Phase Space Prediction of Product Branching Ratios: Canonical Competitive Nonstatistical Model

Abstract

We present a new model for predicting branching ratios of chemical reactions when a branching of the reaction path occurs after the dynamical bottleneck, including the case where it occurs after an intermediate. The model is based on combining nonstatistical phase space theory for the direct component of a reaction with variational transition-state theory for an indirect component of reaction. The competition between direct and indirect processes is treated by an extension of the unified statistical model. This new method provides a way to understand the factors that control this kind of chemical reaction and to perform calculations using high-level electronic structure methods for complex systems. The model is based on quantized energy levels of transition states and products, and it involves the same information as required for calculating transition-state rate constants and equilibrium constants plus a phenomenological relaxation time, which was taken from previous work. For the textbook reaction of the hydroboration of propene by BH(3) it has recently been inferred that the selectivity can only be understood by consideration of dynamical trajectories. However, the calculated branching fraction of this prototype reaction increases from 2%-3% when calculated under the inappropriate assumption of complete equilibration of the intermediate to from 8%-9% when calculated with the new theory, which requires only limited information about the system and does not involve running trajectories. The calculated result is in reasonable agreement with experiment (approximately 10%).