(258a) Virial Coefficients and Virial Equation of State As a Stringent Method for Validation of Intermolecular Potentials of Pure Fluids and Mixtures

The virial equation of state (VEOS) is unique in its ability to provide a rigorous thermodynamic equation of state from a model of the intermolecular potential-energy surface (PES). Virial coefficients B_n that enter into the VEOS are specified as integrals of the PES for 2, 3, etc. molecules. The PES may be based on semi-empirical force fields, or developed from ab initio quantum chemical calculations that are increasingly being employed as an input to machine-learning based PES representations. In the latter application, the VEOS then provides a thermodynamic model that is built completely on first principles. In either case, knowledge of the VEOS from a PES provides a critical tool for evaluating the quality of the PES, because the properties computed from the VEOS (including some of the coefficients themselves) can be compared directly to experiment. This provides a precise determination of the quality of two-body, three-body, etc. components of the PES, presenting a rigorous assessment of its accuracy while guiding improvements.

In this study, we investigate the accuracy of several established molecular models by computing pure and mixture gas-phase virial coefficients for 30 compounds, including common alkanes, alcohols, benzene-derivatives and small-molecule gases. In contrast to coefficients computed from a first-principles PES, which should in principle match virial coefficients from experiment directly, coefficients computed from pairwise-additive semi-empirical force fields are expected to exhibit a cancellation of errors that lead them to provide values of B₂, B₃, etc. that are inaccurate, but in an offsetting manner. Therefore, we consider as well comparison of the VEOS derived from the potentials to PVT property data, as well as the coefficients themselves. For several models, we calculate gas-phase pure and mixed virial coefficients up to the fourth virial coefficient over a range of temperatures from 100 K to 1000 K using Mayer-sampling Monte Carlo with application of the correction for flexibility as necessary. We have also computed temperature derivatives of these virial coefficient to enable calculation of thermal properties such as the Joule-Thomson coefficient and heat capacities. We validated our calculated virial coefficients with experimental PVT-data provided by the NIST ThermoData Engine, showing convergence of the pressure-density isotherms constructed with the VEOS truncated up to various orders. The comparison points to strengths and weaknesses of these force-field models. We expect that this work would bring more awareness to the effectiveness of the VEOS as an alternative property prediction tool to traditional molecular simulation, and its value in validating and guiding development of molecular models.