Reactive flux theory for finite potential barriers

Area of Science:

• Chemical Kinetics
• Statistical Mechanics
• Physical Chemistry

Background:

• Calculating escape rates from potential wells is crucial in many chemical and physical processes.
• Existing reactive flux theories often simplify barrier potentials, limiting accuracy for finite barriers.

Purpose of the Study:

• To develop a simple, accurate, and widely applicable analytical method for incorporating finite barrier corrections into escape rate calculations.
• To propose a modified reactive flux theory that accounts for finite barrier effects more realistically.

Main Methods:

• The proposed theory adjusts the starting point for Brownian particle trajectories to an equilibrium distribution position within the potential well.
• Finite potential barriers are replaced with equivalent parabolic potentials, with two schemes for determining the equivalent frequency.
• The method was tested using Brownian dynamics simulations of a particle in a cubic metastable potential with Gaussian white noise.

Main Results:

• The modified reactive flux theory provides a more realistic calculation of population dynamics for finite barriers.
• Numerical simulations confirmed the theoretical approach's satisfactory accuracy, particularly for reduced barrier heights above a certain threshold.
• The method demonstrates good agreement with simulation results, validating its applicability.

Conclusions:

• The developed reactive flux theory for finite barriers offers a significant improvement over existing methods.
• This approach provides a robust framework for analytical calculations of escape rates in systems with finite potential barriers.
• The theory is validated by simulations and shows promise for broad applications in chemical kinetics and statistical mechanics.