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Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

Schatz, George C. and Kuppermann, Aron (1976) Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory. Journal of Chemical Physics, 65 (11). pp. 4642-4667. ISSN 0021-9606. doi:10.1063/1.432918.

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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 in three dimensions on a single Born–Oppenheimer potential energy surface. The Schrödinger equation is first expressed in body‐fixed coordinates. The wavefunction is then expanded in a set of vibration–rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. Next, these are smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wavefunctions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes several types of differential and integral cross sections are obtained. Simplifications arising from the use of parity symmetry to decouple the coupled‐channel equations, the matching procedures and the asymptotic analysis are discussed in detail. Relations between certain important angular momentum operators in body‐fixed coordinate systems are derived and the asymptotic solutions to the body‐fixed Schrödinger equation are analyzed extensively. Application of this formalism to the three‐dimensional H+H_2 reaction is considered including the use of arrangement channel permutation symmetry, even–odd rotational decoupling and postantisymmetrization. The range of applicability and limitations of the method are discussed.

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Additional Information:© 1976 American Institute of Physics. Received 22 December 1975. Online Publication Date: 28 August 2008. Research supported in part by the United States Air Force Office of Scientific Research (Grant No. AFOSR-73-2539). Work performed in partial fulfillment of the requirements for the Ph. D. in Chemistry at the California Institute of Technology. Contribution No. 5250.
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Air Force Office of Scientific Research (AFOSR)AFOSR-73-2539
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Caltech Arthur Amos Noyes Laboratory of Chemical Physics 5250
Issue or Number:11
Classification Code:PACS: 34.20.-b, 82.20.Kh
Record Number:CaltechAUTHORS:20120808-102852220
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Official Citation: Quantum mechanical reactive scattering for three‐dimensional atom plus diatom systems. I. Theory George C. Schatz and Aron Kuppermann J. Chem. Phys. 65, 4642 (1976);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33014
Deposited By: Ruth Sustaita
Deposited On:08 Aug 2012 17:48
Last Modified:09 Nov 2021 21:31

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