Consequently, the VEOS can play an important role in connecting molecular and thermodynamic modeling. The value of the VEOS has grown in recent years with advances in computational chemistry and the advent of machine-learning methods to represent the PES. Because the thermodynamic equation of state can be measured experimentally, comparison of the VEOS to experimental data can provide an assessment of the molecular model used to compute the Bn. An effective way to do this is to infer values of the virial coefficients from the experimental data, and compare them to corresponding values computed from the PES. In this manner the VEOS can be applied systematically to pinpoint specific weaknesses in the PES.
A key requirement for the application of the VEOS to assess the PES is the availability of accurate values of the virial coefficients as obtained from experiment. While it may be possible to fit a polynomial to experimental PV data for a given temperature, the coefficients of the fit are not guaranteed to equal the true virial coefficients Bn, even considering experimental uncertainty. The correct values are given via a limiting process, considering the behavior as the density goes to zero. However, experimental data are necessarily recorded at finite density, so the limit must be obtained by extrapolation. Furthermore, a full characterization of the virial coefficients must consider their temperature dependence. This dependence is non-trivial, and would not be well characterized by a simple polynomial.
Given the central role of experimentally-derived Bn in any project to assess the PES through comparison to experiment, it is worthwhile to examine methods to estimate the virial coefficients from experimental PVT data. This presentation examines and develops methods for doing so, considering new approaches made possible by recent advances in machine learning.