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PreprintCC BY-NC-NDChemRxiv

Herzberg–Teller effect as a phonon-assisted optical transition in molecules

  • Takeaki Zaima1,2,3
  • Wataru Ota1,2,3
  • Takumi Yagi1,2,3
  • Tatsuhisa Kato1
  • Tohru Sato1,2,3
  1. 1Fukui Institute for Fundamental Chemistry, Kyoto University, Takano Nishibiraki-cho 34-4, Sakyo-ku, Kyoto, Japan, 606-8103
  2. 2Graduate School of Engineering
  3. 3Kyoto University
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Abstract

This study derives expressions for the photophysics of a molecule exhibiting the Herzberg–Teller (HT) effect. The derivation is based on Fermi’s golden rule, and the Longuet-Higgins representation, where the electron–photon and vibronic couplings are treated as perturbations, is used. All the vibrational modes are included, thus enabling the assignment of vibronic progressions in the spectrum originating from Franck–Condon factors. A forbidden transition is regarded as the photon absorption or emission accompanied by phonon absorption or emission, clarifying the contribution of vibronic structures to the transition. The derived expressions are applied to the absorption from S0 to S1 and fluorescence from S2 to S0 for azulene, a molecule known to exhibit the HT effect. Using the S4 state as an intermediate state, the calculated fluorescence spectrum and rate constant agree well with the experimental results. The in-plane stretching vibration of the five-membered ring contributes to phonon emission, whereas that at the junction of the five-and seven-membered rings contributes to the acceptance of the excess excitation energy. Furthermore, the vibronic coupling density analyses reveal that the vibronic couplings originate from the five-membered ring. This study presents a theory that allows for a detailed assignment of vibronic structures involved in the HT effect, providing design guidelines for HT molecules.

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Cite

BibTeXRIS
BibTeX
@misc{zaima2026herzbergteller,
  title = {{Herzberg–Teller effect as a phonon-assisted optical transition in molecules}},
  author = {Takeaki Zaima and Wataru Ota and Takumi Yagi and Tatsuhisa Kato and Tohru Sato},
  howpublished = {ChemRxiv},
  year = {2026},
  month = oct,
  doi = {10.26434/chemrxiv.15009939/v1},
  url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009939/v1},
  note = {CC BY-NC-ND},
}
RIS
TY  - UNPB
TI  - Herzberg–Teller effect as a phonon-assisted optical transition in molecules
AU  - Takeaki Zaima
AU  - Wataru Ota
AU  - Takumi Yagi
AU  - Tatsuhisa Kato
AU  - Tohru Sato
PY  - 2026
DA  - 2026/10/05
PB  - ChemRxiv
DO  - 10.26434/chemrxiv.15009939/v1
UR  - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009939/v1
AB  - This study derives expressions for the photophysics of a molecule exhibiting the Herzberg–Teller (HT) effect. The derivation is based on Fermi’s golden rule, and the Longuet-Higgins representation, where the electron–photon and vibronic couplings are treated as perturbations, is used. All the vibrational modes are included, thus enabling the assignment of vibronic progressions in the spectrum originating from Franck–Condon factors. A forbidden transition is regarded as the photon absorption or emission accompanied by phonon absorption or emission, clarifying the contribution of vibronic structures to the transition. The derived expressions are applied to the absorption from S0 to S1 and fluorescence from S2 to S0 for azulene, a molecule known to exhibit the HT effect. Using the S4 state as an intermediate state, the calculated fluorescence spectrum and rate constant agree well with the experimental results. The in-plane stretching vibration of the five-membered ring contributes to phonon emission, whereas that at the junction of the five-and seven-membered rings contributes to the acceptance of the excess excitation energy. Furthermore, the vibronic coupling density analyses reveal that the vibronic couplings originate from the five-membered ring. This study presents a theory that allows for a detailed assignment of vibronic structures involved in the HT effect, providing design guidelines for HT molecules.
ER  -