A systematic treatment of three-dimensional quantum mechanical reaction coordinates |
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Authors: | Norman M. Witriol Gary H. Herling |
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Affiliation: | (1) Naval Research Laboratory, 20375-5000 Washington, DC;(2) Department of Physics, Louisiana Tech. University, 71270 Ruston, LA, USA;(3) Naval Research Laboratory, 20375-500 Washington, DC, USA |
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Abstract: | Summary The rigorous, collinear, canonical point transformation method with hyper-hyperbolic coordinates is extended to the infinite central mass problem in three dimensions. The initial transformation performed is (xA, yA, zA, xC, yC, zC) ( , , , r, R, ), where ( , , ) are the Euler angles; r and R are the AB and BC interatomic distances, respectively, and is the angle between r and R. A second transformation is then performed to ( , , , , , ), where is the reaction coordinate mimicking the reaction path, and is the vibrational coordinate of the diatom. The transformed spaces are all one-to-one mappings from the original spaces, and thus do not have any three-to-one regions. The transformed momenta and Hamiltonians are derived, and are Hermitian in their respective transformed spaces. |
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Keywords: | Reactive scattering Reaction coordinates Molecular scattering |
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