Journal of Chemical Physics vol:106 issue:16 pages:6564-6573
The kinetic master equation for the title processes can be formulated as a traditional deterministic set of coupled differential reaction-rate equations, or, alternatively, as a stochastic process in which each reaction is a random-walk transition in energy-species space. This stochastic description is the basis for three methods we describe here to numerically solve the kinetic master equation for chemically activated unimolecular reactions. The first method allows the calculation of the complete time evolution within a given mechanism, and is based an Gillespie's exact stochastic method (ESM). It is essentially a Monte Carlo simulation of the stochastic reaction processes, The second method allows for the direct calculation of the steady-state product distribution (DCPD), II describes the random walk within the framework of a discrete time Markov chain, and reduces the calculation of the steady-state product distribution to a fairly simple matrix algebra problem, The third method calculates the steady-state population of the intermediates (CSSPI), reformulating the solution of the master equation as an eigenvector problem generated by the description as a continuous time Markov chain, To our knowledge, the DCPD method has not been described before. Also, this is the first time that a CSSPI model is used explicitly in this type of calculation, The three methods are illustrated using the simple H+HNCO reaction, important in the RAPRENO(x) mechanism for NOx removal from flue gases. (C) 1997 American Institute of Physics.