Representations of dispersion energy damping functions for interactions of closed shell atoms and molecules Original Research Article

Analytical expressions are developed for the individual partial wave components of the non-expanded second-order dispersion energy for the H(1s)H(1s) interaction and the results are used to obtain analytical expressions for the related damping functions f(la, lb, R). The average or overall damping functions f2n(R), for each R−2n expanded dispersion energy, are given as a weighted average of the f(la, lb, R) with n=la+lb+1. The analytical results, and related numerical calculations, are used to discuss the nature of the average and the partial wave damping functions as a function of la, lb, n and R. For example it is shown that the individual partial wave components of the f2n(R) are essentially independent of la and lb for all relevant values of the interatomic distance R. Reliable representations of the average damping functions are of considerable importance in the construction of potential energy models and the various literature representations are compared and contrasted with each other and with a new representation of the f2n(R) given in this paper. The discussion includes general comments on the use of the H(1s)H(1s) damping functions in the construction of potential energy models for other interactions through the use of interspecies distance scaling methods.