Short-Time Dynamics of Optical Processes in Multidimensional Molecular Systems.

Theoretical studies are described of several short -time optical processes in systems with a few coordinates. The systems studied are small enough to be amenable to quantum and semiclassical treatment, but contain some of the features of chromophores in solution. The first part sets forth a new semiclassical approximation of short-time dynamics in a multi-dimensional system that explicitly includes multiple coupled anharmonic wells in the ground electronic state. The nuclear eigenstates are approximated using van Vleck perturbation theory as a linear combination of multi-dimensional harmonic oscillator eigenstates in each well. Coherent states formed by electronic excitation of the system are propagated in a locally quadratic approximation to the excited state potential using variationally optimized equations of motion for a common set of parameters for each ground state well. Initial applications of this method are to the optical response of small van der Waals clusters. In the second part, quantum mechanical and semiclassical (wave packet) treatments are used to simulate and interpret time resolved fluorescence signals. The method includes effects of ultrafast excitation and transform-limited time and frequency resolved detection via fluorescence upconversion. The initial Gaussian decrease in the Stokes shift is examined using a wave packet picture, and its generality and origin due to the potential difference between ground and excited states are quantitatively explored. Quantum simulations of the peak fluorescence frequency for model systems with few coordinates show qualitative behavior highly dependent on pulse length and center frequency. Derivations and simulations of the time dependent transition energy for the same systems using a full quantum treatment, semiclassical wave packets, nonequilibrium classical molecular dynamics, equilibrium classical correlation functions, and instantaneous normal modes illustrate the ranges of validity and the similarities and differences among these approximations. Inclusion of a bath via Redfield theory introduces the effects of dissipation and damping, and allows the comparison of different forms of system-bath coupling.