Molecular Monte Carlo simulation method of systems connected to three reservoirs

TL;DR

This paper introduces a novel molecular Monte Carlo simulation method that connects three reservoirs—chemical potential, pressure, and temperature—to better simulate equilibrium states and ordered structures, overcoming metastability and defects common in traditional methods.

Contribution

The proposed method uniquely allows simultaneous tuning of system size and particle number, enabling stable ordered structures and reducing preliminary simulation efforts compared to existing techniques.

Findings

Enables stable ordered structures by connecting three reservoirs.

Reduces defects and metastability in simulations.

Requires fewer computational efforts for free energy measurements.

Abstract

In conventional molecular simulation, metastable structures often survive over considerable computational time, resulting in difficulties in simulating equilibrium states. In order to overcome this difficulty, here we propose a newly devised method, molecular Monte Carlo simulation of systems connected to three reservoirs: chemical potential, pressure, and temperature. Gibbs-Duhem equation thermodynamically limits the number of reservoirs to 2 for single component systems. However, in conventional simulations utilizing 2 or fewer reservoirs, the system tends to be trapped in metastable states. Even if the system is allowed to escape from such metastable states in conventional simulations, the fixed system size and/or the fixed number of particles result in creation of defects in ordered structures. This situation breaks global anisotropy of ordered structures and forces the periodicity of the structure to be commensurate to the system size. Here we connect the such three reservoirs to overcome these difficulties. A method of adjusting the three reservoirs and obtaining thermodynamically stable states is also designed, based on Gibbs-Duhem equation. Unlike the other conventional simulation techniques utilizing no more than 2 reservoirs, our method allows the system itself to simultaneously tune the system size and the number of particles to periodicity and anisotropy of ordered structures. Our method requires fewer efforts for preliminary simulations prior to production runs, compared with the other advanced simulation techniques such as multicanonical method. A free energy measurement method, suitable for the system with the three reservoirs, is also discussed, based on Euler equation of thermodynamics. This measurement method needs fewer computational efforts than other free energy measurement methods do.