  A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert
space and their recently developed counterparts in Wigner representation is
presented. It is shown that the numerical protocol for the Herman-Kluk
propagator, which contains the van Vleck one as a particular case, coincides in
both representations. The flexibility of the Wigner version in choosing the
Gaussians' width for the underlying coherent states, being not bound to minimal
uncertainty, is investigated numerically on prototypical potentials. Exploiting
this flexibility provides neither qualitative nor quantitative improvements.
Thus, the well-established Herman-Kluk propagator in Hilbert space remains the
best choice to date given the large number of semiclassical developments and
applications based on it.
