Relationship between gradient expansion terms in the kinetic and exchange energy-density functionals in statistical models of an atom with shell structure

Abstract

In a recent paper Pathak and Gadre have established lower bounds for the first gradient-expansion corrections to the kinetic- and exchange-energy terms of the Thomas-Fermi-Dirac model of an atom. In the present report, with the use of the Na atom as an example, the bounds are calculated with the recent electron (number) densities of Wang and Parr, Csavinszky, and Wang, who considered statistical energy-density functionals for atoms with shell structure.