Steady-state approximation to the master equation for thermal dissociation reactions

A steady-state method is proposed for solving one-dimensional master equations for dissociation reactions. The reactant energy space is divided at a suitable energy (below threshold) and states below this energy are assumed to be Boltzmann populated. The steady-state method involves inversion of a reduced master equation matrix, rather than the usual diagonalisation of the full matrix, and is consequently much faster. It is also shown to be extremely accurate under normal conditions. As a corollary the method explains how the rate constants obtained from a relaxation analysis of a reversible dissociation/association equilibration can be given valid interpretation in terms of irreversible dissociation/association master equations, resolving a long-standing controversy in the literature.