Locating Instantons in Many Degrees of Freedom

We implemented and compared four algorithms to locate instantons, i.e., the most likely tunneling paths at a given temperature. These allow to calculate reaction rates, including atom tunneling, down to very low temperature. An instanton is a first-order saddle point of the Euclidean action in the space of closed Feynman paths. We compared the Newton−Raphson method to the partitioned rational function optimization (P-RFO) algorithm, the dimer method, and a newly proposed mode-following algorithm, where the unstable mode is directly estimated from the instanton path. We tested the algorithms on three chemical systems, each including a hydrogen transfer, at different temperatures. Overall, the Newton−Raphson turned out to be the most promising method, with our newly proposed mode following, being the fall-back option.