Quantum Theory of Rearrangement Collisions with Applications to Elementary Chemical Reactions.

A three-dimensional, quantum mechanical, coupled channel distorted wave approximation is developed for calculating cross sections for rearrangement collisions between an atom and a diatomic molecule based on the transition (T matrix) formulation of molecular scattering. In this approximation, both entrance and exit channel wave functions are calculated from the inelastic vibrational and rotational close-coupling approximation, and these wave functions are used in the calculation of the T matrix elements for rearrangement. This method allows for the internal states of both the target and product molecule to be dynamically coupled following the motion of the atom, and the wave functions for the exit and entrance channel have the proper asymptotic behavior. Therefore, this method is capable of yielding more accurate results than those from most of the T matrix schemes employed so far. An efficient computational procedure for calculating cross sections is given utilizing parity conservation and by reducing the six-dimensional integral over complex-valued functions to a real-valued three-dimensional integral. Cross sections calculated from this method are presented for the isotopic reactions H+H(,2), D+H(,2), H+H(,2), and Mu+H(,2) using the most accurate available potential surface for energies in the threshold regions of these reactions, and these are compared to other theoretical results when possible. The calculated cross sections for the H+H(,2) reaction are found to be in excellent agreement with the converged close coupling results. Rate constants obtained from the cross sections show the same temperature dependence and are of the same order of magnitude as experimental results; however, the present results are about a factor of 2-3 smaller than the experimental values at lower temperatures for all systems studied. The results of this study indicate that the present method is capable of correctly predicting all reaction attributes of the elementary chemical reactions studied as long as the collision energy is small so that the probability for rearrangement is much smaller than the elastic and inelastic processes.