Multidimensional reaction rate theory with anisotropic diffusion.

Area of Science:

• Chemical Physics
• Physical Chemistry
• Theoretical Chemistry

Background:

• Diffusive transitions between potential wells are fundamental in chemical reactions and molecular dynamics.
• Kramers-Langer theory provides a framework for calculating these transition rates but has limitations in anisotropic diffusion scenarios.
• Understanding these transitions is crucial for predicting reaction kinetics and molecular behavior.

Purpose of the Study:

• To derive a novel analytical expression for the rate constant of diffusive transitions between two deep wells in multidimensional potentials.
• To develop a method that is valid even when diffusion is highly anisotropic, overcoming limitations of existing theories.
• To provide a more accurate theoretical tool for studying complex chemical and physical processes.

Main Methods:

• Utilized a variational principle applied to the reactive flux.
• Employed a trial function for the splitting probability (commitor) within the variational framework.
• Validated the derived analytical expression through Brownian dynamics simulations.

Main Results:

• An analytical expression for the rate constant of diffusive transitions was successfully derived.
• The new expression demonstrates validity in cases of highly anisotropic diffusion, unlike the conventional Kramers-Langer formula.
• Brownian dynamics simulations confirmed the accuracy and applicability of the theoretical results.

Conclusions:

• The derived analytical expression offers a more general and accurate method for calculating transition rates in multidimensional systems.
• This work provides a valuable theoretical advancement for studying systems with anisotropic diffusion, relevant to various fields.
• The validated approach enhances the predictive power of theoretical models in chemical kinetics and molecular dynamics.