Calculation of Virial Coefficients On Graphics Processors

Evaluation of virial coefficients from a molecular model can be performed by Monte Carlo sampling of configurations of a small number of molecules, typically on the order of ten or fewer.  Such calculations can have relatively low memory requirements, and are perfectly parallelizable, making this ideal for implementation on graphical processors and other multicore architectures. We describe our experiences performing such calculations in a variety of contexts. We consider first the use of Mayer Sampling Monte Carlo for computation of coefficients up to at least eighth order (B8) for the Lennard-Jones model, and sixth order (B6) for a semiclassical model of helium. We then examine implementation of a remarkable algorithm due to Wheatley, which is particularly effective in application to hard potentials. We examine the strengths and limitations of Wheatley's algorithm in the context of GPU architectures, and consider its performance for a variety of potential models. Ultimately memory limits the order to which coefficients can be computed; we report on the level of capability provided by existing architectures, and consider prospects for these high-order virial calculations as the hardware continues to improve.