Calculating thermodynamic properties from perturbation theory: I. An analytic representation of square-well potential hard-sphere perturbation theory

The Barker–Henderson macroscopic compressibility approximation of the second-order perturbation term is improved by assuming that the numbers of molecules in every two neighbour shells are correlated, based upon the original assumptions. The results are better than those for the original macroscopic compressibility and local compressibility approximation, especially at high densities. A simple analytic representation of square-well potential hard-sphere perturbation theory is derived based upon this improvement. The method is tested by calculating thermodynamic properties with the four-term truncated form, and the results are in good agreement with those of Monte Carlo and Molecular Dynamics simulation.