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

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.