Density functional theory: An introduction
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 wellknown 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 HohenbergKohn 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 KohnSham equations are derived. The exchangecorrelation part of this functional is discussed, including both the local density approximation to it, and its formally exact expression in terms of the exchangecorrelation hole. A very brief survey of various applications and extensions is included.
 Publication:

American Journal of Physics
 Pub Date:
 January 2000
 DOI:
 10.1119/1.19375
 arXiv:
 arXiv:physics/9806013
 Bibcode:
 2000AmJPh..68...69A
 Keywords:

 01.50.i;
 31.15.Ew;
 05.70.a;
 Educational aids;
 Densityfunctional theory;
 Thermodynamics;
 Physics  Physics Education;
 Condensed Matter;
 Physics  Chemical Physics;
 Physics  Computational Physics
 EPrint:
 Substantially revised to improve pedagogical value