Analysis of the Large Z Exchange Expansion of Atoms and Ions Beyond the Leading Order

Lieb-Simon zeta-scaling, which describes the scaling of neutral closed-shell atoms as Z approaches infinity, has been used with marked success to provide theoretical constraints on density functionals and to help generate perturbative expansions with Z. The exact large Z expansion for the exchange energy has never been explicitly calculated beyond the leading order Z^5/3 term. We have recently provided consistent numerical and analytical evidence of a ZlnZ term beyond the LDA. Further the numerical evidence suggests the LDA has a Z^4/3 term. We propose an analytical model for ions, and compare with numerical results for N=1 and N/Z=1/2 atoms, and find that the model agrees with the results within 10%. These results improve as Z increases. We also provide an analysis of the Z^4/3 behavior in the LDA using the Thomas-Fermi potential and Kohn-Sham orbitals.