1/Z expansion, correlation energy, and shannon entropy of heavy atoms in nonrelativistic limit

It has been known since the work of March and White that the simplest nonrelativistic density functional theory, namely, the statistical method of Thomas, Fermi, and Dirac, sums subseries of the so-called 1/Z expansion to yield, for heavy neutral atoms, the ground-state energy E = -a(0)Z(7/3) + a(1)Z(2) - a(2)Z(5/3) + .... The term of 0(Z(5/3)) is the Dirac-Slater exchange energy E-exc, and it is of considerable interest to know at what order the correlation energy E-corr enters this expansion. Dimensional scaling considerations by Kais et al. suggested E-corr proportional to Z(4/3) in the limit of large Z. Here, attention is focused on whether this can be distinguished empirically from a term of the form (aZ In Z + bZ) for neutral atoms. If the latter term is correct, then a relationship between E-corr and the Shannon information entropy can be forged analytically for large atomic number Z in nonrelativistic theory. (C) 1998 John Wiley & Sons, Inc.