Simulating Molecular Single Vibronic Level Fluorescence Spectra with ab initio Hagedorn Wavepacket Dynamics

TL;DR

The paper develops an ab initio time-dependent method using Hagedorn wavepackets to compute single vibronic level fluorescence spectra from arbitrary vibrational preparations. By propagating on a global harmonic potential derived from DFT and representing initial states with a single Hagedorn function, the approach naturally incorporates mode distortion and Duschinsky rotation within a harmonic framework, enabling spectra from multiply excited levels with a single trajectory. Validation on anthracene shows good agreement for singly excited levels and reasonable agreement for higher excitations, while analysis isolates the roles of mode coupling and anharmonicity in shaping peak intensities. The method provides a computationally efficient, transparent route to SVL spectra and offers a pathway to incorporate anharmonicity and non-adiabatic effects in future work, with potential applications to related vibronic spectroscopies.

Abstract

We present a practical, ab initio time-dependent method using Hagedorn wavepackets to efficiently simulate single vibronic level (SVL) fluorescence spectra of polyatomic molecules from arbitrary initial vibrational levels. We apply the method to compute SVL spectra of anthracene by performing wavepacket dynamics on a 66-dimensional harmonic potential energy surface constructed from density functional theory calculations. The Hagedorn approach captures both mode distortion (frequency changes) and mode mixing (Duschinsky rotation) within the harmonic approximation. We not only reproduce the previously reported simulation results for singly excited $12^1$ and $\overline{11}^1$ levels, but are also able to compute SVL spectra from multiply excited levels in good agreement with experiments. Notably, all spectra were obtained from the same wavepacket trajectory without any additional propagation beyond what is required for the emission spectrum from the ground vibrational level of the electronically excited state.

Figures (6)

• Figure 1: SVL fluorescence spectra of anthracene from initial vibrational levels $12^{j}$ and $\overline{11}^{j}$ ($j=1,2$) computed from Hagedorn wavepacket dynamics in the adiabatic harmonic model; a scaling factor of 0.97 was applied to the wavenumbers of the computed spectra (red dashed line); the experimental reference (black solid line) is taken from ref Lambert_Zewail:1984.
• Figure 2: Effects of displacement, mode distortion, and mode mixing on the simulated (red dashed line) $12^{2}$ SVL fluorescence spectra of anthracene; a scaling factor of 0.97 was applied to the wavenumbers of the computed spectra. All spectra are compared to experiment (ref Lambert_Zewail:1984, black solid line).
• Figure 3: Effects of an artificially enhanced Duschinsky coupling between modes $\overline{11}$ and $\overline{10}$ on the computed $\overline{11}^{1}$ and $\overline{11}^{2}$ SVL fluorescence spectra of anthracene; a scaling factor of 0.97 was applied to the wavenumbers of the computed spectra (red dashed line); the experimental reference (black solid line) is taken from ref Lambert_Zewail:1984.
• Figure 4: $12^{2}$ SVL fluorescence spectra of anthracene evaluated with the vertical (left, green dashed line) and local harmonic (right, blue dashed line) approaches. The spectra are compared to the adiabatic harmonic (first row, red solid line) and the experimental (ref Lambert_Zewail:1984, second row, black solid line) spectra; a scaling factor of 0.97 was applied to all computed spectra.
• Figure 5: Evolution of the position along mode 12 ($q_\text{mode 12}$) of the center of the wavepacket in the on-the-fly local harmonic dynamics (blue solid line), compared to the vertical (left panel, green dashed line) and adiabatic (right panel, red dashed line) harmonic dynamics.