Truncated minimum energy path method for finding first order saddle points

A method for finding a selected region of the minimum energy path between two local minima on an energy surface is presented. It can be used to find the highest saddle point and thereby estimate the activation energy for the corresponding transition when the shape of the path is known reasonably well and a good guess can be made of the approximate location of the saddle point. The computational effort is then reduced significantly as compared with a calculation of the full minimum energy path by focusing the images on the selected part of the path and making one of the images, the climbing image, converge rigorously on the saddle point. Unlike the commonly used implementation where a restraint is used to distribute the images along the path, the present implementation makes use of a constraint where the distance between images is controlled based on a predefined overall length of the path. A relatively even density of images on each side of the climbing image is maintained by allowing images to move from one side to the other. Applications to magnetic skyrmion annihilation and escape through boundary are used to illustrate the savings in computational effort as compared with full minimum energy path calculations.