Pressure-dependent rate rules for cycloaddition, intramolecular H-shift, and concerted elimination reactions of alkenyl peroxy radicals at low temperature

The reactions of cycloaddition, intramolecular H-shift and concerted elimination of alkenyl peroxy radicals are three kinds of important reactions in the low temperature combustion of alkenes. In this study, the cycloaddition reactions are divided into classes considering endo-cycloaddition, exo-cycloaddition and the size of the transition states; the intramolecular H-shift reactions are divided into classes depending upon the ring size of the transition states and the type of C–H bonds from which the hydrogen atom is transferred; the concerted elimination reactions are divided into classes according to the type of H–CβCαOO bond that is broken. All geometry optimizations are performed at the B3LYP/6-31G(2df,p) level. With the electronic structure calculations being performed using the composite Gaussian-4 (G4) method, high pressure limit rate constants and pressure-dependent rate constants at pressures varying from 0.01 to 100 atm are calculated by using canonical transition state theory and the Rice–Ramsberger–Kassel–Marcus/master equation method, respectively. All rate constants are given in the form of the modified Arrhenius expression. The high pressure limit rate rules and the pressure-dependent rate rules are derived by averaging the rate constants of a representative set of reactions in each class. The results show that the rate rules for these three classes of reactions have a large uncertainty and the impact of the pressure on the rate constants increases as temperature increases.