Non-equilibrium hybrid insertion/extraction through the 4th dimension in grand-canonical simulation

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Materials Science

Background:

• Grand-canonical Monte Carlo (MC) simulations are crucial for modeling systems with variable particle numbers.
• Standard particle insertion/deletion methods in MC can be inefficient, leading to low acceptance rates.
• The relaxation of the surrounding environment during particle insertion/deletion is critical for accurate simulations.

Purpose of the Study:

• To develop a novel, efficient technique for particle insertion and deletion in grand-canonical MC simulations.
• To improve the success rate of particle insertion/deletion by allowing gradual environmental relaxation.
• To adapt the method for calculating chemical potentials and solvation free energies.

Main Methods:

• A hybrid algorithm combining MC and nonequilibrium molecular dynamics (MD) is proposed.
• A 4th dimension coordinate 'w' is introduced for gradual particle insertion/deletion via an MD trajectory.
• Acceptance probability is governed by chemical potential and applied work during the MD trajectory.

Main Results:

• The novel technique achieves a significant increase in the success rate of particle insertion/deletion.
• The method demonstrates effectiveness across hard sphere, water, and electrolyte systems.
• The approach is adaptable for measuring chemical potential and solvation free energy using Jarzynski's theorem.

Conclusions:

• The hybrid 'H4D' algorithm offers a powerful and efficient method for particle insertion/deletion in simulations.
• This technique allows for gradual environmental adjustments, overcoming limitations of sudden particle creation/deletion.
• The method provides a versatile tool for advanced calculations in computational chemistry and statistical mechanics.