Introduction to Density Functional Theory

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 textbook presents the basic concepts and features of DFT at an introductory level, suitable for undergraduate and beginning graduate students in science and engineering. Beginning with a brief review of elementary quantum mechanics, the book 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 formulated and explained, 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 reviewed, 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, together with a brief review of chemical reactivity indices. The book ends with a chapter on time-dependent DFT, discussing real-time electron dynamics and excitation energies, and additional resources are provided in several appendices. Written in an accessible and student-friendly style, the book covers the essentials of DFT and electronic structure calculations in a fully self-contained manner and without overburdening readers with formal and technical details. The book also contains many end-of-chapter exercises, including hands-on computer simulations using Python, as well as many suggestions for further reading.

Carsten A. Ullrich received his PhD in 1995 at the University of Würzburg and, after several postdoctoral positions, joined the faculty at the University of Missouri in 2001. He received tenure in 2007 and became a full professor in 2013. In 2023 he was appointed Curator's Distinguished Professor of Physics. His research focuses on the study of the foundations and the development of new methodologies in time-dependent density functional theory (TDDFT) and spin-DFT. He has over 125 publications, including a book on TDDFT, and he is a Fellow of the American Physical Society. Adam Wasserman is Professor of Chemistry at Purdue University, where he has taught since 2008. His research focuses on understanding why some chemical bonds are weak while others are strong. To do this, he and his research group develop methods based on Density Functional Theory to calculate the electronic properties of molecules directly from those of their constituent atoms. A Purdue University Faculty Scholar, Dr Wasserman holds a courtesy appointment in the Department of Physics and Astronomy, and has been a recipient of numerous awards, including an Alfred P. Sloan research Fellowship and a Camille and Henry Dreyfus Teacher-Scholar award.