Quantum Dynamical Averaging Over an Ensemble of Molecular Orientations by a Singular Value Decomposition of the Density Matrix

We report a robust and compact methodology for averaging quantum photoexcitation dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the density matrix of the excited molecules which allows identifying the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The massive compaction of the 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.