Semiclassical treatments for small-molecule dynamics in low-temperature crystals using fixed and adiabatic...

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 calculations of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Without resorting to a simple harmonic analysis, both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath. Both approaches 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 intermolecular 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. Computational demands for propagation of the parameter equations of motion appear quite manageable for tens or hundreds of atoms and scale similarly with system size in the two cases. Because of the time-scale separation between intermolecular and lattice vibrations, the AVB/GB theory may in some instances require fewer vibrational basis states than the FVB/GB approach. Either framework should enable practical first-principles calculations of nonlinear optical signals from molecules in cryogenic matrices and their semiclassical interpretation in terms of electronic and vibrational decoherence and vibrational population relaxation, all within a pure-state description of the macroscopic many-body complex.