Full rate constant matrix contraction method for obtaining branching ratio of unimolecular decomposition

• Published in: Journal of computational chemistry Vol. 38; no. 2; pp. 101 - 109
• Main Authors: Sumiya, Yosuke, Taketsugu, Tetsuya, Maeda, Satoshi
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 15.01.2017
• Subjects: Automation; branching ratio; Computer simulation; Construction methods; Decomposition; kinetic simulation; Kinetics; Mathematical analysis; Mathematical models; Matrix; Molecules; Quantum chemistry; Quantum theory; rate constant matrix contraction; rate equation; Search methods; Searching; Simulation; unimolecular decomposition; rate equation; rate constant matrix contraction; branching ratio; kinetic simulation; unimolecular decomposition
• ISSN: 0192-8651; 1096-987X; 1096-987X
• DOI: 10.1002/jcc.24526

The branching ratio of unimolecular decomposition can be evaluated by solving the rate equations. Recent advances in automated reaction path search methods have enabled efficient construction of the rate equations based on quantum chemical calculations. However, it is still difficult to solve the rate equations composed of hundreds or more elementary steps. This problem is especially serious when elementary steps that occur in highly different timescales coexist. In this article, we introduce an efficient approach to obtain the branching ratio from a given set of rate equations. It has been derived from a recently proposed rate constant matrix contraction (RCMC) method, and termed full‐RCMC (f‐RCMC). The f‐RCMC gives the branching ratio without solving the rate equations. Its performance was tested numerically for unimolecular decomposition of C3H5 and C4H5. Branching ratios obtained by the f‐RCMC precisely reproduced the values obtained by numerically solving the rate equations. It took about 95 h to solve the rate equations of C4H5 consisting of 234 elementary steps. In contrast, the f‐RCMC gave the branching ratio in less than 1 s. The f‐RCMC would thus be an efficient alternative of the conventional kinetic simulation approach. © 2016 Wiley Periodicals, Inc. Predicting the branching ratio of unimolecular decomposition is one of the most important subjects in computational chemistry. In this paper, an efficient and robust approach to evaluate the branching ratio from given rate equations for unimolecular decomposition is introduced. The present approach, which was derived from a rate constant matrix contraction (RCMC) method proposed recently by the authors, was termed full‐RCMC (f‐RCMC). The f‐RCMC method can be a highly efficient alternative to the conventional kinetic simulation approach.