Arctangent Approximation to the Intermolecular Potential

The form ${\overline{V}}^{\mathrm{AB}}\mathrm{}\left(R\right)=-\left(\frac{C^{\mathrm{AB}}}{R^6}\right)$ [$2{\pi }^{-1\mathrm{}}invtan\left(\frac{d}{R}\right)$] is proposed as an approximation to the retarded van der Waals potential $V^{\mathrm{AB}}\mathrm{}\left(R\right)\mathrm{}$ acting between atoms or molecules $A$ and $B$. Here $C^{\mathrm{AB}}$ is the London-van der Waals constant and $d=\frac{23{{\alpha }_E}^A{{\alpha }_E}^B\hslash c}{8C^{\mathrm{AB}}}$, with the ${\alpha }_E\text{'}\mathrm{s}$ denoting static electric polarizabilities. ${\overline{V}}^{\mathrm{AB}}$ is shown to be in excellent agreement with available numerical calculations of $V^{\mathrm{AB}}\mathrm{}\left(R\right)\mathrm{}$ based on the Casimir-Polder formula, which requires infinite summation over excited atomic states. A heuristic explanation for the validity of the formula is given.