{"product_id":"introduction-to-computational-chemistry-isbn-9781118825990","title":"Introduction to Computational Chemistry","description":"\u003cp\u003eIntroduction to Computational Chemistry 3rd Edition provides a comprehensive account of the fundamental principles underlying different computational methods. Fully revised and updated throughout to reflect important method developments and improvements since publication of the previous edition, this timely update includes the following significant revisions and new topics:\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePolarizable force fields\u003c\/li\u003e \u003cli\u003eTight-binding DFT\u003c\/li\u003e \u003cli\u003eMore extensive DFT functionals, excited states and time dependent molecular properties\u003c\/li\u003e \u003cli\u003eAccelerated Molecular Dynamics methods\u003c\/li\u003e \u003cli\u003eTensor decomposition methods\u003c\/li\u003e \u003cli\u003eCluster analysis\u003c\/li\u003e \u003cli\u003eReduced scaling and reduced prefactor methods\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eAdditional information is available at: \u003ca href=\"http:\/\/www.wiley.com\/go\/jensen\/computationalchemistry3\"\u003ewww.wiley.com\/go\/jensen\/computationalchemistry3\u003c\/a\u003e\u003c\/p\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 \u003cb\u003eProfessor Frank Jensen, Department of Chemistry, Aarhus University, Denmark\u003c\/b\u003e\u003cbr\u003eFrank Jensen obtained his Ph.D. from UCLA in 1987 with Professors C. S. Foote and K. N. Houk, and is currently an Associate Professor in the Department of Chemistry, Aarhus University, Denmark. He has published over 120 papers and articles, and has been a member of the editorial boards of \u003ci\u003eAdvances in Quantum Chemistry\u003c\/i\u003e (2005 - 2011) and the \u003ci\u003eInternational Journal of Quantum Chemistry\u003c\/i\u003e (2006-2011).","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989457551589,"sku":"NP9781118825990","price":72.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118825990.jpg?v=1761784178","url":"https:\/\/k12savings.com\/es\/products\/introduction-to-computational-chemistry-isbn-9781118825990","provider":"K12savings","version":"1.0","type":"link"}