Perturbed normal-mode analysis of induction times, relaxation times, and reaction rates in unimolecular reactions

Abstract

A perturbed normal-mode analysis is presented of the induction (or incubation) time, the relaxation rate, and the reaction rate of a diluted unimolecular system. At high temperature, the unimolecular rate approaches the Lindemann behaviour and the low-pressure rate is related to the normal modes of relaxation of the reactive states in a simple manner. In a step-ladder model system, the network relationship between the normal modes and the microscopic transition probabilities leads to explicit theoretical correlations between the respective experimental quantities. Illustrative calculations of such correlations are presented for the decomposition reactions of N2O and CO2 diluted in Ar at shock wave temperatures, and are compared with experiment.