Mayer-sampling Monte Carlo calculations of uniquely flexible contributions to virial coefficients

We present methods for computing contributions to the virial coefficients uniquely associated with molecular flexibility, and we demonstrate their use with application to the third, fourth, and fifth virial coefficients of united-atom models of linear alkanes and methanol belonging to the suite of transferrable potentials for phase equilibria (TraPPE-UA). We find that these uniquely flexible contributions are more difficult to compute than the remainder of the coefficient, especially for the conditions at which they appear to be most important. The significance of these contributions relative to the full virial coefficient grows with the number of sites (the size of the molecule), the number of molecules, and, to a certain extent, the temperature. The nature of the site-site interactions is of great importance: the significance of the uniquely flexible contribution at third and fourth order is orders of magnitude larger for TraPPE-UA methanol, which has Coulombic interactions, than for TraPPE-UA propane, which does not, even though both models have three sites per molecule and comparable bending potentials. While the uniquely flexible contribution of TraPPE-UA propane has a negligible impact on its third-order virial-equation-of-state estimate of the critical point, the uniquely flexible contribution of TraPPE-UA methanol increases this estimate of its critical pressure by about 5%.