Density Functional Theory

David S. Sholl leads the Transformational Decarbonization Initiative at the Oak Ridge National Laboratory and is a Professor of Chemical & Biomolecular Engineering at the Georgia Institute of Technology. Janice A. Steckel is a Physical Scientist at the United States Department of Energy, National Energy Technology Laboratory in Pittsburgh, Pennsylvania.

• 1 What Is Density Functional Theory?1.1 How to Approach This Book1.2 Examples of DFT in Action1.2.1 Ammonia Synthesis by Heterogeneous Catalysis1.2.2 Embrittlement of Metals by Trace Impurities1.2.3 Materials Properties for Modeling Planetary Formation1.2.4 High Throughput/Big Data Case Study1.3 The Schrödinger Equation1.4 Density Functional Theory—From Wave Functions to Electron Density1.5 Exchange– Correlation Functional1.6 The Quantum Chemistry Tourist1.6.1 Localized and Spatially Extended Functions1.6.2 Wave-Function-Based Methods1.6.3 Hartree– Fock Method1.6.4 Beyond Hartree–Fock1.7 What Can DFT Not Do?1.8 Which DFT Code Should I Use?1.9 Density Functional Theory in Other Fields1.10 How to Approach This Book  2 DFT Calculations for Simple Solids2.1 Periodic Structures, Supercells, and Lattice Parameters2.2 Face-Centered Cubic Materials2.3 Hexagonal Close-Packed Materials2.4 Crystal Structure Prediction2.5 Phase TransformationsExercises  3 Nuts and Bolts of DFT Calculations3.1 Reciprocal Space and k Points3.1.1 Plane Waves and the Brillouin Zone3.1.2 Integrals in k Space3.1.3 Choosing k Points in the Brillouin Zone3.1.4 Metals—Special Cases in k Space; DFT+U3.1.5 Summary of k Space3.2 Energy Cutoffs3.2.1 Pseudopotentials3.3 Numerical Optimization3.3.1 Optimization in One Dimension3.3.2 Optimization in More than One Dimension3.3.3 What Do I Really Need to Know about Optimization?3.4 DFT Total Energies—An Iterative Optimization Problem3.5 Geometry Optimization3.5.1 Internal Degrees of Freedom3.5.2 Geometry Optimization with Constrained Atoms3.5.3 Optimizing Supercell Volume and ShapeAppendix: Calculation Details  4 Thinking About Accuracy and Choosing Functionals for DFT Calculations4.1 How Accurate Are DFT Calculations?4.2 Choosing a Functional4.3 Examples of Physical Accuracy4.3.1 Benchmark Calculations for Molecular Systems—Energy and Geometry4.3.2 Benchmark Calculations for Molecular Systems—Vibrational Frequencies4.3.3 Crystal Structures and Cohesive Energies4.3.4 Adsorption Energies and Bond Strengths4.4 How to Use the Rest of this Book  5 DFT Calculations for Surfaces of Solids and Interfaces in Crystals5.1 Importance of Surfaces5.2 Periodic Boundary Conditions and Slab Models5.3 Choosing k Points for Surface Calculations5.4 Classification of Surfaces by Miller Indices5.5 Surface Relaxation5.6 Calculation of Surface Energies5.7 Symmetric and Asymmetric Slab Models5.8 Surface Reconstruction5.9 Adsorbates on Surfaces5.9.1 Accuracy of Adsorption Energies5.10 Effects of Surface Coverage5.11 Grain Boundaries in SolidsExercisesAppendix: Calculation Details  6 DFT Calculations of Vibrational Frequencies6.1 Isolated Molecules6.2 Vibrations of a Collection of Atoms6.3 Molecules on Surfaces6.4 Zero-Point Energies6.5 Phonons and Delocalized ModesExercises  7 Calculating Rates of Chemical Processes Using Transition State Theory7.1 One-Dimensional Example7.2 Multidimensional Transition State Theory7.3 Finding Transition States7.3.1 Elastic Band Method7.3.2 Nudged Elastic Band Method and the Dimer Method7.3.3 Initializing NEB Calculations7.4 Finding the Right Transition States7.5 Connecting Individual Rates to Overall Dynamics7.6 Quantum Effects and Other Complications7.6.1 High Temperatures/Low Barriers7.6.2 Quantum Tunneling7.6.3 Zero-Point EnergiesExercisesAppendix: Calculation Details  8 Equilibrium Phase Diagrams and Electrochemistry with Open Ensemble Methods8.1 Stability of Bulk Metal Oxides8.1.1 Examples Including Disorder—Configurational Entropy8.2 Stability of Metal and Metal Oxide Surfaces8.3 Multiple Chemical Potentials and Coupled Chemical Reactions8.4 DFT for ElectrochemistryExercisesAppendix: Calculation Details  9 Electronic Structure and Magnetic Properties9.1 Electronic Density of States9.2 Local Density of States and Atomic Charges9.3 MagnetismExercises  10 Ab Initio Molecular Dynamics10.1 Classical Molecular Dynamics10.1.1 Molecular Dynamics with Constant Energy10.1.2 Molecular Dynamics in the Canonical Ensemble10.1.3 Practical Aspects of Classical Molecular Dynamics10.2 Ab Initio Molecular Dynamics: Gaussian Basis Sets in Non-Plane Wave Codes10.3 Applications of Ab Initio Molecular Dynamics10.3.1 Exploring Structurally Complex Materials: Liquids and Amorphous Phases10.3.2 Exploring Complex Energy Surfaces10.4 Time-Dependent Density Functional TheoryExercisesAppendix: Calculation Details  11 Methods beyond “Standard” Calculations11.1 Choosing a Functional (Revisited)11.2 Estimating Uncertainties in DFT Results Using the BEEF Approach11.3 DFT+X Methods for Improved Treatment of Electron Correlation11.3.1 Dispersion Interactions and DFT-D and D2, D3, TS methods11.4 Self-Interaction Error, Strongly Correlated Electron Systems, and DFT+U11.5 RPA11.6 Larger System Sizes with Linear Scaling Methods and Classical Force Fields11.7 Conclusion