Original method used to investigate process of inserting/deleting a particle during Grand-Canonical Monte Carlo Simulations

The study of the insertion/deletion of particles in statistical thermodynamics has faced several challenges. Specifically, within numerical simulations, the ability to impose the chemical potential provides valuable extra information, which is out of reach using the standard canonical or isobaric conditions. Within the Grand Canonical ensemble, the usual procedures based on sudden creation/deletion of a particle fail in dense, cohesive systems, often leading to rejection.

Using non-equilibrium hybrid insertion/extraction through the fourth dimension within a Grand Canonical Monte Carlo simulation, Belloni developed a new strategy for changing the particle number and successfully slowed the time for particles to react to the insertion/extraction process. Belloni compares this to the set up of a billiards game.

Contrary to the standard instantaneous process, the new technique investigates continuous insertion/extraction through an artificial frontier of a cubic cell, obtained by the addition of a fourth dimension. This gives time for the fluid to relax around the created molecule or cavity before the Grand Canonical Monte Carlo acception decision. The H4D approach has increased the success rate by orders of magnitude.

“In the absence of efficient Grand Canonical techniques, one is forced to work at constant particle number and manipulate pair correlations automatically affected by systematic finite-size errors. The H4D approach also solves this problem.” Belloni said.

In the same spirit, this procedure will help in measuring the solvation free energy of solute molecules immersed in bulk solvent. Belloni explained that the H4D algorithm needs in that case only one or two simulations with non-equilibrium solvent-solute coupling and provides a powerful application of Jarzynski’s fundamental theorem.

Source: “Non-equilibrium hybrid insertion/extraction through the 4th dimension in Grand-Canonical Simulation,” by Luc Belloni, Journal of Chemical Physics (2019). The article can be accessed at https://doi.org/10.1063/1.5110478 .