Comparison of Variational Solutions of the Thomas-Fermi Model in Terms of the Corrected Ionization Energy

Abstract

It is shown that leading corrections, to the ionization energy, o f many-electrons atom , can be expressed as leading corrections of initial slope of trial variational solutions o f the Thomas-Fermi equation. Some variational solutions with different initial slopes are compared. A com parison o f the results shows, that as far as the binding energies are concerned a trial function with its slope not close to the (negative) Baker's constant may not be suited.

A Z-dependent variational solution of Thomas-Fermi-Dirac equation

“…According to these findings, the inclusion of Z in the trial solution is expected to improve the electronic structure of solids within TFD. Despite much available works for TF and TFD methods (Tomishima and Tonei, 1966;Lieb, 1981;Agil et al, 1987;Alhendi et al, 1989;Sabirov, 1993;Porras and Moya, 1999), no Z-dependent exponential solutions, to the best of our knowledge, have been reported for the TFD equation using the electron exchange-correlation scheme.…”