Comparisons of Dispersion Force Bounding Methods with Applications to Anisotropic Interactions

Abstract

Comparisons and applications are made of the various procedures which have been devised recently for obtaining bounds to dispersion force coefficients. Particular attention is given to the methods based on approximate Gaussian quadratures and on Padé approximants, both of which require oscillator-strength sum rule values for their implementation. The equivalence of the bounds obtained from the two procedures, when identical input information is employed, is demonstrated to all orders, and the improvements that can result from the introduction of additional information, in the form of experimental transition frequencies and other sum rules, is investigated in the course of numerical applications. Comparisons with alternative bounding methods, such as those based on variational principles and related inner projection techniques, show that these procedures, which can also employ sum rule values for their implementation, are similar to the Gaussian quadrature and Padé methods and provide identical results if the same input information is employed. There also exists a second class of procedures which provides bounding inter-relations directly among the dispersion force coefficients, without reference to sum rule values, thus forming a useful complement to the former procedures. Numerical applications to molecular hydrogen, nitrogen, and oxygen, and the inert gases and alkali atoms, using both theoretical and semiempirical sum rule values, indicate that the bounding procedures can provide anisotropic dispersion force estimates of greater accuracy than those which can currently be extracted from rotational relaxation and related experiments. Comparison with more approximate methods for estimating the anisotropies in dispersion interactions, based on static polarizability anisotropies, serves to delineate the limits of accuracy of such approximations. The polarizability anisotropy approximation is found to provide overestimates in every case.