Electron–vibrational resonance and optical lineshapes: Complex time-dependent Redfield theory vs vibronic picture

Abstract

We study the validity of the complex time-dependent Redfield (ctR) theory in describing optical lineshapes near electron–vibrational resonance, when a mixing of the electronic states is promoted by a vibrational quantum. We explore the model system containing an electronically excited state coupled to a red-shifted charge-transfer (CT) state. When the vibrational sublevels of the CT are in resonance with the zero-phonon line of the excited state, they can borrow a significant part of the dipole strength, thus producing a mixed configuration with splitting and shifting of the excited state transitions. Comparing the ctR lineshapes with explicit exciton–vibrational structure and with nonperturbative absorption spectra, we have found that ctR theory reproduces (at least qualitatively) the main features of the vibronic picture emerging from resonant exciton–vibrational mixing. On the contrary, these resonant phenomena cannot be explained by the modified Redfield theory, where the off-diagonal phonon-induced modulations of the exciton transitions are treated in a simplified way. On the other hand, we reveal shortcomings of the ctR approaches that are working in a pure exciton basis, where the exciton-CT mixing is supposed to be uniform (i.e., not dependent on nuclear coordinates). As a result, the degree of exciton-CT mixing is typically overestimated in the ctR model, thus leading to the appearance of spectral components with the intensities and energies deviating from the exact (nonperturbative) solution.