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Quantum mechanical reactive scattering for planar atom plus diatom systems. I. Theory

Kuppermann, Aron and Schatz, George C. and Baer, M. (1976) Quantum mechanical reactive scattering for planar atom plus diatom systems. I. Theory. Journal of Chemical Physics, 65 (11). pp. 4596-4623. ISSN 0021-9606. doi:10.1063/1.432916.

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A method is presented for accurately solving the Schrödinger equation for the reactive collision of an atom with a diatomic molecule on a space-fixed plane. The procedure consists primarily of two steps. First, the Schrödinger equation in each of the three arrangement channel regions is transformed into a set of coupled differential equations and numerically integrated in each of these regions to generate primitive solutions. The rotational part of the vibration–rotation basis functions involved is not changed from its asymptotic form during this propagation, but the vibrational eigenfunctions as well as the integration variable are changed periodically so as to follow the vibrational motions in a nearly adiabatic manner. In the second step, the primitive solutions generated in each of the three arrangement channels are smoothly matched to each other on a set of appropriately chosen matching surfaces. The resulting solutions are then linearly combined to satisfy the proper asymptotic boundary conditions, and the scattering matrix, scattering amplitudes, and cross sections are determined. Application of this procedure to the special case of the H+H2 reaction is discussed in detail including simplifications arising from the additional symmetries involved, and the inclusion of effects resulting from indistinguishability of identical particles.

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Additional Information:Copyright © 1976 American Institute of Physics. Received 22 December 1975. One of us (A.K.) wished to thank Professor R. P. Feynman for useful discussions on postantisymmetrization. He is also greatly indebted to Professor J.D. Roberts who, as Chairman of the Division of Chemistry and Chemical Engineering at Caltech during the crucial stages of this research, mustered the financial resources and offered the encouragement which were central to its successful completion. We also thank Professor Donald G. Truhlar for useful comments. Work supported in part by the United States Air Force Office of Scientific Research (Grant No. AFOSR-73-2539). Work performed [by G.C.S.] in partial fulfillment of the requirements for the Ph.D. degree in Chemistry at the California Institilte of Technology. Arthur Amos Noyes Laboratory of Chemical Physics, Contribution No. 5248.
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Division of Chemistry and Chemical Engineering, CaltechUNSPECIFIED
Air Force Office of Scientific ResearchAFOSR-73-2539
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Arthur Amos Noyes Laboratory of Chemical Physics5248
Issue or Number:11
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Deposited On:16 Oct 2008 20:11
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