Fourth Virial Coefficients for the 12–6 Potential

Abstract

A satisfactory numerical method for evaluating fourth virial coefficients for angle-independent intermolecular potential energy functions is developed. The method is based on an expansion in Legendre polynomials which reduces the numerical problem from sixfold integration to triple integration, thus bringing it within the capacity of modern computers. The method is tested by some calculations for square-well potentials and then used to calculate fourth virial coefficients for the Lennard-Jones 12–6 potential. Using the fourth virial coefficients, critical constants for a 12–6 fluid are calculated and compared with experimental values for argon. The calculated and experimental critical temperatures and pressures agree to within 5% and the critical volumes to within 15%.