On product state distributions in triatomic unimolecular reactions: Beyond phase space theory and the adiabatic assumption

Our goal is to derive a simple dynamically corrected statistical treatment of state distributions in the products of triatomic unimolecular reactions involving efficient energy transfers between rotation and translation motions en route to products. For, phase space theory or the adiabatic channel model-the only statistical approaches of final state distributions-may not be applicable to such processes. We thus analyze and model how the departing atom perturbs the rotation of the diatomic molecule. Since the general problem is intricate, we limit our study to the basic, yet realistic and instructive case where the bending force is harmonic and the total angular momentum is zero. A remarkable fact is the one-to-one relation between the perturbation and a coefficient chi, related in a simple way to the mechanical parameters of the system. Transition state theory combined with our model-the linear transformation model-leads to the desired treatment of product state distributions. Its predictions are in good agreement with dynamical calculations. We also show that there is a close relation between the final shape of state distributions and the angular dependence of the potential energy at the transition state. (C) 2001 American Institute of Physics.