Comparison of the Perdew–Wang exchange with the Dirac exchange

Abstract

AbstractRecently, Perdew and Wang presented an expression for the exchange energy of a many‐electron system. This functional has been adapted in the present work in variational density functional calculations of the total atomic binding energy of the Ne atom. For this atom similar calculations have been done earlier using the Dirac expression for the exchange energy. Three different total energy functionals have been considered: (1) the Thomas‐Fermi‐Perdew‐Wang functional, (2) the above functional augmented by (1/9) of the original Weizsäcker correction to the Thomas‐Fermi kinetic energy, and (3) the same functional as in 1 augmented by (1/5.3) of the original Weizsäcker correction to the Thomas‐Fermi kinetic energy. The electron (number) density of the Ne atom has been constructed from hydrogen‐like one‐electron wave functions containing three variational parameters. Each of three total energy functionals have been minimized with respect to these parameters. Comparison of the Perdew‐Wang and Dirac exchange energies shows that, in each of the three model pairs, the Perdew‐Wang exchange energy is larger in magnitude than the Dirac exchange energy. It is also found that the exchange energy obtained by 2, ‐12.31 a.u., is in excellent agreement with the value of ‐12.22 a.u. calculated by Perdew and Wang with the Clementi and Roetti near‐Hartree‐Fock density.