  We present a methodology for computing vibrationally and time-resolved
pump-probe spectra, which takes into account all vibrational degrees of freedom
and is based on the combination of the thawed Gaussian approximation with
on-the-fly ab initio evaluation of the electronic structure. The method is
applied to the phenyl radical and compared with two more approximate approaches
based on the global harmonic approximation - the global harmonic method expands
both the ground- and excited-state potential energy surfaces to the second
order about the corresponding minima, while the combined global
harmonic/on-the-fly method retains the on-the-fly scheme for the excited-state
wavepacket propagation. We also compare the spectra by considering their means
and widths, and show analytically how these measures are related to the
properties of the semiclassical wavepacket. We find that the combined approach
is better than the global harmonic one in describing the vibrational structure,
while the global harmonic approximation estimates better the overall means and
widths of the spectra due to a partial cancellation of errors. Although the
full-dimensional on-the-fly ab initio result seems to reflect the dynamics of
only one mode, we show, by performing exact quantum calculations, that this
simple structure cannot be recovered using a one-dimensional model. Yet, the
agreement between the quantum and semiclassical spectra in this simple, but
anharmonic model lends additional support for the full-dimensional ab initio
thawed Gaussian calculation of the phenyl radical spectra. We conclude that the
thawed Gaussian approximation provides a viable alternative to the expensive or
unfeasible exact quantum calculations in cases, where low-dimensional models
are not sufficiently accurate to represent the full system.
