Are Unoccupied Kohn-Sham Eigenvalues Related to Excitation Energies?

Abstract

In the Kohn-Sham density functional method [1,2,3,4], the true interacting-electron system is replaced by a system of non-interacting electrons in an effective potential, v _eff, defined by the requirement that the density of the non-interacting electrons equals the true density. The single particle orbitals and their eigenenergies were originally introduced as a mathematical artifact in order to achieve a good approximation to the kinetic energy, leaving only a relatively small term, the exchange-correlation energy E _xc, to be approximated in practical implementations of the theory. It was later shown [5] that the energy of the highest occupied orbital is in fact the negative of the ionization energy. However, most approximate functionals (such as the commonly used local density approximation [2,3,4]) yield poor approximations to it. The energies of the other occupied orbitals and of the unoccupied orbitals do not have a rigorous correspondence to excitation energies. Nevertheless, it is common practice to compare eigenvalue differences to optical spectra of molecules and solids. Since these comparisons are made using Kohn-Sham eigenvalues obtained from approximate exchange-correlation functionals, it is not clear how much of the discrepancy between theory and experiment would persist if the true Kohn-Sham eigenvalues were to be used. In this paper we show that there is a surprising degree of agreement between the exact ground-state Kohn-Sham eigenvalue differences and excitation energies, for excitations from the highest occupied orbital to the unoccupied orbitals.