Cylindrical manifolds and reactive island kinetic theory in the time domain

Abstract

In a series of recent publications we discussed the concept of cylindrical manifolds and their role in mediating the reaction dynamics of chemical reactions. The cylindrical manifolds were used to develop a chemical reaction rate theory we called reactive island (RI) theory. RI theory was cast in terms of the map dynamics between n Poincaré mapping planes—which were referred to as the ‘‘n-map.’’ Therefore ‘‘time’’ did not explicitly appear within n-map RI theory. In this paper we extend n-map RI theory to the time domain. The formal theory, cast as a master equation, is used to obtain the temporal RI model. Temporal RI theory is applied to a two degree-of-freedom system exhibiting dynamical chaos. The results of temporal RI theory are compared with classical Rice–Ramsberger–Kassel–Marcus (RRKM) theory and it is found that even under, presumably, ‘‘ideal’’ dynamical conditions, RRKM theory can be in serious error with numerical simulation. It is also seen that temporal RI theory accurately accounts for the rates at energies far above the barrier, where RRKM theory is not expected to be applicable. We also discuss some rigorous comparisons between the decay rates obtained from n-map and temporal RI theories.