Energy 35610.3 Ensemble Properties and Basic Statistical Mechanics 35710.3.1 Ideal Gas Assumption 35810.3.2 Separability of Energy Components 35910.3.3 Molecular Electronic Partition Function 36010.3.4 Molecular Translational Partition Function 36110.3.5 Molecular Rotational Partition Function 36210.3.6 Molecular Vibrational Partition Function 36410.4 Standard-state Heats and Free Energies of Formation and Reaction 36610.4.1 Direct Computation 36710.4.2 Parametric Improvement 37010.4.3 Isodesmic Equations 37210.5 Technical Caveats 37510.5.1 Semiempirical Heats of Formation 37510.5.2 Low-frequency Motions 37510.5.3 Equilibrium Populations over Multiple Minima 37710.5.4 Standard-state Conversions 37810.5.5 Standard-state Free Energies, Equilibrium Constants, and Concentrations 37910.6 Case Study: Heat of Formation of H2NOH 381Bibliography and Suggested Additional Reading 383References 38311 Implicit Models for Condensed Phases 38511.1 Condensed-phase Effects on Structure and Reactivity 38511.1.1 Free Energy of Transfer and Its Physical Components 38611.1.2 Solvation as It Affects Potential Energy Surfaces 38911.2 Electrostatic Interactions with a Continuum 39311.2.1 The Poisson Equation 39411.2.2 Generalized Born 40211.2.3 Conductor-like Screening Model 40411.3 Continuum Models for Non-electrostatic Interactions 40611.3.1 Specific Component Models 40611.3.2 Atomic Surface Tensions 40711.4 Strengths and Weaknesses of Continuum Solvation Models 41011.4.1 General Performance for Solvation Free Energies 41011.4.2 Partitioning 41611.4.3 Non-isotropic Media 41611.4.4 Potentials of Mean Force and Solvent Structure 41911.4.5 Molecular Dynamics with Implicit Solvent 42011.4.6 Equilibrium vs. Non-equilibrium Solvation 42111.5 Case Study: Aqueous Reductive Dechlorination of Hexachloroethane 422Bibliography and Suggested Additional Reading 424References 42512 Explicit Models for Condensed Phases 42912.1 Motivation 42912.2 Computing Free-energy Differences 42912.2.1 Raw Differences 43012.2.2 Free-energy Perturbation 43212.2.3 Slow Growth and Thermodynamic Integration 43512.2.4 Free-energy Cycles 43712.2.5 Potentials of Mean Force 43912.2.6 Technical Issues and Error Analysis 44312.3 Other Thermodynamic Properties 44412.4 Solvent Models 44512.4.1 Classical Models 44512.4.2 Quantal Models 44712.5 Relative Merits of Explicit and Implicit Solvent Models 44812.5.1 Analysis of Solvation Shell Structure and Energetics 44812.5.2 Speed/Efficiency 45012.5.3 Non-equilibrium Solvation 45012.5.4 Mixed Explicit/Implicit Models 45112.6 Case Study: Binding of Biotin Analogs to Avidin 452Bibliography and Suggested Additional Reading 454References 45513 Hybrid Quantal/Classical Models 45713.1 Motivation 45713.2 Boundaries Through Space 45813.2.1 Unpolarized Interactions 45913.2.2 Polarized QM/Unpolarized MM 46113.2.3 Fully Polarized Interactions 46613.3 Boundaries Through Bonds 46713.3.1 Linear Combinations of Model Compounds 46713.3.2 Link Atoms 47313.3.3 Frozen Orbitals 47513.4 Empirical Valence Bond Methods 47713.4.1 Potential Energy Surfaces 47813.4.2 Following Reaction Paths 48013.4.3 Generalization to QM/MM 48113.5 Case Study: Catalytic Mechanism of Yeast Enolase 482Bibliography and Suggested Additional Reading 484References 48514 Excited Electronic States 48714.1 Determinantal/Configurational Representation of Excited States 48714.2 Singly Excited States 49214.2.1 SCF Applicability 49314.2.2 CI Singles 49614.2.3 Rydberg States 49814.3 General Excited State Methods 49914.3.1 Higher Roots in MCSCF and CI Calculations 49914.3.2 Propagator Methods and Time-dependent DFT 50114.4 Sum and Projection Methods 50414.5 Transition Probabilities 50714.6 Solvatochromism 51114.7 Case Study: Organic Light Emitting Diode Alq3 513Bibliography and Suggested Additional Reading 515References 51615 Adiabatic Reaction Dynamics 51915.1 Reaction Kinetics and Rate Constants 51915.1.1 Unimolecular Reactions 52015.1.2 Bimolecular Reactions 52115.2 Reaction Paths and Transition States 52215.3 Transition-state Theory 52415.3.1 Canonical Equation 52415.3.2 Variational Transition-state Theory 53115.3.3 Quantum Effects on the Rate Constant 53315.4 Condensed-phase Dynamics 53815.5 Non-adiabatic Dynamics 53915.5.1 General Surface Crossings 53915.5.2 Marcus Theory 54115.6 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 571Reference 574Appendix D Orbital Localization 575D.1 Orbitals as Empirical Constructs 575D.2 Natural Bond Orbital Analysis 578References 579Index 581