Master equation analysis of intermolecular energy transfer in multiple-well, multiple-channel unimolecular reactions. II. Numerical methods and application to the mechanism of the C₂H₅+O₂ reaction

Having elucidated a full theoretical analysis of the master equation for intermolecular and intramolecular energy transfer in multiple-well, multiple-channel chemically or thermally activated reactions [J. Chem. Phys. 107, 8904 (1997)], we now present efficient methods of numerical analysis for the computational examination of the dynamics of the master equation. We suggest the use of a Krylov-subspace method to determine the uppermost portions of the internal spectrum of the master equation kernel. Such a computation is pivotal in determining whether there exists a state of secular equilibrium for the population of the moieties and whether there exists within the possible state of secular equilibrium, a state wherein the dynamics are represented by an isolated dominating mode; for only in the state of secular equilibrium can one write rate equations for the dissociating processes that are local in time. And, if such a state is possible, we suggest the use of a Hermite-Laguerre orthogonal collocation method for obtaining highly accurate solutions to the population of the moieties. The theory and numerical analysis is then applied to study the dynamics of the chemically-activated reaction C₂H₅+O₂. Comparison of the master equation treatment with modified strong-collision theory is also given for this system of multiple-well, multiple-channel reactions.