submitted to TCA 2015

The Variational Nature of the Gentlest Ascent Dynamics and
the Relation of a Variational Minimum of a Curve and the Minimum Energy Path

by

Josep Maria Bofill     and     Wolfgang Quapp


abstract:

It is shown that the path described by the gentlest ascent dynamics to find
transition states [W. E and X. Zhou, 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, that some
former reaction pathways possess, and the minimum energy path is discussed.