1With support from the Theoretical and Computational Chemistry Program and the Materials Theory Program, Professor Silby will investigate three problems in quantum mechanics: (1) tunneling in gas and condensed phases, (2) spectroscopy of guest molecules in low temperature glasses, and (3) competing electron-phonon and electron-electron interactions in molecular systems. The theoretical models that result will lead to a better understanding of the important experimental data generated in the above areas. Tunneling in molecules and condensed phases will be studied for both symmetric and asymmetric potentials. Hole burning in glasses will be investigated focusing on the basic aspects of energy states in glasses (interacting vs. non-interacting two-level systems) and their ramifications for imhomogeneous broadening. The dynamics in low dimensional molecular crystals and polymeric systems with competing interactions will be studied. These systems show a rich variety of possible states, such as charge density waves, spin density waves, and solitonic, polaronic, and bipolaronic defect states.