1 What Is Density Functional Theory?
1.1 How to Approach This Book
1.2 Examples of DFT in Action
1.2.1 Ammonia Synthesis by Heterogeneous Catalysis
1.2.2 Embrittlement of Metals by Trace Impurities
1.2.3 Materials Properties for Modeling Planetary Formation
1.2.4 High Throughput/Big Data Case Study
1.3 The Schr¶dinger Equation
1.4 Density Functional Theoryâ"From Wave Functions to Electron Density
1.5 Exchangeâ" Correlation Functional
1.6 The Quantum Chemistry Tourist
1.6.1 Localized and Spatially Extended Functions
1.6.2 Wave-Function-Based Methods
1.6.3 Hartreeâ" Fock Method
1.6.4 Beyond Hartreeâ"Fock
1.7 What Can DFT Not Do?
1.8 Which DFT Code Should I Use?
1.9 Density Functional Theory in Other Fields
1.10 How to Approach This Book
2 DFT Calculations for Simple Solids
2.1 Periodic Structures, Supercells, and Lattice Parameters
2.2 Face-Centered Cubic Materials
2.3 Hexagonal Close-Packed Materials
2.4 Crystal Structure Prediction
2.5 Phase Transformations
Exercises
3 Nuts and Bolts of DFT Calculations
3.1 Reciprocal Space and k Points
3.1.1 Plane Waves and the Brillouin Zone
3.1.2 Integrals in k Space
3.1.3 Choosing k Points in the Brillouin Zone
3.1.4 Metalsâ"Special Cases in k Space; DFT+U
3.1.5 Summary of k Space
3.2 Energy Cutoffs
3.2.1 Pseudopotentials
3.3 Numerical Optimization
3.3.1 Optimization in One Dimension
3.3.2 Optimization in More than One Dimension
3.3.3 What Do I Really Need to Know about Optimization?
3.4 DFT Total Energiesâ"An Iterative Optimization Problem
3.5 Geometry Optimization
3.5.1 Internal Degrees of Freedom
3.5.2 Geometry Optimization with Constrained Atoms
3.5.3 Optimizing Supercell Volume and Shape
Appendix: Calculation Details
4 Thinking About Accuracy and Choosing Functionals for DFT Calculations
4.1 How Accurate Are DFT Calculations?
4.2 Choosing a Functional
4.3 Examples of Physical Accuracy
4.3.1 Benchmark Calculations for Molecular Systemsâ"Energy and Geometry
4.3.2 Benchmark Calculations for Molecular Systemsâ"Vibrational Frequencies
4.3.3 Crystal Structures and Cohesive Energies
4.3.4 Adsorption Energies and Bond Strengths
4.4 How to Use the Rest of this Book
5 DFT Calculations for Surfaces of Solids and Interfaces in Crystals
5.1 Importance of Surfaces
5.2 Periodic Boundary Conditions and Slab Models
5.3 Choosing k Points for Surface Calculations
5.4 Classification of Surfaces by Miller Indices
5.5 Surface Relaxation
5.6 Calculation of Surface Energies
5.7 Symmetric and Asymmetric Slab Models
5.8 Surface Reconstruction
5.9 Adsorbates on Surfaces
5.9.1 Accuracy of Adsorption Energies
5.10 Effects of Surface Coverage
5.11 Grain Boundaries in Solids
Exercises
Appendix: Calculation Details
6 DFT Calculations of Vibrational Frequencies
6.1 Isolated Molecules
6.2 Vibrations of a Collection of Atoms
6.3 Molecules on Surfaces
6.4 Zero-Point Energies
6.5 Phonons and Delocalized Modes
Exercises
7 Calculating Rates of Chemical Processes Using Transition State Theory
7.1 One-Dimensional Example
7.2 Multidimensional Transition State Theory
7.3 Finding Transition States
7.3.1 Elastic Band Method
7.3.2 Nudged Elastic Band Method and the Dimer Method
7.3.3 Initializing NEB Calculations
7.4 Finding the Right Transition States
7.5 Connecting Individual Rates to Overall Dynamics
7.6 Quantum Effects and Other Complications
7.6.1 High Temperatures/Low Barriers
7.6.2 Quantum Tunneling
7.6.3 Zero-Point Energies
Exercises
Appendix: Calculation Details
8 Equilibrium Phase Diagrams and Electrochemistry with Open Ensemble Methods
8.1 Stability of Bulk Metal Oxides
8.1.1 Examples Including Disorderâ"Configurational Entropy
8.2 Stability of Metal and Metal Oxide Surfaces
8.3 Multiple Chemical Potentials and Coupled Chemical Reactions
8.4 DFT for Electrochemistry
Exercises
Appendix: Calculation Details
9 Electronic Structure and Magnetic Properties
9.1 Electronic Density of States
9.2 Local Density of States and Atomic Charges
9.3 Magnetism
Exercises
10 Ab Initio Molecular Dynamics
10.1 Classical Molecular Dynamics
10.1.1 Molecular Dynamics with Constant Energy
10.1.2 Molecular Dynamics in the Canonical Ensemble
10.1.3 Practical Aspects of Classical Molecular Dynamics
10.2 Ab Initio Molecular Dynamics: Gaussian Basis Sets in Non-Plane Wave Codes
10.3 Applications of Ab Initio Molecular Dynamics
10.3.1 Exploring Structurally Complex Materials: Liquids and Amorphous Phases
10.3.2 Exploring Complex Energy Surfaces
10.4 Time-Dependent Density Functional Theory
Exercises
Appendix: Calculation Details
11 Methods beyond âStandardâ Calculations
11.1 Choosing a Functional (Revisited)
11.2 Estimating Uncertainties in DFT Results Using the BEEF Approach
11.3 DFT+X Methods for Improved Treatment of Electron Correlation
11.3.1 Dispersion Interactions and DFT-D and D2, D3, TS methods
11.4 Self-Interaction Error, Strongly Correlated Electron Systems, and DFT+U
11.5 RPA
11.6 Larger System Sizes with Linear Scaling Methods and Classical Force Fields
11.7 Conclusion
