Explicit energy density functional for the Crandall two-electron model atom with harmonic confinement and inverse square law inter-particle repulsion

Abstract

Abstract Though density functional theory is already developed in useful practical numerical forms, no explicit simple ground-state energy density functional exists. Here, towards establishing such a theory, we present the ground-state energy of the Crandall et al.'s two-electron spin-compensated model atom in terms of ∇ 2 ρ ( r ) / ρ ( r ) evaluated at r = 0 , where ρ ( r ) is the electron density.