Quasi-Spectral Method for the Solution of the Master Equation for Unimolecular Reaction Systems

Rate constants of elementary reactions involving unimolecular steps can be calculated from molecular data in a most general way by solving appropriate master equations. The conventional numerical solution requires rather a fine discretization applied over a sufficiently large energy range to achieve a reasonable accuracy. This leads to linear but very high-dimensional systems of differential equations. We propose a quasi-spectral method that uses Gaussian radial basis functions to establish a low-dimensional linear model to speed up the numerical integration. The combination with an iterative adaptation provides a further improvement of computational efficiency. The suggested approach is illustrated and exemplified by means of the unimolecular decomposition of 2,3-dihydro-2,5-dimethylfuran-3-yl, an intermediate radical occurring in the pyrolysis and oxidation of 2,5-dimethylfuran. A comparison of the conventional and the proposed method is presented to validate the novel approach and to demonstrate its performance.