Starting from the secondhyphen;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 state sum rule values of the separated atoms for two sets of basis functions. The resulting bounds are narrower than those obtained starting from the Casimirhyphen;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 Padeacute; approximants. The bounds obtained here from the larger basis set are of comparable quality to those reported using Gaussian quadrature or the 2,1 Padeacute; approximants to bound the polarizabilities in the Casimirhyphen;Polder formula. A derivation of the Kramerhyphen;Herschbach combination rule from one of the bounds is also presented.
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