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Coherence phenomena arise from interference, or the addition, of wave-like amplitudes with fixed phase differences. Although coherence has been shown to yield transformative ways for improving function, advances have been confined to pristine matter and coherence was considered fragile. However, recent evidence of coherence in chemical and biological systems suggests that the phenomena are robust and can survive in the face of disorder and noise. Here we survey the state of recent discoveries, present viewpoints that suggest that coherence can be used in complex chemical systems, and discuss the role of coherence as a design element in realizing function.

Coupling among chromophores in molecular assemblies is responsible for phenomena such as resonant energy transfer and intermolecular charge transfer. These processes are central to the fields of organic photovoltaics and photocatalysis, where it is necessary to funnel energy or charge to specific regions within the system. As such, a fundamental understanding of these transport processes is essential for developing new materials for photovoltaic and photocatalytic applications. Recently, photocatalytic systems based on photosensitizing perylene monomimide (PMI) chromophore amphiphiles were found to show variation in hydrogen gas (H2) production as a function of nanostructure crystallinity. The 2D crystalline systems form in aqueous electrolyte solution, which provides a high dielectric environment where the Coulomb potential between charges is mitigated. This results in relatively weakly bound excitons that are ideal for reducing protons. In order to understand how variations in crystalline structure affect H2 generation, two representative PMI systems are investigated theoretically using a modified Holstein Hamiltonian. The Hamiltonian includes both molecular Frenkel excitations (FE) and charge-transfer excitations (CTE) coupled nonadiabatically to local intramolecular vibrations. Signatures of FE/CTE mixing and the extent of electron/hole separation are identified in the optical absorption spectrum and are found to correlate strongly to the observed H2 production rates. The absorption spectral signatures are found to sensitively depend on the relative phase between the electron and hole transfer integrals, as well as the diabatic energy difference between the Frenkel and CT exciton bands. Our analysis provides design rules for artificial photosynthetic systems based on organic chromophore arrays.

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. [ABSTRACT FROM AUTHOR]

Polaritons in an ensemble of permutationally symmetric chromophores confined to an optical microcavity are investigated numerically. The analysis is based on the Holstein–Tavis–Cummings Hamiltonian which accounts for the coupling between an electronic excitation on each chromophore and a single cavity mode, as well as the coupling between the electronic and nuclear degrees of freedom on each chromophore. A straightforward ensemble partitioning scheme is introduced, which, along with an intuitive ansatz, allows one to obtain accurate evaluations of the lowest-energy polaritons using a subset of collective states. The polaritons include all three degrees of freedom—electronic, vibronic, and photonic—and can therefore be described as exciton–phonon polaritons. Applications focus on the limiting regimes where the Rabi frequency is small or large compared to the nuclear relaxation energy subsequent to optical excitation, with relaxation occurring mainly along the vinyl stretching coordinate in conjugated organic chromophores. Comparisons are also made to the more conventional vibronic polariton approach, which does not take into account two-particle excitations and vibration–photon states. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Molecular doping of conjugated polymers causes bleaching of the neutral absorbance and results in new polaron absorbance transitions in the mid and near infrared. Here, the concentration dependent changes in the spectra for a series of molecularly doped diketopyrrolopyrrole (DPP) co‐polymers with a series of ultra‐high electron affinity cyanotrimethylenecyclopropane‐based dopants is analyzed. With these strong dopants the polaron mole fraction (Θ) reaches saturation. Analysis of the full spectrum enables separation of neutral and polaron signals and quantification of the polaron mole fraction using a simple noninteracting site model. The peak ratios for both neutral and polaron peaks change systematically with increasing polaron mole fraction for all measured polymers. Analysis of the spectral changes indicates that the polaron mole fraction can be quantified to within 5%. While the total change in the absorbance spectrum with increasing polaron mole fraction is linear, the lowest energy polaron peak (P1) grows nonlinearly, which indicates increased polarization/delocalization. Molecular doping of polymers that form either H‐ or J‐aggregates shows systematically different spectral changes in the vibronic peak ratios of the neutral spectra and provides insights into the polymer configuration at undoped sites in the film. [ABSTRACT FROM AUTHOR]

The technologically important unsubstituted oligo-phenylene vinylenes (OPVn) and oligo-thiophenes (OTn), which display side-by-side herringbone crystal, are discussed. The key photophysical properties displayed by OPVn and OTn solid phases, including the large Davydov splitting, the variety of peaks due to vibronic coupling in both absorption and emission, and the unusual behavior of the emission origin, are accounted for in a model including excitonic coupling between molecules, linear exciton-phonon coupling, and disorder.

The spectroscopic differences between J and H-aggregates are traditionally attributed to the spatial dependence of the Coulombic coupling, as originally proposed by Kasha. However, in tightly packed molecular aggregates wave functions on neighboring molecules overlap, leading to an additional charge transfer (CT) mediated exciton coupling with a vastly different spatial dependence. The latter is governed by the nodal patterns of the molecular LUMOs and HOMOs from which the electron (te) and hole (th) transfer integrals derive. The sign of the CT-mediated coupling depends on the sign of the product teth and is therefore highly sensitive to small (sub-Angstrom) transverse displacements or slips. Given that Coulombic and CT-mediated couplings exist simultaneously in tightly packed molecular systems, the interference between the two must be considered when defining J and H-aggregates. Generally, such p-stacked aggregates do not abide by the traditional classification scheme of Kasha: for example, even when the Coulomb coupling is strong the presence of a similarly strong but destructively interfering CT-mediated coupling results in "null-aggregates" which spectroscopically resemble uncoupled molecules. Based on a Frenkel/CT Holstein Hamiltonian that takes into account both sources of electronic coupling as well as intramolecular vibrations, vibronic spectral signatures are developed for integrated Frenkel/CT systems in both the perturbative and resonance regimes. In the perturbative regime, the sign of the lowest exciton band curvature, which rigorously defines J and H-aggregation, is directly tracked by the ratio of the first two vibronic peak intensities. Even in the resonance regime, the vibronic ratio remains a useful tool to evaluate the J or H nature of the system. The theory developed is applied to the reversible H to J-aggregate transformations recently observed in several perylene bisimide systems. [ABSTRACT FROM AUTHOR]

Infrared absorption of positively charged polarons in conjugated polymer chains and π-stacked aggregates is investigated theoretically, employing a Holstein-based Hamiltonian which treats electronic coupling, electron-vibrational coupling, and disorder on equal footing. The spectra evaluated from the Hamiltonian expressed in a one- and two-particle basis set are essentially exact, insofar as the main, aromatic-quinoidal vibrational mode is treated fully nonadiabatically. Diagonal and off-diagonal ("paracrystalline") disorder are resolved along the polymer axis (x) and the aggregate stacking axis (y). Disorder along the polymer axis selectively attenuates the x-polarized spectrum, which is dominated by the polaron peak P1. Disorder along the stacking axis selectively attenuates the y-polarized spectrum, which is dominated by the lower-energy charge-transfer peak, DP1. Calculated spectra are in excellent agreement with the measured induced-absorption and charge-modulation spectra, reproducing the peak positions and relative peak intensities within a line shape rich in vibronic structure. Our nonadiabatic approach predicts the existence of a weak, x-polarized peak P0, slightly blueshifted from DP1. The peak is intrinsic to single polymer chains and appears in a region of the spectrum where narrow infrared active vibrational modes have been observed in nonaggregated conjugated polymers. The polaron responsible for P0 is composed mainly of two-particle wave functions and cannot be accounted for in the more conventional adiabatic treatments. [ABSTRACT FROM AUTHOR]