Thermodynamic consistency and integral equations for the liquid structure

Within an assumed pair potential framework, it has been generally accepted for a long time that far from the critical point the asymptotic form of the direct correlation function c(r) at large r is given by [− ϕ(r)/k_BT]. Here ϕ(r) is the pair potential and k_BT the thermal energy. Subsequently, Kumar, March, and Wasserman [Phys. Chem. Liquids 11, 271 (1982)] examined the condition for thermodynamic consistency between virial and compressibility equations of state. Their study, together with later work by Senatore, Rashid, and March [Phys. Chem. Liquids 16, 1 (1986)], resulted in a decomposition of c(r) into a potential part c_p(r) given by Kumar et al. for all r and involving the pair function g(r) and its density derivative, plus a “collective” part c_c(r), which must obey a simple Sum rule to satisfy thermodynamic consistency. The more recent study of B. C. Eu and K. Rah [J. Chem. Phys. 3, 3327 (1999)] prompts us to bring their results into direct contact with the study of Kumar et al. The work of Eu and Rah gives a prominent place to the Mayer function f(r) = e^{(−[ϕ(r) / k_BT]}−1 which tends to −[ϕ(r)/k_BT] as r → ∞ for potentials tending to zero at infinity.