  Evaluation of symmetry-forbidden or weakly-allowed vibronic spectra requires
treating the transition dipole moment beyond the Condon approximation. To
include vibronic spectral features not captured in the global harmonic models,
we have recently implemented an on-the-fly ab initio extended thawed Gaussian
approximation, where the propagated wavepacket is a Gaussian multiplied by a
linear polynomial. To include more anharmonic effects, here we represent the
initial wavepacket by a superposition of three independent Gaussian wavepackets
- one for the Condon term and two displaced Gaussians for the Herzberg-Teller
part. Application of this ab initio "three thawed Gaussians approximation" to
vibrationally resolved electronic spectra of the phenyl radical and benzene
shows a clear improvement over the global harmonic and Condon approximations.
The orientational averaging of spectra, the relation between the gradient of
the transition dipole moment and nonadiabatic coupling vectors, and the details
of the extended and three thawed Gaussians approximation are discussed.
