A virial expansion of fluid pressure in powers of the density can be used to calculate a wealth of thermodynamic information, but the $N$th virial coefficient, which multiplies the $N$th power of the density in the expansion, becomes rapidly more complicated with increasing $N$. This Letter shows that the $N$th virial coefficient can be calculated using a method that scales exponentially with $N$ in computer time and memory. This is orders of magnitude more efficient than any existing method for large $N$, and the method is simple and general. New results are presented for $N=11$ and 12 for hard spheres, and $N=9$ and 10 for soft spheres.

• Received 12 March 2013

DOI:https://doi.org/10.1103/PhysRevLett.110.200601