Towards a state-to-state transition state theory
We assume that, having arrived at the transition state, the branching into the different product states is independent of the initial quantum states of the reactants. This assumption plus the familiar transition state approximation (that the reaction rate is the rate of the passage across the barrier) yields an expression for the state-to-state cross section in terms of the state-to-all one, as well as microcanonical rate constants. Models, adiabatic correlations, purely statistical considerations, or collinear computations can provide the required input for the theory. Exact quantal computations on the 3D H + H2 reaction are found to satisfy the assumed factorization quite well. Furthemore, reaction probabilities derived from a line-of-centers model, with a barrier height dependent on the approach angle, account for the probabilities derived from the exact quantal computation.
© 1985 American Institute of Physics. Received 13 February 1985; accepted 30 April 1985. One of us (A.K.) thanks the chairman and staff of the Fritz Haber Research Center for Molecular Dynamics, where this work was performed, for their warm hospitality and help. We thank Dr. Y.M. Engel for carrying out the numerical work necessary to generate Tables II and III. The research of A.K. was supported in part by the United States Air Force Office of Scientific Research (Grant No. AFOSR-82-0341). The Fritz Haber Research Center is supported by the Minerva Gesellshaft für die Forschung, mbH, Munich, West Germany. Arthur Amos Noyes Laboratory of Chemical Physics, Contribution No. 7150.
Published - KUPjcp85.pdf