Collisional transition probability and non-equilibrium unimolecular rate

Abstract

The rate constant for a unimolecular reaction at the low-pressure limit under non-equilibrium conditions (k0†) is a function of the collisional transition probability qi→j. For polyatomic molecules, the form of qi→j can only be surmised at present. We have used six models of qi→j, representing energy transfer that can be termed efficient (bimodal gaussian and bimodal gamma transition probability models), inefficient (exponential and Schwartz-Slawsky-Herzfeld models) and intermediate (unimodal gaussian and unimodal gamma models), and have computed k0†/k0 and Ea0=Ea0†−Ea0, where k0 is the equilibrium low-pressure rate constant, and †Ea0 is the temperature coefficient of k0†/k0, i.e., the difference in the corresponding experimental (Arrhenius) activation energies, for two molecular models based on the pyrolysis of H2O2 and the isomerization of CH3NC at low pressures. It turns out that when compared at the same average energy transferred per deactivating collision, the various transition probability models give results for k0†/k0 and Ea0 that are independent of the nature of the decomposing molecule, are virtually indistinguishable experimentally, and in particular yield ∼-2kT as the maximum Ea0 due to inefficient energy transfer.