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.