Table of contents for Introduction to computational chemistry / Frank Jensen.

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Contents
Preface to the First Edition xv
Preface to the Second Edition xix
1 Introduction 1
1.1 Fundamental Issues 2
1.2 Describing the System 3
1.3 Fundamental Forces 4
1.4 The Dynamical Equation 5
1.5 Solving the Dynamical Equation 8
1.6 Separation of Variables 8
1.6.1 Separating space and time variables 10
1.6.2 Separating nuclear and electronic variables 10
1.6.3 Separating variables in general 11
1.7 Classical Mechanics 12
1.7.1 The Sun?Earth system 12
1.7.2 The solar system 13
1.8 Quantum Mechanics 14
1.8.1 A hydrogen-like atom 14
1.8.2 The helium atom 17
1.9 Chemistry 19
References 21
2 Force Field Methods 22
2.1 Introduction 22
2.2 The Force Field Energy 23
2.2.1 The stretch energy 24
2.2.2 The bending energy 37
2.2.3 The out-of-plane bending energy 30
2.2.4 The torsional energy 30
2.2.5 The van der Waals energy 34 O
2.2.6 The electrostatic energy: charges and dipoles 40
2.2.7 The electrostatic energy: multipoles and polarizabilities 43
2.2.8 Cross terms 47
2.2.9 Small rings and conjugated systems 48
2.2.10 Comparing energies of structurally different molecules 50
2.3 Force Field Parameterization 51
2.3.1 Parameter reductions in force fields 57
2.3.2 Force fields for metal coordination compounds 58
2.3.3 Universal force fields 62
2.4 Differences in Force Fields 62
2.5 Computational Considerations 65
2.6 Validation of Force Fields 67
2.7 Practical Considerations 69
2.8 Advantages and Limitations of Force Field Methods 69
2.9 Transition Structure Modelling 70
2.9.1 Modelling the TS as a minimum energy structure 70
2.9.2 Modelling the TS as a minimum energy structure on the
reactant/product energy seam 71
2.9.3 Modelling the reactive energy surface by interacting force
field functions or by geometry-dependent parameters 73
2.10 Hybrid Force Field Electronic Structure Methods 74
References 77
3 Electronic Structure Methods: Independent-Particle Models 80
3.1 The Adiabatic and Born?Oppenheimer Approximations 82
3.2 Self-Consistent Field Theory 86
3.3 The Energy of a Slater Determinant 87
3.4 Koopmans? Theorem 92
3.5 The Basis Set Approximation 93
3.6 An Alternative Formulation of the Variational Problem 98
3.7 Restricted and Unrestricted Hartree?Fock 99
3.8 SCF Techniques 100
3.8.1 SCF convergence 101
3.8.2 Use of symmetry 104
3.8.3 Ensuring that the HF energy is a minimum, and the
correct minimum 105
3.8.4 Initial guess orbitals 107
3.8.5 Direct SCF 108
3.8.6 Reduced scaling techniques 110
3.9 Periodic Systems 113
3.10 Semi-Empirical Methods 115
3.10.1 Neglect of Diatomic Differential Overlap Approximation
(NDDO) 116
3.10.2 Intermediate Neglect of Differential Overlap
Approximation (INDO) 117
3.10.3 Complete Neglect of Differential Overlap Approximation
(CNDO) 117
3.11 Parameterization 118
3.11.1 Modified Intermediate Neglect of Differential Overlap
(MINDO) 119
3.11.2 Modified NDDO models 119
3.11.3 Modified Neglect of Diatomic Overlap (MNDO) 121
3.11.4 Austin Model 1 (AM1) 121
3.11.5 Modified Neglect of Diatomic Overlap, Parametric
Method Number 3 (PM3) 122
3.11.6 Parametric Method number 5 (PM5) and PDDG/PM3
methods 123
3.11.7 The MNDO/d and AM1/d methods 124
3.11.8 Semi Ab initio Method 1 124
3.12 Performance of Semi-Empirical Methods 125
3.13 H¿ckel Theory 127
3.13.1 Extended H¿ckel theory 127
3.13.2 Simple H¿ckel theory 128
3.14 Limitations and Advantages of Semi-Empirical Methods 129
References 131
4 Electron Correlation Methods 133
4.1 Excited Slater Determinants 135
4.2 Configuration Interaction 137
4.2.1 CI Matrix elements 138
4.2.2 Size of the CI matrix 141
4.2.3 Truncated CI methods 143
4.2.4 Direct CI methods 144
4.3 Illustrating how CI Accounts for Electron Correlation, and the
RHF Dissociation Problem 145
4.4 The UHF Dissociation, and the Spin Contamination Problem 148
4.5 Size Consistency and Size Extensivity 153
4.6 Multi-Configuration Self-Consistent Field 153
4.7 Multi-Reference Configuration Interaction 158
4.8 Many-Body Perturbation Theory 159
4.8.1 M?ller?Plesset perturbation theory 162
4.8.2 Unrestricted and projected M?ller?Plesset methods 168
4.9 Coupled Cluster 169
4.9.1 Truncated coupled cluster methods 172
4.10 Connections between Coupled Cluster, Configuration Interaction
and Perturbation Theory 174
4.10.1 Illustrating correlation methods for the beryllium atom 177
4.11 Methods Involving the Interelectronic Distance 178
4.12 Direct Methods 181
4.13 Localized Orbital Methods 182
4.14 Summary of Electron Correlation Methods 183
4.15 Excited States 186
4.16 Quantum Monte Carlo Methods 187
References 189
5 Basis Sets 192
5.1 Slater and Gaussian Type Orbitals 192
5.2 Classification of Basis Sets 194
5.3 Even- and Well-Tempered Basis Sets 198
5.4 Contracted Basis Sets 200
5.4.1 Pople style basis sets 202
5.4.2 Dunning?Huzinaga basis sets 204
5.4.3 MINI, MIDI and MAXI basis sets 205
5.4.4 Ahlrichs type basis sets 205
5.4.5 Atomic natural orbital basis sets 205
5.4.6 Correlation consistent basis sets 206
5.4.7 Polarization consistent basis sets 207
5.4.8 Basis set extrapolation 208
5.5 Plane Wave Basis Functions 211
5.6 Recent Developments and Computational Issues 212
5.7 Composite Extrapolation Procedures 213
5.8 Isogyric and Isodesmic Reactions 221
5.9 Effective Core Potentials 222
5.10 Basis Set Superposition Errors 225
5.11 Pseudospectral Methods 227
References 229
6 Density Functional Methods 232
6.1 Orbital-Free Density Functional Theory 233
6.2 Kohn?Sham Theory 235
6.3 Reduced Density Matrix Methods 236
6.4 Exchange and Correlation Holes 240
6.5 Exchange?Correlation Functionals 243
6.5.1 Local Density Approximation 246
6.5.2 Gradient-corrected methods 248
6.5.3 Higher order gradient or meta-GGA methods 250
6.5.4 Hybrid or hyper-GGA methods 252
6.5.5 Generalized random phase methods 253
6.5.6 Functionals overview 254
6.6 Performance and Properties of Density Functional Methods 255
6.7 DFT Problems 258
6.8 Computational Considerations 260
6.9 Final Considerations 263
References 264
7 Valence Bond Methods 268
7.1 Classical Valence Bond Theory 269
7.2 Spin-Coupled Valence Bond Theory 270
7.3 Generalized Valence Bond Theory 275
References 276
8 Relativistic Methods 277
8.1 The Dirac Equation 278
8.2 Connections Between the Dirac and Schr¿dinger Equations 280
8.2.1 Including electric potentials 280
8.2.2 Including both electric and magnetic potentials 282
8.3 Many-Particle Systems 284
8.4 Four-Component Calculations 287
8.5 Relativistic Effects 289
References 292
9 Wave Function Analysis 293
9.1 Population Analysis Based on Basis Functions 293
9.2 Population Analysis Based on the Electrostatic Potential 296
9.3 Population Analysis Based on the Electron Density 299
9.3.1 Atoms In Molecules 299
9.3.2 Voronoi, Hirshfeld and Stewart atomic charges 303
9.3.3 Generalized atomic polar tensor charges 304
9.4 Localized Orbitals 304
9.4.1 Computational considerations 306
9.5 Natural Orbitals 308
9.6 Natural Atomic Orbital and Natural Bond Orbital Analysis 309
9.7 Computational Considerations 311
9.8 Examples 312
References 313
10 Molecular Properties 315
10.1 Examples of Molecular Properties 316
10.1.1 External electric field 316
10.1.2 External magnetic field 318
10.1.3 Internal magnetic moments 318
10.1.4 Geometry change 319
10.1.5 Mixed derivatives 319
10.2 Perturbation Methods 321
10.3 Derivative Techniques 321
10.4 Lagrangian Techniques 324
10.5 Coupled Perturbed Hartree?Fock 325
10.6 Electric Field Perturbation 329
10.6.1 External electric field 329
10.6.2 Internal electric field 329
10.7 Magnetic Field Perturbation 329
10.7.1 External magnetic field 331
10.7.2 Nuclear spin 332
10.7.3 Electron spin 333
10.7.4 Classical terms 333
10.7.5 Relativistic terms 334
10.7.6 Magnetic properties 334
10.7.7 Gauge dependence of magnetic properties 338
10.8 Geometry Perturbations 339
10.9 Response and Propagator Methods 343
10.10 Property Basis Sets 348
References 349
11 Illustrating the Concepts 350
11.1 Geometry Convergence 350
11.1.1 Ab Initio methods 350
11.1.2 Density functional methods 353
11.2 Total Energy Convergence 354
11.3 Dipole Moment Convergence 356
11.3.1 Ab Initio methods 356
11.3.2 Density functional methods 357
11.4 Vibrational Frequency Convergence 358
11.4.1 Ab Initio methods 358
11.4.2 Density functional methods 360
11.5 Bond Dissociation Curves 361
11.5.1 Basis set effect at the Hartree?Fock level 361
11.5.2 Performance of different types of wave function 363
11.5.3 Density functional methods 369
11.6 Angle Bending Curves 370
11.7 Problematic Systems 370
11.7.1 The geometry of FOOF 371
11.7.2 The dipole moment of CO 372
11.7.3 The vibrational frequencies of O3 373
11.8 Relative Energies of C4H6 Isomers 374
References 378
12 Optimization Techniques 380
12.1 Optimizing Quadratic Functions 381
12.2 Optimizing General Functions: Finding Minima 383
12.2.1 Steepest descent 383
12.2.2 Conjugate gradient methods 384
12.2.3 Newton?Raphson methods 385
12.2.4 Step control 386
12.2.5 Obtaining the Hessian 387
12.2.6 Storing and diagonalizing the Hessian 388
12.2.7 Extrapolations: the GDIIS method 389
12.3 Choice of Coordinates 390
12.4 Optimizing General Functions: Finding Saddle Points (Transition
Structures) 394
12.4.1 One-structure interpolation methods: coordinate driving,
linear and quadratic synchronous transit, and sphere
optimization 394
12.4.2 Two-structure interpolation methods: saddle, line-thenplane,
ridge and step-and-slide optimizations 397
12.4.3 Multi-structure interpolation methods: chain, locally
updated planes, self-penalty walk, conjugate peak
refinement and nudged elastic band 398
12.4.4 Characteristics of interpolation methods 401
12.4.5 Local methods: gradient norm minimization 402
12.4.6 Local methods: Newton?Raphson 403
12.4.7 Local methods: the dimer method 405
12.4.8 Coordinates for TS searches 405
12.4.9 Characteristics of local methods 406
12.4.10 Dynamic methods 406
12.5 Constrained Optimization Problems 407
12.6 Conformational Sampling and the Global Minimum Problem 409
12.6.1 Stochastic and Monte Carlo methods 411
12.6.2 Molecular dynamics 412
12.6.3 Simulated annealing 413
12.6.4 Genetic algorithms 413
12.6.5 Diffusion methods 414
12.6.6 Distance geometry methods 414
12.7 Molecular Docking 415
12.8 Intrinsic Reaction Coordinate Methods 416
References 419
13 Statistical Mechanics and Transition State Theory 421
13.1 Transition State Theory 421
13.2 Rice?Ramsperger?Kassel?Marcus Theory 424
13.3 Dynamical Effects 425
13.4 Statistical Mechanics 426
13.5 The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation 429
13.5.1 Translational degrees of freedom 430
13.5.2 Rotational degrees of freedom 430
13.5.3 Vibrational degrees of freedom 431
13.5.4 Electronic degrees of freedom 433
13.5.5 Enthalpy and entropy contributions 433
13.6 Condensed Phases 439
References 443
14 Simulation Techniques 445
14.1 Monte Carlo Methods 448
14.1.1 Generating non-natural ensembles 450
14.2 Time-Dependent Methods 450
14.2.1 Molecular dynamics methods 451
14.2.2 Generating non-natural ensembles 454
14.2.3 Langevin methods 455
14.2.4 Direct methods 455
14.2.5 Extended Lagrange techniques (Car?Parrinello methods) 457
14.2.6 Quantum methods using potential energy surfaces 459
14.2.7 Reaction path methods 460
14.2.8 Non-Born?Oppenheimer methods 463
14.2.9 Constrained sampling methods 463
14.3 Periodic Boundary Conditions 464
14.4 Extracting Information from Simulations 468
14.5 Free Energy Methods 472
14.5.1 Thermodynamic perturbation methods 472
14.5.2 Thermodynamic integration methods 473
14.6 Solvation Models 475
14.7 Continuum Solvation Models 476
14.7.1 Poisson?Boltzmann methods 478
14.7.2 Born/Onsager/Kirkwood models 480
14.7.3 Self-consistent reaction field models 481
References 484
15 Qualitative Theories 487
15.1 Frontier Molecular Orbital Theory 487
15.2 Concepts from Density Functional Theory 492
15.3 Qualitative Molecular Orbital Theory 494
15.4 Woodward?Hoffmann Rules 497
15.5 The Bell?Evans?Polanyi Principle/Hammond Postulate/Marcus
Theory 506
15.6 More O?Ferrall?Jencks Diagrams 510
References 512
16 Mathematical Methods 514
16.1 Numbers,Vectors, Matrices and Tensors 514
16.2 Change of Coordinate System 520
16.2.1 Examples of changing the coordinate system 525
16.2.2 Vibrational normal coordinates 526
16.2.3 Energy of a Slater determinant 528
16.2.4 Energy of a CI wave function 529
16.2.5 Computational Consideration 529
16.3 Coordinates, Functions, Functionals, Operators and
Superoperators 530
16.3.1 Differential operators 531
16.4 Normalization, Orthogonalization and Projection 532
16.5 Differential Equations 535
16.5.1 Simple first-order differential equations 535
16.5.2 Less simple first-order differential equations 536
16.5.3 Simple second-order differential equations 536
16.5.4 Less simple second-order differential equations 537
16.5.5 Second-order differential equations depending on the
function itself 537
16.6 Approximating Functions 538
16.6.1 Taylor expansion 539
16.6.2 Basis set expansion 541
16.7 Fourier and Laplace Transformations 541
16.8 Surfaces 543
References 546
17 Statistics and QSAR 547
17.1 Introduction 547
17.2 Elementary Statistical Measures 549
17.3 Correlation Between Two Sets of Data 550
17.4 Correlation between Many Sets of Data 553
17.4.1 Multiple-descriptor data sets and quality analysis 553
17.4.2 Multiple linear regression 555
17.4.3 Principal component and partial least squares analysis 556
17.4.4 Illustrative example 558
17.5 Quantitative Structure?Activity Relationships (QSAR) 559
References 561
18 Concluding Remarks 562
Appendix A 565
Notation 565
Appendix B 570
B.1 The Variational Principle 570
B.2 The Hohenberg?Kohn Theorems 571
B.3 The Adiabatic Connection Formula 572
Reference 573
Appendix C 574
Atomic Units 574
Appendix D 575
Z-Matrix Construction 575
Index 583

Library of Congress Subject Headings for this publication:

Chemistry, Physical and theoretical -- Data processing.
Chemistry, Physical and theoretical -- Mathematics.