Effect of Intra-Atomic Correlation on Long-Range Intermolecular Forces: An Exactly Soluble Model

Using a model system composed of two two-electron atoms whose electrons are bound to the nucleus by Hooke's law forces (of force constant k) but which interact within an atom with one another as A1(x1x2+y1y 2+z1z2), the appropriate crystal-field term to define the components of 1/r12 for this problem (A1 is a constant), the long-range R−6 interaction is exactly −3/(k+A1)R236. Polarizability of these ``atoms'' is 2/(k+A1). Thus the relative contribution of intra-atomic correlation to the R−6 coefficient is related to polarizability calculated with and without correlation (A1=0) as [α(A1≠0)/α(A1=0)]32. This predicts reasonable values for the corrections in Be, He, and even Ne or Ar interactions. The energy through fourth order is also calculated based on a perturbation due to intra- and interatomic correlations,−(3/k32R6)[1−32(A1/k)+(15/8)(A1/k)2+···].Most of the fourth-order energy contributions (proportional to A12) arise from three-electron correlations. The results are also compared with real systems such as He, Be, and Ne.