STOCHASTIC SIMULATION OF CHEMICALLY ACTIVATED UNIMOLECULAR REACTIONS

The kinetic master equation for the title processes can be formulated as a traditional deterministic set of coupled differential reaction-ra te equations, or, alternatively, as a stochastic process in which each reaction is a random-walk transition in energy-species space. This st ochastic description is the basis for three methods we describe here t o numerically solve the kinetic master equation for chemically activat ed 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 C arlo simulation of the stochastic reaction processes, The second metho d allows for the direct calculation of the steady-state product distri bution (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 interme diates (CSSPI), reformulating the solution of the master equation as a n eigenvector problem generated by the description as a continuous tim e Markov chain, To our knowledge, the DCPD method has not been describ ed before. Also, this is the first time that a CSSPI model is used exp licitly in this type of calculation, The three methods are illustrated using the simple H+HNCO reaction, important in the RAPRENO(x) mechani sm for NOx removal from flue gases. (C) 1997 American Institute of Phy sics.