Layered nested Markov chain Monte Carlo.

Area of Science:

• Computational chemistry and physics
• Statistical mechanics
• Materials science

Background:

• Simulating systems with rugged free energy landscapes presents significant computational challenges.
• Existing methods may struggle to efficiently explore complex energy landscapes.

Purpose of the Study:

• To introduce and validate a new configurational sampling algorithm, Layered Nested Markov Chain Monte Carlo (L-NMCMC).
• To demonstrate the algorithm's capability in simulating systems with challenging energy landscapes.

Main Methods:

• Development of the L-NMCMC algorithm utilizing nested layerings of Markov chains.
• Generation of auxiliary potential energy surfaces to guide the sampling process.
• Application to a 2D potential energy surface and a Lennard-Jones fluid system.

Main Results:

• Successful implementation and demonstration of L-NMCMC on model systems.
• Versatile application shown on a Lennard-Jones fluid using various layering schemes and auxiliary potentials.
• Demonstration of L-NMCMC's ability to construct approximate free-energy surfaces at no additional computational cost when combined with free-energy perturbation.

Conclusions:

• L-NMCMC is a general and effective method for configurational sampling in systems with rugged free energy landscapes.
• The algorithm offers a straightforward approach to free-energy surface construction.
• L-NMCMC can complement existing simulation methods that rely on target distribution sampling or hierarchical scale decomposition.