Variational improvement of the statistical model for heavy atoms, with minimization of correlation energy

Abstract

The statistical model of Thomas–Fermi–Dirac treats many-electron atoms in terms of statistical density, and derives the well-known single particle potential US which in turn gives the determinantal function ΦS that carries the many-body feature. This paper presents: (a) a variational improvement of the model is presented by simply modifying the Ritz principle with a special form of trial function that contains both the ΦS and dynamical correlation parts. With the ΦS assuming the principal role, the Ritz principle is improved for treating heavy atoms. (b) Mediated by ΦS, the variational functional reduces immediately to that of the correlation energy Ect, and, when optimized, yields an upper bound on the exact energy. The exact Ec is derived to clarify the contents of the Ect, and, several approximations using the bound property are discussed. (c) Finally, the RRU is critically compared with the density functional theory, indicating that the RRU can be a viable variational alternative, as they are operationally inverse of each other, but with the important feature that the theory can be systematically improved.