A quantum/semiclassical theory for the internal nuclear dynamics of a small molecule and the induced small-amplitude coherent motion of a low-temperature host medium is developed, tested and applied to simulate and interpret ultrafast optical signals. Linear wave-packet interferometry and time-resolved coherent anti-Stokes Raman scattering signals for a model of molecular iodine in a 2D krypton lattice are calculated and used to study the vibrational decoherence and energy dissipation of iodine molecules in condensed media. The total wave function of the whole model is approximately obtained instead of a reduced system density matrix, and therefore the theory enables us to analyze the behavior and the role of the host matrix in quantum dynamics. This dissertation includes previously published co-authored material.

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.