Formulations of the closed-shell interactions in endohedral systems
An attempt is made to express the interaction energy in an endohedral A@B system starting from a one-center (r<)l/(r>)l+1 expansion. Electrostatic, induction, and dispersion contributions are obtained from Rayleigh–Schrödinger perturbation theory. New electric polarizabilities with r−l−1 radial integrals are calculated for l = 0, 1 and 2 for the outer system B. For a ‘breakable’ B, they can be related to the usual London formula. The new polarizabilities are used to successfully estimate the Born-type charge solvation energy and to roughly estimate the lowest-order, l = 1 dispersion term. The latter, London-type expression is now also derived from a Casimir–Polder-type argument. It is applied on A = He–Xe, Zn–Hg, and several molecules with B = C60 and the results are compared against MP2 and SCS-MP2 supramolecular calculations. The l = 2 dispersion terms are smaller than the l = 1 ones.