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BK

Third edition

Chichester ; Hoboken : Wiley, [2017]

xxii, 638 stran : ilustrace ; 24 cm

ISBN 978-1-118-82599-0 (brožováno)

Obsahuje bibliografie a rejstřík

001462610

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 g // 1.6.1 Separating Space and Time Variables 9 // 1.6.2 Separating Nuclear and Electronic Variables 9 // 1.6.3 Separating Variables in General 10 // 1.7 Classical Mechanics // 1.7.1 The Sun-Earth System // 1.7.2 The Solar System 12 // 1.8 Quantum Mechanics 13 // 1.8.1 A Hydrogen-Like Atom 13 // 1.8.2 The Helium Atom 16 // 1.9 Chemistry lg // References // 2 Force Field Methods 20 // 2.1 Introduction 20 // 2 2 The Force Field Energy 21 // 2.2.1 The Stretch Energy 23 // 2.2.2 The Bending Energy 25 // 2.2.3 The Out-of-Plane Bending Energy 28 // 2 2.4 The Torsional Energy 28 // 2.2.5 The van der Waals energy 32 // 2.2.6 The Electrostatic Energy: Atomic Charges 37 // 2.2.7 The Electrostatic Energy: Atomic Multipoles 41 // 2.2.8 The Electrostatic Energy: Polarizability and Charge Penetration Effects 42 // vi Contents // 2.2.9 Cross Terms 48 // 2.2.10 Small Rings and Conjugated Systems 49 // 2.2.11 Comparing Energies of Structurally Different Molecules 51 // 2.3 Force Field Parameterization 53 // 2.3.1 Parameter Reductions in Force Fields 58 // 2.3.2 Force Fields for Metal Coordination Compounds 59 // 2.3.3 Universal Force Fields 62 // 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 // 2.11.1 Modeling the TS as a Minimum Energy Structure 74 //

2.11.2 Modeling the TS as a Minimum Energy Structure on the Reactant/Product // Energy Seam 75 // 2.11.3 Modeling the Reactive Energy Surface by Interacting Force Field Functions 76 // 2.11.4 Reactive Force Fields 77 // 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-Fock Theory 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 // 3.8.1 SCF Convergence 108 // 3.8.2 Use of Symmetry 110 // 3.8.3 Ensuring that the HF Energy Is a Minimum, and the Correct Minimum 111 // 3.8.4 Initial Guess Orbitals 113 // 3.8.5 Direct SCF 113 // 3.8.6 Reduced Scaling Techniques 116 // 3.8.7 Reduced Prefactor Methods 117 // 3.9 Periodic Systems 119 // References 121 // 4 Electron Correlation Methods 124 // 4.1 Excited Slater Determinants 125 // 4.2 Configuration Interaction 128 // 4.2.1 Cl Matrix Elements 129 // 4.2.2 Size of the Cl Matrix 131 // 4.2.3 Truncated Cl Methods // 4.2.4 Direct Cl Methods // Illustrating how Cl Accounts for Electron Correlation, and the RHF Dissociation Problem // The UHF Dissociation and the Spin Contamination Problem Size Consistency and Size Extensivity Multiconfiguration Self-Consistent Field Multireference Configuration Interaction Many-Body Perturbation Theory // 4.8.1 Moller-Plesset Perturbation Theory // 4.8.2 Unrestricted and Projected Moller-Plesset Methods Coupled Cluster // 4.9.1 Truncated coupled cluster methods // Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory // 4.10.1 Illustrating Correlation Methods for the Beryllium Atom Methods Involving the Interelectronic Distance //

Techniques for Improving the Computational Efficiency // 4.12.1 Direct Methods // 4.12.2 Localized Orbital Methods // 4.12.3 Fragment-Based Methods // 4.12.4 Tensor Decomposition Methods Summary of Electron Correlation Methods Excited States // 4.14.1 Excited State Analysis Quantum Monte Carlo Methods References // 5 Basis Sets jgg // 5.1 Slater-and Gaussian-??? Orbitals 189 // 5.2 Classification of Basis Sets 190 // 5.3 Construction of Basis Sets 194 // 5.3.1 Exponents of Primitive Functions 194 // 5.3.2 Parameterized Exponent Basis Sets 195 // 5.3.3 Basis Set Contraction 195 // 5.3.4 Basis Set Augmentation 199 // 5.4 Examples of Standard Basis Sets 200 // 5.4.1 Pople Style Basis Sets 200 // 5.4.2 Dunning-Huzinaga Basis Sets 202 // 5.4.3 Karlsruhe-Type Basis Sets 203 // 5.4.4 Atomic Natural Orbital Basis Sets 203 // 5.4.5 Correlation Consistent Basis Sets 204 // 5.4.6 Polarization Consistent Basis Sets 205 // 5-4.7 Correlation Consistent F12 Basis Sets 206 // 5-4.8 Relativistic Basis Sets 207 // 5.4.9 Property Optimized Basis Sets 207 // 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 // 5.10.1 Gaussian-n Models 216 // 5.10.2 Complete Basis Set Models 217 // 5.10.3 Weizmann-n Models 219 // 5.10.4 Other Composite Models 221 // 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 // 6.5.1 Local Density Approximation 247 //

6.5.2 Generalized Gradient Approximation 248 // 6.5.3 Meta-GGA Methods 251 // 6.5.4 Hybrid or Hyper-GGA Methods 252 // 6.5.5 Double Hybrid Methods 253 // 6.5.6 Range-Separated Methods 254 // 6.5.7 Dispersion-Corrected Methods 255 // 6.5.8 Functional Overview 257 // 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 // 6.9.1 Weak Perturbation - Linear Response 266 // 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 // 7.4.1 Modified Intermediate Neglect of Differential Overlap (MINDO) 278 // 7.4.2 Modified NDDO Models 279 // 7.4.3 Modified Neglect of Diatomic Overlap (MNDO) 280 // 7 4.4 Austin Model 1 (AMI) // 745 Modified Neglect of Diatomic Overlap, Parametric Method Number 3 (PM3) // 7 4.6 The MNDO/d and AMl/d Methods // 7.4.7 Parametric Method Numbers 6 and 7 (PM6 and PM7) // 7.4.8 Orthogonalization Models Hückel Theory // 7.5.1 Extended Hückel theory // 7.5.2 Simple Hückel Theory Tight-Binding Density Functional Theory Performance of Semi-empirical Methods Advantages and Limitations of Semi-empirical Methods References // 8 Valence Bond Methods // 8.1 Classical Valence Bond Theory // 8.2 Spin-Coupled Valence Bond Theory // 8.3 Generalized Valence Bond Theory References // 9 Relativistic Methods // 9.1 The Dirac Equation // 9.2 Connections between the Dirac and Schrödinger Equations // 9.2.1 Including Electric Potentials //

9.2.2 Including Both Electric and Magnetic Potentials // 9.3 Many-Particle Systems // 9.4 Four-Component Calculations // 9.5 Two-Component Calculations // 9.6 Relativistic Effects References // 10 Wave Function Analysis // 10.1 Population Analysis Based on Basis Functions // 10.2 Population Analysis Based on the Electrostatic Potential // 10.3 Population Analysis Based on the Electron Density // 10.3.1 Quantum Theory of Atoms in Molecules // 10.3.2 Voronoi, Hirshfeld, Stockholder and Stewart Atomic Charges // 10.3.3 Generalized Atomic Polar Tensor Charges // 10.4 Localized Orbitals // 10.4.1 Computational considerations // 10.5 Natural Orbitals // 10.5.1 Natural Atomic Orbital and Natural Bond Orbital Analyses •6 Computational Considerations // 10-7 Examples // References // 11 Molecular Properties // 11.1 Examples of Molecular Properties // 11.1.1 External Electric Field // 11.1.2 External Magnetic Field // 11.1.3 Nuclear Magnetic Moments // 11.1.4 Electron Magnetic Moments // 11.1.5 Geometry Change // 11.1.6 Mixed Derivatives // 11.2 Perturbation Methods // 11.3 Derivative Techniques // 11.4 Response and Propagator Methods // 11.5 Lagrangian Techniques // 11.6 Wave Function Response // 11.6.1 Coupled Perturbed Hartree-Fock // 11.7 Electric Field Perturbation // 11.7.1 External Electric Field // 11.7.2 Internal Electric Field // 11.8 Magnetic Field Perturbation // 11.8.1 External Magnetic Field // 11.8.2 Nuclear Spin // 11.8.3 Electron Spin // 11.8.4 Electron Angular Momentum // 11.8.5 Classical Terms // 11.8.6 Relativistic Terms // 11.8.7 Magnetic Properties // 11.8.8 Gauge Dependence of Magnetic Properties // 11.9 Geometry Perturbations // 11.10 Time-Dependent Perturbations // 11.11 Rotational and Vibrational Corrections // 11.12 Environmental Effects // 11.13 Relativistic Corrections References // 12 Illustrating the Concepts // 12.1 Geometry Convergence //

12.1.1 Wave Function Methods // 12.1.2 Density Functional Methods // 12.2 Total Energy Convergence // 12.3 Dipole Moment Convergence // 12.3.1 Wave Function Methods // 12.3.2 Density Functional Methods // 12.4 Vibrational Frequency Convergence // 12.4.1 Wave Function Methods // 12.5 Bond Dissociation Curves // 12.5.1 Wave Function Methods // 12.5.2 Density Functional Methods // 12.6 Angle Bending Curves // 12.7 Problematic Systems 396 // 12.71 The Geometry of FOOF 396 // 12 7.2 The Dipole Moment of CO 397 // 12 7.3 The Vibrational Frequencies of 03 398 // 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 // 13.2.1 Steepest Descent 407 // 13.2.2 Conjugate Gradient Methods 408 // 13.2.3 Newton-Raphson Methods 409 // 13.2.4 Augmented Flessian Methods 410 // 13.2.5 Hessian Update Methods 411 // 13.2.6 Truncated Hessian Methods 413 // 13.2.7 Extrapolation: The DOS Method 413 // 13.3 Choice of Coordinates 415 // 13.4 Optimizing General Functions: Finding Saddle Points (Transition Structures) 418 // 13.4.1 One-Structure Interpolation Methods 419 // 13.4.2 Two-Structure Interpolation Methods 421 // 13.4.3 Multistructure Interpolation Methods 422 // 13.4.4 Characteristics of Interpolation Methods 426 // 13.4.5 Local Methods: Gradient Norm Minimization 427 // 13.4.6 Local Methods: Newton-Raphson 427 // 13.4.7 Local Methods: The Dimer Method 429 // 13.4.8 Coordinates for TS Searches 429 // 13.4.9 Characteristics of Local Methods 430 // 13.4.10 Dynamic Methods 431 // 13.5 Constrained Optimizations 431 // 13.6 Global Minimizations and Sampling 433 // 13.6.1 Stochastic and Monte Carlo Methods 434 // 13.6.2 Molecular Dynamics Methods 436 // 13.6.3 Simulated Annealing 436 // 13.6.4 Genetic Algorithms 437 //

13.6.5 Particle Swarm and Gravitational Search Methods 437 // 13.6.6 Diffusion Methods 438 // 13.6.7 Distance Geometry Methods 439 // 13.6.8 Characteristics of Global Optimization Methods 439 // 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 // xii // Contents // 14.4 Statistical Mechanics 452 // 14.5 The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation 454 // 14.5.1 Translational Degrees of Freedom 455 // 14.5.2 Rotational Degrees of Freedom 455 // 14.5.3 Vibrational Degrees of Freedom 457 // 14.5.4 Electronic Degrees of Freedom 458 // 14.5.5 Enthalpy and Entropy Contributions 459 // 14.6 Condensed Phases 464 // References 468 // 15 Simulation Techniques 469 // 15.1 Monte Carlo Methods 472 // 15.1.1 Generating Non-natural Ensembles 474 // 15.2 Time-Dependent Methods 474 // 15.2.1 Molecular Dynamics Methods 474 // 15.2.2 Generating Non-natural Ensembles 478 // 15.2.3 Langevin Methods 479 // 15.2.4 Direct Methods 479 // 15.2.5 AZ?/??/? Molecular Dynamics 480 // 15.2.6 Quantum Dynamical Methods Using Potential Energy Surfaces 483 // 15.2.7 Reaction Path Methods 484 // 15.2.8 Non-Born-Oppenheimer Methods 487 // 15.2.9 Constrained and Biased Sampling Methods 488 // 15.3 Periodic Boundary Conditions 491 // 15.4 Extracting Information from Simulations 494 // 15.5 Free Energy Methods 499 // 15.5.1 Thermodynamic Perturbation Methods 499 // 15.5.2 Thermodynamic Integration Methods 500 // 15.6 Solvation Models 502 // 15.6.1 Continuum Solvation Models 503 // 15.6.2 Poisson-Boltzmann Methods 505 // 15.6.3 Born/Onsager/Kirkwood Models 506 // 15.6.4 Self-Consistent Reaction Field Models 508 // 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: The Woodward-Hoffmann Rules 526 // 16.6 The Bell-Evans-Polanyi Principle/Hammond Postulate/Marcus Theory 534 // 16.7 More OTerrall-Jencks Diagrams 538 // References 541 // 17 Mathematical Methods 543 // 17.1 Numbers, Vectors, Matrices and Tensors 543 // 17.2 Change of Coordinate System 549 // Contents xiii // 17.2.1 Examples of Changing the Coordinate System 554 // 17.2.2 Vibrational Normal Coordinates 555 // 17.2.3 Energy of a Slater Determinant 557 // 17.2.4 Energy of a Cl Wave Function 558 // 17.2.5 Computational Considerations 558 // 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 // 17.5.1 Simple First-Order Differential Equations 565 // 17.5.2 Less Simple First-Order Differential Equations 566 // 17.5.3 Simple Second-Order Differential Equations 566 // 17.5.4 Less Simple Second-Order Differential Equations 567 // 17.5.5 Second-Order Differential Equations Depending on the Function Itself 568 // 17.6 Approximating Functions 568 // 17.6.1 Taylor Expansion 569 // 17.6.2 Basis Set Expansion 570 // 17.6.3 Tensor Decomposition Methods 572 // 17.6.4 Examples of Tensor Decompositions 574 // 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 // 18.4.1 Quality Measures 589 // 18.4.2 Multiple Linear Regression 590 // 18.4.3 Principal Component Analysis 591 //

18.4.4 Partial Least Squares 593 // 18.4.5 Illustrative Example 594 // 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 // Atomic Units 618 // Appendix D // Z Matrix Construction 619 // Appendix E // First and Second Quantization // References