Effect of mixed Frenkel and charge transfer states in time-gated fluorescence spectra of perylene bisimides H-aggregates: Hierarchical equations of motion approach.

We theoretically investigated the effect of mixed Frenkel (F) and charge transfer (CT) states on the spectral properties of perylene bisimide (PBI) derivatives, focusing on the role of strong electron-phonon interactions. The model consists of a four-level system described by the Holstein Hamiltonian coupled to independent local heat-baths on each site, described by Brownian spectral distribution functions. We employ the reduced hierarchical equations of motion (HEOM) approach to calculate the time evolution of the system and compare it to the pure F exciton cases. We compute the absorption and time-gated fluorescence (TGF) spectra for different exciton transfer integrals and F-CT bandgap conditions. The coherence length of excitons (N) is evaluated employing two different definitions. We observe the presence of an excited hot state peak whose intensity is associated with the delocalization of the excited species and ultrafast dynamics that are solely dependent on the frequency of the local bath. The results indicate that the inclusion of CT states promotes localization of the excitons, which is manifested in a decrease in the intensity of the hot state peak and the 0-1 peak and an increase in the intensity of the 0-0 emission peak in the TGF spectrum, leading to a decrease of N.