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%).

Reaction Path Bifurcation in an Electrocyclic Reaction: Ring-Opening of the Cyclopropyl Radical

“…29−35 For many of these reactions, it is found that conventional statistical theories of reaction, namely transition state theory (TST) and RRKM, 36 fail to predict isotope effects and, often more importantly, product selectivities. 37−39 Dynamical studies of nonstatistical reactions are reshaping our fundamental conceptions of mechanistic physical organic chemistry with profound significance in areas such as synthetic organic chemistry, 38 enzyme catalysis, 40 and reactive roaming.…”

Dynamic Origin of the Stereoselectivity of a Nucleophilic Substitution Reaction

“…25 In the “canonical competitive nonstatistical model” (CCNM), the branching between products is divided into “indirect” and “direct” components, the former being predicted from TST and the later predicted from phase space theory. The absence of an intermediate leads the CCNM model to allocate 100% of the reaction to the indirect component, which is dominated by the stability of the initially formed conformers of the products.…”

Deviation from the anti-Markovnikov rule: a computational study of the regio- and stereoselectivity of diene hydroboration reactions

“…1 and assuming a kinetically controlled mechanism, we can predict the most favorable isomers computationally [21,22]. Previous computational studies have also pointed out the fact that the final thermodynamically favored products might not reflect the selectivity of the kinetically favored hydroboration reactions [23] and emphasized the importance of dynamical effects beyond transition state theory [24][25][26].…”