Fulton, Nicholas Grant; (1995) Graphical and computational analysis of the vibrations of triatomic molecules. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The vibrational motions of triatomic molecules at low energies are well studied both experimentally and theoretically. Advances in computer capability have made it possible to perform fully quantal calculations at ever higher energies, where the motions are less well known and often classically chaotic. Experiments at these energies frequently give very complicated results, for example the photodissociation spectrum of H+3 which has yet to be fully explained. Traditionally much theoretical effort has been concentrated in reproducing transition energies seen experimentally. Graphical and computational techniques presented here are aimed at the analysis of the wavefunctions, which are often calculated with the eigenenergies, but not studied so thoroughly. A discrete variable representation (DVR) method for calculating large amplitude vibrations in symmetrised Radau coordinates is presented and applied to water. The eigenenergies are compared with other calculations, and wavefunctions analysed graphically to find the important motions. Possible convergence problems are then discussed with reference to the local mode O-H stretch. Analysis of normal and local mode vibrational behaviour of H+3 and D+3 is presented with discussion as to how topological considerations of the configuration potential can predict the likely types of motion at low energies. Wavefunctions are examined graphically and localisation is compared to that of a similar classical system. Methods for studying high amplitude vibrations are presented and applied to H+3. New types of wavefunction localisation are shown, and their lifetimes and periods investigated. A new function is defined which gives a measure of the degree of localisation and the way in which wavefunction amplitude may transfer between different modes of localisation. Classical analysis of H+3 is performed in 2D and compared to quantal calculations. The behaviour of the system at different energies is discussed and bifurcation diagrams are examined, showing the appearance of new motions. Important motions are then discussed and considered in the explanation of the H+3 photodissociation experiment.

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