Charge-overlap model of physical interactions and a combining rule for unlike systems

We consider the hypothesis that the repulsive interaction V in van der Waals–type systems is proportional to the charge-density overlap integral S. This hypothesis is shown to be accurate for interatomic interactions, with a proportionality coefficient V/S∼10 a.u. in most cases. It is related to previous results of Kim, Kim, and Lee [Chem. Phys. Lett. 80, 574 (1971)] and Nyeland and Toennies [Chem. Phys. Lett. 127, 172 (1986)]. The hypothesis is consistent with the effective-medium theory result for immersion of an atom or ${\mathrm{H}}_2$ into jellium. For the interatomic problem, the computed values of the decay lengths (${\gamma }^{\mathrm{-}1}$) of V are simply related to those (${\mathrm{\beta }}^{\mathrm{-}1}$) of the asymptotic atomic charge density. This model provides a theoretical basis for an improved combining rule for the minimum position ${\mathit{R}}_{\mathit{A}\mathit{B}}$ of the total interaction ${\mathit{V}}_{\mathit{t}\mathit{o}\mathit{t}}$ between unlike species. It also explains why this quantity depends systematically on the ionization ratio ${\mathit{I}}_{\mathit{B}}$/${\mathit{I}}_{\mathit{A}}$ of the interacting species.