A vibronic exciton model is developed to account for the spectral signatures of HJ-aggregates of oligomers and polymers containing donor–acceptor–donor (DAD) repeat units. In (DAD)N π-stacks, J-aggregate-promoting intrachain interactions compete with H-aggregate-promoting interchain interactions. The latter includes Coulombic coupling, which arises from “side-by-side” fragment transition dipole moments as well as intermolecular charge transfer (ICT), which is enhanced in geometries with substantial overlap between donors on one chain and acceptors on a neighboring chain. J-behavior is dominant in single (DAD)N chains with enhanced intrachain order as evidenced by an increased red-shift in the low-energy absorption band along with a heightened A1/A2 peak ratio, where A1 and A2 are the oscillator strengths of the first two vibronic peaks in the progression sourced by the symmetric quinoidal–aromatic vibration. By contrast, the positive H-promoting interchain Coulomb interactions operative in aggregates cause the vibronic ratio to attenuate, similar to what has been established in H-aggregates of homopolymers such as P3HT. An attenuated A1/A2 ratio can also be caused by H-promoting ICT which occurs when the electron and hole transfer integrals are out-of-phase. In this case, the A1 peak is red-shifted, in contrast to conventional Kasha H-aggregates. With slight modifications, the ratio formula derived previously for P3HT aggregates is shown to apply to (DAD)N aggregates as well, allowing one to determine the effective free-exciton interchain coupling from the A1/A2 ratio. Applications are made to polymers based on 2T-DPP-2T and 2T-BT-2T repeat units, where the importance of the admixture of the excited acceptor state in the lowest energy band is emphasized.
A vibronic exciton model is introduced to describe the excited state band structure and associated absorption spectra of low bandgap donor–acceptor conjugated polymers. The Hamiltonian is represented in a diabatic basis consisting of Frenkel-like donor and acceptor fragment excitations as well as charge-transfer (CT) excitations between neighboring fragments. States are coupled to each other through electron and hole transfer as well as Coulombically, through interacting fragment transition dipole moments. Local vibronic coupling involving the prominent aromatic-quinoidal vibrational mode, which is responsible for pronounced vibronic progressions in most conjugated oligomers and polymers, is also included. The DAD repeat unit is shown to behave like a J-aggregate trimer, driven by both the sizable in-phase electron and hole transfer integrals between donor and acceptor fragments as well as negative Coulomb coupling between donor and acceptor fragment excitations. The J-aggregate behavior is enhanced in the polymer limit through inter-repeat unit coupling, with the 0–0 vibronic peak significantly enhanced in the lowest-energy near-IR band. In addition, the radiative rate is enhanced by the number of coherently connected repeat units. The near-IR band is shown to possess roughly equal admixtures of CT and Frenkel-like excitations. Applications are made to the polymer PffBT4T-2DT, with the simulated absorption spectrum quantitatively capturing the salient features of the measured spectrum.
A Holstein-based model for mid-IR polaron absorption in π-conjugated polymers with nondegenerate ground states is expanded to include singlet bipolarons. In addition to hole hopping, the model includes electron−vibration coupling involving the prominent aromatic-quinoidal mode, as well as Coulombic interactions between (hole) polarons and between polarons and dopant anions. Compared to single polarons, the mid-IR band for bipolarons is red-shifted by up to 0.2 eV depending on the level of disorder. The red shift reflects the enhanced hole delocalization in the bound bipolaron complex and is in good agreement with recent measurements on electrochemically doped P3HT.
A vibronic exciton model is developed to describe low-energy electronic excitations in slip-stack aggregates of donor−acceptor−donor (DAD) chromophores with substantial overlap between the neighboring donor and acceptor fragments. In such stacks, J-and H-aggregate behavior is driven by intermolecular charge transfer (ICT) and not Coulomb coupling as is assumed in the Kasha model. In-phase (out-of-phase) intermolecular charge transfer integrals result in J-aggregate (H-aggregate) behavior, as unambiguously determined by the vibronic spectral signatures. Interestingly, both J-and H-aggregates are red-shifted, in contrast to the predictions of the Kasha model. Simulated spectral line shapes agree well with recent experiments on two derivatives of the bithiophene diketopyrrolopyrrole chromophore, 2T-DPP-2T, with different terminal groups.
For the prototypical two-dimensional hybrid organic–inorganic perovskites (2D HOIPs) (AE4T)PbX4 (X = Cl, Br, and I), we demonstrate that the Frenkel–Holstein Hamiltonian (FHH) can be applied to describe the absorption spectrum arising from the organic component. We first model the spectra using only the four nearest neighbor couplings between translationally inequivalent molecules in the organic herringbone lattice as fitting parameters in the FHH. We next use linear-response time-dependent density functional theory (LR-TDDFT) to calculate molecular transition densities, from which extended excitonic couplings are evaluated based on the atomic positions within the 2D HOIPs. We find that both approaches reproduce the experimentally observed spectra, including changes in their shape and peak positions. The spectral changes are correlated with a decrease in excitonic coupling from X = Cl to X = I. Importantly, the LR-TDDFT-based approach with extended excitonic couplings not only gives better agreement with the experimental absorption line shape than the approach using a restricted set of fitted parameters but also allows us to relate the changes in excitonic coupling to the underlying geometry. We accordingly find that the decrease in excitonic coupling from X = Cl to Br to I is due to an increase in molecular separation, which in turn can be related to the increasing Pb–X bond length from Cl to I. Our research opens up a potential pathway to predicting optoelectronic properties of new 2D HOIPs from ab initio calculations and to gain insight into structural relations from 2D HOIP absorption spectra.
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