Angular Momentum Coherences in Molecular Dynamics

With the advent of attosecond science ultrafast probes of excited state dynamics have recently achieved unprecedented time resolution, now sufficient to resolve molecular electronic dynamics. A number of different methods have been proposed to probe physical processes of chemical interest, such as charge migration and passage through conical intersections, using this technology. However, many of these methods rely on the molecule being fixed in space. Here we examine instead the full dimensional, laboratory frame, time evolving probability distribution generated by resonant excitation of an isolated molecule. We find that the excited state molecular dynamics induce time dependent anisotropy in this probability distribution, the moments of which are directly observable by ultrafast scattering experiments. These observable Molecular Angular Distribution Moments (MADMs) are related to density matrix elements in the lab frame, and fully characterize the molecular dynamics. Furthermore, higher order moments, which can be experimentally isolated, exclusively contain the off diagonal electronic density matrix elements, in other words the electronic coherences, allowing separation of these from population dynamics. As a demonstrative example we compute the MADMs and lab frame density matrix elements for the case of an excited state electronic wavepacket in 4-amino-4’-nitrostilbene, a molecule thought to exhibit charge migration in the molecular frame.