A comparison of the correlation functions of the Lennard–Jones fluid for the first-order Duh–Haymet–Henderson closure with molecular simulations

First-order integral equation theories are much more computationally efficient than second-order theories, but the latter are usually much more accurate for computing correlation functions of fluids. We here test the accuracy of the Duh–Haymet–Henderson (DHH) integral equation theory by comparing radial distribution, cavity correlation and bridge functions computed from DHH, first-order and second-order Percus–Yevick theories, with molecular dynamics calculations for the Lennard–Jones fluid. We find that the DHH theory is almost as accurate as the second-order Percus–Yevick theory at liquid-like densities for both sub- and super-critical temperatures. However, the accuracy of the DHH theory decreases with decreasing density. The correlation functions computed from DHH theory are very similar to those computed from first-order Percus–Yevick theory at low densities. The cavity correlation and bridge functions at low densities computed from these two theories are qualitatively different from results computed from molecular simulations. However, the radial distribution functions computed from all three methods are essentially identical at low densities, indicating that errors in the cavity correlation and bridge functions at low densities cancel out to give high accuracy in the radial distribution function.