Optimization methods for finding minimum energy paths

TLDR

The study compares chain‑of‑states methods for locating minimum energy pathways. The authors evaluate NEB, doubly NEB, string, and simplified string methods, each coupled with common optimizers, by relaxing images along initial pathways between minima using a pairwise Morse potential for a Pt(111) heptamer and plane‑wave DFT for a Pd tetramer on MgO(100) and oxygen on Au(111). NEB and string methods are essentially equivalent and most efficient when paired with a suitable optimizer, with limited‑memory BFGS providing the best performance; a climbing‑image facilitates saddle‑point identification with few images, and for high‑accuracy MEPs it is more efficient to descend from the saddle to the minima than to use many images.

Abstract

A comparison of chain-of-states based methods for finding minimum energy pathways (MEPs) is presented. In each method, a set of images along an initial pathway between two local minima is relaxed to find a MEP. We compare the nudged elastic band (NEB), doubly nudged elastic band, string, and simplified string methods, each with a set of commonly used optimizers. Our results show that the NEB and string methods are essentially equivalent and the most efficient methods for finding MEPs when coupled with a suitable optimizer. The most efficient optimizer was found to be a form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno method in which the approximate inverse Hessian is constructed globally for all images along the path. The use of a climbing-image allows for finding the saddle point while representing the MEP with as few images as possible. If a highly accurate MEP is desired, it is found to be more efficient to descend from the saddle to the minima than to use a chain-of-states method with many images. Our results are based on a pairwise Morse potential to model rearrangements of a heptamer island on Pt(111), and plane-wave based density functional theory to model a rollover diffusion mechanism of a Pd tetramer on MgO(100) and dissociative adsorption and diffusion of oxygen on Au(111).