Hartree-Fock densities in Thomas-Fermi-Dirac formulas including the inhomogeneity term

Hartree-Fock-Roothaan-Clementi (HFRC) densities are used to calculate the total kinetic energies and the total binding energies of neutral atoms according to the Thomas-Fermi-Dirac formulas with inhomogeneity corrections. The strength of the Weizs\"acker inhomogeneity correction is multiplied by the Kompaneets and Pavlovskii, and Kirzhnits factor of 1/9. Of the atoms considered ($Z=2$ to $Z=36$; $Z=54$) almost all the total kinetic energies agree with the HFRC expectation values to better than 1%, and the largest disagreement is 1.7%. Except for He, Li, Be, and B, the total binding energies agree with the HFRC expectation values to better than 0.7%. Higher-order corrections of the Thomas-Fermi-Dirac-Weizs\"acker formulas are therefore very small.