  We modify the pre-factor of the semiclassical propagator to improve its
efficiency in practical implementations. The new pre-factor represents the
smooth portion of an orbit's contribution, and leads to fast convergence in
numerical calculations. As an illustration of the accuracy and efficiency of
the resultant propagator, we numerically calculate overlaps between quantum and
semiclassical wave functions, as well as low-lying spectrum density in a
10-dimensional system contains unstable classical orbits. This sheds light on
applying semiclassical propagator to high dimensional systems.
