Bounds to dispersion energy coefficients

Abstract

Starting from the second‐order perturbation energy expression and utilizing inner projection and operator inequalities techniques, easy to evaluate expressions for the bounds to dispersion energy coefficients are obtained in terms of ground statesum rule values of the separated atoms for two sets of basis functions. The resulting bounds are narrower than those obtained starting from the Casimir‐Polder integral formula and bounding each of the polarizabilities in that expression by using either the present technique and basis set or the [1,0] Padé approximants. The bounds obtained here from the larger basis set are of comparable quality to those reported using Gaussian quadrature or the [2,1] Padé approximants to bound the polarizabilities in the Casimir‐Polder formula. A derivation of the Kramer‐Herschbach combination rule from one of the bounds is also presented.