On-the-fly string method for minimum free energy paths calculation

An improved and simplified version of the string method in collective variables for computing minimum free energy paths is proposed. The string is discretized into a finite number of images and in the new method these images are evolved concurrently with replicas of the original system while keeping their inter-distances equal via reparametrization. There is no need to compute the mean force by time-averaging, nor to project the force perpendicularly to the string. In this Letter, the algorithmic aspects of the on-the-fly string method are presented in detail and the method is tested on the solvated alanine dipeptide molecule.