Semiempirical Atomic-Energy Formula

We study the Thomas-Fermi-Dirac statistical model of the atom in the energy-functional formulation. We obtain minima of the total energy for five analytic-screening-function-density combinations. Total energies, average radii, and rms radii vary from model to model quite markedly, and depart quite substantially from "data" based upon Hartree-Fock or Hartree-Fock-Slater calculations. For the model based upon the analytic screening function due to Green, Sellin, and Zachor and for a closely related "regularized" model, the dependence of the component energies upon the electron number $N$, the model parameters, and certain integral constants is represented analytically. Minimization of the total energy with respect to the potential parameters leads to simple algebraic equations. The results again are poor. However, by making reasonable semiempirical modifications in the component terms, we find we can achieve stability with binding energies and potential parameters which are close to the data obtained from Hartree-Fock (HF) or Hartree-Fock-Slater (HFS) studies.