Introduction to Computational Chemistry (eBook)

Frank Jensen (Autor)

eBook Download: PDF

2016 | 3. Auflage
John Wiley & Sons (Verlag)
9781118825983 (ISBN)

Infos

Introduction 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:

• Polarizable force fields
• Tight-binding DFT
• More extensive DFT functionals, excited states and time dependent molecular properties
• Accelerated Molecular Dynamics methods
• Tensor decomposition methods
• Cluster analysis
• Reduced scaling and reduced prefactor methods

Additional information is available at: www.wiley.com/go/jensen/computationalchemistry3

Professor Frank Jensen, Department of Chemistry, Aarhus University, Denmark
Frank 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 Advances in Quantum Chemistry (2005 - 2011) and the International Journal of Quantum Chemistry (2006-2011).

Inhalt

Introduction to Computational Chemistry 3
Contents 7
Preface to the First Edition 17
Preface to the Second Edition 21
Preface to the Third Edition 23
1 Introduction 25
1.1 Fundamental Issues 26
1.2 Describing the System 27
1.3 Fundamental Forces 27
1.4 The Dynamical Equation 29
1.5 Solving the Dynamical Equation 31
1.6 Separation of Variables 32
1.6.1 Separating Space and Time Variables 33
1.6.2 Separating Nuclear and Electronic Variables 33
1.6.3 Separating Variables in General 34
1.7 Classical Mechanics 35
1.7.1 The Sun–Earth System 35
1.7.2 The Solar System 36
1.8 Quantum Mechanics 37
1.8.1 A Hydrogen-Like Atom 37
1.8.2 The Helium Atom 40
1.9 Chemistry 42
References 43
2 Force Field Methods 44
2.1 Introduction 44
2.2 The Force Field Energy 45
2.2.1 The Stretch Energy 47
2.2.2 The Bending Energy 49
2.2.3 The Out-of-Plane Bending Energy 52
2.2.4 The Torsional Energy 52
2.2.5 The van der Waals energy 56
2.2.6 The Electrostatic Energy: Atomic Charges 61
2.2.7 The Electrostatic Energy: Atomic Multipoles 65
2.2.8 The Electrostatic Energy: Polarizability and Charge Penetration Effects 66
2.2.9 Cross Terms 72
2.2.10 Small Rings and Conjugated Systems 73
2.2.11 Comparing Energies of Structurally Different Molecules 75
2.3 Force Field Parameterization 77
2.3.1 Parameter Reductions in Force Fields 82
2.3.2 Force Fields for Metal Coordination Compounds 83
2.3.3 Universal Force Fields 86
2.4 Differences in Atomistic Force Fields 86
2.5 Water Models 90
2.6 Coarse Grained Force Fields 91
2.7 Computational Considerations 93
2.8 Validation of Force Fields 95
2.9 Practical Considerations 97
2.10 Advantages and Limitations of Force Field Methods 97
2.11 Transition Structure Modeling 98
2.11.1 Modeling the TS as a Minimum Energy Structure 98
2.11.2 Modeling the TS as a Minimum Energy Structure on the Reactant/Product Energy Seam 99
2.11.3 Modeling the Reactive Energy Surface by Interacting Force Field Functions 100
2.11.4 Reactive Force Fields 101
2.12 Hybrid Force Field Electronic Structure Methods 102
References 106
3 Hartree–Fock Theory 112
3.1 The Adiabatic and Born–Oppenheimer Approximations 114
3.2 Hartree–Fock Theory 118
3.3 The Energy of a Slater Determinant 119
3.4 Koopmans’ Theorem 124
3.5 The Basis Set Approximation 125
3.6 An Alternative Formulation of the Variational Problem 129
3.7 Restricted and Unrestricted Hartree–Fock 130
3.8 SCF Techniques 132
3.8.1 SCF Convergence 132
3.8.2 Use of Symmetry 134
3.8.3 Ensuring that the HF Energy Is a Minimum, and the Correct Minimum 135
3.8.4 Initial Guess Orbitals 137
3.8.5 Direct SCF 137
3.8.6 Reduced Scaling Techniques 140
3.8.7 Reduced Prefactor Methods 141
3.9 Periodic Systems 143
References 145
4 Electron Correlation Methods 148
4.1 Excited Slater Determinants 149
4.2 Configuration Interaction 152
4.2.1 CI Matrix Elements 153
4.2.2 Size of the CI Matrix 155
4.2.3 Truncated CI Methods 157
4.2.4 Direct CI Methods 158
4.3 Illustrating how CI Accounts for Electron Correlation, and the RHF Dissociation Problem 159
4.4 The UHF Dissociation and the Spin Contamination Problem 162
4.5 Size Consistency and Size Extensivity 166
4.6 Multiconfiguration Self-Consistent Field 167
4.7 Multireference Configuration Interaction 172
4.8 Many-Body Perturbation Theory 172
4.8.1 Møller–Plesset Perturbation Theory 175
4.8.2 Unrestricted and Projected Møller–Plesset Methods 180
4.9 Coupled Cluster 181
4.9.1 Truncated coupled cluster methods 184
4.10 Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory 186
4.10.1 Illustrating Correlation Methods for the Beryllium Atom 189
4.11 Methods Involving the Interelectronic Distance 190
4.12 Techniques for Improving the Computational Efficiency 193
4.12.1 Direct Methods 194
4.12.2 Localized Orbital Methods 196
4.12.3 Fragment-Based Methods 197
4.12.4 Tensor Decomposition Methods 197
4.13 Summary of Electron Correlation Methods 198
4.14 Excited States 200
4.14.1 Excited State Analysis 205
4.15 Quantum Monte Carlo Methods 207
References 209
5 Basis Sets 212
5.1 Slater- and Gaussian-Type Orbitals 213
5.2 Classification of Basis Sets 214
5.3 Construction of Basis Sets 218
5.3.1 Exponents of Primitive Functions 218
5.3.2 Parameterized Exponent Basis Sets 219
5.3.3 Basis Set Contraction 220
5.3.4 Basis Set Augmentation 223
5.4 Examples of Standard Basis Sets 224
5.4.1 Pople Style Basis Sets 224
5.4.2 Dunning–Huzinaga Basis Sets 226
5.4.3 Karlsruhe-Type Basis Sets 227
5.4.4 Atomic Natural Orbital Basis Sets 227
5.4.5 Correlation Consistent Basis Sets 228
5.4.6 Polarization Consistent Basis Sets 229
5.4.7 Correlation Consistent F12 Basis Sets 230
5.4.8 Relativistic Basis Sets 231
5.4.9 Property Optimized Basis Sets 231
5.5 PlaneWave Basis Functions 232
5.6 Grid andWavelet Basis Sets 234
5.7 Fitting Basis Sets 235
5.8 Computational Issues 235
5.9 Basis Set Extrapolation 236
5.10 Composite Extrapolation Procedures 239
5.10.1 Gaussian-n Models 240
5.10.2 Complete Basis Set Models 241
5.10.3 Weizmann-n Models 243
5.10.4 Other Composite Models 245
5.11 Isogyric and Isodesmic Reactions 246
5.12 Effective Core Potentials 247
5.13 Basis Set Superposition and Incompleteness Errors 250
References 252
6 Density Functional Methods 257
6.1 Orbital-Free Density FunctionalTheory 258
6.2 Kohn–Sham Theory 259
6.3 Reduced Density Matrix and Density Cumulant Methods 261
6.4 Exchange and Correlation Holes 265
6.5 Exchange–Correlation Functionals 268
6.5.1 Local Density Approximation 271
6.5.2 Generalized Gradient Approximation 272
6.5.3 Meta-GGA Methods 275
6.5.4 Hybrid or Hyper-GGA Methods 276
6.5.5 Double Hybrid Methods 277
6.5.6 Range-Separated Methods 278
6.5.7 Dispersion-Corrected Methods 279
6.5.8 Functional Overview 281
6.6 Performance of Density Functional Methods 282
6.7 Computational Considerations 284
6.8 Differences between Density Functional Theory and Hartree-Fock 286
6.9 Time-Dependent Density Functional Theory (TDDFT) 287
6.9.1 Weak Perturbation – Linear Response 290
6.10 Ensemble Density Functional Theory 292
6.11 Density Functional Theory Problems 293
6.12 Final Considerations 293
References 294
7 Semi-empirical Methods 299
7.1 Neglect of Diatomic Differential Overlap (NDDO) Approximation 300
7.2 Intermediate Neglect of Differential Overlap (INDO) Approximation 301
7.3 Complete Neglect of Differential Overlap (CNDO) Approximation 301
7.4 Parameterization 302
7.4.1 Modified Intermediate Neglect of Differential Overlap (MINDO) 302
7.4.2 Modified NDDO Models 303
7.4.3 Modified Neglect of Diatomic Overlap (MNDO) 304
7.4.4 Austin Model 1 (AM1) 305
7.4.5 Modified Neglect of Diatomic Overlap, Parametric Method Number 3 (PM3) 305
7.4.6 The MNDO/d and AM1/d Methods 306
7.4.7 Parametric Method Numbers 6 and 7 (PM6 and PM7) 306
7.4.8 Orthogonalization Models 307
7.5 Hückel Theory 307
7.5.1 Extended Hückel theory 307
7.5.2 Simple Hückel Theory 308
7.6 Tight-Binding Density Functional Theory 309
7.7 Performance of Semi-empirical Methods 311
7.8 Advantages and Limitations of Semi-empirical Methods 313
References 314
8 Valence Bond Methods 315
8.1 Classical Valence Bond Theory 316
8.2 Spin-Coupled Valence Bond Theory 317
8.3 Generalized Valence Bond Theory 321
References 322
9 Relativistic Methods 323
9.1 The Dirac Equation 324
9.2 Connections between the Dirac and Schrödinger Equations 326
9.2.1 Including Electric Potentials 326
9.2.2 Including Both Electric and Magnetic Potentials 328
9.3 Many-Particle Systems 330
9.4 Four-Component Calculations 333
9.5 Two-Component Calculations 334
9.6 Relativistic Effects 337
References 339
10 Wave Function Analysis 341
10.1 Population Analysis Based on Basis Functions 341
10.2 Population Analysis Based on the Electrostatic Potential 344
10.3 Population Analysis Based on the Electron Density 347
10.3.1 Quantum Theory of Atoms in Molecules 348
10.3.2 Voronoi, Hirshfeld, Stockholder and Stewart Atomic Charges 351
10.3.3 Generalized Atomic Polar Tensor Charges 353
10.4 Localized Orbitals 353
10.4.1 Computational considerations 356
10.5 Natural Orbitals 357
10.5.1 Natural Atomic Orbital and Natural Bond Orbital Analyses 358
10.6 Computational Considerations 361
10.7 Examples 362
References 363
11 Molecular Properties 365
11.1 Examples of Molecular Properties 367
11.1.1 External Electric Field 367
11.1.2 External Magnetic Field 368
11.1.3 Nuclear Magnetic Moments 369
11.1.4 Electron Magnetic Moments 369
11.1.5 Geometry Change 370
11.1.6 Mixed Derivatives 370
11.2 Perturbation Methods 371
11.3 Derivative Techniques 373
11.4 Response and Propagator Methods 375
11.5 Lagrangian Techniques 375
11.6 Wave Function Response 377
11.6.1 Coupled Perturbed Hartree–Fock 378
11.7 Electric Field Perturbation 381
11.7.1 External Electric Field 381
11.7.2 Internal Electric Field 382
11.8 Magnetic Field Perturbation 382
11.8.1 External Magnetic Field 384
11.8.2 Nuclear Spin 385
11.8.3 Electron Spin 385
11.8.4 Electron Angular Momentum 386
11.8.5 Classical Terms 386
11.8.6 Relativistic Terms 387
11.8.7 Magnetic Properties 387
11.8.8 Gauge Dependence of Magnetic Properties 390
11.9 Geometry Perturbations 391
11.10 Time-Dependent Perturbations 396
11.11 Rotational and Vibrational Corrections 401
11.12 Environmental Effects 402
11.13 Relativistic Corrections 402
References 402
12 Illustrating the Concepts 404
12.1 Geometry Convergence 404
12.1.1 Wave Function Methods 404
12.1.2 Density Functional Methods 406
12.2 Total Energy Convergence 407
12.3 Dipole Moment Convergence 409
12.3.1 Wave Function Methods 409
12.3.2 Density Functional Methods 409
12.4 Vibrational Frequency Convergence 410
12.4.1 Wave Function Methods 410
12.5 Bond Dissociation Curves 413
12.5.1 Wave Function Methods 413
12.5.2 Density Functional Methods 418
12.6 Angle Bending Curves 418
12.7 Problematic Systems 420
12.7.1 The Geometry of FOOF 420
12.7.2 The Dipole Moment of CO 421
12.7.3 The Vibrational Frequencies of O3 422
12.8 Relative Energies of C4H6 Isomers 423
References 426
13 Optimization Techniques 428
13.1 Optimizing Quadratic Functions 429
13.2 Optimizing General Functions: Finding Minima 431
13.2.1 Steepest Descent 431
13.2.2 Conjugate Gradient Methods 432
13.2.3 Newton–Raphson Methods 433
13.2.4 Augmented Hessian Methods 434
13.2.5 Hessian Update Methods 435
13.2.6 Truncated Hessian Methods 437
13.2.7 Extrapolation: The DIIS Method 437
13.3 Choice of Coordinates 439
13.4 Optimizing General Functions: Finding Saddle Points (Transition Structures) 442
13.4.1 One-Structure Interpolation Methods 443
13.4.2 Two-Structure Interpolation Methods 445
13.4.3 Multistructure Interpolation Methods 446
13.4.4 Characteristics of Interpolation Methods 450
13.4.5 Local Methods: Gradient Norm Minimization 451
13.4.6 Local Methods: Newton–Raphson 451
13.4.7 Local Methods: The Dimer Method 453
13.4.8 Coordinates for TS Searches 453
13.4.9 Characteristics of Local Methods 454
13.4.10 Dynamic Methods 455
13.5 Constrained Optimizations 455
13.6 Global Minimizations and Sampling 457
13.6.1 Stochastic and Monte Carlo Methods 458
13.6.2 Molecular Dynamics Methods 460
13.6.3 Simulated Annealing 460
13.6.4 Genetic Algorithms 461
13.6.5 Particle Swarm and Gravitational Search Methods 461
13.6.6 Diffusion Methods 462
13.6.7 Distance Geometry Methods 463
13.6.8 Characteristics of Global Optimization Methods 463
13.7 Molecular Docking 464
13.8 Intrinsic Reaction Coordinate Methods 465
References 468
14 Statistical Mechanics and Transition State Theory 471
14.1 Transition State Theory 471
14.2 Rice–Ramsperger–Kassel–Marcus Theory 474
14.3 Dynamical Effects 475
14.4 Statistical Mechanics 476
14.5 The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation 478
14.5.1 Translational Degrees of Freedom 479
14.5.2 Rotational Degrees of Freedom 479
14.5.3 Vibrational Degrees of Freedom 481
14.5.4 Electronic Degrees of Freedom 482
14.5.5 Enthalpy and Entropy Contributions 483
14.6 Condensed Phases 488
References 492
15 Simulation Techniques 493
15.1 Monte Carlo Methods 496
15.1.1 Generating Non-natural Ensembles 498
15.2 Time-Dependent Methods 498
15.2.1 Molecular Dynamics Methods 498
15.2.2 Generating Non-natural Ensembles 502
15.2.3 Langevin Methods 503
15.2.4 Direct Methods 503
15.2.5 Ab Initio Molecular Dynamics 504
15.2.6 Quantum Dynamical Methods Using Potential Energy Surfaces 507
15.2.7 Reaction Path Methods 508
15.2.8 Non-Born–Oppenheimer Methods 511
15.2.9 Constrained and Biased Sampling Methods 512
15.3 Periodic Boundary Conditions 515
15.4 Extracting Information from Simulations 518
15.5 Free Energy Methods 523
15.5.1 Thermodynamic Perturbation Methods 523
15.5.2 Thermodynamic Integration Methods 524
15.6 Solvation Models 526
15.6.1 Continuum Solvation Models 527
15.6.2 Poisson–Boltzmann Methods 529
15.6.3 Born/Onsager/Kirkwood Models 530
15.6.4 Self-Consistent Reaction Field Models 532
References 535
16 Qualitative Theories 539
16.1 Frontier Molecular Orbital Theory 539
16.2 Concepts from Density Functional Theory 543
16.3 Qualitative Molecular Orbital Theory 546
16.4 Energy Decomposition Analyses 548
16.5 Orbital Correlation Diagrams: The Woodward–Hoffmann Rules 550
16.6 The Bell–Evans–Polanyi Principle/Hammond Postulate/Marcus Theory 558
16.7 More O’Ferrall–Jencks Diagrams 562
References 565
17 Mathematical Methods 567
17.1 Numbers, Vectors, Matrices and Tensors 567
17.2 Change of Coordinate System 573
17.2.1 Examples of Changing the Coordinate System 578
17.2.2 Vibrational Normal Coordinates 579
17.2.3 Energy of a Slater Determinant 581
17.2.4 Energy of a CI Wave Function 582
17.2.5 Computational Considerations 582
17.3 Coordinates, Functions, Functionals, Operators and Superoperators 584
17.3.1 Differential Operators 586
17.4 Normalization, Orthogonalization and Projection 587
17.5 Differential Equations 589
17.5.1 Simple First-Order Differential Equations 589
17.5.2 Less Simple First-Order Differential Equations 590
17.5.3 Simple Second-Order Differential Equations 590
17.5.4 Less Simple Second-Order Differential Equations 591
17.5.5 Second-Order Differential Equations Depending on the Function Itself 592
17.6 Approximating Functions 592
17.6.1 Taylor Expansion 593
17.6.2 Basis Set Expansion 594
17.6.3 Tensor Decomposition Methods 596
17.6.4 Examples of Tensor Decompositions 598
17.7 Fourier and Laplace Transformations 601
17.8 Surfaces 601
References 604
18 Statistics and QSAR 605
18.1 Introduction 605
18.2 Elementary Statistical Measures 607
18.3 Correlation between Two Sets of Data 609
18.4 Correlation between Many Sets of Data 612
18.4.1 Quality Measures 613
18.4.2 Multiple Linear Regression 614
18.4.3 Principal Component Analysis 615
18.4.4 Partial Least Squares 617
18.4.5 Illustrative Example 618
18.5 Quantitative Structure–Activity Relationships (QSAR) 619
18.6 Non-linear Correlation Methods 621
18.7 Clustering Methods 622
References 628
19 Concluding Remarks 629
Appendix A 632
Notation 632
Appendix B 638
The Variational Principle 638
The Hohenberg–Kohn Theorems 639
The Adiabatic Connection Formula 640
Reference 641
Appendix C 642
Atomic Units 642
Appendix D 643
Z Matrix Construction 643
Appendix E 651
First and Second Quantization 651
References 652
Index 653
EULA 663

Produkt-Details

• Erscheint lt. Verlag: 28.11.2016
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie ► Physikalische Chemie
• Themenwelt: Technik
• Schlagworte: Accelerated Molecular Dynamic methods • Chemie • Chemistry • Computational Chemistry • Computational Chemistry & Molecular Modeling • Computational Chemistry u. Molecular Modeling • computational methods • Custer Analysis • density functional theory • Electron Correlation • electronic structure methods • Force Fields • Hartree-Fock • Mathematical & Computational Physics • Mathematische Physik • Molecular Properties • Optimization • Physics • Physik • Quantenchemie • Quantum Chemistry • quantum mechanics • Simulations • Tensor Decomposition Methods
• ISBN-13: 9781118825983 / 9781118825983