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.

Preparation of Polymer Nanoparticles by Ring Opening Metathesis Polymerization in Aqueous Dispersed Systems with Water-Soluble Ruthenium-based Catalyst

Ring opening metathesis polymerization (ROMP) is a variant of olefin metathesis used to polymerize strained cyclic olefins. Ruthenium-based Grubbs’ catalysts are widely used in ROMP to produce industrially important products. While highly efficient in organic solvents such as dichloromethane and toluene, these hydrophobic catalysts are not typically applied in aqueous systems. With the advancements in emulsion and miniemulsion polymerization, it is promising to conduct ROMP in an aqueous dispersed phase to generate well-defined latex nanoparticles while improving heat transfer and reducing the use of volatile organic solvents (VOCs). Herein I report the efforts made using a PEGylated ruthenium alkylidene as the catalyst to initiate ROMP in an oil-in-water miniemulsion. 1H NMR revealed that the synthesized PEGylated catalyst was stable and reactive in water. Using 1,5-cyclooctadiene (COD) as monomer, we showed the highly efficient catalyst yielded colloidally stable polymer latexes with ~ 100% conversion at room temperature. Kinetic studies demonstrated first-order kinetics with good livingness as confirmed by the shift of gel permeation chromatography (GPC) traces. Depending on the surfactants used, the particle sizes ranged from 100 to 300 nm with monomodal distributions. The more strained cyclic olefin norbornene (NB) could also be efficiently polymerized with a PEGylated ruthenium alkylidene in miniemulsion to full conversion and with minimal coagulum formation.