On the role of nonergodicity and slow IVR in unimolecular reaction rate theory—A review and a view

A review of the history of unimolecular reaction rate theory reveals a strong reliance upon an assumption of ergodicity and rapid internal vibrational energy redistribution (IVR). The notable exception is the theory of N. B. Slater wherein fully separable harmonic dynamics was assumed. Recently realistic intermediate theories have been sought. A simple analysis will be presented here which systematizes the mechanism and the expected effects. The problem of nonergodicity and slow IVR is analyzed within the framework of the classical RRK theory. A phenomenological model, the RRK-S(n) model, previously applied to the study of the isomerization of trans-stilbene, is extended to account for an energy dependent internal energy transfer rate between a reactive oscillator and the remaining oscillators. The reaction dynamics is expected to show character transitions at three different energies. Below Eerg the dynamics will be predominantly nonergodic while above Eerg it will be predominantly ergodic. At the energy E0, the barrier height, the specific rate coefficient ka(E) becomes nonzero and generally rising with energy. Depending on the number of “reactive ” oscillators n, the rate of energy transfer between reactive and unreactive oscillators, the external collision frequency and the rate of decay of the reactive set of oscillators the specific rate coefficient shows a degree of IVR limitation which is in turn reflected in the total reaction rate coefficient k(ω). Illustrative calculations delineating expected behaviour within the confines of the model are presented.