# A Two Transition State Model for Radical−Molecule Reactions: A Case Study of the
Addition of OH to C_{2}H_{4}

journal contribution

posted on 14.07.2005, 00:00 by Erin E. Greenwald, Simon W. North, Yuri Georgievskii, Stephen J. KlippensteinA two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This
reaction serves as a prototypical example of a radical−molecule reaction with a negative activation energy
in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition
states. The outer transition state is treated with a recently derived long-range transition state theory approach
focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated
in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner
transition state region are explored with direct phase space integration. A two-dimensional master equation
is employed in treating the pressure dependence of the addition process. 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 predicted to occur at about 130 K, with significant effects from both
transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner
saddle point energy yields theoretical predictions which are in quantitative agreement with the available
experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the
expression [4.93 × 10

^{-12}(*T*/298)^{-2.488}exp(−107.9/*RT*) + 3.33 × 10^{-12}(*T*/298)^{0.451}exp(117.6/*RT*); with*R*= 1.987 and*T*in K] cm^{3}molecules^{-1}s^{-1}over the 10−600 K range.