A simple Chain-of-States method in acceleration space for the efficient location of Minimum Energy Paths

We describe a robust and efficient chain-of-states method for computing Minimum Energy Paths~(MEPs) associated to barrier-crossing events in poly-atomic systems. The path is parametrized in terms of a continuous variable $t \in [0,1]$ that plays the role of time. In contrast to previous chain-of-states algorithms such as the Nudged Elastic Band or String methods, where the positions of the states in the chain are taken as variational parameters in the search for the MEP, our strategy is to formulate the problem in terms of the second derivatives of the coordinates with respect to $t$, {\em i.e.\/} the state {\em accelerations\/}. We show this to result in a very transparent and efficient method for determining the MEP. We describe the application of the method in a series of test cases, including two low-dimensional problems and the Stone-Wales transformation in $\mbox{C}_{60}$.