Monte Carlo Methods for the Development of Ab Initio Virial Equations of State
Shaul, Katherine R. S.
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The virial equation of state provides a rigorous connection between molecular potentials and the macroscopic behavior of a gas. Classical approximations to the second and third virial coefficients, B 2 and B 3 , have long played a role in the development of empirical potentials for simple fluids because their values can be both extracted with sufficient reliability from experimental data and computed readily from potentials using their definitions as integrals over configuration space. We demonstrate how the virial coefficients can be used to analyze the effect of truncation and shift on the Lennard-Jones potential and the importance of electrostatic interactions to methanol potentials. We also demonstrate how empirical B 2 data can be used to improve a dispersion-corrected density functional theory treatment for the pair potential of argon, and how the integrands of the virial coefficient can be used to facilitate development of ab initio potentials. With accurate ab initio potentials becoming increasingly available, it is now possible to obtain ab initio virial coefficients and thus a truly predictive equation of state for the gas phase. Consideration of virial coefficients is expanding to higher orders and more complex potentials as the advancement of tailored Monte Carlo methods facilitates their computation. Mayer-sampling Monte Carlo has made possible the computation of classical virial coefficients for a wide range of potentials. We demonstrate how the method can be made more efficient for atomic, pairwise-additive models, how it can be applied to molecular models with flexibility, and how it can be applied to quantum molecules. Inclusion of quantum contributions is essential for the validity of ab initio virial equations of state at low temperature.