On-the-Fly Ab Initio Hagedorn Wavepacket Dynamics: Single Vibronic Level Fluorescence Spectra of Difluorocarbene

Hagedorn wavepackets have been used with local harmonic approximation to partially capture the anharmonic effects on single vibronic level (SVL) spectra in model potentials. To make the Hagedorn approach practical for realistic anharmonic polyatomic molecules, here we combine local harmonic Hagedorn wavepacket dynamics with on-the-fly ab initio dynamics. We then test this method by computing the SVL fluorescence spectra of difluorocarbene, a small, floppy molecule with a very anharmonic potential energy surface. Our time-dependent approach obtains the emission spectra of all initial vibrational levels from a single anharmonic semiclassical wavepacket trajectory without the need to fit individual anharmonic vibrational wavefunctions and to calculate the Franck--Condon factors for all vibronic transitions. We show that, whereas global harmonic models are inadequate for CF$_2$, the spectra computed with the on-the-fly local harmonic Hagedorn wavepacket dynamics agree well with experimental data, especially for low initial excitations.