Estimating time-correlation functions by sampling and unbiasing dynamically activated events.

Area of Science:

• Computational Physics
• Materials Science
• Statistical Mechanics

Background:

• Transition path sampling (TPS) is crucial for rare-event simulations in many-body systems.
• Estimating state-to-state time-correlation functions requires sampling short trajectories.
• Existing methods can be computationally intensive for rare events.

Purpose of the Study:

• To develop an improved biasing strategy for transition path sampling.
• To enhance the efficiency of sampling rare reactive trajectories.
• To accurately estimate time-correlation functions and reaction rates.

Main Methods:

• Biasing the importance function using the lowest Jacobian eigenvalue moduli along dynamical trajectories.
• Utilizing the Lanczos algorithm to evaluate the lowest eigenvalue modulus.
• Employing the multi-state Bennett acceptance ratio (MBAR) method for trajectory unbiasing.
• Recycling information from rejected trajectories for computational speed-up.

Main Results:

• The proposed method effectively favors sampling of activated and rare reactive trajectories.
• Accurate estimation of time-correlation functions for vacancy migration in α-iron.
• Calculated migration rates agree with transition state theory predictions.
• Significant speed-up achieved by recycling rejected trajectory data.

Conclusions:

• The novel biasing strategy enhances the efficiency of transition path sampling for rare-event simulations.
• This method provides accurate estimates of dynamic properties like migration rates.
• The approach offers a computationally advantageous alternative to traditional TPS by avoiding reversible work calculations.