## Abstract

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 C_{3}H_{5} and C_{4}H_{5}. 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 C_{4}H_{5} 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.

Original language | English |
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Pages (from-to) | 101-109 |

Number of pages | 9 |

Journal | Journal of Computational Chemistry |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 15 2017 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Computational Mathematics