Dual Grid Methods for Finding the Reaction Path on Reduced Potential Energy Surfaces

Area of Science:

• Computational Chemistry
• Theoretical Chemistry
• Chemical Kinetics

Background:

• Determining the minimum energy reaction path (MEP) is crucial for understanding chemical reaction mechanisms.
• Traditional methods like the fast marching method (FMM) can be computationally expensive due to the exponential growth of grid points with dimensionality.
• Accurate interpolation techniques are essential for managing computational costs in exploring reduced potential energy surfaces (RPES).

Purpose of the Study:

• To develop novel algorithms for efficiently determining the MEP and identifying the rate-limiting transition state (TS) on RPES.
• To improve upon existing FMM-based approaches by focusing computational effort on TS localization rather than precise MEP tracing.
• To minimize extrapolation errors by performing most interpolation on a finer grid.

Main Methods:

• Development of two new algorithms based on the fast marching method (FMM) and modified Shepard interpolation.
• Mapping the RPES on a coarse grid followed by refining a least action path on a finer grid.
• Iterative localization of the transition state (TS) on the estimated fine potential energy surface (PES).

Main Results:

• The new algorithms rapidly approximate the MEP and locate the rate-limiting TS in under 30 constrained optimization cycles.
• Successful application to three diverse systems: a 4-well potential, N-hydroxymethyl-methylnitrosamine (HMMN), and a DNA-uracil glycosylase model.
• Demonstrated capability to handle complex potential energy landscapes.

Conclusions:

• The presented algorithms offer a computationally efficient alternative for exploring reaction pathways and identifying key transition states.
• Modified Shepard interpolation effectively addresses overfitting issues, enhancing the reliability of the methods.
• These approaches provide valuable tools for computational studies in chemistry and related fields.