The variational nature of the gentlest ascent dynamics and the relation of a variational minimum of a curve and the minimum energy path

摘要

It is shown that the path described by the gentlest ascent dynamics to find transition states (Weinan and Zhou in Nonlinearity 24:1831, 2011) is an example of a quickest nautical path for a given stationary wind or current, the so-called Zermelo navigation variational problem. In the present case, the current is the gradient of the potential energy surface. The result opens the possibility to propose new curves based on Zermelo's theory for two tasks: locate transition states and define reaction paths. The relation between a minimal variational character, which some former reaction pathways possess, and the minimum energy path is discussed.