Monte Carlo Calculations of the Virial Coefficients for Development of Potential Models

The second and third virial coefficients, B₂ and B₃, have long played a role in the development of simple pair potentials because these quantities can be computed rapidly as integrals over configuration space and extracted reliably from experimental data.  Consideration of the virial coefficients during model development is expanding to larger numbers of molecules and more complex model forms as the advancement of targeted Monte Carlo methods facilitates their computation.  Path-integral Monte Carlo has enabled computation of the uniquely quantum contributions to B₂ and B₃ for monatomic gases [1], which are required for meaningful comparisons to experimental data at low temperature.  Mayer-sampling Monte Carlo has made possible computation of classical virial coefficients for a wide range of models, including B₄ for the TraPPE-UA model of icosane [2], B₅ for the Gaussian charge polarizable model of water [3], and B₈ for the Lennard-Jones model [4]. 

Here we present two extensions of the Mayer-sampling Monte Carlo approach designed to facilitate development of potential models.  The first provides an estimate of the error in the classical virial coefficient for an ab initio potential model relative to that of the quantum-mechanical model it approximates and identifies configurations appropriate for inclusion within the fitting procedure.  The second is designed to facilitate path-integral Monte Carlo calculations of quantum contributions to the virial coefficients beyond third order.

[1]        G. Garberoglio and A. H. Harvey, "Path-integral calculation of the third virial coefficient of quantum gases at low temperatures," Journal of Chemical Physics, vol. 134, 2011.

[2]        A. J. Schultz and D. A. Kofke, "Virial coefficients of model alkanes," Journal of Chemical Physics, vol. 133, 2010.

[3]        K. M. Benjamin, et al., "Fourth and Fifth Virial Coefficients of Polarizable Water," Journal of Physical Chemistry B, vol. 113, pp. 7810-7815, 2009.

[4]        A. J. Schultz and D. A. Kofke, "Sixth, seventh and eighth virial coefficients of the Lennard-Jones model," Molecular Physics, vol. 107, pp. 2309-2318, 2009.