Efficiency Comparison of Single- and Multiple-Macrostate Grand Canonical Ensemble Transition-Matrix Monte Carlo...

Area of Science:

• Computational chemistry and physics
• Statistical mechanics
• Materials science

Background:

• Flat-histogram Monte Carlo simulations are effective for studying phase behavior, self-assembly, and adsorption.
• Single-macrostate simulations, a parallelized extreme, simulate each macrostate independently.

Purpose of the Study:

• To compare the efficiency of single-macrostate versus multiple-macrostate flat-histogram Monte Carlo simulations.
• To identify reasons for efficiency differences in parallelized simulation approaches.

Main Methods:

• Utilized the open-source simulation toolkit FEASST.
• Compared single-macrostate and multiple-macrostate simulations across various systems: supercritical fluids, Lennard-Jones models, water models, patchy trimers, and confined fluids.
• Analyzed different Monte Carlo trial move sets.

Main Results:

• Multiple-macrostate simulations are up to 3 orders of magnitude (1000x) more efficient than single-macrostate simulations.
• This efficiency gain holds even with low acceptance probabilities for biased insertions/deletions.
• Existing parallelization for multiple-macrostate simulations is ~10x more efficient than parallel single-macrostate simulations.

Conclusions:

• Single-macrostate simulations are significantly less efficient due to wasted computational expense on ghost trials, lack of biased macrostate change trials, and reduced sampling possibilities.
• Multiple-macrostate flat-histogram simulations offer superior performance for complex systems.
• The findings underscore the importance of efficient sampling strategies in computational simulations.