| |
| |
| Preface | |
| |
| |
| |
| What Is Density Functional Theory? | |
| |
| |
| |
| How to Approach This Book | |
| |
| |
| |
| Examples of DFT in Action | |
| |
| |
| |
| Ammonia Synthesis by Heterogeneous Catalysis | |
| |
| |
| |
| Embrittlement of Metals by Trace Impurities | |
| |
| |
| |
| Materials Properties for Modeling Planetary Formation | |
| |
| |
| |
| The Schr&ooddot;dinger Equation | |
| |
| |
| |
| Density Functional Theory-From Wave Functions to Electron Density | |
| |
| |
| |
| Exchange-Correlation Functional | |
| |
| |
| |
| The Quantum Chemistry Tourist | |
| |
| |
| |
| Localized and Spatially Extended Functions | |
| |
| |
| |
| Wave-Function-Based Methods | |
| |
| |
| |
| Hartree-Fock Method | |
| |
| |
| |
| Beyond Hartree-Fock | |
| |
| |
| |
| What Can DFT Not Do? | |
| |
| |
| |
| Density Functional Theory in Other Fields | |
| |
| |
| |
| How to Approach This Book (Revisited) | |
| |
| |
| References | |
| |
| |
| Further Reading | |
| |
| |
| |
| DFT Calculations for Simple Solids | |
| |
| |
| |
| Periodic Structures, Supercells, and Lattice Parameters | |
| |
| |
| |
| Face-Centered Cubic Materials | |
| |
| |
| |
| Hexagonal Close-Packed Materials | |
| |
| |
| |
| Crystal Structure Prediction | |
| |
| |
| |
| Phase Transformations | |
| |
| |
| Exercises | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| Nuts and Bolts of DFT Calculations | |
| |
| |
| |
| Reciprocal Space and k Points | |
| |
| |
| |
| Plane Waves and the Brillouin Zone | |
| |
| |
| |
| Integrals in k Space | |
| |
| |
| |
| Choosing k Points in the Brillouin Zone | |
| |
| |
| |
| Metals-Special Cases in k Space | |
| |
| |
| |
| Summary of k Space | |
| |
| |
| |
| Energy Cutoffs | |
| |
| |
| |
| Pseudopotentials | |
| |
| |
| |
| Numerical Optimization | |
| |
| |
| |
| Optimization in One Dimension | |
| |
| |
| |
| Optimization in More than One Dimension | |
| |
| |
| |
| What Do I Really Need to Know about Optimization? | |
| |
| |
| |
| DFT Total Energies-An Iterative Optimization Problem | |
| |
| |
| |
| Geometry Optimization | |
| |
| |
| |
| Internal Degrees of Freedom | |
| |
| |
| |
| Geometry Optimization with Constrained Atoms | |
| |
| |
| |
| Optimizing Supercell Volume and Shape | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| DFT Calculations for Surfaces of Solids | |
| |
| |
| |
| Importance of Surfaces | |
| |
| |
| |
| Periodic Boundary Conditions and Slab Models | |
| |
| |
| |
| Choosing k Points for Surface Calculations | |
| |
| |
| |
| Classification of Surfaces by Miller Indices | |
| |
| |
| |
| Surface Relaxation | |
| |
| |
| |
| Calculation of Surface Energies | |
| |
| |
| |
| Symmetric and Asymmetric Slab Models | |
| |
| |
| |
| Surface Reconstruction | |
| |
| |
| |
| Absorbates on Surfaces | |
| |
| |
| |
| Accuracy of Adsorption Energies | |
| |
| |
| |
| Effects of Surface Coverage | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| DFT Calculations of Vibrational Frequencies | |
| |
| |
| |
| Isolated Molecules | |
| |
| |
| |
| Vibrations of a Collection of Atoms | |
| |
| |
| |
| Molecules on Surfaces | |
| |
| |
| |
| Zero-Point Energies | |
| |
| |
| |
| Phonons and Delocalized Modes | |
| |
| |
| Exercises | |
| |
| |
| Reference | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| Calculating Rates of Chemical Processes Using Transition State Theory | |
| |
| |
| |
| One-Dimensional Example | |
| |
| |
| |
| Multidimensional Transition State Theory | |
| |
| |
| |
| Finding Transition States | |
| |
| |
| |
| Elastic Band Method | |
| |
| |
| |
| Nudged Elastic Band Method | |
| |
| |
| |
| Initializing NEB Calculations | |
| |
| |
| |
| Finding the Right Transition States | |
| |
| |
| |
| Connecting Individual Rates to Overall Dynamics | |
| |
| |
| |
| Quantum Effects and Other Complications | |
| |
| |
| |
| High Temperatures/Low Barriers | |
| |
| |
| |
| Quantum Tunneling | |
| |
| |
| |
| Zero-Point Energies | |
| |
| |
| Exercises | |
| |
| |
| Reference | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| Equilibrium Phase Diagrams from Ab Initio Thermodynamics | |
| |
| |
| |
| Stability of Bulk Metal Oxides | |
| |
| |
| |
| Examples Including Disorder-Configurational Entropy | |
| |
| |
| |
| Stability of Metal and Metal Oxide Surfaces | |
| |
| |
| |
| Multiple Chemical Potentials and Coupled Chemical Reactions | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| Electronic Structure and Magnetic Properties | |
| |
| |
| |
| Electronic Density of States | |
| |
| |
| |
| Local Density of States and Atomic Charges | |
| |
| |
| |
| Magnetism | |
| |
| |
| Exercises | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| Ab Initio Molecular Dynamics | |
| |
| |
| |
| Classical Molecular Dynamics | |
| |
| |
| |
| Molecular Dynamics with Constant Energy | |
| |
| |
| |
| Molecular Dynamics in the Canonical Ensemble | |
| |
| |
| |
| Practical Aspects of Classical Molecular Dynamics | |
| |
| |
| |
| Ab Initio Molecular Dynamics | |
| |
| |
| |
| Applications of Ab Initio Molecular Dynamics | |
| |
| |
| |
| Exploring Structurally Complex Materials: Liquids and Amorphous Phases | |
| |
| |
| |
| Exploring Complex Energy Surfaces | |
| |
| |
| Exercises | |
| |
| |
| References | |
| |
| |
| Further Reading | |
| |
| |
| Appendix Calculation Details | |
| |
| |
| |
| Accuracy and Methods beyond "Standard" Calculations | |
| |
| |
| |
| How Accurate Are DFT Calculations? | |
| |
| |
| |
| Choosing a Functional | |
| |
| |
| |
| Examples of Physical Accuracy | |
| |
| |
| |
| Benchmark Calculations for Molecular Systems-Energy and Geometry | |
| |
| |
| |
| Benchmark Calculations for Molecular Systems-Vibrational Frequencies | |
| |
| |
| |
| Crystal Structures and Cohesive Energies | |
| |
| |
| |
| Adsorption Energies and Bond Strengths | |
| |
| |
| |
| DFT + X Methods for Improved Treatment of Electron Correlation | |
| |
| |
| |
| Dispersion Interactions and DFT-D | |
| |
| |
| |
| Self-Interaction Error, Strongly Correlated Electron Systems, and DFT+U | |
| |
| |
| |
| Larger System Sizes with Linear Scaling Methods and Classical Force Fields | |
| |
| |
| |
| Conclusion | |
| |
| |
| References | |
| |
| |
| Further Reading | |
| |
| |
| Index | |