Eighth-Order Virial Equation of State for Methane from Accurate Two-Body and Nonadditive Three-Body Intermolecular Potentials

The second to eighth
virial coefficients of methane were determined
for temperatures up to 1200 K using an existing ab initio-based and
empirically fine-tuned two-body potential combined with a new empirical
nonadditive three-body potential. Nuclear quantum effects were accounted
for by the semiclassical Feynman–Hibbs approach. The numerical
evaluation of the high-dimensional integrals through which the virial
coefficients are expressed was performed employing the Mayer-sampling
Monte Carlo technique. By fitting suitable mathematical functions
to the calculated virial coefficients, an analytical eighth-order
virial equation of state (VEOS8) was obtained. Pressures p computed as a function of temperature T and density
ρ using VEOS8 agree highly satisfactorily with p(ρ, T) values obtained with the experimentally
based reference equation of state for methane of Setzmann and Wagner
(SWEOS) at state points at which VEOS8 is sufficiently converged.
It is shown that it is essential to account for nonadditive three-body
interactions in the calculations in order to achieve good agreement
with the SWEOS.