Calculation of the atomic kinetic energy from a density functional virial relationship

The kinetic energies of a series of atoms and ions have been calculated with a high degree of accuracy using some known exchange energy functional and the electrostatic potential. They are related to the kinetic energy functional through the virial equations. The kinetic energy contribution to the ionization potential has also been calculated to a very high degree of accuracy. It has also been shown that the Hartree - Fock kinetic energy density is very well reproduced. This method, however, does not generate an Euler equation because the electrostatic potential as a function of the density is unknown. All the calculations have been performed using Hartree - Fock densities.