Energy levels in modified quantum statistical potentials

We calculate one-electron energy levels in potentials derived from the solution of the atomic Thomas-Fermi-Dirac equation. A local exchange potential is used. Corrections are made to a previous theory, which joins a TFD density to a quantum mechanical electron density near the nucleus, where the Thomas-Fermi-Dirac density has an incorrect singularity. Use of a potential derived from this theory leads to improvement in inner-shell energies. Changes in the potential, suggested in the literature as being reasonable for valence electrons, do not always give the expected improvement. Nor does naively correcting for self-energy lead to improved one-electron energy levels in general.