Modified string method for finding minimum energy path

TL;DR

This paper introduces an improved string method algorithm for efficiently calculating minimum energy paths and energy barriers on potential energy surfaces, enhancing transition pathway analysis between metastable states.

Contribution

The paper presents a modified string method that employs constrained minimization on hyperplanes, allowing faster algorithms and a more direct analogy to the finite temperature string method.

Findings

Algorithm effectively computes MEPs on complex PES.

Demonstrated flexibility with various minimization algorithms.

Validated on multiple example systems.

Abstract

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition pathways between metastable states. Our method relies on the original formulation of the string method [Phys. Rev. B ${\bf 66}$, 052301 (2002)], i.e. to evolve a smooth curve along a direction normal to the curve. The algorithm works by performing minimization steps on hyperplanes normal to the curve. Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems. This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method [J. Chem. Phys., ${\bf 126}$(16),164103 (2007)]. At the same time, it provides a more direct analog of the finite temperature string method. The applicability of the algorithm is demonstrated using various examples.