Generalized Local Density Approximation in an Inhomogeneous Electron Liquid

Abstract

A differential equation relating an unknown, but local, function of ground-state electron density ρ, say S(ρ), is shown first to have an analytical solution for S(r) in terms of ρ(r) for spherically symmetric systems. For closed shell atoms Kr and Xe, S(r) and S(ρ) over the density range 0<ρ<ρ(r = 0) are plotted and examined. S(r) has a roughly monotonically decreasing behaviour with small additional features reflecting electronic shell structure. the general shape of S(ρ) is also found to be the same for these atoms, use of which is made to present an approach to the non-relativisitic limit of large numbers of electrons via these closed shell atoms. Relaxing spherical symmetry, it is proposed that the resulting partial differential equation should be powerful enough to describe the ground-state electron density in neutral homonuclear molecules and clusters for large number of electrons.

Key Words:

• Inhomogeneous electron liquid
• Thomas-Fermi theory