Three Dimensional Atom-Diatom Reactive Scattering Calculations Using Symmetrized Hyperspherical Coordinates
<p>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 coordinate...
| Summary: | <p>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.</p>
<p>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 (<i>J</i> = 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 <i>H</i> + <i>H₂</i>. The numerical stability of the treatment is sufficiently high to permit the first lifetime matrix analysis of the resonance structure of <i>H</i> + <i>H₂</i> based on scattering matrices from our accurate calculations. This analysis reveals a series of 6 resonance states in the <i>J</i> = 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 <i>J</i> = 0 <i>H</i> + <i>H₂</i> 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.</p>
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