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.