Thermodynamic properties of Ar, Kr and Xe from a Monte Carlo-based perturbation theory with an effective two-body Lennard-Jones potential

A third-order perturbation theory is used to obtain the equilibrium properties of Ar, Kr and Xe over wide ranges of temperatures and densities. The theory belongs to the framework of the inverse temperature expansion of the Helmholtz free energy, with the perturbation terms determined from Monte Carlo simulation. The interactions are modeled by an effective two-body Lennard-Jones potential incorporating the main contribution of the three-body interactions. To this end, the ratio of three-body to two-body configuration energies have been determined also from Monte Carlo simulation. The results for the pressure and energy at supercritical temperatures are in quite good agreement with experimental data. The liquid–vapor coexistence is also reproduced fairly well, although for Ar and Kr the critical temperature is slightly overestimated as well as the liquid densities at low temperatures, and the coexistence densities of Xe are slightly overestimated for the vapor and underestimated for the liquid near the critical point. In any case, the calculations show a remarkable improvement in the predicted coexistence curve with including the three-body contribution.