A Two Transition State Model for Radical−Molecule Reactions: Applications to Isomeric Branching in the OH−Isoprene Reaction

Abstract

A two transition state model is applied to the prediction of the isomeric branching in the addition of hydroxyl radical to isoprene. The outer transition state is treated with phase space theory fitted to long-range transition state theory calculations on an electrostatic potential energy surface. High-level quantum chemical estimates are applied to the treatment of the inner transition state. A one-dimensional master equation based on an analytic reduction from two-dimensions for a particular statistical assumption about the rotational part of the energy transfer kernel is employed in the calculation of the pressure dependence of the addition process. We find that an accurate treatment of the two separate transition state regions, at the energy and angular momentum resolved level, is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is shown to occur at about 275 K, with significant effects from both transition states over the 30-500 K temperature range. Modest adjustments in the ab initio predicted inner saddle point energies yield predictions that are in quantitative agreement with the available high-pressure limit experimental observations and qualitative agreement with those in the falloff regime. The theoretically predicted capture rate is reproduced to within 10% by the expression [1.71 x 10(-10)(T/298)(-2.58) exp(-608.6/RT) + 5.47 x 10(-11)(T/298)-1.78 exp(-97.3/RT); with R = 1.987 and T in K] cm3 molecule(-1) s(-1) over the 30-500 K range. A 300 K branching ratio of 0.67:0.02:0.02:0.29 was determined for formation of the four possible OH-isoprene adduct isomers 1, 2, 3, and 4, respectively, and was found to be relatively insensitive to temperature. An Arrhenius activation energy of -0.77 kcal/mol was determined for the high-pressure addition rate constants around 300 K.