A reexamination of virial coefficients of the Lennard-Jones fluid

The fourth-order virial coefficients have been calculated exactly to five decimal places for pure fluids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more significance than was thought from previous studies, especially in the low-temperature range. This result was confirmed by direct evaluation of the diagrams which construct the virial coefficients, as given by Rowlinson, Barker, and coworkers. This calculation confirmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These differences, though minor at higher temperatures, can be seen to be more significant at the lower temperature ranges.