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

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 H and C H . 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 H 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.

Understanding the Acetalization Reaction Based on its Reaction Path Network

“…As we reported previously, propagation of the initial population can also be studied by the RCMC method . Furthermore, we introduced so called a traffic volume index Λ i , which is calculated as the sum of the population influx to MIN i and outflow from MIN i during the M times contraction procedure .…”

“…The obtained multiple reaction paths form a network called reaction path network. We have developed the artificial force induced reaction (AFIR) method for obtaining reaction path networks and the rate constant matrix contraction (RCMC) method for analyzing them . In this study, we applied the AFIR and RCMC methods to the acetalization reaction with R 1 =CH 3 and R 2 =H in Scheme .…”

Designing the Backbone of Hexasilabenzene Derivatives with a High Unimolecular Kinetic Stability

“…In this study, we have designed a kinetically stable hexasilabenene derivative with a planar, monocyclic Si 6 backbone. The key methodologies to achieve the design are the artificial force induced reaction (AFIR) method combined with the rate constant matrix contraction (RCMC) method . Using these methods, we evaluated unimolecular lifetimes of hexasilabenzene (Si 6 H 6 ), a sila‐substituted dicyclic compound decasilanaphthalene (Si 10 H 8 ), and lithium‐substituted hexasilabenzene (Si 6 Li 6 ).…”

“…The RCMC method regards MINs that interconvert to each other within a certain timescale belong to the same superstate and gives a few superstates that interconvert in the longer timescale. Details of the RCMC method are described in our previous papers …”

“…The key methodologies to achievet he design are the artificial force induced reaction (AFIR)m ethod combined with the rate constant matrixc ontraction (RCMC)m ethod. [35][36][37][38][39][40] Using these methods, we evaluated unimolecular lifetimes of hexasilabenzene (Si 6 H 6 ), asila-substituted dicyclic compound decasilanaphthalene( Si 10 H 8 ), and lithium-substituted hexasilabenzene (Si 6 Li 6 ). Then, we came up with ac ompound Si 6 H 4 Li 2 ,b ased on the most stable Si 6 Li 6 structure containing ap lanar Si 6 monocyclic backbone.…”