Mayer-sampling Monte Carlo

Mayer-sampling Monte Carlo for estimating virial coefficients.

This project is in early development.

Background

This implementation is based on the Mayer sampling method introduced by Singh and Kofke:

J. K. Singh and D. A. Kofke, "Mayer Sampling: Calculation of Cluster Integrals using Free-Energy Perturbation Methods," Phys. Rev. Lett. 92, 220601 (2004).

Hard-sphere reference virial coefficients are taken from:

F. H. Ree and W. G. Hoover, "Seventh Virial Coefficients for Hard Spheres and Hard Disks," J. Chem. Phys. 46, 4181–4197 (1967).

Compared to the original method, this implementation:

• Exploits symmetry in the cluster integrands instead of full explicit summation over all graphs.
• Perturbs all particles simultaneously per MC step, rather than a random subset.
• Does not perform adaptive step-size tuning.
• Uses the full cluster sum (rather than just the ring cluster) as the hard-sphere reference integrand, with known HS virial coefficients from Ree & Hoover as normalization.

Results vs Literature

The results were compared with data from:

J. A. Barker, P. J. Leonard, and A. Pompe, J. Chem. Phys. 44, 4206 (1966) (as cited in Singh and Kofke)

Virial coefficient	Literature	Implementation
$B_2 / b$	-2.5381	-2.5309
$B_3 / b^2$	0.4297	0.4469
$B_4 / b^3$	-0.2769	-1.7438

Getting started

Requires Python 3.11+ and uv.

uv sync

Run the example script:

uv run python scripts/msmc_example.py --T_reduced 1.0

Development

Set up pre-commit hooks:

uv run pre-commit install

For clangd support, install just and run just configure.