Density functional theory: An introduction
1998/06/30 by Nathan Argaman, Guy Makov · 358 citations
Chemistry · Engineering · Materials Science · Physics and Astronomy · #Ab initio #Advanced Physical and Chemical Molecular Interactions #Density functional theory #Generalization #Legendre polynomials #Legendre transformation #Machine Learning in Materials Science #Orbital-free density functional theory #Phase Equilibria and Thermodynamics #Simple (philosophy) #Theme (computing) #Time-dependent density functional theory #cond-mat #physics.chem-ph #physics.comp-ph #physics.ed-ph
paper · pdf · doi:10.1119/1.19375
published in American Journal of Physics 68(1), 69-79 (American Institute of Physics) · Substantially revised to improve pedagogical value; explicit examples added. 14 twocolumn pages, 4 figures, American Journal of Physics (in press)
arxiv created 1999/07/19 · openalex publication_date 2000/01/01 · arxiv updated 2010/12/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.
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