A bird's-eye view of density-functional theory

TL;DR

This paper provides an accessible overview of density-functional theory (DFT), focusing on its conceptual foundations, recent developments, and applications relevant to both physics and chemistry, aimed at students and researchers new to the field.

Contribution

It offers a non-technical, balanced introduction to DFT's core principles, recent advances, and extensions, bridging the gap between foundational theory and practical applications.

Findings

Discussion of Hohenberg-Kohn theorem and Kohn-Sham equations

Overview of approximate density functionals and extensions

Insight into applications of DFT in physics and chemistry

Abstract

This paper is the outgrowth of lectures the author gave at the Physics Institute and the Chemistry Institute of the University of Sao Paulo at Sao Carlos, Brazil, and at the VIII'th Summer School on Electronic Structure of the Brazilian Physical Society. It is an attempt to introduce density-functional theory (DFT) in a language accessible for students entering the field or researchers from other fields. It is not meant to be a scholarly review of DFT, but rather an informal guide to its conceptual basis and some recent developments and advances. The Hohenberg-Kohn theorem and the Kohn-Sham equations are discussed in some detail. Approximate density functionals, selected aspects of applications of DFT, and a variety of extensions of standard DFT are also discussed, albeit in less detail. Throughout it is attempted to provide a balanced treatment of aspects that are relevant for chemistry and aspects relevant for physics, but with a strong bias towards conceptual foundations. The paper is intended to be read before (or in parallel with) one of the many excellent more technical reviews available in the literature.