Force −∂Vxc/∂r associated with the exchange-correlation potential Vxc(r) in the neutral Ne atom

Abstract

Following an electrostatic interpretation of the force Fxc = −∂Vxc/∂r associated with the exchange-correlation potential Vxc(r), we present both analytical and numerical results for Fxc(r) in the Ne atom. The basic input is an existing quantum Monte Carlo (QMC) calculation of the ground-state electron density ρ(r) in this atom. The analytic form of ∂Vxc/∂r is in terms of the number of electrons Q(r) enclosed in a sphere of radius r centred on the nucleus, plus two phases needed to characterize the radial wavefunctions of density functional theory. Eigenvalue equations are presented for these phases, and used numerically. A brief discussion is added on the result of replacing the QMC ground-state density by its Hartree–Fock counterpart.