Hierarchy of reaction dynamics in a thermally fluctuating environment

Nonlinear dynamics in the passage over a rank-one saddle is investigated as a function of temperature in the presence of stochastic, thermal fluctuation. The analyses are based on a framework we developed recently adopting a multidimensional underdamped Langevin equation (without any assumption for the form of the potential of mean force). The framework can in principle provide a single coordinate to enable us to predict the final destination of the reaction in a thermally fluctuating media. At each temperature, the preciseness or the error of the reaction coordinate is evaluated in capturing the true reaction dynamics at different levels of approximations. By using the Müller-Brown potential as an illustrative example, it is found that a hierarchy of dynamical structure exists in the region of a rank-one saddle, in which the crossing dynamics qualitatively changes as the temperature increases. We discuss the mechanism of how the reaction coordinate persists, which provides a boundary of the reaction to divide the phase space into the reactive and the nonreactive regions, even in the presence of thermal fluctuation.