Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

Analysis of Evidence from Core Sample Fractures in Stewardson Lake Uranium Prospect

This study was performed to characterize evidence of potential unconformity-type U mineralizing fluids in drill core fractures from the Stewardson Lake prospect, in the Athabasca Basin, located in Northern Saskatchewan and Alberta, Canada. Fractures were visually classified into eight varieties. This classification scheme was improved with the use of mineralogical characterization through SEM (Scanning Electron Microscope) and XRD analyses of the fracture fills and resulted in the identification of various oxides, hydroxides, sulfides, and clays or clay-sized minerals. Fractures were tallied to a total of ten categories with some commonalities in color. The oxidative, reductive or mixed nature of the fluids interacting with each fracture was determined based on its fill mineralogy. The measured Pb isotopic signature of samples was used to distinguish fractures affected solely by fluids emanating from a U mineralization source, from those affected by mixed fluids. Anomalies in U and U-pathfinder elements detected in fractures assisted with attributing them to the secondary dispersion halo of potential mineralization. Three types of fracture functions (chimney, composite and drain) were defined based on their interpreted flow vector and history. A secondary dispersion halo boundary with a zone of dominance of infiltrating fluids was suggested for two boreholes. The control of fill mineralogy on fracture color was investigated and the indicative and non-indicative colors and minerals, with respect to a secondary dispersion halo, were formally described. The fracture colors and fills indicative of proximity to the basement host of the potential mineralization were also identified. In addition, three zones of interest were delineated in the boreholes with respect to their geochemical dynamics and their relationship to the potential mineralization: a shallow barren overburden zone, a dispersion and alteration zone at intermediate depth, and a second deeper zone of dispersion and alteration.