Convergence of Intermolecular Force Series

Abstract

The commonly used perturbation method of estimating the Van der Waals forces between atoms is shown to lead, when carried to the extreme, to divergent results. The method employs an expansion of the classical electrostatic interaction between the atoms in a series of inverse powers of the internuclear distance. The divergence arises because this expansion is utilized in regions of configuration space where it is not convergent. In this paper, the resulting divergent intermolecular force series are shown to be asymptotic to the true molecular interaction. The divergence is removed in an approximate way and the second-order attractive energy so obtained is added to the first-order exchange energy between the atoms. The method results in an electronic energy curve for $\mathrm{H}_2^{}{}_{}{}^{+}$ in reasonable accord with the exact result of Hylleraas and in a new interaction between helium atoms in good agreement with recent low temperature experiment.