Cooperative singlet and triplet exciton transport in tetracene crystals visualized by ultrafast microscopy

Slowed Singlet Exciton Fission Enhances Triplet Exciton Transport in Select Perylenediimide Crystals

Singlet fission (SF) materials used in light-harvesting devices must not only efficiently produce spin-triplet excitons but also transport them to an energy acceptor. N,N'-Bis(2-phenylethyl)-3,4,9,10-perylenedicarboximide (EP-PDI) is a promising SF chromophore due to its photostability, large extinction coefficient, and high triplet yield, but the energy transport mechanisms in EP-PDI solids are minimally understood. Herein, we use transient absorption microscopy to directly characterize exciton transport in EP-PDI crystals. We find evidence for singlet-mediated transport in which pairs of triplet excitons undergo triplet fusion (TF), producing spin-singlet excitons that rapidly diffuse. This interchange of singlet and triplet excitons shuttles triplets as far as 205 nm within the first 500 ps after photoexcitation. This enhanced transport comes at a cost, however, as it necessitates favoring triplet recombination and thus requires fine-tuning of SF dynamics to balance triplet yields with triplet transport lengths. Through numerical modeling, we predict tuning the ratio of SF and TF rate constants, kSF/kTF, to between 1.9 and 3.8 allows for an optimized triplet transport length (425-563 nm) with minimal loss (7-10%) in triplet yield. Interestingly, by adjusting the size of EP-PDI crystals, we find that we can subtly tune their crystal structure and thereby alter their SF and TF rates. By slowing SF within small EP-PDI crystals, we are able to boost their triplet transport length by ∼20%. Although counterintuitive, our work suggests slowing SF by introducing moderate structural distortions can be preferential when optimizing triplet exciton transport, provided singlet exciton transport is not significantly hindered.

Exciton diffusion in organic semiconductors: precision and pitfalls

Nanometer exciton diffusion is a fundamental process important in virtually all applications of organic semiconductors. Many measurement techniques have been developed to measure exciton diffusion length (LD) at the nanometer scale; however, these techniques have common challenges that the community has worked for decades to overcome. In this perspective, we lay out the principal challenges researchers need to overcome to obtain an accurate measurement of LD. We then examine the most common techniques used to measure LD with respect to these challenges and describe solutions developed to overcome them. This analysis leads to the suggestion that static quenching techniques underestimate LD due to uncertainties in the quenching behavior, while time-resolved exciton-exciton annihilation (EEA) techniques overestimate LD based on experimental conditions, we advance steady-state EEA techniques as an alternative that overcome many of the challenges of these other techniques while preserving accuracy. We support this hypothesis with a meta-analysis of LD measured across various organic semiconductors and measurement techniques. We intend this investigation to provide a framework for researchers to interpret and compare findings across measurement techniques and to guide researchers on how to obtain the most accurate results for each technique in question.

Chirality in Singlet Fission: Controlling Singlet Fission in Aqueous Nanoparticles of Tetracenedicarboxylic Acid Ion Pairs

The singlet fission characteristics of aqueous nanoparticles, self-assembled from ion pairs of tetracene dicarboxylic acid and various amines with or without chirality, are thoroughly investigated. The structure of the ammonium molecule, the counterion, is found to play a decisive role in determining the molecular orientation of the ion pairs and its regularity, spectroscopic properties, the strength of the intermolecular coupling between the tetracene chromophores, and the consequent singlet fission process. Using chiral amines has led to the formation of crystalline nanosheets and efficient singlet fission with a triplet quantum yield as high as 133% ±20% and a rate constant of 6.99 × 109 s-1. The chiral ion pairs also provide a separation channel to free triplets with yields as high as 33% ±10%. In contrast, nanoparticles with achiral counterions do not show singlet fission, which gave low or high fluorescence quantum yields depending on the size of the counterions. The racemic ion pair produces a correlated triplet pair intermediate by singlet fission, but no decorrelation into two free triplets is observed, as triplet-triplet annihilation dominates. The introduction of chirality enables higher control over orientation and singlet fission in self-assembled chromophores. It provides new design guidelines for singlet fission materials.

Surface Loading Dictates Triplet Production via Singlet Fission in Anthradithiophene Sensitized TiO2 Films

Singlet fission, the process of transforming a singlet excited state into two lower energy triplet excited states, is a promising strategy for improving the efficiency of dye-sensitized solar cells. The difficulty in utilizing singlet fission molecules in this architecture is understanding and controlling the orientation of dyes on mesoporous metal oxide surfaces to maximize triplet production and minimize detrimental deactivation pathways, such as electron injection from the singlet or excimer formation. Here, we varied the concentration of loading solutions of two anthradithiophene dyes derivatized with either one or two carboxylic acid groups for binding to a metal oxide surface and studied their photophysics using ultrafast transient absorption spectroscopy. For the single carboxylic acid case, an increase in dye surface coverage led to an increase in apparent triplet excited-state growth via singlet fission, while the same increase in coverage with two carboxylic acids did not. This study represents a step toward controlling the interactions between molecules at mesoporous interfaces.

Transport, trapping, triplet fusion: thermally retarded exciton migration in tetracene single crystals

Efficient exciton migration is crucial for optoelectronic organic devices. While the transport of triplet excitons is generally slow compared to singlet excitons, triplet exciton migration in certain molecular semiconductors with endothermic singlet fission appears to be enhanced by a time-delayed regeneration of the more mobile singlet species via triplet fusion. This combined transport mechanism could be exploited for devices, but the interplay between singlet fission and triplet fusion, as well as the role of trap states is not yet well understood. Here, we study the spatiotemporal exciton dynamics in the singlet fission material tetracene by means of time resolved photoluminescence micro-spectroscopy on crystalline samples of different quality. Varying the temperature allows us to modify the dynamic equilibrium between singlet, triplet and trapped excitons. Supported by a kinetic model, we find that thermally activated dissociation of triplet pairs into free triplet excitons can account for an increase of the diffusion length below room temperature. Moreover, we demonstrate that trapping competes efficiently with exciton migration.

Hot Carrier Trapping and It's Influence to the Carrier Diffusion in CsPbBr3 Perovskite Film Revealed by Transient Absorption Microscopy

The defects in perovskite film can cause charge carrier trapping which shortens carrier lifetime and diffusion length. So defects passivation has become promising for the perovskite studies. However, how defects disturb the carrier transport and how the passivating affects the carrier transport in CsPbBr3 are still unclear. Here the carrier dynamics and diffusion processes of CsPbBr3 and LiBr passivated CsPbBr3 films are investigated by using transient absorption spectroscopy and transient absorption microscopy. It's found that there is a fast hot carrier trapping process with the above bandgap excitation, and the hot carrier trapping would decrease the population of cold carriers which are diffusible, then lower the carrier diffusion constant. It's proved that LiBr can passivate the defect and lower the trapping probability of hot carriers, thus improve the carrier diffusion rate. The finding demonstrates the influence of hot carrier trapping to the carrier diffusion in CsPbBr3 film.

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe-Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

Giant magneto-photoluminescence at ultralow field in organic microcrystal arrays for on-chip optical magnetometer

Optical detection of magnetic field is appealing for integrated photonics; however, the light-matter interaction is usually weak at low field. Here we observe that the photoluminescence (PL) decreases by > 40% at 10 mT in rubrene microcrystals (RMCs) prepared by a capillary-bridge assembly method. The giant magneto-PL (MPL) relies on the singlet-triplet conversion involving triplet-triplet pairs, through the processes of singlet fission (SF) and triplet fusion (TF) during radiative decay. Importantly, the size of RMCs is critical for maximizing MPL as it influences on the photophysical processes of spin state conversion. The SF/TF process is quantified by measuring the prompt/delayed PL with time-resolved spectroscopies, which shows that the geminate SF/TF associated with triplet-triplet pairs are responsible for the giant MPL. Furthermore, the RMC-based magnetometer is constructed on an optical chip, which takes advantages of remarkable low-field sensitivity over a broad range of frequencies, representing a prototype of emerging opto-spintronic molecular devices.

Long-Lived Charge Separation in Single Crystals of an Electron Donor Covalently Linked to Four Acceptor Molecules

Crystalline donor-acceptor (D-A) systems serve as an excellent platform for studying CT exciton creation, migration, and dissociation into free charge carriers for solar energy conversion. Donor-acceptor cocrystals have been utilized to develop an understanding of CT exciton formation in ordered organic solids; however, the strong electronic coupling of the D and A units can sometimes limit charge separation lifetimes due to their close proximity. Covalent D-A systems that preorganize specific donor-acceptor structures can assist in engineering crystal morphologies that promote long-lived charge separation to overcome this limitation. Here we investigate photogenerated CT exciton formation in a single crystal of a 2,5,8,11-tetraphenylperylene (PerPh4) donor to which four identical naphthalene-(1,4:5,8)-bis(dicarboximide) (NDI) electron acceptors are covalently attached at the para positions of the PerPh4 phenyl groups to yield PerPh4-NDI4. X-ray crystallography shows that the four NDIs pack pairwise into two distinct motifs. Two NDI acceptors of one PerPh4-NDI4 are positioned over the PerPh4 donors of adjacent PerPh4-NDI4 molecules with the donor and acceptor π-systems having a large dihedral angle between them, while the other two NDIs of PerPh4-NDI4 form xylene-NDI van der Waals π-stacks with the corresponding NDIs in adjacent PerPh4-NDI4 molecules. Upon selective photoexcitation of PerPh4 in the single crystal, CT exciton formation occurs in <300 fs yielding electron-hole pairs that live for more than ∼16 μs. This demonstrates the effectiveness of covalently linked D-A systems for engineering single crystal structures that promote efficient and long-lived charge separation for solar energy conversion.

Phonon-Driven Femtosecond Dynamics of Excitons in Crystalline Pentacene from First Principles

Nonradiative exciton relaxation processes are critical for energy transduction and transport in optoelectronic materials, but how these processes are connected to the underlying crystal structure and the associated electron, exciton, and phonon band structures, as well as the interactions of all these particles, is challenging to understand. Here, we present a first-principles study of exciton-phonon relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyze key scattering channels. We find that both exciton intraband scattering and interband scattering to parity-forbidden dark states occur on the same ∼100  fs timescale as a direct consequence of the longitudinal-transverse splitting of the bright exciton band. Consequently, exciton-phonon scattering exists as a dominant nonradiative relaxation channel in pentacene. We further show how the propagation of an exciton wave packet is connected with crystal anisotropy, which gives rise to the longitudinal-transverse exciton splitting and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding the role of exciton-phonon interactions in exciton nonradiative lifetimes in molecular crystals and beyond.

Efficient Spin Interconversion by Molecular Conformation Dynamics of a Triplet Pair for Photon Up-Conversion in an Amorphous Solid

Solid-state materials with improved light-to-energy conversions in organic photovoltaics and in optoelectronics are expected to be developed by realizing efficient triplet-triplet annihilation (TTA) by manipulating the spin conversion processes to the singlet state. In this study, we elucidate the spin conversion mechanism for delayed fluorescence by TTA from a microscopic view of the molecular conformations. We examine the time evolution of the electron spin polarization of the triplet-pair state (TT state) in an amorphous solid-state system exhibiting highly efficient up-conversion emission by using time-resolved electron paramagnetic resonance. We clarified that the spin-state population of the singlet TT increased through the spin interconversion from triplet and quintet TT states during exciton diffusion with random orientation dynamics between the two triplets for the modulation of the exchange interaction, achieving a high quantum yield of up-conversion emission. This understanding provides us with a guide for the development of efficient light-to-energy conversion devices utilizing TTA.

Impact of Photoluminescence Imaging Methodology on Transport Parameters in Semiconductors

Triplet-triplet annihilation-induced delayed emission provides a pathway for investigating triplets via emission spectroscopy. This bimolecular annihilation depends directly on the transport properties of triplet excitons in disordered organic semiconductors. Photoluminescence (PL) imaging is a direct method for studying exciton and charge-carrier diffusivity. However, most of these studies neglect dispersive transport. Early time scale measurements using this technique can lead to an overestimation of the diffusion coefficient (DT) or diffusion length (Ld). In this study, we investigated the time-dependent triplet DT using PL imaging. We observed an overestimation of Ld in classical delayed PL imaging, often 1 order of magnitude higher than the actual Ld value. We compared various thicknesses of polymeric thin films to study the dispersive nature of triplet excitons. Transient analysis of delayed PL imaging and steady state imaging reveals the importance of considering the time-dependent nature of DT for the triplet excitons in disordered electronic materials.

Structured Excitation Energy Transfer: Tracking Exciton Diffusion below Sunlight Intensity

With the increasing demand for new materials for light-harvesting applications, spatiotemporal microscopy techniques are receiving increasing attention as they allow direct observation of the nanoscale diffusion of excitons. However, the use of pulsed and tightly focused laser beams generates light intensities far above those expected under sunlight illumination, leading to photodamage and nonlinear effects that seriously limit the accuracy and applicability of these techniques, especially in biological or atomically thin materials. In this work, we present a novel spatiotemporal microscopy technique that exploits structured excitation in order to dramatically decrease the excitation intensity, up to 10,000-fold when compared with previously reported spatiotemporal photoluminescence microscopy experiments. We tested our method in two different systems, reporting the first exciton diffusion measurement at illumination conditions below sunlight, both considering average power and peak exciton densities in an organic photovoltaic sample (Y6), where we tracked the excitons for up to five recombination lifetimes. Next, nanometer-scale energy transport was directly observed for the first time in both space and time in a printed monolayer of the light-harvesting complex 2 from purple bacteria.

Time-Resolved Spectroscopy for Dynamic Investigation of Photoresponsive Metal-Organic Frameworks

Photoresponsive MOFs with precise and adjustable reticular structures are attractive for light conversion applications. Uncovering the photoinduced carrier dynamics lays the essential foundation for the further development and optimization of the MOF material. With the application of time-resolved spectroscopy, photophysical processes including excimer formation, energy transfer/migration, and charge transfer/separation have been widely investigated. However, the identification of distinct photophysical processes in real experimental MOF spectra still remains difficult due to the spectral and dynamic complexity of MOFs. In this Perspective, we summarize the typical spectral features of these photophysical processes and the related analysis methods for dynamic studies performed by time-resolved photoluminescence (TR-PL) and transient absorption (TA) spectroscopy. Based on the recent understanding of excited-state properties of photoresponsive MOFs and the discussion of challenges and future outlooks, this Perspective aims to provide convenience for MOF kinetic analysis and contribute to the further development of photoresponsive MOF material.

Methylation of Si(111) Modulates Molecular Orientation in Perylenediimide Thin Films

Singlet fission produces a pair of low-energy spin-triplet excitons from a single high-energy spin-singlet exciton. While this process offers the potential to enhance the efficiency of silicon solar cells by ∼30%, meeting this goal requires overlayer materials that can efficiently transport triplet excitons to an underlying silicon substrate. Herein, we demonstrate that the chemical functionalization of silicon surfaces controls the structure of vapor-deposited thin films of perylenediimide (PDI) dyes, which are prototypical singlet fission materials. Using a combination of atomic force microscopy (AFM) and grazing-incidence wide-angle X-ray scattering (GIWAXS), we find terminating Si(111) with either a thin, polar oxide layer (SiOx) or with hydrophobic methyl groups (Si-CH3) alters the structures of the resulting PDI films. While PDI films grown on SiOx are comprised of small crystalline grains that largely adopt an "edge-on" orientation with respect to the silicon surface, films grown on Si-CH3 contain large grains that prefer to align in a "face-on" manner with respect to the substrate. This "face-on" orientation is expected to enhance exciton transport to silicon. Interestingly, we find that the preferred mode of growth for different PDIs correlates with the space group associated with bulk crystals of these compounds. While PDIs that inhabit a monoclinic (P21/c) space group nucleate films by forming tall and sparse crystalline columns, PDIs that inhabit triclinic (P1̅) space groups afford films comprised of uniform, lamellar PDI domains. The results highlight that silicon surface functionalization profoundly impacts PDI thin film growth, and rational selection of a hydrophobic surface that promotes "face-on" adsorption may improve energy transfer to silicon.

Dual-Hyperspectral Optical Pump-Probe Microscopy with Single-Nanosecond Time Resolution

In recent years, optical pump-probe microscopy (PPM) has become a vital technique for spatiotemporally imaging electronic excitations and charge-carrier transport in metals and semiconductors. However, existing methods are limited by mechanical delay lines with a probe time window up to several nanoseconds (ns) or monochromatic pump and probe sources with restricted spectral coverage and temporal resolution, hindering their amenability in studying relatively slow processes. To bridge these gaps, we introduce a dual-hyperspectral PPM setup with a time window spanning from nanoseconds to milliseconds and single-nanosecond resolution. Our method features a wide-field probe tunable from 370 to 1000 nm and a pump spanning from 330 nm to 16 μm. We apply this PPM technique to study various two-dimensional metal-halide perovskites (2D-MHPs) as representative semiconductors by imaging their transient responses near the exciton resonances under both above-band gap electronic pump excitation and below-band gap vibrational pump excitation. The resulting spatially and temporally resolved images reveal insights into heat dissipation, film uniformity, distribution of impurity phases, and film-substrate interfaces. In addition, the single-nanosecond temporal resolution enables the imaging of in-plane strain wave propagation in 2D-MHP single crystals. Our method, which offers extensive spectral tunability and significantly improved time resolution, opens new possibilities for the imaging of charge carriers, heat, and transient phase transformation processes, particularly in materials with spatially varying composition, strain, crystalline structure, and interfaces.

Above 100% Efficiency Photocharge Generation in Monolayer Semiconductors by Singlet Fission Sensitization

Sensitizing inorganic semiconductors using singlet fission (SF) materials, which produce two excitons from one absorbed photon, can potentially boost their light-to-electricity conversion efficiency. The SF sensitization is particularly exciting for two-dimensional (2D) layered semiconductors with atomically flat surface and high carrier mobility but limited light absorption. However, efficiently harnessing triplet excitons from SF by charge transfer at organic/inorganic interface has been challenging, and the intricate interplay among competing processes remains unresolved. Here, we investigate SF sensitization in high-quality organic/2D bilayer heterostructures featuring TIPS-Pc single crystals. Through transient magneto-optical spectroscopy, we demonstrate that despite an ultrafast SF process in sub-100 fs, a significant fraction of singlet excitons in TIPS-Pc dissociate at the interface before fission, while triplet excitons from SF undergo diffusion-limited charge transfer at the interface in ∼10 ps to ns. Remarkably, the photocharge generation efficiency reaches 126% in heterostructures with optimal thickness, resulting from the competitive interplay between singlet exciton fission, dissociation, and triplet exciton transport. This presents a promising strategy for advancing SF-enhanced 2D optoelectronics beyond the conventional limits.

Exciton annihilation in molecular aggregates suppressed through qu antum interference

Exciton-exciton annihilation (EEA), an important loss channel in optoelectronic devices and photosynthetic complexes, has conventionally been assumed to be an incoherent, diffusion-limited process. Here we challenge this assumption by experimentally demonstrating the ability to control EEA in molecular aggregates using the quantum phase relationships of excitons. We employed time-resolved photoluminescence microscopy to independently determine exciton diffusion constants and annihilation rates in two substituted perylene diimide aggregates featuring contrasting excitonic phase envelopes. Low-temperature EEA rates were found to differ by more than two orders of magnitude for the two compounds, despite comparable diffusion constants. Simulated rates based on a microscopic theory, in excellent agreement with experiments, rationalize this EEA behaviour based on quantum interference arising from the presence or absence of spatial phase oscillations of delocalized excitons. These results offer an approach for designing molecular materials using quantum interference where low annihilation can coexist with high exciton concentrations and mobilities.

Theoretical Description of Attosecond X-ray Absorption Spectroscopy of Frenkel Exciton Dynamics

Frenkel excitons are responsible for the transport of light energy in many molecular systems. Coherent electron dynamics govern the initial stage of Frenkel-exciton transfer. Capability to follow coherent exciton dynamics in real time will help to reveal their actual contribution to the efficiency of light-harvesting. Attosecond X-ray pulses are the tool with the necessary temporal resolution to resolve pure electronic processes with atomic sensitivity. We describe how attosecond X-ray pulses can probe coherent electronic processes during Frenkel-exciton transport in molecular aggregates. We analyze time-resolved absorption cross section taking broad spectral bandwidth of an attosecond pulse into account. We demonstrate that attosecond X-ray absorption spectra can reveal delocalization degree of coherent exciton transfer dynamics.

From enhanced diffusion to ultrafast ballistic motion of hybrid light-matter excitations

Transport of excitons and charge carriers in molecular systems can be enhanced by coherent coupling to photons, giving rise to the formation of hybrid excitations known as polaritons. Such enhancement has far-reaching technological implications; however, the enhancement mechanism and the transport nature of these hybrid excitations remain elusive. Here we map the ultrafast spatiotemporal dynamics of polaritons formed by mixing surface-bound optical waves with Frenkel excitons in a self-assembled molecular layer, resolving polariton dynamics in energy/momentum space. We find that the interplay between the molecular disorder and long-range correlations induced by coherent mixing with light leads to a mobility transition between diffusive and ballistic transport, which can be controlled by varying the light-matter composition of the polaritons. Furthermore, we show that coupling to light enhances the diffusion coefficient of molecular excitons by six orders of magnitude and even leads to ballistic flow at two-thirds the speed of light.

Singlet fission preserves polarisation correlation of excitons

Singlet fission (SF) holds the promise to circumvent the photovoltaic efficiency limit to reach a power-conversion efficiency above 34%. SF of TIPS-pentacene (TIPS-Pn) has been investigated but its mechanism is yet to be well elucidated. Recently, we developed a nanoparticle (NP) system, in which doping of TIPS-Pn in a host matrix yields a range of average intermolecular distances, d, to study the dependence of SF in TIPS-Pn on d. At large d values, where the bimolecular SF process should be unfavourable, a relatively high SF quantum yield (Φ_SF) is still observed, which implies a deviation from a random distribution of TIPS-Pn throughout the NP. Here, using polarisation-sensitive femtosecond time-resolved spectroscopy and Monte Carlo simulations of exciton migration and SF, we quantify the level of clustering of TIPS-Pn in the host matrix, which is responsible for the higher than expected Φ_SF. The experimental data indicate a preservation of polarisation correlation by SF, which is uncommon because energy transfer in amorphous materials tends to result in depolarisation. We show that the preservation of polarisation correlation is due to SF upon exciton migration. Although exciton migration decorrelates polarisation, SF acts to remove decorrelated excitons to give an overall preservation of polarisation correlation.

A pre-time-zero spatiotemporal microscopy technique for the ultrasensitive determination of the thermal diffusivity of thin films

Diffusion is one of the most ubiquitous transport phenomena in nature. Experimentally, it can be tracked by following point spreading in space and time. Here, we introduce a spatiotemporal pump-probe microscopy technique that exploits the residual spatial temperature profile obtained through the transient reflectivity when probe pulses arrive before pump pulses. This corresponds to an effective pump-probe time delay of 13 ns, determined by the repetition rate of our laser system (76 MHz). This pre-time-zero technique enables probing the diffusion of long-lived excitations created by previous pump pulses with nanometer accuracy and is particularly powerful for following in-plane heat diffusion in thin films. The particular advantage of this technique is that it enables quantifying thermal transport without requiring any material input parameters or strong heating. We demonstrate the direct determination of the thermal diffusivities of films with a thickness of around 15 nm, consisting of the layered materials MoSe₂ (0.18 cm²/s), WSe₂ (0.20 cm²/s), MoS₂ (0.35 cm²/s), and WS₂ (0.59 cm²/s). This technique paves the way for observing nanoscale thermal transport phenomena and tracking diffusion of a broad range of species.

Direct Exciton Harvesting from a Bound Triplet Pair

Singlet fission is commonly defined as the generation of two triplet excitons from a single absorbed photon. However, ambiguities within this definition arise due to the complexity of the various double triplet states that exist in SF chromophores and the corresponding interconversion processes. To clarify this process, singlet fission is frequently depicted as sequential two-step conversion in which a singlet exciton decays into a bound triplet-pair biexciton state that dissociates into two "free" triplet excitons. However, this model discounts the potential for direct harvesting from the coupled biexciton state. Here, it is demonstrated that individual triplet excitons can be extracted directly from a bound triplet pair. It is demonstrated that due to the requirement for geminate triplet-triplet annihilation in intramolecular singlet fission compounds, unique spectral and kinetic signatures can be used to quantify triplet-pair harvesting yields. An internal quantum efficiency for triplet exciton transfer from the triplet pair of >50%, limited only by the solubility of the compounds is achieved. The harvesting process is not dependent on the net multiplicity of the triplet-pair state, suggesting that an explicit, independent dissociation step is not a requirement for using triplet pairs to do chemical or electrical work.

Decrypting Material Performance by Wide-field Femtosecond Interferometric Imaging of Energy Carrier Evolution

Energy carrier evolution is crucial for material performance. Ultrafast microscopy has been widely applied to visualize the spatiotemporal evolution of energy carriers. However, direct imaging of a small amount of energy carriers on the nanoscale remains difficult due to extremely weak transient signals. Here, we present a method for ultrasensitive and high-throughput imaging of energy carrier evolution in space and time. This method combines femtosecond pump-probe techniques with interferometric scattering microscopy (iSCAT), named Femto-iSCAT. The interferometric principle and unique spatially modulated contrast enhancement enable the exploration of new science. We address three important and challenging problems: transport of different energy carriers at various interfaces, heterogeneous hot-electron distribution and relaxation in single plasmonic resonators, and distinct structure-dependent edge-state dynamics of carriers and excitons in optoelectronic semiconductors. Femto-iSCAT holds great potential as a universal tool for ultrasensitive imaging of energy carrier evolution in space and time.

High ambipolar mobility in cubic boron arsenide revealed by transient reflectivity microscopy

Semiconducting cubic boron arsenide (c-BAs) has been predicted to have carrier mobility of 1400 square centimeters per volt-second for electrons and 2100 square centimeters per volt-second for holes at room temperature. Using pump-probe transient reflectivity microscopy, we monitored the diffusion of photoexcited carriers in single-crystal c-BAs to obtain their mobility. With near-bandgap 600-nanometer pump pulses, we found a high ambipolar mobility of 1550 ± 120 square centimeters per volt-second, in good agreement with theoretical prediction. Additional experiments with 400-nanometer pumps on the same spot revealed a mobility of >3000 square centimeters per volt-second, which we attribute to hot electrons. The observation of high carrier mobility, in conjunction with high thermal conductivity, enables an enormous number of device applications for c-BAs in high-performance electronics and optoelectronics.

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.

Quantifying Exciton Transport in Singlet Fission Diblock Copolymers

Singlet fission (SF) is a mechanism of exciton multiplication in organic chromophores, which has potential to drive highly efficient optoelectronic devices. Creating effective device architectures that operate by SF critically depends on electronic interactions across multiple length scales─from individual molecules to interchromophore interactions that facilitate multiexciton dephasing and exciton diffusion toward donor-acceptor interfaces. Therefore, it is imperative to understand the underpinnings of multiexciton transport and interfacial energy transfer in multichromophore systems. Interestingly, block copolymers (BCPs) can be designed to control multiscale interactions by tailoring the nature of the building blocks, yet SF dynamics are not well understood in these macromolecules. Here, we designed diblock copolymers comprising an inherent energy cleft at the interface between a block with pendent pentacene chromophores and an additional block with pendent tetracene chromophores. The singlet and triplet energy offset between the two blocks creates a driving force for exciton transport along the BCP chain in dilute solution. Using time-resolved optical spectroscopy, we have quantified the yields of key energy transfer steps, including both singlet and triplet energy transfer processes across the pentacene-tetracene interface. From this modular BCP architecture, we correlate the energy transfer time scales and relative yields with the length of each block. The ability to quantify these energy transfer processes provides valuable insights into exciton transport at critical length scales between bulk crystalline systems and small-molecule dimers─an area that has been underexplored.

Singlet fission and triplet pair recombination in bipentacenes with a twist

We investigate triplet pair dynamics in pentacene dimers that have varying degrees of coplanarity (pentacene-pentacene twist angle). The fine-tuning of the twist angle was achieved by alternating connectivity at the 1-position or 2-positions of pentacene. This mix-and-match connectivity leads to tunable twist angles between the two covalently linked pentacenes. These twisted dimers allow us to investigate the subtle effects that the dihedral angle between the covalently linked pentacenes imparts on singlet fission and triplet pair recombination dynamics. We observe that as the dihedral angle between the two bonded pentacenes is increased, the rates of singlet fission decrease, while the accompanying decrease in triplet recombination rates is stark. Temperature-dependent transient optical studies combined with theoretical calculations show that the triplet pair recombination proceeds primarily through a direct multiexciton internal conversion process. Calculations further show that the significant decrease in recombination rates can be directly attributed to a corresponding decrease in the magnitude of the nonadiabatic coupling between the singlet multiexcitonic state and the ground state. These results highlight the importance of the twist angle in designing systems that exhibit rapid singlet fission, while maintaining long triplet pair lifetimes in pentacene dimers.

Efficient long-range triplet exciton transport by metal-metal interaction at room temperature

Efficient and long-range exciton transport is critical for photosynthesis and opto-electronic devices, and for triplet-harvesting materials, triplet exciton diffusion length ( [[EQUATION]] ) and coefficient ( [[EQUATION]] ) are key parameters in determining their performances. Herein, we observed that PtII and PdII organometallic nanowires exhibit long-range anisotropic triplet exciton LD of 5-7 μm along the M-M direction using direct photoluminescence (PL) imaging technique by low-power continuous wave (CW) laser excitation. At room temperature, via a combined triplet-triplet annihilation (TTA) analysis and spatial PL imaging, an efficient triplet exciton diffusion was observed for the PtII and PdII nanowires with extended close M-M contact, while is absent in nanowires without close M-M contact. Two-dimensional electronic spectroscopy (2DES) and calculations revealed a significant contribution of the delocalized 1/3[dσ*(M-M)→π*] excited state during the exciton diffusion modulated by the M-M distance.

All-optical manipulation of singlet exciton transport in individual supramolecular nanostructures by triplet gating

Directed transport of singlet excitation energy is a key process in natural light-harvesting systems and a desired feature in assemblies of functional organic molecules for organic electronics and nanotechnology applications. However, progress in this direction is hampered by the lack of concepts and model systems. Here we demonstrate an all-optical approach to manipulate singlet exciton transport pathways within supramolecular nanostructures via singlet-triplet annihilation, i.e., to enforce an effective motion of singlet excitons along a predefined direction. For this proof-of-concept, we locally photo-generate a long-lived triplet exciton population and subsequently a singlet exciton population on single bundles of H-type supramolecular nanofibres using two temporally and spatially separated laser pulses. The local triplet exciton population operates as a gate for the singlet exciton transport since singlet-triplet annihilation hinders singlet exciton motion across the triplet population. We visualize this manipulation of singlet exciton transport via the fluorescence signal from the singlet excitons, using a detection-beam scanning approach combined with time-correlated single-photon counting. Our reversible, all-optical manipulation of singlet exciton transport can pave the way to realising new design principles for functional photonic nanodevices.

Revealing the Contest between Triplet-Triplet Exchange and Triplet-Triplet Energy Transfer Coupling in Correlated Triplet Pair States in Singlet Fission

Understanding the separation of the correlated triplet pair state ¹(TT) intermediate is critical for leveraging singlet fission to improve solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into ¹(TT),³(TT) and ⁵(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state ¹(T···T). We develop a simple ab initio technique to compute both the biexciton exchange (K) and biexciton transfer coupling. Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene.

Exciton Modulation in Perylene-Based Molecular Crystals Upon Formation of a Metal-Organic Interface From Many-Body Perturbation Theory

Excited-state processes at organic-inorganic interfaces consisting of molecular crystals are essential in energy conversion applications. While advances in experimental methods allow direct observation and detection of exciton transfer across such junctions, a detailed understanding of the underlying excitonic properties due to crystal packing and interface structure is still largely lacking. In this work, we use many-body perturbation theory to study structure-property relations of excitons in molecular crystals upon adsorption on a gold surface. We explore the case of the experimentally-studied octyl perylene diimide (C8-PDI) as a prototypical system, and use the GW and Bethe-Salpeter equation (BSE) approach to quantify the change in quasiparticle and exciton properties due to intermolecular and substrate screening. Our findings provide a close inspection of both local and environmental structural effects dominating the excitation energies and the exciton binding and nature, as well as their modulation upon the metal-organic interface composition.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reineker model to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Signatures of Dimensionality and Symmetry in Exciton Band Structure: Consequences for Exciton Dynamics and Transport

Exciton dynamics, lifetimes, and scattering are directly related to the exciton dispersion or band structure. Here, we present a general theory for exciton band structure within both ab initio and model Hamiltonian approaches. We show that contrary to common assumption, the exciton band structure contains nonanalytical discontinuities-a feature which is impossible to obtain from the electronic band structure alone. These discontinuities are purely quantum phenomena, arising from the exchange scattering of electron-hole pairs. We show that the degree of these discontinuities depends on materials' symmetry and dimensionality, with jump discontinuities occurring in 3D and different orders of removable discontinuities in 2D and 1D, whose details depend on the exciton degeneracy and material thickness. We connect these features to the early stages of exciton dynamics, radiative lifetimes, and diffusion constants, in good correspondence with recent experimental observations, revealing that the discontinuities in the band structure lead to ultrafast ballistic transport and suggesting that measured exciton diffusion and dynamics are influenced by the underlying exciton dispersion.

Formally exact simulations of mesoscale exciton dynamics in molecular materials

Excited state carriers, such as excitons, can diffuse on the 100 nm to micron length scale in molecular materials but only delocalize over short length scales due to coupling between electronic and vibrational degrees-of-freedom. Here, we leverage the locality of excitons to adaptively solve the hierarchy of pure states equations (HOPS). We demonstrate that our adaptive HOPS (adHOPS) methodology provides a formally exact and size-invariant (i.e., ) scaling algorithm for simulating mesoscale quantum dynamics. Finally, we provide proof-of-principle calculations for exciton diffusion on linear chains containing up to 1000 molecules.

The adaptive hierarchy of pure states (adHOPS) algorithm leverages the locality of excitons in molecular materials to perform formally-exact simulations with size-invariant (i.e., ) scaling, enabling efficient simulations of mesoscale exciton dynamics.

Fully Quantum Modeling of Exciton Diffusion in Mesoscale Light Harvesting Systems

It has long been a challenge to accurately and efficiently simulate exciton-phonon dynamics in mesoscale photosynthetic systems with a fully quantum mechanical treatment due to extensive computational resources required. In this work, we tackle this seemingly intractable problem by combining the Dirac-Frenkel time-dependent variational method with Davydov trial states and implementing the algorithm in graphic processing units. The phonons are treated on the same footing as the exciton. Tested with toy models, which are nanoarrays of the B850 pigments from the light harvesting 2 complexes of purple bacteria, the methodology is adopted to describe exciton diffusion in huge systems containing more than 1600 molecules. The superradiance enhancement factor extracted from the simulations indicates an exciton delocalization over two to three pigments, in agreement with measurements of fluorescence quantum yield and lifetime in B850 systems. With fractal analysis of the exciton dynamics, it is found that exciton transfer in B850 nanoarrays exhibits a superdiffusion component for about 500 fs. Treating the B850 ring as an aggregate and modeling the inter-ring exciton transfer as incoherent hopping, we also apply the method of classical master equations to estimate exciton diffusion properties in one-dimensional (1D) and two-dimensional (2D) B850 nanoarrays using derived analytical expressions of time-dependent excitation probabilities. For both coherent and incoherent propagation, faster energy transfer is uncovered in 2D nanoarrays than 1D chains, owing to availability of more numerous propagating channels in the 2D arrangement.

Free-triplet generation with improved efficiency in tetracene oligomers through spatially separated triplet pair states

Singlet fission (SF) can potentially boost the efficiency of solar energy conversion by converting a singlet exciton (S₁) into two free triplets (T₁ + T₁) through an intermediate state of a correlated triplet pair (TT). Although efficient TT generation has been recently realized in many intramolecular SF materials, their potential applications have been hindered by the poor efficiency of TT dissociation. Here we demonstrate that this can be overcome by employing a spatially separated ¹(T…T) state with weak intertriplet coupling in tetracene oligomers with three or more chromophores. By using transient magneto-optical spectroscopic methods, we show that free-triplet generation can be markedly enhanced through the SF pathway that involves the spatially separated ¹(T…T) state rather than the pathway mediated by the spatially adjacent TT state, leading to a marked improvement in free-triplet generation with an efficiency increase from 21% for the dimer to 85% (124%) for the trimer (tetramer).

Direct Transition from Triplet Excitons to Hybrid Light-Matter States via Triplet-Triplet Annihilation

Strong light–matter coupling generates hybrid states that inherit properties of both light and matter, effectively allowing the modification of the molecular potential energy landscape. This phenomenon opens up a plethora of options for manipulating the properties of molecules, with a broad range of applications in photochemistry and photophysics. In this article, we use strong light–matter coupling to transform an endothermic triplet–triplet annihilation process into an exothermic one. The resulting gradual on–off photon upconversion experiment demonstrates a direct conversion between molecular states and hybrid light–matter states. Our study provides a direct evidence that energy can relax from nonresonant low energy molecular states directly into hybrid light–matter states and lays the groundwork for tunable photon upconversion systems that modify molecular properties in situ by optical cavities rather than with chemical modifications.

Nanoscale Disorder Generates Subdiffusive Heat Transport in Self-Assembled Nanocrystal Films

Investigating the impact of nanoscale heterogeneity on heat transport requires a spatiotemporal probe of temperature on the length and time scales intrinsic to heat navigating nanoscale defects. Here, we use stroboscopic optical scattering microscopy to visualize nanoscale heat transport in disordered films of gold nanocrystals. We find that heat transport appears subdiffusive at the nanoscale. Finite element simulations show that tortuosity of the heat flow underlies the subdiffusive transport, owing to a distribution of nonconductive voids. Thus, while heat travels diffusively through contiguous regions of the film, the tortuosity causes heat to navigate circuitous pathways that make the observed mean-squared expansion of an initially localized temperature distribution appear subdiffusive on length scales comparable to the voids. Our approach should be broadly applicable to uncover the impact of both designed and unintended heterogeneities in a wide range of materials and devices that can affect more commonly used spatially averaged thermal transport measurements.

Effective Negative Diffusion of Singlet Excitons in Organic Semiconductors

Using diffraction-limited ultrafast imaging techniques, we investigate the propagation of singlet and triplet excitons in single-crystal tetracene. Instead of an expected broadening, the distribution of singlet excitons narrows on a nanosecond time scale after photoexcitation. This narrowing results in an effective negative diffusion in which singlet excitons migrate toward the high-density region, eventually leading to a singlet exciton distribution that is smaller than the laser excitation spot. Modeling the excited-state dynamics demonstrates that the origin of the anomalous diffusion is rooted in nonlinear triplet-triplet annihilation (TTA). We anticipate that this is a general phenomenon that can be used to study exciton diffusion and nonlinear TTA rates in semiconductors relevant for organic optoelectronics.

Device-Based Probe of Triplet Exciton Diffusion in Singlet Fission Materials

Probing triplet transport in singlet fission materials can be challenging due to the presence of multiple diffusing species. We present a device-based method to measure the intrinsic triplet diffusion length (L_D) in organic semiconductor thin films exhibiting singlet fission. Triplet states are optically injected into the singlet fission material of interest via energy transfer from an adjacent thin film characterized by strong spin-orbit coupling. Injected triplets migrate through the full thickness of the material before undergoing dissociation at a donor-acceptor interface. By modeling the ratio of injector and acceptor photocurrent as a function of layer thickness, the triplet L_D is extracted separate from processes of unknown efficiency including singlet fission and diffusion. In considering three archetypical fission systems, a wide range is found for the triplet L_D, ranging from 3.3 ± 0.4 nm for 5,12-bis((triisopropylsilyl)ethynyl)tetracene to 17.1 ± 1.3 nm for pentacene and 32.1 ± 2.6 nm for tetracene.

Using temperature dependent fluorescence to evaluate singlet fission pathways in tetracene single crystals

The temperature-dependent fluorescence spectrum, decay rate, and spin quantum beats are examined in single tetracene crystals to gain insight into the mechanism of singlet fission. Over the temperature range of 250 K-500 K, the vibronic lineshape of the emission indicates that the singlet exciton becomes localized at 400 K. The fission process is insensitive to this localization and exhibits Arrhenius behavior with an activation energy of 550 ± 50 cm^-1. The damping rate of the triplet pair spin quantum beats in the delayed fluorescence also exhibits an Arrhenius temperature dependence with an activation energy of 165 ± 70 cm^-1. All the data for T > 250 K are consistent with direct production of a spatially separated ¹(T⋯T) state via a thermally activated process, analogous to spontaneous parametric downconversion of photons. For temperatures in the range of 20 K-250 K, the singlet exciton continues to undergo a rapid decay on the order of 200 ps, leaving a red-shifted emission that decays on the order of 100 ns. At very long times (≈1 µs), a delayed fluorescence component corresponding to the original S₁ state can still be resolved, unlike in polycrystalline films. A kinetic analysis shows that the redshifted emission seen at lower temperatures cannot be an intermediate in the triplet production. When considered in the context of other results, our data suggest that the production of triplets in tetracene for temperatures below 250 K is a complex process that is sensitive to the presence of structural defects.

Singlet Fission Dynamics in Tetracene Single Crystals Probed by Polarization-Dependent Two-Dimensional Electronic Spectroscopy

The exact mechanism of endothermic singlet fission in crystalline polyacene remains to be clarified. It has been elusive whether the excess energy of vibrational hot states and the upper branch of Davydov splitting is important for the energy compensation. Here, we probe the excited-state specified singlet fission dynamics in tetracene single crystals by polarization-dependent two-dimensional electronic spectroscopy (2DES). While a major spectral transfer with a characteristic lifetime of 86 ps is observed to be largely independent of the excitation energy due to formation of the spatially separated triplet pairs (¹(T···T)), the excitation-energy dependent subpicosecond dynamics show marked differences for different states probed, implying the possible involvement of a coherently formed triplet pair state (¹(TT)). Analysis of coherent vibrational modes suggests the coupling to high energy modes may offset the energy difference between singlet and triplet pair states. Moreover, the beating map of the low frequency mode indicates a vibrational hot state violating the aggregation behavior of Davydov exciton, which can be explained as a resonance of the ¹(TT) state. These results suggest that the coherent vibronic mixing between local excitation and triplet pair states is essential for the singlet fission dynamics in molecule aggregates.

Energy transport and light propagation mechanisms in organic single crystals

Unambiguous information about spatiotemporal exciton dynamics in three-dimensional nanometer- to micrometer-sized organic structures is difficult to obtain experimentally. Exciton dynamics can be modified by annihilation processes, and different light propagation mechanisms can take place, such as active waveguiding and photon recycling. Since these various processes and mechanisms can lead to similar spectroscopic and microscopic signatures on comparable time scales, their discrimination is highly demanding. Here, we study individual organic single crystals grown from thiophene-based oligomers. We use time-resolved detection-beam scanning microscopy to excite a local singlet exciton population and monitor the subsequent broadening of the photoluminescence (PL) signal in space and on pico- to nanosecond time scales. Combined with Monte Carlo simulations, we were able to exclude photon recycling for our system, whereas leakage radiation upon active waveguiding leads to an apparent PL broadening of about 20% compared to the initial excitation profile. Exciton-exciton annihilation becomes important at high excitation fluence and apparently accelerates the exciton dynamics leading to apparently increased diffusion lengths. At low excitation fluences, the spatiotemporal PL broadening results from singlet exciton diffusion with diffusion lengths of up to 210 nm. Surprisingly, even in structurally highly ordered single crystals, the transport dynamics is subdiffusive and shows variations between different crystals, which we relate to varying degrees of static and dynamic electronic disorders.

Triplet Exciton Transfers and Triplet-Triplet Annihilation in Anthracene Derivatives via Direct versus Superexchange Pathways Governed by Molecular Packing

Triplet exciton transfer (TET) and triplet-triplet annihilations (TTAs) in anthracene derivatives, namely, one of the polymorphs of 9,10-bis(triisopropylsilylethynyl)anthracene (TIPS-ANTp) and 1,2,3,4-tetrafluoro-5,8-bis(trimethylsilylethynyl)anthracene (F4-TMS-ANT), are analyzed theoretically. The electronic couplings for TET and TTA are evaluated by means of the diabatization scheme in conjunction with the time-dependent density functional theory and the multireference second-order Møller-Plesset method. The TET rate is estimated on the basis of Fermi's golden rule considering the Franck-Condon factor of intramolecular modes. TTA is analyzed by means of quantum dynamics calculations with the multiconfiguration time-dependent Hartree method. TET in the cofacially stacked F4-TMS-ANT is faster than that of the slip-stacked TIPS-ANTp. In the anthracene derivatives, a singlet exciton is lower in energy than a pair of triplets. F4-TMS-ANT can exhibit an ultrafast TTA via the superexchange pathway mediated by higher lying charge transfer (CT) states, owing to strong electronic couplings. In contrast, TIPS-ANTp exhibits an inefficient TTA via the direct pathway with a small two-electron coupling. The cofacial stacking decreases the energy gap to the intermediate CT states, thereby facilitating TET and TTA via the superexchange pathway.

Polaritons and excitons: Hamiltonian design for enhanced coherence

The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian-connections between sites (or molecules) made by electronic coupling-is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.