{"product_id":"introduction-to-computational-chemistry-9781118825990","title":"Introduction to Computational Chemistry","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIntroduction to Computational Chemistry 3rd Edition provides a comprehensive account of the fundamental principles underlying different computational methods.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface to the First Edition xv\u003c\/p\u003e \u003cp\u003ePreface to the Second Edition xix\u003c\/p\u003e \u003cp\u003ePreface to the Third Edition xxi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Fundamental Issues 2\u003c\/p\u003e \u003cp\u003e1.2 Describing the System 3\u003c\/p\u003e \u003cp\u003e1.3 Fundamental Forces 3\u003c\/p\u003e \u003cp\u003e1.4 The Dynamical Equation 5\u003c\/p\u003e \u003cp\u003e1.5 Solving the Dynamical Equation 7\u003c\/p\u003e \u003cp\u003e1.6 Separation of Variables 8\u003c\/p\u003e \u003cp\u003e1.6.1 Separating Space and Time Variables 9\u003c\/p\u003e \u003cp\u003e1.6.2 Separating Nuclear and Electronic Variables 9\u003c\/p\u003e \u003cp\u003e1.6.3 Separating Variables in General 10\u003c\/p\u003e \u003cp\u003e1.7 Classical Mechanics 11\u003c\/p\u003e \u003cp\u003e1.7.1 The Sun–Earth System 11\u003c\/p\u003e \u003cp\u003e1.7.2 The Solar System 12\u003c\/p\u003e \u003cp\u003e1.8 Quantum Mechanics 13\u003c\/p\u003e \u003cp\u003e1.8.1 A Hydrogen-Like Atom 13\u003c\/p\u003e \u003cp\u003e1.8.2 The Helium Atom 16\u003c\/p\u003e \u003cp\u003e1.9 Chemistry 18\u003c\/p\u003e \u003cp\u003eReferences 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Force Field Methods 20\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 20\u003c\/p\u003e \u003cp\u003e2.2 The Force Field Energy 21\u003c\/p\u003e \u003cp\u003e2.2.1 The Stretch Energy 23\u003c\/p\u003e \u003cp\u003e2.2.2 The Bending Energy 25\u003c\/p\u003e \u003cp\u003e2.2.3 The Out-of-Plane Bending Energy 28\u003c\/p\u003e \u003cp\u003e2.2.4 The Torsional Energy 28\u003c\/p\u003e \u003cp\u003e2.2.5 The van der Waals energy 32\u003c\/p\u003e \u003cp\u003e2.2.6 The Electrostatic Energy: Atomic Charges 37\u003c\/p\u003e \u003cp\u003e2.2.7 The Electrostatic Energy: Atomic Multipoles 41\u003c\/p\u003e \u003cp\u003e2.2.8 The Electrostatic Energy: Polarizability and Charge Penetration Effects 42\u003c\/p\u003e \u003cp\u003e2.2.9 Cross Terms 48\u003c\/p\u003e \u003cp\u003e2.2.10 Small Rings and Conjugated Systems 49\u003c\/p\u003e \u003cp\u003e2.2.11 Comparing Energies of Structurally Different Molecules 51\u003c\/p\u003e \u003cp\u003e2.3 Force Field Parameterization 53\u003c\/p\u003e \u003cp\u003e2.3.1 Parameter Reductions in Force Fields 58\u003c\/p\u003e \u003cp\u003e2.3.2 Force Fields for Metal Coordination Compounds 59\u003c\/p\u003e \u003cp\u003e2.3.3 Universal Force Fields 62\u003c\/p\u003e \u003cp\u003e2.4 Differences in Atomistic Force Fields 62\u003c\/p\u003e \u003cp\u003e2.5 Water Models 66\u003c\/p\u003e \u003cp\u003e2.6 Coarse Grained Force Fields 67\u003c\/p\u003e \u003cp\u003e2.7 Computational Considerations 69\u003c\/p\u003e \u003cp\u003e2.8 Validation of Force Fields 71\u003c\/p\u003e \u003cp\u003e2.9 Practical Considerations 73\u003c\/p\u003e \u003cp\u003e2.10 Advantages and Limitations of Force Field Methods 73\u003c\/p\u003e \u003cp\u003e2.11 Transition Structure Modeling 74\u003c\/p\u003e \u003cp\u003e2.11.1 Modeling the TS as a Minimum Energy Structure 74\u003c\/p\u003e \u003cp\u003e2.11.2 Modeling the TS as a Minimum Energy Structure on the Reactant\/Product Energy Seam 75\u003c\/p\u003e \u003cp\u003e2.11.3 Modeling the Reactive Energy Surface by Interacting Force Field Functions 76\u003c\/p\u003e \u003cp\u003e2.11.4 Reactive Force Fields 77\u003c\/p\u003e \u003cp\u003e2.12 Hybrid Force Field Electronic Structure Methods 78\u003c\/p\u003e \u003cp\u003eReferences 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Hartree–Fock Theory 88\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Adiabatic and Born–Oppenheimer Approximations 90\u003c\/p\u003e \u003cp\u003e3.2 Hartree–Fock Theory 94\u003c\/p\u003e \u003cp\u003e3.3 The Energy of a Slater Determinant 95\u003c\/p\u003e \u003cp\u003e3.4 Koopmans’ Theorem 100\u003c\/p\u003e \u003cp\u003e3.5 The Basis Set Approximation 101\u003c\/p\u003e \u003cp\u003e3.6 An Alternative Formulation of the Variational Problem 105\u003c\/p\u003e \u003cp\u003e3.7 Restricted and Unrestricted Hartree–Fock 106\u003c\/p\u003e \u003cp\u003e3.8 SCF Techniques 108\u003c\/p\u003e \u003cp\u003e3.8.1 SCF Convergence 108\u003c\/p\u003e \u003cp\u003e3.8.2 Use of Symmetry 110\u003c\/p\u003e \u003cp\u003e3.8.3 Ensuring that the HF Energy Is a Minimum, and the Correct Minimum 111\u003c\/p\u003e \u003cp\u003e3.8.4 Initial Guess Orbitals 113\u003c\/p\u003e \u003cp\u003e3.8.5 Direct SCF 113\u003c\/p\u003e \u003cp\u003e3.8.6 Reduced Scaling Techniques 116\u003c\/p\u003e \u003cp\u003e3.8.7 Reduced Prefactor Methods 117\u003c\/p\u003e \u003cp\u003e3.9 Periodic Systems 119\u003c\/p\u003e \u003cp\u003eReferences 121\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Electron Correlation Methods 124\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Excited Slater Determinants 125\u003c\/p\u003e \u003cp\u003e4.2 Configuration Interaction 128\u003c\/p\u003e \u003cp\u003e4.2.1 ci Matrix Elements 129\u003c\/p\u003e \u003cp\u003e4.2.2 Size of the CI Matrix 131\u003c\/p\u003e \u003cp\u003e4.2.3 Truncated CI Methods 133\u003c\/p\u003e \u003cp\u003e4.2.4 Direct CI Methods 134\u003c\/p\u003e \u003cp\u003e4.3 Illustrating how CI Accounts for Electron Correlation, and the RHF Dissociation Problem 135\u003c\/p\u003e \u003cp\u003e4.4 The UHF Dissociation and the Spin Contamination Problem 138\u003c\/p\u003e \u003cp\u003e4.5 Size Consistency and Size Extensivity 142\u003c\/p\u003e \u003cp\u003e4.6 Multiconfiguration Self-Consistent Field 143\u003c\/p\u003e \u003cp\u003e4.7 Multireference Configuration Interaction 148\u003c\/p\u003e \u003cp\u003e4.8 Many-Body Perturbation Theory 148\u003c\/p\u003e \u003cp\u003e4.8.1 Møller–Plesset Perturbation Theory 151\u003c\/p\u003e \u003cp\u003e4.8.2 Unrestricted and Projected Møller–Plesset Methods 156\u003c\/p\u003e \u003cp\u003e4.9 Coupled Cluster 157\u003c\/p\u003e \u003cp\u003e4.9.1 Truncated coupled cluster methods 160\u003c\/p\u003e \u003cp\u003e4.10 Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory 162\u003c\/p\u003e \u003cp\u003e4.10.1 Illustrating Correlation Methods for the Beryllium Atom 165\u003c\/p\u003e \u003cp\u003e4.11 Methods Involving the Interelectronic Distance 166\u003c\/p\u003e \u003cp\u003e4.12 Techniques for Improving the Computational Efficiency 169\u003c\/p\u003e \u003cp\u003e4.12.1 Direct Methods 170\u003c\/p\u003e \u003cp\u003e4.12.2 Localized Orbital Methods 172\u003c\/p\u003e \u003cp\u003e4.12.3 Fragment-Based Methods 173\u003c\/p\u003e \u003cp\u003e4.12.4 Tensor Decomposition Methods 173\u003c\/p\u003e \u003cp\u003e4.13 Summary of Electron Correlation Methods 174\u003c\/p\u003e \u003cp\u003e4.14 Excited States 176\u003c\/p\u003e \u003cp\u003e4.14.1 Excited State Analysis 181\u003c\/p\u003e \u003cp\u003e4.15 Quantum Monte Carlo Methods 183\u003c\/p\u003e \u003cp\u003eReferences 185\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Basis Sets 188\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Slater- and Gaussian-Type Orbitals 189\u003c\/p\u003e \u003cp\u003e5.2 Classification of Basis Sets 190\u003c\/p\u003e \u003cp\u003e5.3 Construction of Basis Sets 194\u003c\/p\u003e \u003cp\u003e5.3.1 Exponents of Primitive Functions 194\u003c\/p\u003e \u003cp\u003e5.3.2 Parameterized Exponent Basis Sets 195\u003c\/p\u003e \u003cp\u003e5.3.3 Basis Set Contraction 196\u003c\/p\u003e \u003cp\u003e5.3.4 Basis Set Augmentation 199\u003c\/p\u003e \u003cp\u003e5.4 Examples of Standard Basis Sets 200\u003c\/p\u003e \u003cp\u003e5.4.1 Pople Style Basis Sets 200\u003c\/p\u003e \u003cp\u003e5.4.2 Dunning–Huzinaga Basis Sets 202\u003c\/p\u003e \u003cp\u003e5.4.3 Karlsruhe-Type Basis Sets 203\u003c\/p\u003e \u003cp\u003e5.4.4 Atomic Natural Orbital Basis Sets 203\u003c\/p\u003e \u003cp\u003e5.4.5 Correlation Consistent Basis Sets 204\u003c\/p\u003e \u003cp\u003e5.4.6 Polarization Consistent Basis Sets 205\u003c\/p\u003e \u003cp\u003e5.4.7 Correlation Consistent F12 Basis Sets 206\u003c\/p\u003e \u003cp\u003e5.4.8 Relativistic Basis Sets 207\u003c\/p\u003e \u003cp\u003e5.4.9 Property Optimized Basis Sets 207\u003c\/p\u003e \u003cp\u003e5.5 Plane Wave Basis Functions 208\u003c\/p\u003e \u003cp\u003e5.6 Grid and Wavelet Basis Sets 210\u003c\/p\u003e \u003cp\u003e5.7 Fitting Basis Sets 211\u003c\/p\u003e \u003cp\u003e5.8 Computational Issues 211\u003c\/p\u003e \u003cp\u003e5.9 Basis Set Extrapolation 212\u003c\/p\u003e \u003cp\u003e5.10 Composite Extrapolation Procedures 215\u003c\/p\u003e \u003cp\u003e5.10.1 Gaussian-n Models 216\u003c\/p\u003e \u003cp\u003e5.10.2 Complete Basis Set Models 217\u003c\/p\u003e \u003cp\u003e5.10.3 Weizmann-n Models 219\u003c\/p\u003e \u003cp\u003e5.10.4 Other Composite Models 221\u003c\/p\u003e \u003cp\u003e5.11 Isogyric and Isodesmic Reactions 222\u003c\/p\u003e \u003cp\u003e5.12 Effective Core Potentials 223\u003c\/p\u003e \u003cp\u003e5.13 Basis Set Superposition and Incompleteness Errors 226\u003c\/p\u003e \u003cp\u003eReferences 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Density Functional Methods 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Orbital-Free Density Functional Theory 234\u003c\/p\u003e \u003cp\u003e6.2 Kohn–Sham Theory 235\u003c\/p\u003e \u003cp\u003e6.3 Reduced Density Matrix and Density Cumulant Methods 237\u003c\/p\u003e \u003cp\u003e6.4 Exchange and Correlation Holes 241\u003c\/p\u003e \u003cp\u003e6.5 Exchange–Correlation Functionals 244\u003c\/p\u003e \u003cp\u003e6.5.1 Local Density Approximation 247\u003c\/p\u003e \u003cp\u003e6.5.2 Generalized Gradient Approximation 248\u003c\/p\u003e \u003cp\u003e6.5.3 Meta-GGA Methods 251\u003c\/p\u003e \u003cp\u003e6.5.4 Hybrid or Hyper-GGA Methods 252\u003c\/p\u003e \u003cp\u003e6.5.5 Double Hybrid Methods 253\u003c\/p\u003e \u003cp\u003e6.5.6 Range-Separated Methods 254\u003c\/p\u003e \u003cp\u003e6.5.7 Dispersion-Corrected Methods 255\u003c\/p\u003e \u003cp\u003e6.5.8 Functional Overview 257\u003c\/p\u003e \u003cp\u003e6.6 Performance of Density Functional Methods 258\u003c\/p\u003e \u003cp\u003e6.7 Computational Considerations 260\u003c\/p\u003e \u003cp\u003e6.8 Differences between Density Functional Theory and Hartree-Fock 262\u003c\/p\u003e \u003cp\u003e6.9 Time-Dependent Density Functional Theory (TDDFT) 263\u003c\/p\u003e \u003cp\u003e6.9.1 Weak Perturbation – Linear Response 266\u003c\/p\u003e \u003cp\u003e6.10 Ensemble Density Functional Theory 268\u003c\/p\u003e \u003cp\u003e6.11 Density Functional Theory Problems 269\u003c\/p\u003e \u003cp\u003e6.12 Final Considerations 269\u003c\/p\u003e \u003cp\u003eReferences 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Semi-empirical Methods 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Neglect of Diatomic Differential Overlap (NDDO) Approximation 276\u003c\/p\u003e \u003cp\u003e7.2 Intermediate Neglect of Differential Overlap (INDO) Approximation 277\u003c\/p\u003e \u003cp\u003e7.3 Complete Neglect of Differential Overlap (CNDO) Approximation 277\u003c\/p\u003e \u003cp\u003e7.4 Parameterization 278\u003c\/p\u003e \u003cp\u003e7.4.1 Modified Intermediate Neglect of Differential Overlap (MINDO) 278\u003c\/p\u003e \u003cp\u003e7.4.2 Modified NDDO Models 279\u003c\/p\u003e \u003cp\u003e7.4.3 Modified Neglect of Diatomic Overlap (MNDO) 280\u003c\/p\u003e \u003cp\u003e7.4.4 Austin Model 1 (AM1) 281\u003c\/p\u003e \u003cp\u003e7.4.5 Modified Neglect of Diatomic Overlap, Parametric Method Number 3 (PM3) 281\u003c\/p\u003e \u003cp\u003e7.4.6 The MNDO\/d and AM1\/d Methods 282\u003c\/p\u003e \u003cp\u003e7.4.7 Parametric Method Numbers 6 and 7 (PM6 and PM7) 282\u003c\/p\u003e \u003cp\u003e7.4.8 Orthogonalization Models 283\u003c\/p\u003e \u003cp\u003e7.5 Hückel Theory 283\u003c\/p\u003e \u003cp\u003e7.5.1 Extended Hückel theory 283\u003c\/p\u003e \u003cp\u003e7.5.2 Simple Hückel Theory 284\u003c\/p\u003e \u003cp\u003e7.6 Tight-Binding Density Functional Theory 285\u003c\/p\u003e \u003cp\u003e7.7 Performance of Semi-empirical Methods 287\u003c\/p\u003e \u003cp\u003e7.8 Advantages and Limitations of Semi-empirical Methods 289\u003c\/p\u003e \u003cp\u003eReferences 290\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Valence Bond Methods 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Classical Valence Bond Theory 292\u003c\/p\u003e \u003cp\u003e8.2 Spin-Coupled Valence Bond Theory 293\u003c\/p\u003e \u003cp\u003e8.3 Generalized Valence Bond Theory 297\u003c\/p\u003e \u003cp\u003eReferences 298\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Relativistic Methods 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 The Dirac Equation 300\u003c\/p\u003e \u003cp\u003e9.2 Connections between the Dirac and Schrödinger Equations 302\u003c\/p\u003e \u003cp\u003e9.2.1 Including Electric Potentials 302\u003c\/p\u003e \u003cp\u003e9.2.2 Including Both Electric and Magnetic Potentials 304\u003c\/p\u003e \u003cp\u003e9.3 Many-Particle Systems 306\u003c\/p\u003e \u003cp\u003e9.4 Four-Component Calculations 309\u003c\/p\u003e \u003cp\u003e9.5 Two-Component Calculations 310\u003c\/p\u003e \u003cp\u003e9.6 Relativistic Effects 313\u003c\/p\u003e \u003cp\u003eReferences 315\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Wave Function Analysis 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Population Analysis Based on Basis Functions 317\u003c\/p\u003e \u003cp\u003e10.2 Population Analysis Based on the Electrostatic Potential 320\u003c\/p\u003e \u003cp\u003e10.3 Population Analysis Based on the Electron Density 323\u003c\/p\u003e \u003cp\u003e10.3.1 Quantum Theory of Atoms in Molecules 324\u003c\/p\u003e \u003cp\u003e10.3.2 Voronoi, Hirshfeld, Stockholder and Stewart Atomic Charges 327\u003c\/p\u003e \u003cp\u003e10.3.3 Generalized Atomic Polar Tensor Charges 329\u003c\/p\u003e \u003cp\u003e10.4 Localized Orbitals 329\u003c\/p\u003e \u003cp\u003e10.4.1 Computational considerations 332\u003c\/p\u003e \u003cp\u003e10.5 Natural Orbitals 333\u003c\/p\u003e \u003cp\u003e10.5.1 Natural Atomic Orbital and Natural Bond Orbital Analyses 334\u003c\/p\u003e \u003cp\u003e10.6 Computational Considerations 337\u003c\/p\u003e \u003cp\u003e10.7 Examples 338\u003c\/p\u003e \u003cp\u003eReferences 339\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Molecular Properties 341\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Examples of Molecular Properties 343\u003c\/p\u003e \u003cp\u003e11.1.1 External Electric Field 343\u003c\/p\u003e \u003cp\u003e11.1.2 External Magnetic Field 344\u003c\/p\u003e \u003cp\u003e11.1.3 Nuclear Magnetic Moments 345\u003c\/p\u003e \u003cp\u003e11.1.4 Electron Magnetic Moments 345\u003c\/p\u003e \u003cp\u003e11.1.5 Geometry Change 346\u003c\/p\u003e \u003cp\u003e11.1.6 Mixed Derivatives 346\u003c\/p\u003e \u003cp\u003e11.2 Perturbation Methods 347\u003c\/p\u003e \u003cp\u003e11.3 Derivative Techniques 349\u003c\/p\u003e \u003cp\u003e11.4 Response and Propagator Methods 351\u003c\/p\u003e \u003cp\u003e11.5 Lagrangian Techniques 351\u003c\/p\u003e \u003cp\u003e11.6 Wave Function Response 353\u003c\/p\u003e \u003cp\u003e11.6.1 Coupled Perturbed Hartree–Fock 354\u003c\/p\u003e \u003cp\u003e11.7 Electric Field Perturbation 357\u003c\/p\u003e \u003cp\u003e11.7.1 External Electric Field 357\u003c\/p\u003e \u003cp\u003e11.7.2 Internal Electric Field 358\u003c\/p\u003e \u003cp\u003e11.8 Magnetic Field Perturbation 358\u003c\/p\u003e \u003cp\u003e11.8.1 External Magnetic Field 360\u003c\/p\u003e \u003cp\u003e11.8.2 Nuclear Spin 361\u003c\/p\u003e \u003cp\u003e11.8.3 Electron Spin 361\u003c\/p\u003e \u003cp\u003e11.8.4 Electron Angular Momentum 362\u003c\/p\u003e \u003cp\u003e11.8.5 Classical Terms 362\u003c\/p\u003e \u003cp\u003e11.8.6 Relativistic Terms 363\u003c\/p\u003e \u003cp\u003e11.8.7 Magnetic Properties 363\u003c\/p\u003e \u003cp\u003e11.8.8 Gauge Dependence of Magnetic Properties 366\u003c\/p\u003e \u003cp\u003e11.9 Geometry Perturbations 367\u003c\/p\u003e \u003cp\u003e11.10 Time-Dependent Perturbations 372\u003c\/p\u003e \u003cp\u003e11.11 Rotational and Vibrational Corrections 377\u003c\/p\u003e \u003cp\u003e11.12 Environmental Effects 378\u003c\/p\u003e \u003cp\u003e11.13 Relativistic Corrections 378\u003c\/p\u003e \u003cp\u003eReferences 378\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Illustrating the Concepts 380\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Geometry Convergence 380\u003c\/p\u003e \u003cp\u003e12.1.1 Wave Function Methods 380\u003c\/p\u003e \u003cp\u003e12.1.2 Density Functional Methods 382\u003c\/p\u003e \u003cp\u003e12.2 Total Energy Convergence 383\u003c\/p\u003e \u003cp\u003e12.3 Dipole Moment Convergence 385\u003c\/p\u003e \u003cp\u003e12.3.1 Wave Function Methods 385\u003c\/p\u003e \u003cp\u003e12.3.2 Density Functional Methods 385\u003c\/p\u003e \u003cp\u003e12.4 Vibrational Frequency Convergence 386\u003c\/p\u003e \u003cp\u003e12.4.1 Wave Function Methods 386\u003c\/p\u003e \u003cp\u003e12.5 Bond Dissociation Curves 389\u003c\/p\u003e \u003cp\u003e12.5.1 Wave Function Methods 389\u003c\/p\u003e \u003cp\u003e12.5.2 Density Functional Methods 394\u003c\/p\u003e \u003cp\u003e12.6 Angle Bending Curves 394\u003c\/p\u003e \u003cp\u003e12.7 Problematic Systems 396\u003c\/p\u003e \u003cp\u003e12.7.1 The Geometry of FOOF 396\u003c\/p\u003e \u003cp\u003e12.7.2 The Dipole Moment of CO 397\u003c\/p\u003e \u003cp\u003e12.7.3 The Vibrational Frequencies of O\u003csub\u003e3\u003c\/sub\u003e 398\u003c\/p\u003e \u003cp\u003e12.8 Relative Energies of C\u003csub\u003e4\u003c\/sub\u003eH\u003csub\u003e6\u003c\/sub\u003e Isomers 399\u003c\/p\u003e \u003cp\u003eReferences 402\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Optimization Techniques 404\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Optimizing Quadratic Functions 405\u003c\/p\u003e \u003cp\u003e13.2 Optimizing General Functions: Finding Minima 407\u003c\/p\u003e \u003cp\u003e13.2.1 Steepest Descent 407\u003c\/p\u003e \u003cp\u003e13.2.2 Conjugate Gradient Methods 408\u003c\/p\u003e \u003cp\u003e13.2.3 Newton–Raphson Methods 409\u003c\/p\u003e \u003cp\u003e13.2.4 Augmented Hessian Methods 410\u003c\/p\u003e \u003cp\u003e13.2.5 Hessian Update Methods 411\u003c\/p\u003e \u003cp\u003e13.2.6 Truncated Hessian Methods 413\u003c\/p\u003e \u003cp\u003e13.2.7 Extrapolation: The DIIS Method 413\u003c\/p\u003e \u003cp\u003e13.3 Choice of Coordinates 415\u003c\/p\u003e \u003cp\u003e13.4 Optimizing General Functions: Finding Saddle Points (Transition Structures) 418\u003c\/p\u003e \u003cp\u003e13.4.1 One-Structure Interpolation Methods 419\u003c\/p\u003e \u003cp\u003e13.4.2 Two-Structure Interpolation Methods 421\u003c\/p\u003e \u003cp\u003e13.4.3 Multistructure Interpolation Methods 422\u003c\/p\u003e \u003cp\u003e13.4.4 Characteristics of Interpolation Methods 426\u003c\/p\u003e \u003cp\u003e13.4.5 Local Methods: Gradient Norm Minimization 427\u003c\/p\u003e \u003cp\u003e13.4.6 Local Methods: Newton–Raphson 427\u003c\/p\u003e \u003cp\u003e13.4.7 Local Methods: The Dimer Method 429\u003c\/p\u003e \u003cp\u003e13.4.8 Coordinates for TS Searches 429\u003c\/p\u003e \u003cp\u003e13.4.9 Characteristics of Local Methods 430\u003c\/p\u003e \u003cp\u003e13.4.10 Dynamic Methods 431\u003c\/p\u003e \u003cp\u003e13.5 Constrained Optimizations 431\u003c\/p\u003e \u003cp\u003e13.6 Global Minimizations and Sampling 433\u003c\/p\u003e \u003cp\u003e13.6.1 Stochastic and Monte Carlo Methods 434\u003c\/p\u003e \u003cp\u003e13.6.2 Molecular Dynamics Methods 436\u003c\/p\u003e \u003cp\u003e13.6.3 Simulated Annealing 436\u003c\/p\u003e \u003cp\u003e13.6.4 Genetic Algorithms 437\u003c\/p\u003e \u003cp\u003e13.6.5 Particle Swarm and Gravitational Search Methods 437\u003c\/p\u003e \u003cp\u003e13.6.6 Diffusion Methods 438\u003c\/p\u003e \u003cp\u003e13.6.7 Distance Geometry Methods 439\u003c\/p\u003e \u003cp\u003e13.6.8 Characteristics of Global Optimization Methods 439\u003c\/p\u003e \u003cp\u003e13.7 Molecular Docking 440\u003c\/p\u003e \u003cp\u003e13.8 Intrinsic Reaction Coordinate Methods 441\u003c\/p\u003e \u003cp\u003eReferences 444\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Statistical Mechanics and Transition State Theory 447\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Transition State Theory 447\u003c\/p\u003e \u003cp\u003e14.2 Rice–Ramsperger–Kassel–Marcus Theory 450\u003c\/p\u003e \u003cp\u003e14.3 Dynamical Effects 451\u003c\/p\u003e \u003cp\u003e14.4 Statistical Mechanics 452\u003c\/p\u003e \u003cp\u003e14.5 The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation 454\u003c\/p\u003e \u003cp\u003e14.5.1 Translational Degrees of Freedom 455\u003c\/p\u003e \u003cp\u003e14.5.2 Rotational Degrees of Freedom 455\u003c\/p\u003e \u003cp\u003e14.5.3 Vibrational Degrees of Freedom 457\u003c\/p\u003e \u003cp\u003e14.5.4 Electronic Degrees of Freedom 458\u003c\/p\u003e \u003cp\u003e14.5.5 Enthalpy and Entropy Contributions 459\u003c\/p\u003e \u003cp\u003e14.6 Condensed Phases 464\u003c\/p\u003e \u003cp\u003eReferences 468\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Simulation Techniques 469\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Monte Carlo Methods 472\u003c\/p\u003e \u003cp\u003e15.1.1 Generating Non-natural Ensembles 474\u003c\/p\u003e \u003cp\u003e15.2 Time-Dependent Methods 474\u003c\/p\u003e \u003cp\u003e15.2.1 Molecular Dynamics Methods 474\u003c\/p\u003e \u003cp\u003e15.2.2 Generating Non-natural Ensembles 478\u003c\/p\u003e \u003cp\u003e15.2.3 Langevin Methods 479\u003c\/p\u003e \u003cp\u003e15.2.4 Direct Methods 479\u003c\/p\u003e \u003cp\u003e15.2.5 Ab Initio Molecular Dynamics 480\u003c\/p\u003e \u003cp\u003e15.2.6 Quantum Dynamical Methods Using Potential Energy Surfaces 483\u003c\/p\u003e \u003cp\u003e15.2.7 Reaction Path Methods 484\u003c\/p\u003e \u003cp\u003e15.2.8 Non-Born–Oppenheimer Methods 487\u003c\/p\u003e \u003cp\u003e15.2.9 Constrained and Biased Sampling Methods 488\u003c\/p\u003e \u003cp\u003e15.3 Periodic Boundary Conditions 491\u003c\/p\u003e \u003cp\u003e15.4 Extracting Information from Simulations 494\u003c\/p\u003e \u003cp\u003e15.5 Free Energy Methods 499\u003c\/p\u003e \u003cp\u003e15.5.1 Thermodynamic Perturbation Methods 499\u003c\/p\u003e \u003cp\u003e15.5.2 Thermodynamic Integration Methods 500\u003c\/p\u003e \u003cp\u003e15.6 Solvation Models 502\u003c\/p\u003e \u003cp\u003e15.6.1 Continuum Solvation Models 503\u003c\/p\u003e \u003cp\u003e15.6.2 Poisson–Boltzmann Methods 505\u003c\/p\u003e \u003cp\u003e15.6.3 Born\/Onsager\/Kirkwood Models 506\u003c\/p\u003e \u003cp\u003e15.6.4 Self-Consistent Reaction Field Models 508\u003c\/p\u003e \u003cp\u003eReferences 511\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Qualitative Theories 515\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Frontier Molecular Orbital Theory 515\u003c\/p\u003e \u003cp\u003e16.2 Concepts from Density Functional Theory 519\u003c\/p\u003e \u003cp\u003e16.3 Qualitative Molecular Orbital Theory 522\u003c\/p\u003e \u003cp\u003e16.4 Energy Decomposition Analyses 524\u003c\/p\u003e \u003cp\u003e16.5 Orbital Correlation Diagrams: The Woodward–Hoffmann Rules 526\u003c\/p\u003e \u003cp\u003e16.6 The Bell–Evans–Polanyi Principle\/Hammond Postulate\/Marcus Theory 534\u003c\/p\u003e \u003cp\u003e16.7 More O’Ferrall–Jencks Diagrams 538\u003c\/p\u003e \u003cp\u003eReferences 541\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Mathematical Methods 543\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Numbers, Vectors, Matrices and Tensors 543\u003c\/p\u003e \u003cp\u003e17.2 Change of Coordinate System 549\u003c\/p\u003e \u003cp\u003e17.2.1 Examples of Changing the Coordinate System 554\u003c\/p\u003e \u003cp\u003e17.2.2 Vibrational Normal Coordinates 555\u003c\/p\u003e \u003cp\u003e17.2.3 Energy of a Slater Determinant 557\u003c\/p\u003e \u003cp\u003e17.2.4 Energy of a CI Wave Function 558\u003c\/p\u003e \u003cp\u003e17.2.5 Computational Considerations 558\u003c\/p\u003e \u003cp\u003e17.3 Coordinates, Functions, Functionals, Operators and Superoperators 560\u003c\/p\u003e \u003cp\u003e17.3.1 Differential Operators 562\u003c\/p\u003e \u003cp\u003e17.4 Normalization, Orthogonalization and Projection 563\u003c\/p\u003e \u003cp\u003e17.5 Differential Equations 565\u003c\/p\u003e \u003cp\u003e17.5.1 Simple First-Order Differential Equations 565\u003c\/p\u003e \u003cp\u003e17.5.2 Less Simple First-Order Differential Equations 566\u003c\/p\u003e \u003cp\u003e17.5.3 Simple Second-Order Differential Equations 566\u003c\/p\u003e \u003cp\u003e17.5.4 Less Simple Second-Order Differential Equations 567\u003c\/p\u003e \u003cp\u003e17.5.5 Second-Order Differential Equations Depending on the Function Itself 568\u003c\/p\u003e \u003cp\u003e17.6 Approximating Functions 568\u003c\/p\u003e \u003cp\u003e17.6.1 Taylor Expansion 569\u003c\/p\u003e \u003cp\u003e17.6.2 Basis Set Expansion 570\u003c\/p\u003e \u003cp\u003e17.6.3 Tensor Decomposition Methods 572\u003c\/p\u003e \u003cp\u003e17.6.4 Examples of Tensor Decompositions 574\u003c\/p\u003e \u003cp\u003e17.7 Fourier and Laplace Transformations 577\u003c\/p\u003e \u003cp\u003e17.8 Surfaces 577\u003c\/p\u003e \u003cp\u003eReferences 580\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Statistics and QSAR 581\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 581\u003c\/p\u003e \u003cp\u003e18.2 Elementary Statistical Measures 583\u003c\/p\u003e \u003cp\u003e18.3 Correlation between Two Sets of Data 585\u003c\/p\u003e \u003cp\u003e18.4 Correlation between Many Sets of Data 588\u003c\/p\u003e \u003cp\u003e18.4.1 Quality Measures 589\u003c\/p\u003e \u003cp\u003e18.4.2 Multiple Linear Regression 590\u003c\/p\u003e \u003cp\u003e18.4.3 Principal Component Analysis 591\u003c\/p\u003e \u003cp\u003e18.4.4 Partial Least Squares 593\u003c\/p\u003e \u003cp\u003e18.4.5 Illustrative Example 594\u003c\/p\u003e \u003cp\u003e18.5 Quantitative Structure–Activity Relationships (QSAR) 595\u003c\/p\u003e \u003cp\u003e18.6 Non-linear Correlation Methods 597\u003c\/p\u003e \u003cp\u003e18.7 Clustering Methods 598\u003c\/p\u003e \u003cp\u003eReferences 604\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Concluding Remarks 605\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A 608\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eNotation 608\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B 614\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Variational Principle 614\u003c\/p\u003e \u003cp\u003eThe Hohenberg–Kohn Theorems 615\u003c\/p\u003e \u003cp\u003eThe Adiabatic Connection Formula 616\u003c\/p\u003e \u003cp\u003eReference 617\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C 618\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAtomic Units 618\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D 619\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eZ Matrix Construction 619\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E 627\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eFirst and Second Quantization 627\u003c\/p\u003e \u003cp\u003eReferences 628\u003c\/p\u003e \u003cp\u003eIndex 629\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406929666391,"sku":"9781118825990","price":69.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118825990.jpg?v=1730497591","url":"https:\/\/bookcurl.com\/products\/introduction-to-computational-chemistry-9781118825990","provider":"Book Curl","version":"1.0","type":"link"}