List of Contributors xi Foreword 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 Δ-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 ML4 Compounds along the Planarization Path 334 Conclusions 343 Acknowledgment 344 References 344 Index 353.