Three Dimensional Atom-Diatom Reactive Scattering Calculations Using Symmetrized Hyperspherical Coordinates

Author: Hipes, Paul Gregory

Year: 1988

Degree: Dissertation (Ph.D.)

Advisor: Kuppermann, Aron

Committee Members: Marcus, Rudolph A.; Beauchamp, Jesse L.; Bercaw, John E.; Dervan, Peter B.; Kuppermann, Aron

Option: Chemistry

DOI: 10.7907/2S8G-PJ87

Abstract

The focus of this thesis is the use of symmetrized hyperspherical coordinate techniques in the accurate calculation of differential cross sections for the reactive collision of an atom with a diatomic molecule in three-dimensional space. A single set of symmetrized hyperspherical coordinates treats all regions of configuration space in an equivalent inelastic scattering problem which is conceptually and computationally easier to handle.

The work described here represents the first successful application of any accurate hyperspherical coordinate methodology to atom-diatom reactive scattering in three-dimensional space. This methodology has permitted the calculation of zero total angular momentum (J = 0) partial wave transition probabilities and associated phases over a significantly larger range of collision energies (up to 1.6 eV total energy) than previously possible for the system H + H₂. The numerical stability of the treatment is sufficiently high to permit the first lifetime matrix analysis of the resonance structure of H + H₂ based on scattering matrices from our accurate calculations. This analysis reveals a series of 6 resonance states in the J = 0 partial wave, some of which have not been seen before. The symmetrized hyperspherical coordinate methodology is presented in detail. A selection of surface functions and scattering results for J = 0 H + H₂ using the LSTH potential energy surface are presented and discussed. In addition, a small number of results from the Porter-Karplus potential energy surface are also given.

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