Solving the unimolecular master equation with a weighted subspace projection method

A weighted subspace projection method for solving the unimolecular master equation over a wide range of temperatures and pressures is developed. Sample calculations modeling the dissociation of ethane at 300 K and pressures as low as 0.65 Torr demonstrates the utility of the method in regimes where standard projection methods fail. For the sample calculations the weighted Arnoldi method was able to reliably calculate the smallest eigenvalue of the rate matrix in excellent agreement with calculations using the Nesbet algorithm. Extremely small eigenvalues of the order of -10(-48) could be calculated without difficulty. The formal equivalence between various weighting schemes and common matrix transformations is shown. The point that merely taking the transpose of the rate matrix can be extremely beneficial is made, commenting on the relationship between the left and right eigenvectors of the rate matrix. (C) 2000 John Wiley & Sons, Inc.