Exact asymptotic form of the site-site direct correlation function for linear triatomic molecules

In a recent article [1] (hereafter denoted I) examining the interaction-site model (ISM) for molecular fluids, Cummings and Stell have argued that one cannot in general expect he site-site direct correlation function c~B(r) to exhibit the asymptotic decay [2], c~p(r)~ _-k f fT), r-+~. (1) Here k B is Boltzmann's constant, T is the absolute temperature, and u~(r) is the site-site interaction potential between sites ~ and /3 on distinct molecules. Rather, the asymptotic form of c~p(r) is expressed by equation (45) in I (denoted (I.45)), which contains additional large-r contributions of a state-dependent nature. This follows from a key assumption made in I, embodied in (I.29), namely that the particle-particle direct correlation function, which is distinct from c~(r), decays at large r as-1/kBT times the particle-particle potential, where the latter must in general be state-dependent i order to maintain the binding and saturation of rigid polyatomics over the entire range of T and number density p. On the basis of this assumption, Cummings and Stell derive the following asymptotic form of c~(r) for rigid diatomic molecules, c~(r)~_A~/r, r-+ov, (2) and provide explicit expressions for the coefficients ~/ ~ in terms of the dielectric constant, for a polar fluid, or in terms of the angular correlation parameter G1 [3] in the case of a non-polar fluid. These results would not be anticipated on the basis of equation (1). An even more strikingly singular behaviour was conjectured by these authors to hold for linear triatomic molecules, namely c~(r)~r, r-+oo. (3) Using their methods, Cummings and Stell were unable to verify explicitly t Author for correspondence.