Hagedorn wave packets have been used to compute single vibronic level (SVL) spectra efficiently in model harmonic potentials. To make the Hagedorn approach practical for realistic polyatomic molecules with anharmonicity, here we combine local harmonic Hagedorn wave-packet 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 wave-packet trajectory without the need to fit individual anharmonic vibrational wave functions 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 wave-packet dynamics agree well with experimental data, especially for low initial excitations.