Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition

We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Sigma and Pi states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.