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The exciton band dispersion in π-stacks of conjugated organic chromophores is a critical factor in determining the photophysical response and transport properties. In such stacks, the exciton band ...

The essential states model (ESM) for donor–acceptor–donor (D–A–D) chromophores is used to explore absorption and photoluminescence (PL) in molecular dimers composed of centrosymmetric and non-centrosymmetric squaraine molecules. The spectral line shapes and shifts relative to the monomer spectrum are due to an interesting interplay between three-center charge distributions responsible for ground- and excited-state (permanent) dipole and quadrupole moments and two-center charge distributions responsible for transition dipole moments. The Davydov splitting is sensitive only to the interactions between the (extended) transition dipoles , whereas the permanent dipole-dipole and quadruple-quadrupole interactions impact the midpoint frequency of the two Davydov components, leading to a generally asymmetric splitting relative to the peak monomer transition frequency. The theory accurately reproduces the steady-state absorption and PL line shapes recently obtained for covalently bound squaraine dimers. The ESM also predicts an extreme type of non-Kasha behavior, where both Davydov components are blue-shifted above the monomer transition frequency.

An extension of the essential states model is developed to investigate the absorption and electronic properties of a highly dipolar merocyanine dye and double and quadruple π-stacks formed upon the...

The shape of the mid-IR absorption spectrum provides valuable information about the “hole” polaron coherence length in doped and undoped conjugated polymer films. In poly(3-hexylthiophene) (P3HT) f...

ConspectusExcitons and polarons play a central role in the electronic and optical properties of organic semiconducting polymers and molecular aggregates and are of fundamental importance in understanding the operation of organic optoelectronic devices such as solar cells and light-emitting diodes. For many conjugated organic molecules and polymers, the creation of neutral electronic excitations or ionic radicals is associated with significant nuclear relaxation, the bulk of which occurs along the vinyl-stretching mode or the aromatic-quinoidal stretching mode when conjugated rings are present. Within a polymer chain or molecular aggregate, nuclear relaxation competes with energy- and charge-transfer, mediated by electronic interactions between the constituent units (repeat units for polymers and individual chromophores for a molecular aggregate); for neutral electronic excitations, such inter-unit interactions lead to extended excited states or excitons, while for positive (or negative) charges, interactions lead to delocalized hole (or electron) polarons. The electronic coupling as well as the local coupling between electronic and nuclear degrees of freedom in both excitons and polarons can be described with a Holstein Hamiltonian. However, although excitons and polarons derive from similarly structured Hamiltonians, their optical signatures are quite distinct, largely due to differing ground states and optical selection rules.In this Account, we explore the similarities and differences in the spectral response of excitons and polarons in organic polymers and molecular aggregates. We limit our analysis to the subspace of excitons and hole polarons containing at most one excitation; hence we omit the influence of bipolarons, biexcitons, and higher multiparticle excitations. Using a generic linear array of coupled units as a model host for both excitons and polarons, we compare and contrast the optical responses of both quasiparticles, with a particular emphasis on the spatial coherence length, the length over which an exciton or polaron possesses wave-like properties important for more efficient transport. For excitons, the UV-vis absorption spectrum is generally represented by a distorted vibronic progression with H-like or J-like signatures depending on the sign of the electronic coupling, Jex. The spectrum broadens with increasing site disorder, with the spectral area preserved due to an oscillator strength sum rule. For (hole) polarons, the generally stronger electronic coupling results in a mid-IR spectrum consisting of a narrow, low-energy peak (A) with energy near a vibrational quantum of the vinyl stretching mode, and a broader, higher-energy feature (B). In contrast to the UV-vis spectrum, the mid-IR spectrum is invariant to the sign of the electronic coupling, th, and completely resistant to long-range disorder, where it remains entirely homogeneously broadened. Even in the presence of short-range disorder, the width of peak A remains surprisingly narrow as long as |th| remains sufficiently large, a property that can be understood in terms of Herzberg-Teller coupling. Unlike for excitons, for polarons, the absorption spectral area decreases with increasing short-range disorder σ (i.e., there is no oscillator sum rule) reflective of a decreasing polaron coherence length. The intensity of the low-energy peak A in relation to B is an important signature of polaron coherence. By contrast, for excitons, the absorption spectrum contains no unambiguous signs of exciton coherence. One must instead resort to the shape of the steady-state photoluminescence spectrum. The Holstein-based model has been highly successful in accounting for the spectral properties of molecular aggregates as well as conjugated polymers like poly(3-hexylthiophene) (P3HT) in the mid-IR and UV-vis spectral regions.

Aggregates of quadrupolar DAD-type chromophores are investigated theoretically using the essential states model (ESM) enhanced to include vibronic coupling. On the basis of vibronic signatures in the absorption and photoluminescence spectra, important connections are made to the Frenkel exciton model, which is the basis for defining conventional H- and J-aggregates. In contrast to the exciton theory, the ESM allows for an unusual type of the red-shifted H-aggregate, driven by the large quadrupole–quadrupole interaction. Except for the red shift of the main absorption peak, such aggregates display all of the characteristics of conventional H-aggregates, including suppressed radiative decay rates and all of the vibronic signatures in the absorption and photoluminescence spectra consistent with Frenkel exciton models. Red-shifted H-dimers occur for a range of slip angles, which separate conventional H- and J-aggregate behavior, with the slip range diminishing with increasing intermolecular separation. Davydo...

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

Small conjugated molecules are of great interest as promising alternatives to semiconducting polymers in organic photovoltaics (OPV). In this work, we introduce a more accurate assignment of the excited state of a promising squaraine (SQ) targeted for OPV application. From this assignment, we conclude that a mixed population of monomers and aggregates exists in spin-cast SQ:PC 61 BM bulk heterojunction (BHJ) films, where monomers indicate the presence of amorphous regions that could act as traps. Since crystallinity is critically important for efficient charge transport and exciton diffusion in the BHJ, we thermally anneal the as-cast films to reduce the amorphous regions. Our analysis of annealed films demonstrates a delicate trade-off between increased crystallinity and larger domain sizes. Crystallinity improves but often at the expense of larger crystal size, as supported by XRD and TEM study. Therefore, to achieve optimal OPV efficiency, we controlled the tradeoff to improve the crystallinity while maintaining a small, highly mixed BHJ morphology. We thus highlight the importance of chemical compatibility when designing small molecules for use in high efficiency BHJ devices. Significantly, we have connected theoretically validated spectroscopic assignment with the first full study of morphology and domain size control as they affect small molecule OPV active layers.

The importance of spatial coherence in energy and charge transfer processes in biological systems and photovoltaic devices has been hotly debated over the past several years. While larger spatial coherences are thought to benefit transport, a clear correlation has yet to be established, partly because a simple and accurate measure of the coherence length has remained elusive. Previously, it was shown that the number of coherently connected chromophores, N Coh , can be determined directly from the ratio ( S R ) of the 0-0 and 0-1 vibronic line strengths in the photoluminescence (PL) spectrum. The relation N Coh = λ 0 2 S R , where λ 0 2 is the associated monomeric Huang–Rhys parameter, was derived in the Frenkel exciton limit. Here, it is shown that S R remains a highly accurate measure of coherence for systems characterized by significant charge transfer interactions (e.g. conjugated π-stacked systems). The only requirement is that the exciton band curvature must be positive, as in a J-aggregate.

The impact of chain bending on the photophysical properties of emissive conjugated polymers (CPs) is studied theoretically using Holstein-style Hamiltonians which treat vibronic coupling involving the ubiquitous vinyl/ring stretching mode nonadiabatically. The photophysical impact of chain bending is already evident at the level of an effective Frenkel Hamiltonian, where the positive exciton band curvature in CPs translates to negative excitonic coupling between monomeric units, as in J-aggregates. It is shown that the absorption and photoluminescence (PL) spectral line shapes respond very differently to chain bending. The misalignment of monomeric transition dipole moments with bending selectively attenuates the 0-0 PL peak intensity while leaving the 0-1 intensity practically unchanged, a property which is ultimately due to the uniquely coherent nature of the 0-0 peak. Hence, the 0-0/0-1 PL ratio, as well as the radiative decay rate, decrease with chain bending, effects that are more pronounced at lower temperatures where exciton coherence extends over a larger portion of the chain. Increasing temperature and/or static disorder reduces the exciton coherence number, Ncoh, thereby reducing the sensitivity to bending. In marked contrast, the absorption vibronic progression is far less sensitive to morphological changes, even at low temperatures, and is mainly responsive to the exciton bandwidth. The above results also hold when using a more accurate 1D semiconductor Hamiltonian which allows for electron-hole separation along the CP chain. The findings may suggest unique ways of controlling the radiative properties of conjugated polymer chains useful in applications such as organic light emitting diodes (OLEDs) and low-temperature sensors.

Aggregates of conjugated polymers exhibit two classes of fundamental electronic interactions: those occurring within a given chain and those occurring between chains. The impact of such excitonic interactions on the photophysics of polymer films can be understood using concepts of J- and H-aggregation originally developed by Kasha and coworkers to treat aggregates of small molecules. In polymer assemblies, intrachain through-bond interactions lead to J-aggregate behavior, whereas interchain Coulombic interactions lead to H-aggregate behavior. The photophysics of common emissive conjugated polymer films are determined by a competition between intrachain, J-favoring interactions and interchain, H-favoring interactions. We review formalisms describing absorption and photoluminescence lineshapes, based on intra- and intermolecular excitonic coupling, electron-vibrational coupling, and correlated energetic disorder. Examples include regioregular polythiophenes, pheneylene-vinylenes, and polydiacetylene.

The absorption line shapes of a series of linear and star-shaped perylene diimide (PDI) complexes are evaluated theoretically and compared to experiment. The cyclic trimer and tetrahedral complexes are part of the symmetric series, characterized by a single interchromophoric coupling, J(0), between any two PDI chromophores. The measured spectra of all complexes show pronounced vibronic progressions based on the symmetric ring stretching mode at ~1400 cm(-1). The spectral line shapes are accurately reproduced using a Holstein Hamiltonian parametrized with electronic couplings calculated using time-dependent density functional transition charge densities. Although the "head-to-tail" linear complexes display classic J-aggregate behavior, the star-shaped complexes display a unique photophysical response, which is neither J- nor H-like. In the symmetric N-mers (N = 2-4), absorption and emission are polarized along N - 1 directions in contrast to linear complexes where absorption and emission remain polarized along the long molecular axis. In the symmetric complexes the red-shift of the 0-0 peak with increasing |J(0)|, as well as the initial linear rise of the 0-0/1-0 oscillator strength ratio with increasing |J(0)|, are independent of the number of PDI chromophores, N, and are markedly smaller than what is found in the linear series, where the shifts and ratios depend on N. Moreover, whereas the radiative decay rate, γ(r), scales with N and is therefore superradiant in linear complexes, γ(r) scales with N/(N - 1) in the symmetric complexes. Vibronic/vibrational pair states (two-particle states) are found to profoundly affect the absorption line shapes of both linear and symmetric complexes for sufficiently large coupling.

We present a theory for the dynamics of excitons in molecular aggregates in presence of polaronic effects caused by a strong coupling to an intramolecular vibration. Transitions between exciton states are assumed to occur by weak coupling to low-energy acoustic phonons. The theory can describe measurements of the polarization anisotropy decay of helical aggregates of oligo(p-phenylene-vinylene) derivatives in solution. The fitted cut-off frequency of the acoustic phonons agrees well with an estimate of the Debye frequency of the solvent. The inclusion of polaronic effects leads for long times to a slower, but for short times to a faster exciton dynamics.

The extreme sensitivity of circularly polarized luminescence (CPL) to long-range excitonic interactions inside a helical aggregate is investigated. It is found to persist even in the presence of strong energetic disorder and coupling of the exciton to molecular vibrations, when the emitting exciton is localized to only a few chromophores. The CPL dissymmetry, g(lum), is found to depend on a modulated sum over the excitonic couplings, Sigma(n,s)J(n,n+s) s sin(phi s), where J(n,n+s) is the coupling between molecules separated by s lattice spacings and 4, is the pitch angle between adjacent chromophores. The validity of this relation is confirmed through full-scale numerical simulations of helical MPOV4 aggregates using the disordered Holstein Hamiltonian. In addition, an analytical expression for g(lum) is obtained for a helical chain containing a single, energetically detuned chromophore to represent strong disorder. Subsequently, the resulting expression is generalized to include full distributed disorder. Our results demonstrate that the spatial dependence of extended interactions can be extracted from experimental spectra, without having details on disorder or exciton-vibrational coupling.

Absorption in conjugated polymer aggregates is studied theoretically, taking into account excitonic (intermolecular) coupling, exciton–phonon (EP) coupling and site-energy disorder, all treated on equal footing within a generalized Holstein Hamiltonian with numerically generated eigenmodes and energies. The analysis deals primarily with the weak excitonic coupling regime, which for polymers, corresponds to J 0 ≲ 0.4 ω 0 where J 0 is the nearest neighbor excitonic coupling and ω 0 (≈1400 cm −1 ) is the frequency of the ring breathing/stretching mode coupled to the molecular electronic transition with Huang–Rhys factor, λ 2 ≈ 1. Disorder is characterized by a Gaussian distribution of molecular transition frequencies of width σ . Absorption spectra are calculated under the two-particle approximation (TPA) as well as the less accurate, but computationally more efficient single-particle approximation (SPA). Fermi resonances (FRs) arise due to the coupling between the optically allowed single-particle states (vibronic excitons) and the dark two-particle states. In the motional narrowing limit FRs are clearly resolved. Further increases in σ cause the FRs to merge into a single peak for each vibronic band. At this point the SPA becomes accurate for the entire spectrum. The SPA also provides the basis for simplified analytical expressions for the peak intensity ratios, from which the free exciton bandwidth, W , can be determined. Analytical expressions are also obtained for the peak-positions within the vibronic progression. Application to regio-regular poly(3-hexyl)thiophene films shows the exciton bandwidth, W , to be in the range 0.8 ω 0 – ω 0 . The model also accounts for the irregular peak spacings observed in experiment.

A model accounting for the simultaneous presence of static and dynamic disorder is developed for herringbone (HB) aggregates and thin films of conjugated oligomers such as oligo-phenylene vinylene and oligothiophene. Short-range orientational defects as well as stacking faults (SFs) are considered within the motional narrowing regime. Temperature effects are included under the fast scattering approximation. Adding orientational defects attenuates 0–0 emission in HB aggregates while enhancing 0–0 emission when stacking faults are already present.

In this work, the effect of temperature, exciton bandwidth, and size on the photoluminescence spectra of defect-free two-dimensional herringbone aggregates of pi-conjugated oligomers such as oligophenylene vinylene and oligothiophene is investigated theoretically. The model is based on exciton-phonon coupling in two-dimensional herringbone lattices with the exciton deriving from the lowest optical (1Ag-->1Bu) transition and the phonon from the most strongly coupled intramolecular vibrational mode with frequency omega0. Simple analytical expressions are obtained for the line strengths of the emission origin (0-0) and first replica (0-1) as a function of the number of molecules comprising the aggregate, N, the free exciton bandwidth, WD, and the temperature, T. At a given temperature, the 0-0 emission intensity initially scales as N/Nth, where Nth is the superradiant threshold number, but eventually converges to NT/Nth, where NT is the size independent thermal coherence number. NT is inversely proportional to temperature and proportional to the exciton band curvature (omegac) near the band bottom; NT=1+4piomegac/kbT. In striking contrast, the 0-1 line strength is relatively insensitive to temperature and size, but scales as the inverse square of WD+omega0. The insensitivity of the first replica to the exciton coherence number makes the ratio of the 0-0 to 0-1 line strengths a measure of the exciton coherence number. The ratio can be used to test for crystal purity. Comparison to experiments on thin films of quaterthiophene shows that the thermal coherence size is given by NT approximately 1+450/T (K) and that superradiance, which requires NT>Nth, can only be observed at temperatures less than 1 K.

The photophysical properties of defect-free herringbone aggregates of π-conjugated oligomers are investigated theoretically using a two-particle basis set consisting of vibronic excitons and coupled vibronic–vibrational excitons. Incorporation of periodic boundary conditions allows the treatment of aggregates containing up to 1000 molecules. The vibrational distortion fields for the optically allowed excitons, including those responsible for the upper and lower Davydov components, are evaluated. The herringbone lattice supports both vibrationally dressed, heavy excitons as well as nearly free, light excitons. The former are responsible for the b-polarized absorption origin as well as two ac-polarized peaks slightly higher in energy. The strongly blueshifted main absorption peak is due to an exciton which travels with almost no nuclear distortion. The main absorption features are studied as a function of aggregate size and exciton bandwidth. The vibronic replicas in the aggregate emission spectrum are foun...

The impact of exciton-phonon coupling and defect states on the photophysical properties of p-distyrylbenzene nanoaggregates is studied numerically. Molecular packing within aggregates is based on the known crystal structures of poly-p-phenylene vinylene (Type I) and the five phenyl group oligomer (Type II). Calculations of absorption and emission are conducted using a reduced basis set consisting of all one- and two-particle vibronic states. The calculated spectra are very similar for both aggregate types, the only substantial difference being the polarization directions for the J-band and 0-0 emission line. Under the noninteracting domains approximation the calculated nanoaggregate absorption spectrum is in excellent agreement with experiment, assuming an exciton coherence length of approximately 20 A. In the calculated emission spectrum the 0-0 emission is uniquely polarized compared with the rest of the vibronic progression, also in agreement with experiment. The 0-0 emission intensity in defect-free Type I and II aggregates is linearly proportional to the total number of molecules, becoming superradiant beyond a certain size threshold. The 0-0 emission is highly sensitive to stacking faults and dislocations. These defects account for the measured Stokes shift, but quench the 0-0 emission (and superradiance) while only slightly affecting the rest of the vibronic progression. Adding orientational point defects to an aggregate with stacking faults and/or dislocations enhances the 0-0 oscillator strength, bringing the 0-0 emission intensity into good agreement with experiment.

The effects of exciton-vibrational coupling and point defects on the absorption and emission of distyrylbenzene nanoaggregates are treated theoretically. Two aggregate types based on a two-dimensional array of cyclic tetramers (pinwheels) are considered: type A aggregates, composed of chiral pinwheels, and type B aggregates, composed of achiral pinwheels. The low-energy vibronic features in the experimental excitation spectrum arise from vibrationally dressed K=(0,0) excitons, while the more intense blue shifted H-band is due to nearly free K=(0,0) excitons. The K=(0,0) features are polarized primarily along the herringbone plane normal. The lowest Davydov component is polarized in the herringbone plane and is due to the lowest energy K=(π,π) exciton. This state is also responsible for the aggregate emission. The 0-v peaks for v>0 are mainly due to indirect transitions to the ground electronic state containing v phonons, with wave vector sum equal to (π,π). These peaks are largely independent of defect fr...

Absorption and spontaneous emission from exciton states in ordered aggregates of π-conjugated polymers are studied theoretically. Each polymer contains N carbon atoms with average bond length a and is treated using a Pariser–Parr–Pople Hamiltonian. Coulombic interactions between molecules are treated to first order using an effective Hamiltonian approach. The aggregate electronic excited states are Wannier–Frenkel (WF) excitons with intramolecular Wannier exciton character and intermolecular Frenkel exciton character. For aggregates with in-phase double bond alignment, interpolymer interactions cause a blue shift of the optically allowed (νB−) WF excitons. The blue shift increases with N, peaks, and ultimately tends to a small value when the polymer length greatly exceeds d, the nearest neighbor separation. The radiative decay rate γνB− of the optically allowed νB− WF exciton is proportional to the number of polymers, M. Intermolecular interactions have little effect on the exciton sizes and energies when...