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
