Stability and convergence of the string method for computing minimum energy paths
arXiv:1807.060945 citationsh-index: 42
Originality Synthesis-oriented
AI Analysis
Provides theoretical convergence guarantees for a widely used method in computational chemistry and materials science.
The paper proves that the string method for computing minimum energy paths converges to a minimum energy path when initialized nearby, with convergence improving as the number of images increases.
We analyze the convergence of the string method of E, Ren, and Vanden-Eijnden to a minimum energy path. Under some assumptions relating to the critical points on the minimum energy path, we show that the string method initialized in a neighborhood of the minimum energy path converges to an arbitrarily small neighborhood of the minimum energy path as the number of images is increased.