  Revealing possible long-living coherence in ultrafast processes allows
detecting genuine quantum mechanical effects in molecules. To investigate such
effects from a quantum chemistry perspective, we have developed a method for
simulating the time evolution of molecular systems, based on ab initio
calculations that includes relaxation and environment-induced dephasing of the
molecular wave function, whose rates are external parameters. The proposed
approach combines a quantum chemistry description of the molecular target with
a real-time propagation scheme within the time-dependent stochastic
Schroedinger equation. Moreover, it allows a quantitative characterization of
the state and dynamics coherence, through the l1-norm of coherence and the
linear entropy, respectively. To test the approach, we have simulated
femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well
studied fluorophore in single-molecule spectroscopy. Our approach is able to
reproduce the experimental findings [R. Hildner et al.,Nature Phys., 7, 172
(2011)], confirming the usefulness of the approach and the correctness of the
implementation.
