Density-functional theory for excited states in a quasi-local-density approximation

Abstract

The starting point of this paper is a recent extension by Theophilou of the Hohenberg-Kohn-Sham (HKS) density-functional theory to ensembles of systems consisting of the M lowest eigenstates, equally weighted. As in the HKS theory the key quantities are the exchange-correlation energy, $E_{\mathrm{xc}{}^M\left[\mathrm{n}\right(\mathrm{r}\left)\right]}$, and potential, $v_{\mathrm{xc}{}^M(\mathit{r};[\mathit{n}\left(\mathit{r}\mathcal{’}\right)\left]\right)}$. The present paper provides expressions for these quantities, valid for systems of slowly varying density. Even for such systems, however, there are essential nonlocal effects. Nevertheless both $E_{\mathrm{xc}{}^M}$ and $v_{\mathrm{xc}{}^M}$ can be calculated in terms of quantities characteristic of appropriate uniform thermal ensembles. This theory is the analog of the ground-state local-density approximation and allows calculation of excited-state energies and densities.