Study of the electron gas approximation

We test the applicability to atoms of the uniform electron gas energy expression in terms of the local atomic electron density. By using the known atomic electron densities obtained from an independent method (Hartree-Fock) for the density in the electron gas energy expression, we calculate some atomic energies, one-electron energies, and atomic ionization potentials and compare the results with the Hartree-Fock energy values. We calculate the local kinetic energy and exchange energy densities in Hartree-Fock atoms, and compare these results with the corresponding electron gas energy densities. We suggest a simple correction to the electron gas energy to be used for systems not paired in spin, and test this correction. We examine the effect of the finiteness of the atoms by treating a uniform electron gas with a finite number of electrons.