Computation of high-order virial coefficients in high-dimensional hard-sphere fluids by Mayer sampling

Abstract

The Mayer sampling method was used to compute the virial coefficients of high-dimensional hard-sphere fluids. The first 64 virial coefficients for dimensions 12 < D ⩽ 100 were obtained to high precision, and several lower dimensional virial coefficients were computed. The radii of convergence of the virial series in 13, 15, 17 and 19 dimensions agreed well with the analytical results from the Percus–Yevick closure.

Keywords:

• liquid state
• equation of state

Acknowledgements

It is a pleasure to thank Dr Chun-Liang Lai for helpful discussions. The authors are also grateful for the support of the Texas Advanced Computing Center at the University of Texas at Austin and that of the National Institute for Computational Sciences at the University of Tennessee for the computational time on the Stampede [46] and Kraken [47] supercomputers, respectively (TG-MCA93S001).

Additional information

Funding

The authors gratefully acknowledge the financial support of the National Science Foundation [grant number CHE-1152876]; the Robert A. Welch Foundation [grant number H-0037].