Excitonic coupling in polythiophenes: Comparison of different calculation methods

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

Assessing the effects of increasing conjugation length on exciton diffusion: from small molecules to the polymeric limit

Organic solar cells (OSC) generally contain long-chain π-conjugated polymers as donor materials, but, more recently, small-molecule donors have also attracted considerable attention. The nature of these compounds is of crucial importance concerning the various processes that determine device performance, among which singlet exciton diffusion is one of the most relevant. The efficiency of the diffusion mechanism depends on several aspects, from system morphology to electronic structure properties, which vary importantly with molecular size. In this work, we investigated the effects of conjugation length on the exciton diffusion length through electronic structure calculations and an exciton diffusion model. By applying extrapolation procedures to thiophene and phenylene vinylene oligomer series, we investigate their electronic and optical properties from the small-molecule point of view to the polymeric limit. Several properties are calculated as a function of oligomer size, including transition energies, absorption and emission spectra, reorganization energies, exciton coupling and Förster radii. Finally, an exciton diffusion model is used to estimate diffusion lengths as a function of oligomer size and for the polymeric limit showing agreement with experimental data. Results also show that longer conjugation lengths correlate with longer exciton diffusion lengths in spite of also being associated with shorter exciton lifetimes.

Spatially Resolved Photogenerated Exciton and Charge Transport in Emerging Semiconductors

We review recent advances in the characterization of electronic forms of energy transport in emerging semiconductors. The approaches described all temporally and spatially resolve the evolution of initially localized populations of photogenerated excitons or charge carriers. We first provide a comprehensive background for describing the physical origin and nature of electronic energy transport both microscopically and from the perspective of the observer. We introduce the new family of far-field, time-resolved optical microscopies developed to directly resolve not only the extent of this transport but also its potentially temporally and spatially dependent rate. We review a representation of examples from the recent literature, including investigation of energy flow in colloidal quantum dot solids, organic semiconductors, organic-inorganic metal halide perovskites, and 2D transition metal dichalcogenides. These examples illustrate how traditional parameters like diffusivity are applicable only within limited spatiotemporal ranges and how the techniques at the core of this review,especially when taken together, are revealing a more complete picture of the spatiotemporal evolution of energy transport in complex semiconductors, even as a function of their structural heterogeneities.

Comparative Computational Study of Electronic Excitations of Neutral and Charged Small Oligothiophenes and Their Extrapolations Based on Simple Models

This work reports electronic excitation energies of neutral and charged oligothiophenes (OT n ) with repeat unit n = 2-6 computed by routinely used semiempirical and time-dependent density functional theory (TD-DFT) methods. More specifically, for OT n , OTn +, and OTn -, we calculated vertical transition energies for electronic absorption spectroscopy employing the Zerner's version of intermediate neglect differential overlap method for structures optimized by the PM6 semiempirical method and the TD-DFT method with three different functionals, B3LYP, BVP86, and M06-2X, for structures optimized by the ground-state DFT method employing the same functionals. We also calculated vertical transition energies for the emission spectroscopy from the lowest singlet excited states by employing the TD-DFT method for the structures optimized for the lowest singlet excited states. In addition to computational results in vacuum, solution phase data calculated at the level of polarizable continuum model are reported and compared with available experimental data. Most of the data are fitted reasonably well by two simple model functions, one based on a Frenkel exciton theory and the other based on the model of independent electrons in a box with sinusoidal modulation of potential. Despite similar levels of fitting performance, the two models produce distinctively different asymptotic values of excitation energies. Comparison of these with available experimental and computational data suggests that the values based on the exciton model, while seemingly overestimating, are closer to true values than those based on the other model. This assessment is confirmed by additional calculations for a larger oligomer. The fitting parameters offer new means to understand the relationship between electronic excitations of OTs and their sizes and suggest the feasibility of constructing simple coarse-grained exciton-bath models applicable for aggregates of OTs.

Photoinduced charge transfer by one and two-photon absorptions: physical mechanisms and applications

We review photoinduced charge transfer in organic solar cells without and with an external electric field and then we introduce the visualization methods of the transition density, charge difference density and transition density matrix for the analysis of the photoinduced charge transfer in a neutral system and a charged system excited by one-photon and two-photon absorption. This review will not only promote a deeper understanding of the available theories and methods of PICT, but also lead to further developments in this field.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

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.

Theory of FRET "Spectroscopic Ruler" for Short Distances: Application to Polyproline

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory.

Light Harvesting for Organic Photovoltaics

The field of organic photovoltaics has developed rapidly over the last 2 decades, and small solar cells with power conversion efficiencies of 13% have been demonstrated. Light absorbed in the organic layers forms tightly bound excitons that are split into free electrons and holes using heterojunctions of electron donor and acceptor materials, which are then extracted at electrodes to give useful electrical power. This review gives a concise description of the fundamental processes in photovoltaic devices, with the main emphasis on the characterization of energy transfer and its role in dictating device architecture, including multilayer planar heterojunctions, and on the factors that impact free carrier generation from dissociated excitons. We briefly discuss harvesting of triplet excitons, which now attracts substantial interest when used in conjunction with singlet fission. Finally, we introduce the techniques used by researchers for characterization and engineering of bulk heterojunctions to realize large photocurrents, and examine the formed morphology in three prototypical blends.

Size-Independent Energy Transfer in Biomimetic Nanoring Complexes

Supramolecular antenna-ring complexes are of great interest due to their presence in natural light-harvesting complexes. While such systems are known to provide benefits through robust and efficient energy funneling, the relationship between molecular structure, strain (governed by nuclear coordinates and motion), and energy dynamics (arising from electronic behavior) is highly complex. We present a synthetic antenna-nanoring system based on a series of conjugated porphyrin chromophores ideally suited to explore such effects. By systematically varying the size of the acceptor nanoring, we reveal the interplay between antenna-nanoring binding, local strain, and energy dynamics on the picosecond time scale. Binding of the antenna unit creates a local strain in the nanoring, and this strain was measured as a function of the size of the nanoring, by UV-vis-NIR titration, providing information on the conformational flexibility of the system. Strikingly, the energy-transfer rate is independent of nanoring size, indicating the existence of strain-localized acceptor states, spread over about six porphyrin units, arising from the noncovalent antenna-nanoring association.

Quantum Chemical Studies of Light Harvesting

The design of optimal light-harvesting (supra)molecular systems and materials is one of the most challenging frontiers of science. Theoretical methods and computational models play a fundamental role in this difficult task, as they allow the establishment of structural blueprints inspired by natural photosynthetic organisms that can be applied to the design of novel artificial light-harvesting devices. Among theoretical strategies, the application of quantum chemical tools represents an important reality that has already reached an evident degree of maturity, although it still has to show its real potentials. This Review presents an overview of the state of the art of this strategy, showing the actual fields of applicability but also indicating its current limitations, which need to be solved in future developments.

Photoinduced Electron Transfer in Organic Solar Cells

Electron transfer (ET) is the key process in light-driven charge separation reactions in organic solar cells. The current review summarizes the progress in theoretical modelling of ET in these materials. First we give an account of ET, with a description originating from Marcus theory. We systematically go through all the relevant parameters and show how they depend on different material properties, and discuss the consequences such dependencies have for the performance of the devices. Finally, we present a set of visualization methods which have proven to be very useful in analyzing the elementary processes in absorption and charge separation events. Such visualization tools help us to understand the properties of the photochemical and photobiological systems in solar cells.

Excited state analysis of absorption processes in metal decorated graphene nanoribbons

Transition density matrix (TDM) based excited state analysis presented for single metal atom doped graphene C₂₉H₁₄-X. Natural transition orbitals (NTOs) and e–h correlation plots of Ti-doped graphene are shown below.

Quantifying highly efficient incoherent energy transfer in perylene-based multichromophore arrays

Multichromophore perylene arrays were designed and synthesized to have extremely efficient resonance energy transfer, as confirmed by ultrafast spectroscopy.

Cooperative enhancement versus additivity of two-photon-absorption cross sections in linear and branched squaraine superchromophores

Our investigation of the nonlinear optical properties of a series of oligomeric squaraine dyes showed enhanced cross sections for linear oligomers but only additivity for branched systems.

Fluorescence polarization measures energy funneling in single light-harvesting antennas--LH2 vs conjugated polymers

Numerous approaches have been proposed to mimic natural photosynthesis using artificial antenna systems, such as conjugated polymers (CPs), dendrimers, and J-aggregates. As a result, there is a need to characterize and compare the excitation energy transfer (EET) properties of various natural and artificial antennas. Here we experimentally show that EET in single antennas can be characterized by 2D polarization imaging using the single funnel approximation. This methodology addresses the ability of an individual antenna to transfer its absorbed energy towards a single pool of emissive states, using a single parameter called energy funneling efficiency (ε). We studied individual peripheral antennas of purple bacteria (LH2) and single CP chains of 20 nm length. As expected from a perfect antenna, LH2s showed funneling efficiencies close to unity. In contrast, CPs showed lower average funneling efficiencies, greatly varying from molecule to molecule. Cyclodextrin insulation of the conjugated backbone improves EET, increasing the fraction of CPs possessing ε = 1. Comparison between LH2s and CPs shows the importance of the protection systems and the protein scaffold of LH2, which keep the chromophores in functional form and at such geometrical arrangement that ensures excellent EET.

Rapid Energy Transfer Enabling Control of Emission Polarization in Perylene Bisimide Donor-Acceptor Triads

Materials showing rapid intramolecular energy transfer and polarization switching are of interest for both their fundamental photophysics and potential for use in real-world applications. Here, we report two donor-acceptor-donor triad dyes based on perylene-bisimide subunits, with the long axis of the donors arranged either parallel or perpendicular to that of the central acceptor. We observe rapid energy transfer (<2 ps) and effective polarization control in both dye molecules in solution. A distributed-dipole Förster model predicts the excitation energy transfer rate for the linearly arranged triad but severely underestimates it for the orthogonal case. We show that the rapid energy transfer arises from a combination of through-bond coupling and through-space transfer between donor and acceptor units. As they allow energy cascading to an excited state with controllable polarization, these triad dyes show high potential for use in luminescent solar concentrator devices.

On the relation of energy and electron transfer in multidimensional chromophores based on polychlorinated triphenylmethyl radicals and triarylamines

Chromophores with many donors and acceptors show electron transfer which is identical to energy transfer.

Simulations of singlet exciton diffusion in organic semiconductors: a review

Recent advances in exciton diffusion simulations in conjugated materials are presented in this review.

Chromophores in Molecular Nanorings: When Is a Ring a Ring?

The topology of a conjugated molecule plays a significant role in controlling both the electronic properties and the conformational manifold that the molecule may explore. Fully π-conjugated molecular nanorings are of particular interest, as their lowest electronic transition may be strongly suppressed as a result of symmetry constraints. In contrast, the simple Kasha model predicts an enhancement in the radiative rate for corresponding linear oligomers. Here we investigate such effects in linear and cyclic conjugated molecules containing between 6 and 42 butadiyne-linked porphyrin units (corresponding to 600 C-C bonds) as pure monodisperse oligomers. We demonstrate that as the diameter of the nanorings increases beyond ∼10 nm, its electronic properties tend toward those of a similarly sized linear molecule as a result of excitation localization on a subsegment of the ring. However, significant differences persist in the nature of the emitting dipole polarization even beyond this limit, arising from variations in molecular curvature and conformation.

Ultrafast energy transfer in biomimetic multistrand nanorings

We report the synthesis of LH2-like supramolecular double- and triple-stranded complexes based upon porphyrin nanorings. Energy transfer from the antenna dimers to the π-conjugated nanoring occurs on a subpicosecond time scale, rivaling transfer rates in natural light-harvesting systems. The presence of a second nanoring acceptor doubles the transfer rate, providing strong evidence for multidirectional energy funneling. The behavior of these systems is particularly intriguing because the local nature of the interaction may allow energy transfer into states that are, for cyclic nanorings, symmetry-forbidden in the far field. These complexes are versatile synthetic models for natural light-harvesting systems.

Excitonic effects from geometric order and disorder explain broadband optical absorption in eumelanin

Eumelanin is a ubiquitous biological pigment, and the origin of its broadband absorption spectrum has long been a topic of scientific debate. Here, we report a first-principles computational investigation to explain its broadband absorption feature. These computations are complemented by experimental results showing a broadening of the absorption spectra of dopamine solutions upon their oxidation. We consider a variety of eumelanin molecular structures supported by experiments or theoretical studies, and calculate the absorption spectra with proper account of the excitonic couplings based on the Frenkel exciton model. The interplay of geometric order and disorder of eumelanin aggregate structures broadens the absorption spectrum and gives rise to a relative enhancement of absorption intensity at the higher-energy end, proportional to the cube of absorption energy. These findings show that the geometric disorder model is as able as the chemical disorder model, and complements this model, to describe the optical properties of eumelanin.

The structure and dynamics of molecular excitons

The photophysical behavior of organic semiconductors is governed by their excitonic states. In this review, I classify the three different exciton types (Frenkel singlet, Frenkel triplet, and charge transfer) typically encountered in organic semiconductors. Experimental challenges that arise in the study of solid-state organic systems are discussed. The steady-state spectroscopy of intermolecular delocalized Frenkel excitons is described, using crystalline tetracene as an example. I consider the problem of a localized exciton diffusing in a disordered matrix in detail, and experimental results on conjugated polymers and model systems suggest that energetic disorder leads to subdiffusive motion. Multiexciton processes such as singlet fission and triplet fusion are described, emphasizing the role of spin state coherence and magnetic fields in studying singlet ↔ triplet pair interconversion. Singlet fission provides an example of how all three types of excitons (triplet, singlet, and charge transfer) may interact to produce useful phenomena for applications such as solar energy conversion.

Theoretical study of torsional disorder in poly(3-alkylthiophene) single chains: intramolecular charge-transfer character and implications for photovoltaic properties

The role of polymer chain morphology on the optoelectronic properties of polythiophenes is an ongoing investigation with the promise of improving organic photovoltaic performance. Chain morphology is predominantly affected by torsional disorder, which causes localization of holes and electrons in the conjugated backbone. Using the model compound oligo(3-methylthiophene), torsionally disordered oligomers were created to compare with a trans-planar oligomer such as found in crystalline poly(3-hexylthiophene). Low lying electronic excitations are calculated using TD-HF and TD-DFT with various long-range corrected functionals. Probability densities of electron and hole were constructed from natural transition orbitals, giving insight into localization and electron-hole overlap. Overlap is found to be substantially higher in disordered oligomers, indicating a stronger Coulombic interaction between electron and hole. Results suggest that improved photovoltaic performance with increased crystallinity is partially explained by stronger light absorption in crystalline polymers and a higher barrier to charge separation in disordered polymers.

Light-harvesting and ultrafast energy migration in porphyrin-based metal-organic frameworks

Given that energy (exciton) migration in natural photosynthesis primarily occurs in highly ordered porphyrin-like pigments (chlorophylls), equally highly ordered porphyrin-based metal-organic frameworks (MOFs) might be expected to exhibit similar behavior, thereby facilitating antenna-like light-harvesting and positioning such materials for use in solar energy conversion schemes. Herein, we report the first example of directional, long-distance energy migration within a MOF. Two MOFs, namely F-MOF and DA-MOF that are composed of two Zn(II) porphyrin struts [5,15-dipyridyl-10,20-bis(pentafluorophenyl)porphinato]zinc(II) and [5,15-bis[4-(pyridyl)ethynyl]-10,20-diphenylporphinato]zinc(II), respectively, were investigated. From fluorescence quenching experiments and theoretical calculations, we find that the photogenerated exciton migrates over a net distance of up to ~45 porphyrin struts within its lifetime in DA-MOF (but only ~3 in F-MOF), with a high anisotropy along a specific direction. The remarkably efficient exciton migration in DA-MOF is attributed to enhanced π-conjugation through the addition of two acetylene moieties in the porphyrin molecule, which leads to greater Q-band absorption intensity and much faster exciton-hopping (energy transfer between adjacent porphyrin struts). The long distance and directional energy migration in DA-MOF suggests promising applications of this compound or related compounds in solar energy conversion schemes as an efficient light-harvesting and energy-transport component.