Electron Densities for Homonuclear Diatomic Molecules from the Thomas-Fermi-Dirac Theory

Electron densities are calculated from approximate solutions to the Thomas-Fermi-Dirac equation for homonuclear diatomic molecules. The accuracy of expectation values calculated from these densities is assessed. In general, one obtains fair agreement with self-consistent-field and experimental results, but this is insufficient when a property is a difference between electronic and nuclear contributions. An important example is the Hellmann-Feynman force on a nucleus, the net force necessarily being repulsive, as for closed-shell atoms. Forc and energy results for such a situation are compared with experiment. Finally, it is shown that a modified theory, previously applied to atoms, gives improvement in expectation values depending on the electron density near the nuclei