Vibrational wave packets: Molecular state reconstruction in the gas phase and mixed quantum/semiclassical descriptions of small-molecule dynamics in low-temperature solid media

We explore the reconstruction of B-state vibrational wave packets in I2 from simulated two-color nonlinear wave packet interferometry data. As a simplification of earlier proposals, we make use of different vibrational energy ranges in the B-state---rather than different electronic potential surfaces---for the short-pulse preparation and propagation of both target and reference wave packets. Numerical results from noisy interferograms indicate that experimental reconstruction should be possible with high fidelity (>0.99).;Time-resolved coherent nonlinear optical experiments on small molecules in low-temperature host crystals are exposing valuable information on quantum mechanical dynamics in condensed media. We make use of generic features of these systems to frame two simple, comprehensive theories that will enable the efficient calculation of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath and expand the overall wave function as a sum of product states between fully anharmonic vibrational basis states for the system and approximate Gaussian wave packets for the bath degrees of freedom. The theories exploit the fact that ultrafast experiments typically drive large-amplitude motion in a few intramolecular degrees of freedom of higher frequency than the crystal phonons, while these intramolecular vibrations indirectly induce smaller-amplitude---but still perhaps coherent---motion among the lattice modes. The equations of motion for the time-dependent parameters of the bath wave packets are fairly compact in a fixed vibrational basis/Gaussian bath (FVB/GB) approach. An alternative adiabatic vibrational basis/Gaussian bath (AVB/GB) treatment leads to more complicated equations of motion involving adiabatic and nonadiabatic vector potentials.;Numerical tests of the FVB/GB are presented. We consider two bilinearly coupled harmonic oscillators with varying coupling strengths and initial conditions and show that the mixed quantum/semiclassical theory compares favorably with the exact results. Linear absorption spectra and wave-packet interferometry signals calculated using the theory are presented.;This dissertation includes previously published coauthored material.