Density functional theory: An introduction

Nathan Argaman, Guy Makov

Research output: Contribution to journalArticlepeer-review

138 Scopus citations

Abstract

Density functional theory (DFT) is one of the most widely used methods for ab initio calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often considered too lengthy to be included in various curricula. An alternative introduction to DFT is presented here, drawing on ideas which are well-known from thermodynamics, especially the idea of switching between different independent variables. The central theme of DFT, i.e., the notion that it is possible and beneficial to replace the dependence on the external potential v(r) by a dependence on the density distribution n(r), is presented as a straightforward generalization of the familiar Legendre transform from the chemical potential μ to the number of particles N. This approach is used here to introduce the Hohenberg-Kohn energy functional and to obtain the corresponding theorems, using classical nonuniform fluids as simple examples. The energy functional for electronic systems is considered next, and the Kohn-Sham equations are derived. The exchange-correlation part of this functional is discussed, including both the local density approximation to it, and its formally exact expression in terms of the exchange-correlation hole. A very brief survey of various applications and extensions is included.

Original languageEnglish
Pages (from-to)69-79
Number of pages11
JournalAmerican Journal of Physics
Volume68
Issue number1
DOIs
StatePublished - 1 Jan 2000
Externally publishedYes

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