Steady-state master equation methods

This paper investigates the application of the steady-state master equation (SSME) to complex unimolecular reactions. It is shown how the steady-state approximation and the Boltzmann reservoir approximation can be applied, both together or separately, to improve the efficiency and the numerical robustness of simple master equation calculations. The case of a two-well isomerization is considered in detail, and two versions of the SSME are derived for it, one of which shows very clearly and analytically the relationship between the rate coefficients and the flux coefficients. It is shown for a reversible second order recombination reaction that the second order phenomenological equation can be regained in either version of the SSME. It is also shown how, under steady state conditions, the SSME may be used to determine rate coefficients for each reaction in a multiple well scheme.