QC 20100629

A novel method for integrating the time-dependent Schrödinger equation is presented. The moving boundary truncation (MBT) method is a time-dependent adaptive method that can significantly reduce the number of grid points needed to perform accurate wave packet propagation while maintaining stability. Hydrodynamic quantum trajectories are used to adaptively define the boundaries and boundary conditions of a fixed grid. The result is a significant reduction in the number of grid points needed to perform accurate calculations. A variety of model potential energy surfaces are used to evaluate the method. Excellent agreement with fixed boundary grids was obtained for each example. By moving only the boundary points, stability was increased to the level of the full fixed grid. Variations of the MBT method are developed which allow it to be applied to any potential energy surface and used with any propagation method. A variation of MBT is applied to the collinear H+H₂ reaction (using a LEPS potential) to demonstrate the stability and accuracy. Reaction probabilities are calculated for the three dimensional non-rotating O(³P)+H₂ and O(³P)+HD reactions to demonstrate that the MBT can be used with a variety of numerical propagation techniques. / text

Thesis (Ph. D.)--Florida State University, 2003. / Advisor: Dr. Oliver Steinbock, Florida State University, College of Arts and Sciences, Dept. of Chemistry and Biochemistry. Title and description from dissertation home page (Aug. 27, 2004). Includes bibliographical references.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 262-263). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 262-263). Also available on the Internet.

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, August 2002. / Includes bibliographical references (p. 31). Also available on the Internet.

Thesis (Ph. D.)--University of Oregon, 2005. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 79-80). Also available for download via the World Wide Web; free to University of Oregon users.

We present a time-dependent mixed quantum/semiclassical approach to calculating linear absorption spectra. Applying Variational Fixed Vibrational Basis/Gaussian Bath theory (FVB/GB) to the treatment of small molecules isolated in an extended cryogenic medium, an assumed time-scale separation between the few rapid, largely intramolecular modes of the guest and the several slower extended modes of the medium is utilized to partition a system from the surrounding bath. The system dynamics are handled with basis set methods, while the bath degrees of freedom are subject to a semiclasscial thawed Gaussian ansatz. The linear absorption spectrum for a realistic model system is calculated using FVB/GB results and then compared with a numerically exact calculation. Also contained in this dissertation are previously published theoretical works on Transient Absorption and Femtosecond Stimulated Raman Spectroscopy. Both encompass a rebuilding of the theory and elucidate the information content of the respective spectroscopic signals. This dissertation includes previously published co-authored material.

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