Boundary Effect Corrections for the Thomas—Fermi Atomic Interaction Potential

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Abstract
The electronic energies of a neutral diatomic molecule with noninteracting electrons are calculated by two methods: first, using solutions of Schrödinger's equation for a hydrogenlike molecular ion; second, using the assumption of a slowly varying potential, characteristic of the Thomas—Fermi method. Comparison of these solutions serves both as a test of the TF method and as a means of correcting partially for the TF shortcomings. Based on the success of this method as applied by Scott to the TF atom, the corrected interaction energy is believed correct to within 20% for separations up to Z—⅓ Å. Of qualitative interest is the prediction of bound molecules at large separations except for the rare gases which remain repulsive.

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