Introduction to Computational Chemistry

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

Autorentext

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

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 8

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 11

1.7.1 The Sun-Earth System 11

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 18

References 19

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

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 ci Matrix Elements 129

4.2.2 Size of the CI Matrix 131

4.2.3 Truncated CI Methods 133

4.2.4 Direct CI Methods 134

4.3 Illustrating how CI Accounts for Electron Correlation, and the RHF Dissociation Problem 135

4.4 The UHF Dissociation and the Spin Contamination Problem 138

4.5 Size Consistency and Size Extensivity 142

4.6 Multiconfiguration Self-Consistent Field 143

4.7 Multireference Configuration Interaction 148

4.8 Many-Body Perturbation Theory 148

4.8.1 Møller-Plesset Perturbation Theory 151

4.8.2 Unrestricted and Projected Møller-Plesset Methods 156

4.9 Coupled Cluster 157

4.9.1 Truncated coupled cluster methods 160

4.10 Connections between Coupled Cluster, Configuration Interaction and Perturbation Theory 162

4.10.1 Illustrating Correlation Methods for the Beryllium Atom 165

4.11 Methods Involving the Interelectronic Distance 166

4.12 Techniques for Improving the Computational Efficiency 169

4.12.1 Direct Methods 170

4.12.2 Localized Orbital Methods 172

4.12.3 Fragment-Based Methods 173

4.12.4 Tensor Decomposition Methods 173

4.13 Summary of Electron Correlation Methods 174

4.14 Excited States 176

4.14.1 Excited State Analysis 181

4.15 Quantum Monte Carlo Methods 183

References 185

5 Basis Sets 188

5.1 Slater- and Gaussian-Type 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 196

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

5.5 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) Approximati…