Application of (Kohn–Sham) Density-Functional Theory to Real Materials

Abstract

Hohenberg and Kohn proved the existence and uniqueness of a functional of the electron density, whose minimization yields the ground-state density $$n(r)$$ of a bound system of $$N$$ interacting electrons in some external potential $$v(r)$$. The exact expression of the universal density functional is however elusive. In this chapter, I describe the several attempts made for designing an approximation to the density functional that gave accurate results for “real materials” (molecules, clusters, and extended materials). All discussed approximations originate from the Kohn–Sham approach, a particular (but almost universally adopted) formulation of the density-functional theory, in which the variational problem of the $$N$$ interacting electrons is recast into a set of $$N$$ one-particle equations where each electron acts in the mean field generated by all the other electrons.