Bounding and estimation of van der Waals coefficients

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Abstract
Numerous bounds to the induced-dipole induced-dipole van der Waals coefficient C(6)ab are systematically compared on a self-consistent body of data pertaining to 21 atoms and molecules, and 231 pairwise interactions. Only bounds which use no more than five moments of the dipole oscillator strength distribution (DOSD) and possibly the resonance frequency are considered. The sharpest bounds in each of four groups are thus identified. It is shown that, in each of the three groups that require only integer moments of the DOSD as input, the best pair of upper and lower bounds can be supplemented by an estimate with an rms error of less than 1%. These estimates are based on generalized means. The sharpest upper and lower bound of all can both be computed on the basis of merely five moments S(−k) with 1≤k≤5. A two term effective DOSD that reproduces S(−k/4) with 7≤k≤10 is shown to provide an unbounded approximation to C(6)ab with an rms error of only 0.09%. This effective DOSD can form the basis of a very accurate combination rule.

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