Introduction to Density Functional Theory

Abstract

Density functional theory (DFT) is a quantum mechanical framework in which the ground state of interacting electronic systems is completely described in terms of the electron density. This leads to a practical approach for electronic structure calculations which is very widely used in (bio)chemistry, physics, and materials science due to its reasonable computational cost and useful accuracy. This book presents the basic concepts and features of DFT at an introductory level, suitable for undergraduate and beginning graduate students in science and engineering. The book starts with a brief review of quantum mechanics, then introduces essential concepts such as many-body wave functions, orbitals, Slater determinants, functionals, and the variational principle. The fundamental theorems of DFT of Hohenberg and Kohn and Kohn and Sham are then formulated and explained. This is followed by a case study of a one-dimensional model system to illustrate the self-consistent numerical solution of the Kohn-Sham equation. To use DFT in practice, the exchange-correlation energy functional must be approximated; the most important and widely used approximations are covered, including the local-density approximation, generalized gradient approximations, and hybrid functionals, explaining their origin and assessing their performance with many examples. Practical aspects of molecular and solid-state calculations, such as basis sets and pseudopotentials, are introduced. The book ends with a chapter on time-dependent DFT, discussing real-time electron dynamics and excitation energies. Additional resources are provided in several appendices. The book contains many end-of-chapter exercises, including hands-on Python simulations, and suggestions for further reading.