  We numerically compare the semiclassical ``frozen Gaussian'' Herman-Kluk
propagator [Chem. Phys. 91, 27 (1984)] and the ``thawed Gaussian'' propagator
put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by
studying the quantum dynamics in some nonlinear one-dimensional potentials. The
reasons for the lack of long time accuracy and norm conservation in the latter
method are uncovered. We amend the thawed Gaussian propagator with a global
harmonic approximation for the stability of the trajectories and demonstrate
that this revised propagator is a true alternative to the Herman-Kluk
propagator with similar accuracy.
