Capturing anharmonic effects in single vibronic level fluorescence spectra using local harmonic Hagedorn wavepacket dynamics

Abstract

Hagedorn wavepacket dynamics yields exact single vibronic level (SVL) fluorescence spectra in global harmonic models. To partially describe the effects of anharmonicity, important in the spectra of real molecules, we describe a combination of the Hagedorn wavepacket approach to SVL spectroscopy with the local harmonic approximation. In a proof-of-principle study [Phys. Rev. A 111, L010801 (2025)], we successfully demonstrated the utility of this method by computing the SVL spectra of difluorocarbene, a floppy molecule with moderately anharmonic potential. Here, we describe the theory in detail and analyse the method more thoroughly. To assess the accuracy of the method independently of electronic structure errors, we use a two-dimensional Morse-type potential for which exact quantum benchmarks are available, and show that the local harmonic approach yields more accurate results than global harmonic approximations, especially for the emission spectra from higher initial vibrational levels. Next, we compare the global and local harmonic SVL spectra of anthracene, where the more expensive local harmonic corrections turn out to be less important as long as the correct global harmonic model is used. We also present additional local harmonic results for difluorocarbene, where treating anharmonicity is essential for accurate evaluation of the spectra. Yet, we also show that the structure of the difluorocarbene spectra can be explained qualitatively (but not quantitatively) with a reduced-dimensional harmonic model, for which the spectral intensities can be evaluated analytically.