Density functional theory: An introduction

Density functional theory (DFT) is one of the most widely used methods for ab initio calculations of the structure of atoms, molecules, crystals, surf aces, 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 betwee n different independent variables. The central theme of DFT, i.e., the noti on that it is possible and beneficial to replace the dependence on the exte rnal potential upsilon(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 mu to the number of particles N. This approach is used here to introduce the Hohenberg-Kohn energy functional an d to obtain the corresponding theorems, using classical nonuniform fluids a s simple examples. The energy functional for electronic systems is consider ed next, and the Kohn-Sham equations are derived. The exchange-correlation part of this functional is discussed, including both the local density appr oximation to it, and its formally exact expression in terms of the exchange -correlation hole. A very brief survey of various applications and extensio ns is included. (C) 2000 American Association of Physics Teachers.