Large barrier behavior of the rate constant from the diffusion equation

Area of Science:

• Physical Chemistry
• Statistical Mechanics
• Biophysics

Background:

• Thermally activated events are crucial in chemistry, physics, and biology.
• Stochastic modeling often uses parameterized mean field potentials for these events.
• Existing models may not capture the full complexity of energy landscapes.

Purpose of the Study:

• To explore an alternative modeling approach for activated processes.
• To utilize parameterized equilibrium distributions for flexible energy landscapes.
• To investigate the rate constants and asymptotic behavior of these new models.

Main Methods:

• Employing symmetric linear combinations of two Gaussian functions for equilibrium distributions.
• Solving the Fokker-Planck-Smoluchowski equation with parameterized distributions.
• Developing new asymptotic analysis for systems with Gaussian-based equilibrium distributions.

Main Results:

• Parameterized equilibrium distributions provide flexible models for energy landscapes and barriers.
• Rate constants were calculated by solving the Fokker-Planck-Smoluchowski equation.
• Asymptotic limits for large barriers deviate from Kramers theory predictions.

Conclusions:

• The proposed method offers a flexible alternative for modeling activated processes.
• Kramers theory's assumptions are not applicable to models based on parameterized equilibrium distributions.
• New asymptotic theories are required for accurate analysis in these cases.