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

Auteur
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).

Contenu

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 SunEarth 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 HartreeFock Theory 88

3.1 The Adiabatic and BornOppenheimer Approximations 90

3.2 HartreeFock 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 HartreeFock 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 MøllerPlesset Perturbation Theory 151

4.8.2 Unrestricted and Projected MøllerPlesset Methods 156 ...