Several Semiclassical Approaches to Time-resolved Spectroscopy

Ultrafast spectroscopy allows molecular dynamics to be resolved on the femtosecond time scale. Whereas such short time scales obviously pose any experimental challenges, they provide an opportunity for semiclassica methods, which are naturally suited for short time dynamics. Here we review several semiclassical approaches for evaluating vibrationally resolved electronic pump-probe spectra, starting with the simplest, 'phase averaging' or 'dephasing representation'. We continue by discussing several methods developed in our group that allow increasing the efficiency (the cellular dephasing representation) and accuracy (cellular dephasing representation with a prefactor) and end with the Gaussian dephasing representation, which, despite its semiclassical origins, converges to the exact quantum result. The merits as well as shortcomings of the different approaches are demonstrated on time-resolved stimulated emission spectra of NCO and pyrazine.