Phonon-induced spectral line broadening in dye-doped glass in terms of resonant vibrational modes: tetra-tert-butylterrylene in polyisobutylene

Previously [A.O. Savostianov, I.Yu. Eremchev, T. Plakhotnik, and A.V. Naumov, Phys. Rev. B 110, 045430 (2024)], we have shown that the zero-phonon line broadening of single tetra-tert-butylterrylene molecules embedded in the matrix of amorphous polyisobutylene is a result of coupling with resonant vibrational modes arising due to the impurity effect on the host normal modes. However, the question remained whether this model would be compatible with the extensive single-molecule spectroscopy and photon echo data previously obtained for the same host/guest system. In the present work we demonstrate the high predictive power of the resonant mode model treated in the framework of the non-perturbative theory of electron–phonon coupling, and good agreement with all experimental data. Furthermore, for single-molecule data we find an unexpectedly large dispersion of the force constants for impurity molecules. To explain this dispersion, we propose a simple microscopic model that assumes fluctuations in the distance between the impurity molecule and its nearest surroundings.