Analysis of a First-order Perturbation Theory for the Direct Correlation Function of Dense Fluids

An approximate expression for the direct correlation function of a real fluid in terms of its intermolecular potential and hard-sphere distribution functions is examined. Calculations for argon using the Percus–Yevick hard-sphere distribution functions are compared with molecular correlation functions from X-ray scattering data and the macroscopic integral of the correlation function related to the isothermal compressibility. The results are not satisfactory for any pair potential unless the parameters are made state dependent. However, since partial compensation occurs on integration, fairly good correlation of the isothermal compressibility can be obtained up to twice the critical density (except near the critical point itself) using Lennard–Jones (6–12) potential parameters obtained from second virial coefficient data and the Barker–Henderson hard-sphere diameter.