Introduction to Computational Chemistry

Content: Preface to the First Edition xv    Preface to the Second Edition xix    Preface to the Third Edition xxi    1 Introduction 1    1.1 Fundamental Issues 2    1.2 Describing the System 3    1.3 Fundamental Forces 3    1.4 The Dynamical Equation 5    1.5 Solving the Dynamical Equation 7    1.6 Separation of Variables 8    1.7 Classical Mechanics 11    1.8 Quantum Mechanics 13    1.9 Chemistry 18    References 19    2 Force Field Methods 20    2.1 Introduction 20    2.2 The Force Field Energy 21    2.3 Force Field Parameterization 53    2.4 Differences in Atomistic Force Fields 62    2.5 Water Models 66    2.6 Coarse Grained Force Fields 67    2.7 Computational Considerations 69    2.8 Validation of Force Fields 71    2.9 Practical Considerations 73    2.10 Advantages and Limitations of Force Field Methods 73    2.11 Transition Structure Modeling 74    2.12 Hybrid Force Field Electronic Structure Methods 78    References 82    3 Hartree   Fock Theory 88    3.1 The Adiabatic and Born   Oppenheimer Approximations 90    3.2 Hartree   FockTheory 94    3.3 The Energy of a Slater Determinant 95    3.4 Koopmans    Theorem 100    3.5 The Basis Set Approximation 101    3.6 An Alternative Formulation of the Variational Problem 105    3.7 Restricted and Unrestricted Hartree   Fock 106    3.8 SCF Techniques 108    3.9 Periodic Systems 119    References 121    4 Electron Correlation Methods 124    4.1 Excited Slater Determinants 125    4.2 Configuration Interaction 128    4.3 Illustrating how CI Accounts for Electron Correlation, and the RHF Dissociation Problem 135    4.4 The UHF Dissociation and the Spin Contamination Problem 138    4.5 Size Consistency and Size Extensivity 142    4.6 Multiconfiguration Self-Consistent Field 143    4.7 Multireference Configuration Interaction 148    4.8 Many-Body Perturbation Theory 148    4.9 Coupled Cluster 157    4.10 Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory 162    4.11 Methods Involving the Interelectronic Distance 166    4.12 Techniques for Improving the Computational Efficiency 169    4.13 Summary of Electron Correlation Methods 174    4.14 Excited States 176    4.15 Quantum Monte Carlo Methods 183    References 185    5 Basis Sets 188    5.1 Slater- and Gaussian-Type Orbitals 189    5.2 Classification of Basis Sets 190    5.3 Construction of Basis Sets 194    5.4 Examples of Standard Basis Sets 200    5.5 Plane Wave Basis Functions 208    5.6 Grid and Wavelet Basis Sets 210    5.7 Fitting Basis Sets 211    5.8 Computational Issues 211    5.9 Basis Set Extrapolation 212    5.10 Composite Extrapolation Procedures 215    5.11 Isogyric and Isodesmic Reactions 222    5.12 Effective Core Potentials 223    5.13 Basis Set Superposition and Incompleteness Errors 226    References 228    6 Density Functional Methods 233    6.1 Orbital-Free Density Functional Theory 234    6.2 Kohn   Sham Theory 235    6.3 Reduced Density Matrix and Density Cumulant Methods 237    6.4 Exchange and Correlation Holes 241    6.5 Exchange   Correlation Functionals 244    6.6 Performance of Density Functional Methods 258    6.7 Computational Considerations 260    6.8 Differences between Density Functional Theory and Hartree-Fock 262    6.9 Time-Dependent Density Functional Theory (TDDFT) 263    6.10 Ensemble Density Functional Theory 268    6.11 Density Functional Theory Problems 269    6.12 Final Considerations 269    References 270    7 Semi-empirical Methods 275    7.1 Neglect of Diatomic Differential Overlap (NDDO) Approximation 276    7.2 Intermediate Neglect of Differential Overlap (INDO) Approximation 277    7.3 Complete Neglect of Differential Overlap (CNDO) Approximation 277    7.4 Parameterization 278    7.5 Huckel Theory 283    7.6 Tight-Binding Density Functional Theory 285    7.7 Performance of Semi-empirical Methods 287    7.8 Advantages and Limitations of Semi-empirical Methods 289    References 290    8 Valence Bond Methods 291    8.1 Classical Valence Bond Theory 292    8.2 Spin-Coupled Valence Bond Theory 293    8.3 Generalized Valence Bond Theory 297    References 298    9 Relativistic Methods 299    9.1 The Dirac Equation 300    9.2 Connections between the Dirac and Schrodinger Equations 302    9.3 Many-Particle Systems 306    9.4 Four-Component Calculations 309    9.5 Two-Component Calculations 310    9.6 Relativistic Effects 313    References 315    10 Wave Function Analysis 317    10.1 Population Analysis Based on Basis Functions 317    10.2 Population Analysis Based on the Electrostatic Potential 320    10.3 Population Analysis Based on the Electron Density 323    10.4 Localized Orbitals 329    10.5 Natural Orbitals 333    10.6 Computational Considerations 337    10.7 Examples 338    References 339    11 Molecular Properties 341    11.1 Examples of Molecular Properties 343    11.2 Perturbation Methods 347    11.3 Derivative Techniques 349    11.4 Response and Propagator Methods 351    11.5 Lagrangian Techniques 351    11.6 Wave Function Response 353    11.7 Electric Field Perturbation 357    11.8 Magnetic Field Perturbation 358    11.9 Geometry Perturbations 367    11.10 Time-Dependent Perturbations 372    11.11 Rotational and Vibrational Corrections 377    11.12 Environmental Effects 378    11.13 Relativistic Corrections 378    References 378    12 Illustrating the Concepts 380    12.1 Geometry Convergence 380    12.2 Total Energy Convergence 383    12.3 Dipole Moment Convergence 385    12.4 Vibrational Frequency Convergence 386    12.5 Bond Dissociation Curves 389    12.6 Angle Bending Curves 394    12.7 Problematic Systems 396    12.8 Relative Energies of C4H6 Isomers 399    References 402    13 Optimization Techniques 404    13.1 Optimizing Quadratic Functions 405    13.2 Optimizing General Functions: Finding Minima 407    13.3 Choice of Coordinates 415    13.4 Optimizing General Functions: Finding Saddle Points (Transition Structures) 418    13.5 Constrained Optimizations 431    13.6 Global Minimizations and Sampling 433    13.7 Molecular Docking 440    13.8 Intrinsic Reaction Coordinate Methods 441    References 444    14 Statistical Mechanics and Transition State Theory 447    14.1 Transition State Theory 447    14.2 Rice   Ramsperger   Kassel   Marcus Theory 450    14.3 Dynamical Effects 451    14.4 StatisticalMechanics 452    14.5 The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation 454    14.6 Condensed Phases 464    References 468    15 Simulation Techniques 469    15.1 Monte Carlo Methods 472    15.2 Time-Dependent Methods 474    15.3 Periodic Boundary Conditions 491    15.4 Extracting Information from Simulations 494    15.5 Free Energy Methods 499    15.6 Solvation Models 502    References 511    16 Qualitative Theories 515    16.1 Frontier Molecular Orbital Theory 515    16.2 Concepts from Density Functional Theory 519    16.3 Qualitative Molecular Orbital Theory 522    16.4 Energy Decomposition Analyses 524    16.5 Orbital Correlation Diagrams: TheWoodward   Hoffmann Rules 526    16.6 The Bell   Evans   Polanyi Principle/Hammond Postulate/Marcus Theory 534    16.7 More O   Ferrall   Jencks Diagrams 538    References 541    17 Mathematical Methods 543    17.1 Numbers, Vectors, Matrices and Tensors 543    17.2 Change of Coordinate System 549    17.3 Coordinates, Functions, Functionals, Operators and Superoperators 560    17.3.1 Differential Operators 562    17.4 Normalization, Orthogonalization and Projection 563    17.5 Differential Equations 565    17.6 Approximating Functions 568    17.7 Fourier and Laplace Transformations 577    17.8 Surfaces 577    References 580    18 Statistics and QSAR 581    18.1 Introduction 581    18.2 Elementary Statistical Measures 583    18.3 Correlation between Two Sets of Data 585    18.4 Correlation between Many Sets of Data 588    18.5 Quantitative Structure   Activity Relationships (QSAR) 595    18.6 Non-linear Correlation Methods 597    18.7 Clustering Methods 598    References 604    19 Concluding Remarks 605    Appendix A 608    Notation 608    Appendix B 614    The Variational Principle 614    The Hohenberg   Kohn Theorems 615    The Adiabatic Connection Formula 616    Reference 617    Appendix C 618    Atomic Units 618    Appendix D 619    Z Matrix Construction 619    Appendix E 627    First and Second Quantization 627    References 628    Index 629