Revisiting shooting point Monte Carlo methods for transition path sampling

Area of Science:

• Computational chemistry
• Molecular dynamics simulations
• Statistical mechanics

Background:

• Rare event sampling algorithms are vital for studying infrequent molecular processes.
• Transition Path Sampling (TPS) is a standard method for analyzing rare events without prior knowledge of transition regions.
• Existing TPS methods often involve generating new trajectories from old ones via momentum modification and trajectory "shooting".

Purpose of the Study:

• To develop a theoretical framework that accounts for memory effects in TPS algorithms.
• To derive generalized acceptance rules for path sampling within this new framework.
• To identify necessary modifications for specific TPS methods like flexible-length aimless shooting and spring shooting.

Main Methods:

• Introduction of an extended ensemble incorporating both paths and shooting indices.
• Derivation of acceptance rules within the extended ensemble formalism.
• Analysis of memory effects in successive shooting point selection.

Main Results:

• A theoretical framework is established to correctly sample the transition path ensemble, considering memory effects.
• The framework reveals the necessity for amended acceptance criteria in certain TPS algorithms.
• Specific methods like flexible-length aimless shooting and spring shooting require updated acceptance rules.

Conclusions:

• The developed theoretical framework enhances the accuracy of rare event sampling in molecular simulations.
• Accounting for memory effects through an extended ensemble is crucial for reliable TPS.
• Amended acceptance criteria are essential for specific TPS algorithms to ensure proper sampling.