Theory of chemically activated unimolecular reactions. Weak collisions and steady states

Abstract

The prediction of decomposition/stabilization ratios for chemically activated unimolecular reactions is usually based on the assumption of steady state and irreversible deactivation. The levels below the activation energy Eo are treated as a sink. In the present work we assume that the reaction can be described by a weak-collision master equation. An exact analysis shows that one can expect three timescales: an initial transient, an intermediate steady state, and an asymptotic steady state. The intermediate steady state is well defined only if the eigenvalues of the corresponding thermal rate matrix can be separated into two groups one of which contains eigenvalues of substantially smaller magnitude. An efficient and accurate method for the estimation of intermediate steady-state populations and branching ratios is described. It avoids the irreversible deactivation assumption which is shown to lead to errors particularly for weak collisions. The new analysis is illustrated in a series of calculations for a model of the sec-butyl radical system. The numerical solutions are readily obtained by use of a recently developed equilibrium finite-basis-set method.