Best Practices for Developing Monte Carlo Methodologies in Molecular Simulations [Article v1.0]

Abstract

Although Monte Carlo (MC) is a very powerful molecular simulation method in statistical mechanics, the development and application of novel MC trials to optimize sampling in complex systems is hindered by the difficulty in deriving their acceptance probabilities. We present a checklist approach to deriving acceptance probabilities, and apply this approach to a variety of trials in the canonical, isothermal-isobaric, grand-canonical, semi-grand canonical and Gibbs ensembles. The ideal gas is then shown to be a useful test case to compare the results of simulations with those from theoretical expectations, providing a computational benchmark that can be easily and rapidly implemented for determining if the acceptance criteria were derived correctly. More complex models and trials are also considered with this checklist approach, including configurational bias, cavity bias, energy bias, aggregation volume bias, dual-cut configurational bias and rigid cluster moves. The result is a framework designed to help researchers implement and test specialized MC trials that expand the model complexity and length scales currently available in open-source MC molecular simulation software. Sample code is also provided in the GitHub repository [https://github.com/usnistgov/best-practices-mc].