Reviews in Computational Chemistry / Reviews in Computational Chemistry, Volume 30

List of Contributors xi

Preface xiii

Contributors to Previous Volumes xvii

1 Chemical Bonding at High Pressure 1
Andreas Hermann

High-Pressure Science 1

Motivation 1

Pressure in Industrial Processes 2

High-Pressure Experiments 2

Pressure Effects in Materials 5

Close Packing and Metallicity-or Not 6

Hydrogen and Hydrogen-Rich Compounds 7

Molecular Crystals 8

Closed-Shell Reactivity 9

Unusual Chemistry 9

New Electronic States 10

Electronic Structure Calculations on Materials Under Pressure 10

Density and Wave Function-Based Approaches 11

Basis Sets and Pseudopotentials 13

Identifying High-Pressure Crystal Structures 14

Stability of High-Pressure Phases 16

Properties of Materials Under Pressure 20

Mechanical Properties 21

Electronic Properties 23

Spectroscopic Properties 28

Conclusions 29

Acknowledgments 31

References 31

2 Molecular Dynamics Simulations of Shock Loading of Materials: A Review and Tutorial 43
Mitchell A. Wood, Mathew J. Cherukara, Edwin Antillon, and Alejandro Strachan

Introduction 43

Shock Loading of Solids 101 44

Chapter Organization 46

Molecular Simulations of Shockwaves in Solids 46

Molecular Dynamics and Coarse Grain Dynamics 46

Direct Shock Simulations 48

Indirect Shock Simulations: Achieving Longer Timescales 49

Shock-Induced Plasticity and Failure 51

Plastic Deformation 51

Preexisting Defects: Voids and Vacancies 54

Preexisting Defects: Polycrystalline Materials 56

Granular Materials 56

Dynamical Failure 57

Critical Phenomena in Spallation and Cluster Formation 60

Ejecta Formation and the Richtmyer-Meshkov Instability 61

Shock-Induced Phase Transformation and Materials Synthesis 62

Phase Transformations 63

Shock-Induced and Shock-Assisted Chemical Reactions 69

Reactive Composites 70

Energetic Materials and Detonation 73

Model Explosives: Shock to Detonation 74

Reactive MD Simulations of Explosives 75

Electronic Structure-Based Modeling 79

Coarse-Grained Descriptions of Shock-Induced Chemistry 80

Summary and Outlook 83

Acknowledgments 84

Appendix 84

References 85

3 Basis Sets in Quantum Chemistry 93
Balazs Nagy, and Frank Jensen

Introduction 93

The Basis Set Approximation 94

Basis Set Desiderata 96

Types of Basis Functions 98

Slater and Gaussian Type Functions 98

Plane-Wave Functions 101

Real-Space Functions 103

Other Functions 104

Structure and Classification of Gaussian Type Basis Sets 105

Contracted Basis Functions 108

Optimization of Basis Set Parameters 111

Basis Set Augmentation 113

Diffuse Functions 113

Tight Functions 114

Fitting Functions 115

Nonatom-Centered Basis Sets 115

Examples of Basis Sets 116

Segmented Contracted Basis Sets 116

General Contracted Basis Sets 117

Property Basis Sets 119

Electric Properties 121

Magnetic Properties 126

Mixed Properties 128

Relativistic Basis Sets 129

Pseudopotentials 130

Basis Set Convergence 131

Convergence of Electronic Structure Methods with Gaussian Type Basis Sets 132

Composite Extrapolation Methods 133

Basis Set Incompleteness and Superposition Errors 134

Aspects of Choosing A Suitable Basis Set 136

Availability of Basis Sets 139

Acknowledgment 139

References 139

4 The Quantum Chemistry of Open-Shell Species 151
Anna I. Krylov

Introduction and Overview 151

Quantum Chemistry Methods for Open- and Closed-Shell Species 155

Some Aspects of Electronic Structure of Open-Shell Species 159

Spin Contamination of Approximate Open-Shell Wave Functions 159

Jahn-Teller Effect 160

Vibronic Interactions and Pseudo-Jahn-Teller Effect 162

High-Spin Open-Shell States 165

Open-Shell States with Multiconfigurational Character 167

EOM-IP and EOM-EA Methods for Open-Shell Systems 167

Examples 169

Diradicals, Triradicals, and Beyond 174

Excited States of Open-Shell Species 181

Metastable Radicals 186

Bonding in Open-Shell Species 187

Dyson Orbitals 188

Density-Based Wave Function Analysis 189

Insight into Bonding from Physical Observables 192

Properties and Spectroscopy 193

Vibrational Spectroscopy 194

Electronic and Photoelectron Spectroscopy 194

Electronic Transitions 200

Outlook 207

Acknowledgments 208

Appendix: List of Acronyms 209

References 210

5 Machine Learning, Quantum Chemistry, and Chemical Space 225
Raghunathan Ramakrishnan, and O. Anatole von Lilienfeld

Introduction 225

Paradigm 228

Kernel Ridge Regression 230

Representation 232

Data 234

Kernel 236

Electrons 239

¿-Machine Learning 241

Atoms in Molecules 245

Crystals 247

Conclusions and Outlook 248

Acknowledgments 250

References 250

6 The Master Equation Approach to Problems in Chemical and Biological Physics 257
Dmitrii E. Makarov

Introduction 257

The General Form of A Master Equation and its Solution 260

Microscopic Reversibility, Detailed Balance, and Their Consequences 262

The Kinetic Monte Carlo (KMC) Method 265

Quantum Master Equations 270

The Reduced Density Matrix as a Description of a Molecule Interacting with Its Surroundings 270

Diagonal and Off-Diagonal Elements of the Density Matrix and Significance of Dephasing 273

Relaxation 275

Kinetic Monte Carlo for Quantum Master Equations 277

Physical Significance of The Quantum Kinetic Monte Carlo Scheme 282

Concluding Remarks 283

Acknowledgments 284

References 284

7 Continuous Symmetry Measures: A New Tool in Quantum Chemistry 289
Pere Alemany, David Casanova, Santiago Alvarez, Chaim Dryzun, and David Avnir

Introduction 289

Symmetry as a Fundamental Concept in Quantum Chemistry 289

Symmetry, Pseudosymmetry, and Quasisymmetry 292

Continuous Symmetry Measures 295

General Definition of CSMs 295

CSMs in Molecular Quantum Chemistry 299

CSM for the Nuclear Framework 300

CSMs for Matrices and Operators 303

CSM for Functions: Electron Density, Wave Functions, and Molecular Orbitals 304

CSMs for Irreducible Representations of a Group 307

Pseudosymmetry Analysis of Molecular Orbitals 313

Applications 315

The Nature of the Chemical Bond from the Point of View of CSMs 315

CSM Analysis of the Electronic Structure of Conjugated Hydrocarbons and Related Compounds 321

Pseudosymmetry Analysis of the d-Block Molecular Orbitals of "Octahedral" ML₆ Transition Metal Compounds 328

Symmetry, Pseudosymmetry and Walsh Diagrams for ML ₄ Compounds along the Planarization Path 334

Conclusions 343

Acknowledgment 344

References 344

Index 353