Nature of low-lying excited states in H-aggregated perylene bisimide dyes: results of TD-LRC-DFT and the mixed exciton model.

We characterize the nature of the low-lying excited states in H-aggregated perylene bisimide (PBI) dyes in terms of the recently proposed long-range-corrected density functional theory (LRC-DFT) and the mixed intramolecular Frenkel exciton (FE) and the intermolecular charge-transfer exciton (CTE) model. The singlet vertical excitation energies of H-aggregated PBI dimers and multimers are theoretically evaluated by considering the aggregation details. It is found that the dimer absorption follows closely the spectra of PBI aggregates in solution and demonstrates strong mixing of two kinds of excitons. The experimentally observed low-energy absorption peak near 2.3 eV should not be a pure CT state but a mixed excitonic state. To model the electronic excitations of H-aggregated PBI multichromophoric oligomers, we adopt a mixed FE-CTE model Hamiltonian, whose microscopic parameters are determined from LRC-DFT/TD-LRC-DFT calculations performed on an individual chromophore or a chromophore pair. By involving four to five PBI chromophores, we have succeeded in reproducing the experimental trends of optical properties in PBI stacking, such as the large blue shift of the absorption band, the mixed FE-CTE nature of the low-energy absorption bands, and the large Stokes shift of emission spectra. The long-range correction on DFT exchange-correlation energy functionals is crucial to correctly evaluate the photophysical characteristics of pi-pi stacks.