  Irradiation of a molecular system by an intense laser field can trigger
dynamics of both electronic and nuclear subsystems. The lighter electrons
usually move on much faster, attosecond time scale but the slow nuclear
rearrangement damps ultrafast electronic oscillations, leading to the
decoherence of the electronic dynamics within a few femtoseconds. We show that
a simple, single-trajectory semiclassical scheme can evaluate the electronic
coherence time in polyatomic molecules accurately by demonstrating an excellent
agreement with full-dimensional quantum calculations. In contrast to numerical
quantum methods, the semiclassical one reveals the physical mechanism of
decoherence beyond the general blame on nuclear motion. In the propiolic acid,
the rate of decoherence and the large deviation from the static frequency of
electronic oscillations are quantitatively described with just two
semiclassical parameters---the phase space distance and signed area between the
trajectories moving on two electronic surfaces. Because it evaluates the
electronic structure on the fly, the semiclassical technique avoids the "curse
of dimensionality" and should be useful for preselecting molecules for
experimental studies.
