Calculating transition rates from durations of transition paths

Area of Science:

• Computational Chemistry
• Statistical Mechanics
• Molecular Dynamics

Background:

• Calculating kinetic rates for rare molecular transitions is crucial for understanding chemical processes.
• Existing methods often face challenges in accurately predicting these rates due to the infrequent nature of transitions.

Purpose of the Study:

• To establish rigorous equalities linking transition rates to equilibrium free energy and transition path statistics.
• To introduce a novel method for calculating kinetic rates using transition path durations.

Main Methods:

• Derivation of theoretical equalities relating transition rates to free energy and path statistics.
• Utilizing forward and backward simulations to evaluate transition path durations.
• Validation on a model system to confirm predictive accuracy.

Main Results:

• Demonstrated that transition path durations within specific reaction coordinate intervals yield the kinetic pre-factor.
• Showcased a method to rigorously calculate transition rates using free energy and path duration analysis.
• Confirmed the general applicability of the derived relations across different reaction coordinates.

Conclusions:

• The developed approach provides a robust method for calculating kinetic rates in molecular simulations.
• The choice of reaction coordinate significantly impacts the efficiency and reliability of rate calculations.
• This work offers a valuable tool for advancing molecular simulations and chemical kinetics research.