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

On-the-fly ab initio three thawed Gaussians approximation: A semiclassical approach to Herzberg-Teller spectra