On the algorithm to perform Monte Carlo simulations in cells with constant volume and variable shape

TL;DR

This paper presents an algorithm for Monte Carlo simulations that adaptively changes the shape of the simulation cell to better match the system's properties, especially in crystal simulations where shape influences behavior.

Contribution

The work introduces a novel algorithm for dynamically adjusting the simulation cell shape based on geometrical parameter distributions, improving accuracy in crystal simulations.

Findings

Algorithm performance depends on the sampled geometrical parameter range.

Narrow sampling ranges minimize impact of shape adaptation.

Large ranges can cause distribution distortions and free energy estimation errors.

Abstract

In simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of the box on the fly in the course of the simulation as it may not be known ahead of time which geometry fits the studied system best. In this work we derive an algorithm for this task based on the condition that the distribution of specific geometrical parameter observed in simulations at a constant volume matches that observed in the constant-pressure ensemble. The proposed algorithm is tested for the system of hard-core ellipses which makes lattices of different types depending on the asphericity parameter of the particle. It is shown that the performance of the algorithm critically depends on the range of the sampled geometrical parameter. If the range is narrow, the impact of the sampling method is minimal. If the range is large, inadequate sampling can lead to significant distortions of the relevant distribution functions and, as a consequence, errors in the estimates of free energy.