Transition-Path Theory Calculations on Non-Uniform Meshes in Two and Three Dimensions using Finite Elements

Area of Science:

• Complex Systems Analysis
• Chemical Physics
• Computational Science

Background:

• Rare events in complex systems are crucial and studied via reaction pathways.
• Transition-path theory (TPT) provides a framework for analyzing these pathways.
• The committor function, central to TPT, is typically found by solving the backward-Kolmogorov equation.

Purpose of the Study:

• To demonstrate the feasibility of calculating the committor function using the finite element method (FEM).
• To enable efficient TPT calculations on 3D potentials.
• To investigate the impact of temperature and entropic barriers on reaction rates.

Main Methods:

• Application of the finite element method on non-uniform meshes to solve for the committor function.
• Comparison with finite-difference approaches, highlighting reduced degrees of freedom.
• Calculation of committor functions and reaction rates in 2D and 3D systems.

Main Results:

• FEM efficiently calculates committor functions, requiring fewer degrees of freedom than traditional methods.
• TPT calculations are made feasible for complex 3D potentials.
• Temperature and entropic barriers were shown to influence committor structure and reaction rates.

Conclusions:

• The finite element method offers an efficient and scalable approach for TPT calculations.
• This method facilitates the study of rare events in higher-dimensional complex systems.
• Understanding temperature and entropic effects is key for accurate reaction rate predictions.