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

TL;DR

This paper introduces a local harmonic approximation combined with Hagedorn wavepacket dynamics to better capture anharmonic effects in single vibronic level fluorescence spectra, improving accuracy over global harmonic models especially for anharmonic molecules.

Contribution

The paper develops and analyzes a local harmonic approach integrated with Hagedorn wavepacket dynamics for more accurate SVL spectra in anharmonic systems, validated against benchmark potentials.

Findings

Local harmonic approach outperforms global harmonic models for anharmonic spectra.

The method provides more accurate results for higher vibrational levels.

Global harmonic models are sufficient for some molecules like anthracene when correctly chosen.

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.