Reaction coordinates, one-dimensional Smoluchowski equations, and a test for dynamical self-consistency.

Area of Science:

• Chemical Physics
• Computational Chemistry
• Statistical Mechanics

Background:

• Identifying accurate reaction coordinates is crucial for understanding complex chemical dynamics.
• Existing methods may not fully capture the dynamics in systems with anisotropic diffusion.
• The Smoluchowski equation provides a framework for modeling diffusion-controlled processes.

Purpose of the Study:

• To propose and validate a novel method for identifying accurate reaction coordinates.
• To assess the self-predictive dynamical property of reaction coordinates under specific conditions.
• To compare the new method's results with established theories like Kramers-Langer-Berezhkovskii-Szabo.

Main Methods:

• Projecting short trajectory swarms onto trial coordinates.
• Quantifying projection differences using Kullback-Leibler divergence.
• Generating ensembles of trajectories from an initial order parameter with a free energy barrier.

Main Results:

• The proposed method successfully identified accurate reaction coordinates in model systems.
• Results showed agreement with exact solutions derived from Kramers-Langer-Berezhkovskii-Szabo theory.
• The study identified conditions under which the dynamical self-consistency method may fail.

Conclusions:

• The new method offers a reliable approach for validating reaction coordinates in Smoluchowski systems.
• Dynamical self-consistency provides a criterion related to the isocommittor criterion.
• This work advances the computational tools for analyzing chemical reaction dynamics.