Gradient expansion of the exchange energy density functional: A complementary expansion of the atomic energy functional

Abstract

Hartree–Fock–Roothaan–Clementi (HFRC) densities are used to calculate the total exchange energies and the total binding energies of neutral atoms according to the truncated gradient expansion. With the inclusion of the fourth order, the total binding energies for Z=2 to 36 and Z=54 agree very well with the HFRC values. Higher-order corrections for the consistency between HFRC solutions and the density gradient expansions are, therefore, unimportant.