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.

Sydenham Street Revived: A Public Space Experiment

In 2015, the Sydenham Street Revived pop-up park project (SSR) transformed Sydenham Street between Princess and Queen Streets into a temporary pedestrian-only public space. The goal of the project was to test out the idea of permanently pedestrianizing this street section. But what did this urban experiment ultimately prove? Using video footage, photographs, and observations recorded before and during the project, this report analyzes the use of the space in order to evaluate the claim that SSR created a successful public space and to make recommendations for a permanent public space on Sydenham Street. Two research methods were used: quantitative data collection, consisting of headcounts of both pedestrians and stationary users of the space; and a qualitative observational survey, based on the criteria for successful public spaces developed by the Project for Public Spaces. Data collection occurred two days one week prior to the project, and two days during the project, on days that were similar in terms of temperature and weather. The research revealed that the SSR did create a successful public space, although additional research is needed in order to determine how the space would function as a public place throughout different seasons, to study the street closure’s impact on surrounding residents and businesses, and to understand how private commercial activity would influence use. Recommendations for a permanent public space on Sydenham Street include considerations for flexible street design and a continuous, barrier-free surface; ensuring that there is an abundance of places to sit; making opportunities for public and community-created art; and to improve walkability by connecting the grid using a mid-block walkway.