Density Functional Theory: Basic Results and Some Observations

Abstract

We review first the basic results of density functional theory: the lemma of Hohenberg and Kohn establishing the density n(r) as a sufficient variable for a description of a non-degenerate or degenerate ground state; the energy variational principle, including recent reformulations by Levy and Lieb; the self-consistent Kohn-Sham equations and the most recent improved approximations for the exchange-correlation functional. This is followed by a number of observations: the issue of v-representability is discussed, including, depending on the context, its significance and non-significance in the light of recent work by Levy, Lieb, and Kohn; a discussion is presented of two different approaches to the basic functionals F[n(r)] and E_xc[n(r)] -- by means of many-body tech-niques or by using the definition of F[n(r)] as a minimum over a constrained set of antisymmetric functions; other interesting recent developments of density functionals are briefly mentioned; some remarks are offered concerning a proposed concept of generalized local approximations; and finally a few other promising directions for future research are listed.

In these lectures, which come at the beginning of a workshop dedicated to density functional theory (DFT), I would like to attempt two objectives: to refresh your memory about the basic facts of DFT, and to present some remarks about the present situation and the outlook for the future.

Supported in part by the National Science Foundation under Grant No. PHY77-27084, supplemented by funds from the National Aeronautics and Space Administration.