Density Functional Theory

This resource provides a brief, readable introduction to the key concepts and practical applications of density functional theory (DFT), at a level suitable for individuals from a variety of scientific backgrounds whom have never performed DFT calculations before. It includes numerous exercises and worked examples for self study, as well as lists of references to more detailed sources for the topics covered. The text is especially well–suited for students and researchers who want to use DFT in their work, but who do not require extensive knowledge of theory and mathematical details.

Chapter 1: What is Density Functional Theory? 1.1 How To Approach This Book. 1.2 Examples of DFT in Action. 1.3 The Schrödinger Equation. 1.4 Density Functional Theory – From Wavefunctions to Electron Density. 1.5 The Exchange–Correlation Functional. 1.6 The Quantum Chemistry Tourist. 1.7 What Can’t DFT Do?. 1.8 Density Functional Theory in Other Fields. 1.9 How To Approach This Book (Revisited). Chapter 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. Chapter 3: Nuts and Bolts of DFT Calculations. 3.1 Reciprocal Space and k–points. 3.2 Energy Cutoffs. 3.3 Numerical Optimization. 3.4 DFT Total Energies – An Iterative Optimization Problem. 3.5 Geometry Optimization. Chapter 4: DFT Calculations for Surfaces of Solids. 4.1 Why Surfaces Are Important. 4.2 Periodic Boundary Conditions and Slab Models. 4.3 Choosing k–points for Surface Calculations. 4.4 Classification of Surfaces by Miller Indices. 4.5 Surface Relaxation. 4.6 Calculation of Surface Energies. 4.7 Symmetric and Asymmetric Slab Models. 4.8 Surface Reconstruction. 4.9 Adsorbates on Surfaces. 4.10 Effects of Surface Coverage. Chapter 5: DFT Calculations of Vibrational Frequencies. 5.1 Isolated Molecules. 5.2 Vibrations of Collections of Atoms. 5.3 Molecules on Surfaces. 5.4 Zero Point Energies. 5.5 Phonons and Delocalized Modes. Chapter 6: Calculating Rates of Chemical Processes Using Transition State Theory. 6.1 A One–Dimensional Example. 6.2 Multi–dimensional Transition State Theory. 6.3 Finding Transition States. 6.4 Finding the Right Transition State. 6.5 Connecting Individual Rates to Overall Dynamics. 6.6 Quantum Effects and Other Complications. Chapter 7: Equilibrium Phase Diagrams From Ab Initio Thermodynamics. 7.1 Stability of Bulk Metal Oxides. 7.2 Stability of Metal and Metal Oxide Surfaces. 7.3 Multiple Chemical Potentials and Coupled Chemical Potentials. Chapter 8: Electronic Structure and Magnetic Properties. 8.1 Electronic Density of States. 8.2 Local DOS and Atomic Charges. 8.3 Magnetism. Chapter 9: Ab Initio Molecular Dynamics. 9.1 Classical Molecular Dynamics. 9.2 Ab Initio Molecular Dynamics. 9.3 Applications of Ab Initio Molecular Dynamics. Chapter 10: Accuracy and Methods Beyond "Standard" Calculations. 10.1 How Accurate Are DFT Calculations? 10.2 Choosing A Functional. 10.3 Examples of Physical Accuracy. 10.4 DFT+X Methods for Improved Treatment of Electron Correlations. 10.5 Large System Sizes With Linear Scaling Methods and Classical Forcefields. 10.6 Conclusion.