# General numerical solution to the time-dependent master equation for non-steady-state reactions: Application to the photoinitiated isomerization of cycloheptatriene to toluene

## Abstract

An efficient numerical algorithm has been developed to solve the time-dependent master equation. The method may be used to calculate the probability of reaction as a function of pressure for a vibrationally hot reactant produced under non-steady-state reaction conditions. To test the numerical algorithm, calculations were performed on the probability of reaction versus buffer gas pressure for the 260 nm photoinitiated isomerization of cycloheptatriene to toluene, which occurs on the ground state potential surface following internal conversion. The average energy transferred per collision, 〈ΔEcoll〉, from cycloheptatriene to 25 buffer gases was determined via master equation fits to the Stern-Volmer data of Troe and Wieters [J. Chem. Phys. 71 (1979) 3931]. The calculated values of 〈ΔEcoll〉 agree very well with those measured directly by Troe and co-workers. © 1991.