Local spin-density approximation for spin eigenspaces and its application to the excited states of atoms

Abstract

The main objective of this paper is to investigate the applicability of the subspace density-functional theory (SDFT) for the calculation of excited-state energies. The exchange and correlation energy density functionals, ${E}_{\mathrm{xc}}(\ensuremath{\rho}),$ used in the present calculation are local and depend on the polarizability parameter $\ensuremath{\zeta}=2S/N.$ The deviations of the calculated excited-state energies from their corresponding experimental values range from 0.1% to 0.8% for systems with more than two electrons, while for the helium isoelectronic series the corresponding range is from 0.1% to 1.9%. Thus the SDFT accuracy compares well in most cases with that of the ground-state local-density approximation calculations. Virial theorem and other relations concerning atoms are verified in the context of SDFT calculations. In this paper we also present a new formulation of the SDFT. Our new formulation alleviates the initial Kohn and Sham (KS) theory from the constraint of densities representable by single Slater determinants. This is an essential development as there are eigenstates of spin and other quantum operators, not representable by single Slater determinants.