Triplet Pair States in Singlet Fission

Towards multistate multimode landscapes in singlet fission of pentacene: the dual role of charge-transfer states

Singlet fission duplicates triplet excitons for improving light harvesting efficiency. The presence of the interaction between electronic and nuclear degrees of freedom complicates the interpretation of correlated triplet pairs. We report a quantum chemistry study on the significance and subtleties of multistate and multimode pathways in forming triplet pair states of the pentacene dimer through a six-state vibronic-coupling Hamiltonian derived from many-electron adiabatic wavefunctions of an ab initio density matrix renormalization group. The resulting spin values of the singlet manifolds on each pentacene center are computed, and the varying spin nature can be distinguished clearly with respect to dimer stacking and vibronic progression. Our monomer spin assignments reveal the coexistence of both lower-lying weak and higher-lying strong charge transfer states which interact vibronically with the triplet pair state, providing important implications for its generation and separation occurring in vibronic regions. This work conveys the importance of the many-electron process requiring close low-lying singlet manifolds to determine the subtle fission details, and represents an important step for understanding vibronically resolved spin states and conversions underlying efficient singlet fission.

Variations in Complementary Hydrogen Bonds Direct Assembly Patterns of Isosteric Polyheteroaromatics at Surfaces

Intermolecular interactions guide self-assembly on the surface. Precise control over these interactions by rational design of the molecule should allow fine control over the self-assembly patterns. Functional groups installed for electronic modulation often induce significant changes in the molecular dimensions, thereby disrupting the original assembly pattern. To overcome this challenge, we have employed a family of isosteric phenazine derivatives, DHP, DAP, and DBQD, to investigate the impacts of hydrogen bonding on two-dimensional molecular self-assembly. While these molecules are similar in size and chemical composition, the strength and directionality of hydrogen bonding differ significantly depending on the chemical structure of donor-acceptor pairs and prototropic tautomerization from positional isomerism. Scanning tunneling microscopy (STM) characterization of the assembled structures on Ag(111), Au(111), and Cu(100) surfaces revealed that minimal changes in molecular structure have a profound impact on the self-assembly patterns. While DHP exhibits highly ordered and robust assemblies, DAP and DBQD show either spatially confined or ill-defined assemblies. In conjunction with hydrogen bonding, prototropic tautomerism is a potent strategy to modulate molecular 2D lattices on surfaces.

Vacancy control in acene blends links exothermic singlet fission to coherence

The fission of singlet excitons into triplet pairs in organic materials holds great technological promise, but the rational application of this phenomenon is hampered by a lack of understanding of its complex photophysics. Here, we use the controlled introduction of vacancies by means of spacer molecules in tetracene and pentacene thin films as a tuning parameter complementing experimental observables to identify the operating principles of different singlet fission pathways. Time-resolved spectroscopic measurements in combination with microscopic modelling enables us to demonstrate distinct scenarios, resulting from different singlet-to-triplet pair energy alignments. For pentacene, where fission is exothermic, coherent mixing between the photoexcited singlet and triplet-pair states is promoted by vibronic resonances, which drives the fission process with little sensitivity to the vacancy concentration. Such vibronic resonances do not occur for endothermic materials such as tetracene, for which we find fission to be fully incoherent; a process that is shown to slow down with increasing vacancy concentration.

Permanent Dipole Moments Enhance Electronic Coupling and Singlet Fission in Pentacene

Singlet fission (SF), the photophysical process in which one singlet exciton is transformed into two triplets, depends inter alia on the coupling of electronic states. Here, we use fluorination and the resulting changes in partial charge distribution across the chromophore backbone as a particularly powerful tool to control this parameter in pentacene. We find that the introduction of a permanent dipole moment leads to an enhanced coupling of Frenkel exciton and charge transfer states and to an increased SF rate which we probed using ultrafast transient absorption spectroscopy. These findings are contrasted with H-aggregate formation and a significantly reduced triplet-pair state lifetime in a fluorinated pentacene for which the different partial charge distribution leads to a negligible dipole moment.

3D Electron Diffraction Structure Determination of Terrylene, a Promising Candidate for Intermolecular Singlet Fission

Herein we demonstrate the prowess of the 3D electron diffraction approach by unveiling the structure of terrylene, the third member in the series of peri‐condensed naphthalene analogues, which has eluded structure determination for 65 years. The structure was determined by direct methods using electron diffraction data and corroborated by dispersion‐inclusive density functional theory optimizations. Terrylene crystalizes in the monoclinic space group P2₁/a, arranging in a sandwich‐herringbone packing motif, similar to analogous compounds. Having solved the crystal structure, we use many‐body perturbation theory to evaluate the excited‐state properties of terrylene in the solid‐state. We find that terrylene is a promising candidate for intermolecular singlet fission, comparable to tetracene and rubrene.

Exploring the Concept of Dimerization-Induced Intersystem Crossing: At the Origins of Spin-Orbit Coupling Selection Rules

Singlet-triplet interconversions (intersystem crossing, ISC) in organic molecules are at the basis of many important processes in cutting-edge photonic applications (organic light-emitting devices, photodynamic therapy, etc.). Selection rules for these transitions are mainly governed by the spin-orbit coupling (SOC) phenomenon. Although the SOC relies on complex relativistic phenomena, theoreticians have, with time, developed increasingly sophisticated and efficient approaches to gain access to a satisfactory evaluation of its magnitude. However, recent works have highlighted the remarkable and somehow unexpected efficiency of dimers of small conjugated molecules in terms of ISC quantum yields, whose origin has not been completely investigated. In this work, we bring a coupled experimental and theoretical analysis of the origin of the unusually large ISC efficiency on a series of such dimers that differ by their nature (covalent or supramolecular). We show that considering the dynamical nature of the SOC, and especially its dependence on angular orientations between the dimer subunits sometimes overlooked in the literature, it is necessary to rationalize some counterintuitive experimental observations. This combined experimental and theoretical work paves the way for new molecular engineering rules for SOC control.

Enthalpy-Entropy Compensation Effect for Triplet Pair Dissociation of Intramolecular Singlet Fission in Phenylene Spacer-Bridged Hexacene Dimers

Hexacene (Hc) is highly promising for singlet fission (SF). However, the number of SFs in Hc is extremely limited. As far as Hc dimers in solution are concerned, there is no report on the observation of the dissociation process from a correlated triplet pair (TT) to an individual one. The emphasis in this study is on the first observation of the quantitative TT generation together with the orientation-dependent photophysical discussions for TT dissociation using para- and meta-phenyl-bridged Hc dimers. Moreover, the activation enthalpies of Hc dimers in TT dissociation are smaller than those of pentacene (Pc) dimers, whereas the relative entropic contributions for Gibbs free energy of activation are much larger than the enthalpic ones in both Hc and Pc dimers. This implies that the vibrational motions are responsible for the intramolecular conformation changes associated with the TT dissociation. Consequently, "enthalpy-entropy compensation" has a large impact on the rate constants and quantum yields.

Theoretical Study on Singlet Fission Dynamics in Slip-Stack-like Pentacene Ring-Shaped Aggregate Models

We investigate the singlet fission (SF) dynamics of a slip-stack-like pentacene ring-shaped aggregate model, which is constructed by rotating each pentacene unit around its longitudinal axis in an H-aggregate ring. The aggregate size (N) and rotation angle (α) dependences of SF rates and double triplet (TT) yields are clarified using the quantum master equation method. It is found that there exist optimal ranges of the rotation angle α for each N, yielding efficient SF with high SF rates and TT yields. For example, in an 8-mer model, SF rates at α = 23 and 43° are 18.9 and 38.6 times as high as that at α = 30°, respectively, and the TT yields are as high as 0.871, 0.988, and 0.882 at α = 23, 30, and 43°, respectively. Analysis of the relative relaxation factors shows that the many-to-many relaxation paths from adiabatic Frenkel exciton (FE)-like states to TT-like states are opened by tuning α at relevant aggregate sizes, causing fast and high-TT-yield SF, and efficient SF occurs at α = 40° for medium N (7 ≤ N ≤ 10) or at α = 30° for large N (>10). This mechanism is interpreted by the second-order perturbation theory for electronic couplings. Namely, the inequality in the energies of charge-transfer states [CA and AC states, where the cation (C) and anion (A) are located at two neighboring sites in anticlockwise and clockwise directions, respectively] and the change in the amplitude and sign of the couplings between the FE, CT, and TT states are found to cause quantum superposition of the FE and TT states, which contribute to the high TT yield and SF rate. The present results contribute to a deeper understanding of SF dynamics in ring-shaped aggregates as well as to the development of their new design guidelines.

Supramolecular Singlet Fission of Pentacene Dimers within Polyaromatic Capsules

We herein report a new set of supramolecular nanotools for the generation and modulation of singlet fission (SF) of noncovalent/covalent pentacene dimers. Two molecules of a pentacene monomer with bulky substituents are facilely encapsulated by a polyaromatic capsule, composed of naphthalene-based bent amphiphiles, in water. The encapsulated noncovalent dimer converts to otherwise undetectable triplet pairs and an individual triplet in high quantum yields (179% and 53%, respectively) even under high dilution conditions. Within the capsule, a covalently linked pentacene dimer with bulky groups generates two triplet pair intermediates in parallel, which are hardly distinguished in bulk solution, in excellent total quantum yield (196%). The yield of the individual triplet is enhanced by 1.6 times upon encapsulation. For both types of pentacene dimers, the SF features can be readily tuned by changing the polyaromatic panels of the capsule (i.e., anthracene and phenanthrene).

Temperature Tuning of Coherent Mixing between States Driving Singlet Fission in a Spiro-Fused Terrylenediimide Dimer

The excited-state dynamics of a spiro-fused terrylene-3,4:11,12-bis(dicarboximide) (TDI) dimer (sTDI2) in toluene and 2-methyltetrahydrofuran (mTHF) were investigated as a function of temperature using femtosecond- and nanosecond-transient absorption spectroscopy, as well as two-dimensional electronic spectroscopy. The spiro conjugation and the corresponding geometry of this compound guarantee a short intermonomer distance along with a partial orbital overlap between the orthogonal TDI π-electron systems, providing electronic coupling between the TDIs. Photoexcitation of sTDI2 in toluene, a low dielectric solvent, at 295 K, results in the ultrafast formation of a state composed of a coherent mixture of singlet 1(S1S0), multiexciton 1(T1T1), and charge-transfer (CT) electronic characters. This mixed species decays to decorrelated triplet states on the nanosecond timescale, completing the process of intramolecular singlet fission (SF) in sTDI2. Upon decreasing the temperature from 295 to 200 K, the contribution of the 1(T1T1) state to the mixed species decreases concurrently with an increase in the CT state character. We attribute this behavior to the variation in the vibrational energy level alignment between the states comprising the mixture due to changes in the temperature and hence the local dielectric environment. In contrast, photoexcitation of sTDI2 in more polar mTHF at 295 K results in the formation of a mixed singlet and CT state before undergoing symmetry-breaking charge separation, owing to the increased stabilization of the CT state in the medium. However, in glassy mTHF at 85 K, photoexcited sTDI2 exhibits discernible multiexciton character, comparable to that observed in toluene at 200 K, which we rationalize by the similarity of the dielectric constants under these two sets of conditions. These observations of mixed states of varying diabatic contributions over the range of experimental conditions show that the temperature and the static dielectric constant can directly control the composition of the electronically mixed excited state of sTDI2 and thus the fate of the SF process.

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).

Nuclear dynamics of singlet exciton fission in pentacene single crystals

Singlet exciton fission (SEF) is a key process for developing efficient optoelectronic devices. An aspect rarely probed directly, yet with tremendous impact on SEF properties, is the nuclear structure and dynamics involved in this process. Here, we directly observe the nuclear dynamics accompanying the SEF process in single crystal pentacene using femtosecond electron diffraction. The data reveal coherent atomic motions at 1 THz, incoherent motions, and an anisotropic lattice distortion representing the polaronic character of the triplet excitons. Combining molecular dynamics simulations, time-dependent density-functional theory, and experimental structure factor analysis, the coherent motions are identified as collective sliding motions of the pentacene molecules along their long axis. Such motions modify the excitonic coupling between adjacent molecules. Our findings reveal that long-range motions play a decisive part in the electronic decoupling of the electronically correlated triplet pairs and shed light on why SEF occurs on ultrafast time scales.

Women in the Singlet Fission World: Pearls in a Semi-Open Shell

Singlet fission, a multiple exciton generation process, can revolutionize existing solar cell technologies. Offering the possibility to double photocurrent, the process has become a focal point for physicists, chemists, software developers, and engineers. The following review is dedicated to the female investigators, predominantly theorists, who have contributed to the field of singlet fission. We highlight their most significant advances in the subject, from deciphering the mechanism of the process to designing coveted singlet fission materials.

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.

Intrinsic photogeneration of long-lived charges in a donor-orthogonal acceptor conjugated polymer

Efficient charge photogeneration in conjugated polymers typically requires the presence of a second component to act as electron acceptor. Here, we report a novel low band-gap conjugated polymer with a donor/orthogonal acceptor motif: poly-2,6-(4,4-dihexadecyl-4H-cyclopenta [2,1-b:3,4-b']dithiophene)-alt-2,6-spiro [cyclopenta[2,1-b:3,4-b']dithiophene-4,9'-fluorene]-2',7'-dicarbonitrile, referred to as PCPDT-sFCN. The role of the orthogonal acceptor is to spatially isolate the LUMO from the HOMO, allowing for negligible exchange energy between electrons in these orbitals and minimising the energy gap between singlet and triplet charge transfer states. We employ ultrafast and microsecond transient absorption spectroscopy to demonstrate that, even in the absence of a separate electron acceptor, PCPDT-sFCN shows efficient charge photogeneration in both pristine solution and film. This efficient charge generation is a result of an isoenergetic singlet/triplet charge transfer state equilibrium acting as a reservoir for charge carrier formation. Furthermore, clear evidence of enhanced triplet populations, which form in less than 1 ps, is observed. Using group theory, we show that this ultrafast triplet formation is due to highly efficient, quantum mechanically allowed intersystem crossing between the bright, initially photoexcited local singlet state and the triplet charge transfer state. Remarkably, the free charges that form via the charge transfer state are extraordinarily long-lived with millisecond lifetimes, possibly due to the stabilisation imparted by the spatial separation of PCPDT-sFCN's donor and orthogonal acceptor motifs. The efficient generation of long-lived charge carriers in a pristine polymer paves the way for single-material applications such as organic photovoltaics and photodetectors.

Theoretical Study on Singlet Fission in Aromatic Diaza s-Indacene Dimers

We theoretically show that diaza (N₂)-substitution to s-indacene with 4n π-electrons, by which the number of π-electrons in N₂-s-indacene amounts to 4n+2, is a new strategy to design efficient singlet fission (SF) molecules. By N₂-substitution, the diradical character and the exchange integral are found to be tuned moderately, leading to satisfying the excitation energy level matching condition for SF with a large triplet excitation energy. On the basis of the effective electronic coupling related to the SF rate, we explore the optimal slip-stack dimer packings for fast SF. Their underlying mechanisms are well understood from the odd-electron density, resonance structure, and frontier orbital distribution, as the functions of the N₂-substituted positions. Furthermore, aromaticities of N₂-s-indacenes are evaluated explicitly on the basis of the magnetically induced current. Although N₂-s-indacenes display strengths of aromaticities similar to that of anthracene, a local decrease in aromaticity is found to correlate to the spatial feature of diradical character, i.e., odd-electron density. The present findings not only newly propose N₂-s-indacenes as feasible SF molecules but also contribute to comprehending the interplay between aromaticity and diradical electronic structures contributing to SF.

High-Lying 31Ag Dark-State-Mediated Singlet Fission

Singlet fission (SF), the conversion of one high-energy singlet to two low-energy triplets, provides the potential to increase the efficiency of photovoltaic devices. In the SF chromophores with C_2h symmetry, exemplified by polyenes, singlet-to-triplet conversion generally involves a low-lying 2¹A_g dark state, which serves as either a multiexciton (ME) intermediate to promote the SF process or a parasitic trap state to shunt excited-state populations via internal conversion. This controversial behavior calls for a deep understanding of dark-state-related photophysics involving the higher-lying singlet state. However, the optical "dark" and "transient" nature of these dark states and strong correlation feature of double exciton species make their characterization and interpretation challenging from both experimental and computational perspectives. In the present work combining transient spectroscopy and multireference electronic structure calculations (XDW-CASPT2), we addressed a new photophysical model, i.e., a high-lying 3¹A_g dark-state-mediated ultrafast SF process in the benzodipyrrolidone (BDPP) skeleton. Such a 3¹A_g dark state with distinctive double excitation character, described as the ME state, could be populated from the initial 1¹B_u bright state on an ultrafast time scale given the quasi-degeneracy and intersection of the two electronic states. Furthermore, the suitable optical band gap and triplet energy, high triplet yield, and excellent photostability render BDPP a promising SF candidate for photovoltaic devices. These results not only enrich the arsenal of SF materials but also shed new insights into the understanding of dark-state-related photophysics, which could promote the development of new SF-active materials.

Crystal Symmetry and Static Electron Correlation Greatly Accelerate Nonradiative Dynamics in Lead Halide Perovskites

Using a recently developed many-body nonadiabatic molecular dynamics (NA-MD) framework for large condensed matter systems, we study the phonon-driven nonradiative relaxation of excess electronic excitation energy in cubic and tetragonal phases of the lead halide perovskite CsPbI₃. We find that the many-body treatment of the electronic excited states significantly changes the structure of the excited states' coupling, promotes a stronger nonadiabatic coupling of states, and ultimately accelerates the relaxation dynamics relative to the single-particle description of excited states. The acceleration of the nonadiabatic dynamics correlates with the degree of configurational mixing, which is controlled by the crystal symmetry. The higher-symmetry cubic phase of CsPbI₃ exhibits stronger configuration mixing than does the tetragonal phase and subsequently yields faster nonradiative dynamics. Overall, using a many-body treatment of excited states and accounting for decoherence dynamics are important for closing the gap between the computationally derived and experimentally measured nonradiative excitation energy relaxation rates.

Exploring the State Space Structure of Multiple Spins via Modular Tensor Diagram Approach: Going beyond the Exciton Pair State

Fully understanding of multistate quantum systems could become formidable if not impossible as the system dimensionality increases. One ideal strategy to comprehend complex systems is to transform the system representation into a more structural one so that major characteristics, connections, and even underlying mechanisms can stand out from the huge unstructured information, e.g., the construction of spin eigenfunctions for a system of multiple spins through the diagonalization of the system Hamiltonian matrix. Here, instead of direct matrix diagonalization, the recently developed modular tensor diagram approach is applied to reorganize the state space structure of multispin systems, extending previous investigations on exciton pair states to exciton trimer states. This implementation demonstrates that the proposed approach not only provides a systematical way to transform the high dimensional multistate system into a well organized structure based on basic (exciton) modules but also paves the way to further analysis on potential applications. For example, the analysis on the state space of the exciton trimer system suggests a possible scheme to improve the laser performance via single fission involving multiexcitations and/or multiple fission steps.

Ultrafast spectroscopy reveals singlet fission, ionization and excimer formation in perylene film

Singlet exciton fission (SF) is a spin-allowed process whereby two triplet excitons are created from one singlet exciton. This phenomenon can offset UV photon energy losses and enhance the overall efficiency in photovoltaic devices. For this purpose, it requires photostable commercially available SF materials. Excited state dynamics in pure perylene film, ease of commercial production, is studied by time-resolved fluorescence and femtosecond transient absorption techniques under different photoexcitation energies. In film, polycrystalline regions contain perylene in H-type aggregate form. SF takes place from higher excited states of these aggregates in ultrafast time scale < 30 fs, reaching a triplet formation quantum yield of 108%. Moreover, at λ_ex = 450 nm singlet fission was detected as a result of two-quantum absorption. Other competing relaxation channels are excimer (1 ps) and dimer radical cation formation (< 30 fs). Excimer radiatively relaxes within 19 ns and radical cation recombines in 3.2 ns. Besides, exciton self-trapping by crystal lattice distortions occurs within hundreds of picosecond. Our results highlight potential of simple-fabricated perylene films with similar properties as high-cost single crystal in SF based photovoltaic applications.

Singlet fission in naturally-organized carotenoid molecules

We have investigated the photophysics of aggregated lutein/violaxanthin in daffodil chromoplasts. We reveal the presence of three carotenoid aggregate species, the main one composed of a mixture of lutein/violaxanthin absorbing at 481 nm, and two secondary populations of aggregated carotenoids absorbing circa 500 and 402 nm. The major population exhibits an efficient singlet fission process, generating μs-lived triplet states on an ultrafast timescale. The structural organization of aggregated lutein/violaxanthin in daffodil chromoplasts produces well-defined electronic levels that permit the energetic pathways to be disentangled unequivocally, allowing us to propose a consistent mechanism for singlet fission in carotenoid aggregates. Transient absorption measurements on this system reveal for the first time an entangled triplet signature for carotenoid aggregates, and its evolution into dissociated triplet states. A clear picture of the carotenoid singlet fission pathway is obtained, which is usually blurred due to the intrinsic disorder of carotenoid aggregates.

Electronic couplings for singlet fission: Orbital choice and extrapolation to the complete basis set limit

For the search for promising singlet fission candidates, the calculation of the effective electronic coupling, which is required to estimate the singlet fission rate between the initially excited state (S0S1) and the multiexcitonic state (1TT, two triplets on neighboring molecules, coupled into a singlet), should be sufficiently reliable and fast enough to explore the configuration space. We propose here to modify the calculation of the effective electronic coupling using a nonorthogonal configuration interaction approach by: (a) using only one set of orbitals, optimized for the triplet state of the molecules, to describe all molecular electronic states, and (b) only taking the leading configurations into consideration. Furthermore, we also studied the basis set convergence of the electronic coupling, and we found, by comparison to the complete basis set limit obtained using the cc-pVnZ series of basis sets, that both the aug-cc-pVDZ and 6-311++G** basis sets are a good compromise between accuracy and computational feasibility. The proposed approach enables future work on larger clusters of molecules than dimers.

Singlet Fission in a Flexible Bichromophore with Structural and Dynamic Control

Singlet fission (SF), i.e., the splitting of a high-energy exciton into two lower-energy triplet excitons, has the potential to increase the efficiency for harvesting spectrally broad light. The path from the photopopulated singlet state to free triplets is complicated by competing processes that decrease the overall SF efficiency. A detailed understanding of the whole cascade and the nature of the photoexcited singlet state is still a major challenge. Here, we introduce a pentacene dimer with a flexible crown ether spacer enabling a control of the interchromophore coupling upon solvent-induced self-aggregation as well as cation binding. The systematic change of solvent polarity and viscosity and excitation wavelength, as well as the available conformational phase space, allows us to draw a coherent picture of the whole SF cascade from the femtosecond to microsecond time scales. High coupling leads to ultrafast SF (<2 ps), independent of the solvent polarity, and to highly coupled correlated triplet pairs. The absence of a polarity effect indicates that the solvent coordinate does not play a significant role and that SF is driven by intramolecular modes. Low coupling results in much slower SF (∼500 ps), which depends on viscosity, and leads to weakly coupled correlated triplet pairs. These two triplet pairs could be spectrally distinguished and their contribution to the overall SF efficiency, i.e., to the population of free triplets, could be determined. Our results reveal how the overall SF efficiency can be increased by conformational restrictions and control of the structural fluctuation dynamics.

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.

Unconventional singlet fission materials

Singlet fission (SF) is a photophysical downconversion pathway, in which a singlet excitation transforms into two triplet excited states. As such, it constitutes an exciton multiplication generation process, which is currently at the focal point for future integration into solar energy conversion devices. Beyond this, various other exciting applications were proposed, including quantum cryptography or organic light emitting diodes. Also, the mechanistic understanding evolved rapidly during the last year. Unfortunately, the number of suitable SF-chromophores is still limited. This is per se problematic, considering the wide range of envisaged applicability. With that in mind, we emphasize uncommon SF-scaffolds and outline requirements as well as strategies to expand the chromophore pool of SF-materials.

Controlling Intramolecular Förster Resonance Energy Transfer and Singlet Fission in a Subporphyrazine-Pentacene Conjugate by Solvent Polarity

Due its complementary absorptions in the range of 450 and 600 nm, an energy-donating hexaaryl-subporphyrazine has been linked to a pentacene dimer, which acts primarily as an energy acceptor and secondarily as a singlet fission enabler. In the corresponding conjugate, efficient intramolecular Förster resonance energy transfer (i-FRET) is the modus operandi to transfer energy from the subporphyrazine to the pentacene dimer. Upon energy transfer, the pentacene dimer undergoes intramolecular singlet fission (i-SF), that is, converting the singlet excited state, via an intermediate state, into a pair of correlated triplet excited states. Solvatochromic fluorescence of the subporphyrazine is a key feature of this system and features a red-shift as large as 20 nm in polar media. Solvent is thus used to modulate spectral overlap between the fluorescence of subporphyrazine and absorption of the pentacene dimer, which controls the Förster rate constant, on one hand, and the triplet quantum yield, on the other hand. The optimum spectral overlap is realized in xylene, leading to Förster rate constant of 3.52×1011  s-1 and a triplet quantum yield of 171 % ±10 %. In short, the solvent polarity dependence, which is a unique feature of subporphyrazines, is decisive in terms of adjusting spectral overlap, ensuring a sizable Förster rate constant, and maximizing triplet quantum yields. Uniquely, this optimization can be achieved without a need for synthetic modification of the subporphyrazine donor.

Room-Temperature Pentacene Fluids: Oligoethylene Glycol Substituent-Controlled Morphologies and Singlet Fission

We report the first synthesis of solvent-free pentacene fluids at room temperature together with observation of singlet fission (SF). Three pentacenes with different number of ethylene glycol (EG) side chains (n) were employed (denoted as (EG)_n-Pc-(EG)_n: n = 2, 3, and 4). The morphologies of these pentacenes largely depend on the lengths of EG chains (n). (EG)₃-Pc-(EG)₃ and (EG)₄-Pc-(EG)₄ indicate fluid compounds at room temperature, whereas (EG)₂-Pc-(EG)₂ is a solid compound. Microscopic clustering with short-range interactions between pentacene chromophores was confirmed in X-ray diffraction profiles of solvent-free fluids. Such a structural trend is an important origin of SF and consistent with the steady-state spectroscopic results. To one's surprise, femtosecond transient absorption spectroscopy demonstrated that SF occurred in thin films prepared from solvent-free fluids of (EG)₃-Pc-(EG)₃ and (EG)₄-Pc-(EG)₄ in spite of such excessive EG chains.

Charge transfer states impact the triplet pair dynamics of singlet fission polymers

Polymers are desirable optoelectronic materials, stemming from their solution processability, tunable electronic properties, and large absorption coefficients. An exciting development is the recent discovery that singlet fission (SF), the conversion of a singlet exciton to a pair of triplet states, can occur along the backbone of an individual conjugated polymer chain. Compared to other intramolecular SF compounds, the nature of the triplet pair state in SF polymers remains poorly understood, hampering the development of new materials with optimized excited state dynamics. Here, we investigate the effect of solvent polarity on the triplet pair dynamics in the SF polymer polybenzodithiophene-thiophene-1,1-dioxide. We use transient emission measurements to study isolated polymer chains in solution and use the change in the solvent polarity to investigate the role of charge transfer character in both the singlet exciton and the triplet pair multiexciton. We identify both singlet fluorescence and direct triplet pair emission, indicating significant symmetry breaking. Surprisingly, the singlet emission peak is relatively insensitive to solvent polarity despite its nominal "charge-transfer" nature. In contrast, the redshift of the triplet pair energy with increasing solvent polarity indicates significant charge transfer character. While the energy separation between singlet and triplet pair states increases with solvent polarity, the overall SF rate constant depends on both the energetic driving force and additional environmental factors. The triplet pair lifetime is directly determined by the solvent effect on its overall energy. The dominant recombination channel is a concerted, radiationless decay process that scales as predicted by a simple energy gap law.

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.

Wave Function Based Analysis of Dynamics versus Yield of Free Triplets in Intramolecular Singlet Fission

Experiments in several intramolecular singlet fission materials have indicated that the triplet-triplet spin biexciton has a much longer lifetime than believed until recently, opening up loss mechanisms that can annihilate the biexciton prior to its dissociation to free triplets. We have performed many-body calculations of excited state wave functions of hypothetical phenylene-linked anthracene molecules to better understand linker-dependent behavior of dimers of larger acenes being investigated as potential singlet fission candidates. The calculations reveal unanticipated features that we show carry over to the real covalently linked pentacene dimers. Dissociation of the correlated triplet-triplet spin biexciton and free triplet generation may be difficult in acene dimers where the formation of the triplet-triplet spin biexciton is truly ultrafast. Conversely, relatively slower biexciton formation may indicate smaller spin biexciton binding energy and greater yield of free triplets. Currently available experimental results appear to support this conclusion. Whether or not the two distinct behaviors are consequences of distinct mechanisms of triplet-triplet generation from the optical singlet is an interesting theoretical question.

Singlet fission relevant energetics from optimally tuned range-separated hybrids

As a promising idea to design high-efficiency organic photovoltaics, singlet fission (SF) mechanism, i.e., generating two triplet excitons out of a single photon absorption, has recently come into the spotlight. Even though much effort has been devoted to this arena, accurately accounting for the SF process from the theoretical perspective has proven to be challenging. Herein, the SF energetics have thoroughly been investigated with the help of optimally tuned range-separated hybrid functionals (OT-RSHs) in both gas and solvent phases. Taking a series of experimentally known SF chromophores as working models, we have proposed and validated several variants of OT-RSH approximations for the reliable prediction of the energy levels which match the crucial criteria for the SF process, namely, the negative singlet-triplet and triplet-triplet energy gaps. We scrutinize the role of the OT-RSH ingredients, i.e., the underlying density functional approximations, short- and long-range exact-like exchange, as well as the range-separation parameter, for our purpose. The newly designed OT-RSHs outperform the standard RSHs and other related schemes such as screened-exchange approximations as well as other density functionals from different rungs for describing the SF energetics. More importantly, it is unveiled that although the OT-RSH coupled with the polarizable continuum model, OT-RSH-PCM, as well as the screened versions, OT-SRSHs, which account for the screening effect by the electron correlation through the scalar dielectric constant have some advantages over gas-phase computations using OT-RSHs, the energetics criteria of the SF process may not necessarily be satisfied. This in turn corroborates the idea of performing both the optimal tuning procedure and subsequent computations of the SF relevant energetics using OT-RSHs as a more reliable and affordable framework, at least for the present purpose. The applicability of the proposed models is also put into broader perspective, where they are used for the computational design of several chromophores as promising candidates prone to utilization in the SF-based materials. Hopefully, our recommended OT-RSHs can function as efficient models for both the theoretical modeling of SF chromophores and confirming the experimental observations in the field.

Emissive spin-0 triplet-pairs are a direct product of triplet-triplet annihilation in pentacene single crystals and anthradithiophene films

Singlet fission and triplet-triplet annihilation represent two highly promising ways of increasing the efficiency of photovoltaic devices. Both processes are believed to be mediated by a biexcitonic triplet-pair state, ¹(TT). Recently however, there has been debate over the role of ¹(TT) in triplet-triplet annihilation. Here we use intensity-dependent, low-temperature photoluminescence measurements, combined with kinetic modelling, to show that distinct ¹(TT) emission arises directly from triplet-triplet annihilation in high-quality pentacene single crystals and anthradithiophene (diF-TES-ADT) thin films. This work demonstrates that a real, emissive triplet-pair state acts as an intermediate in both singlet fission and triplet-triplet annihilation and that this is true for both endo- and exothermic singlet fission materials.

Modulating the dynamics of Förster resonance energy transfer and singlet fission by variable molecular spacers

In contrast to previous work, the synergy between panchromatic absorption and molecular singlet fission (SF) is exploited to optimize solar energy conversion through evaluation of the distance dependence of intramolecular Förster Resonance Energy Transfer (i-FRET) in a series of subphthalocyanines (SubPcs) linked to pentacene dimers (Pnc2s). To provide control over i-FRET, the molecular spacer rather than the energy donating SubPc is tailored in the corresponding SubPc-Pnc2 conjugates in terms of length (i.e., the number of aryl units) and flexibility (i.e., presence or absence of a CH2 group). AM1-CIS calculations support the experiments, which underline the importance of the molecular spacer to impact not only the i-FRET dynamics, but also the dynamics of intramolecular singlet fission (i-SF). For example, an additional phenyl group slows down both i-FRET and i-SF by a factor of ∼3.8 and ∼1.6, respectively, by a quinone-like conjugation pattern that affords a pentacene acceptor orbital that is fairly delocalized over both pentacenes and the bridging phenyl.

Overlap-Driven Splitting of Triplet Pairs in Singlet Fission

We analyze correlated-triplet-pair (TT) singlet-fission intermediates toward two-triplet separation (T...T) using spin-state-averaged density matrix renormalization group electronic-structure calculations. Specifically, we compare the triplet-triplet exchange (J) for tetracene dimers, bipentacene, a subunit of the benzodithiophene-thiophene dioxide polymer, and a carotenoid (neurosporene). Exchange-split energy gaps of J and 3J separate a singlet from a triplet and a singlet from a quintet, respectively. We draw two new insights: (a) the canonical tetracene singlet-fission unit cell supports precisely three low-lying TT intermediates with order-of-magnitude differences in J, and (b) the separable TT intermediate in carotenoids emanates from a pair of excitations to the second triplet state. Therefore, unlike with tetracenes, carotenoid fission requires above-gap excitations. In all cases, the distinguishability of the molecular triplets-that is, the extent of orbital overlap-determines the splitting within the spin manifold of TT states. Consequently, J represents a spectroscopic observable that distnguishes the resemblance between TT intermediates and the T...T product.

In silico prediction of annihilators for triplet-triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T₀), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Electronic structure theories such as AFQMC can accurately predict the low-lying excited state energetics of organic chromophores involved in triplet–triplet annihilation upconversion. A novel class of benzothiadiazole annihilators is discovered.

An ab initio exciton model for singlet fission

We present an ab initio exciton model that extends the Frenkel exciton model and includes valence, charge-transfer, and multiexcitonic excited states. It serves as a general, parameter-free, yet computationally efficient and scalable approach for simulation of singlet fission processes in multichromophoric systems. A comparison with multiconfigurational methods confirms that our exciton model predicts consistent energies and couplings for the pentacene dimer and captures the correct physics. Calculations of larger pentacene clusters demonstrate the computational scalability of the exciton model and suggest that the mixing between local and charge-transfer excitations narrows the gap between singlet and multiexcitonic states. Local vibrations of pentacene molecules are found to facilitate singlet-multiexcitonic state-crossing and hence are important for understanding singlet fission. The exciton model developed in this work also sets the stage for further implementation of the nuclear gradients and nonadiabatic couplings needed for first principles nonadiabatic quantum molecular dynamics simulations of singlet fission.

Diffusion-Controlled Singlet Fission in a Chlorinated Phenazinothiadiazole by Broadband Femtosecond Transient Absorption

Singlet fission (SF) is a process by which one excited singlet state yields two triplet states upon close interaction with a ground-state chromophore of the same kind. This photoreaction was first observed in solid state and has important implications in organic photovoltaics. Singlet fission was also reported in concentrated solutions, where the need for diffusion of the reaction partners slows the dynamics. This helps to single out reaction stages and to identify the involved species. In this work, ultrafast transient absorption spectroscopy and time-correlated single photon counting are applied to the concentration-dependent (from 10^-1 to 10² mM) photodynamics of a tetrachlorinated phenazinothiadiazole in toluene. Time-resolved emission shows a monoexponential decay, which is constant across the emission band. The corresponding decay rate depends linearly on the concentration of the phenazinothiadiazole. Femtosecond transient absorption demonstrates that a concentration-dependent singlet-to-triplet conversion hides behind the emission decay which is diffusion controlled. Contrary to previous reports on SF in pentacenes and tetracenes, no indication of intermediate states has been found. Efficient, direct and barrierless SF is concluded. The strong enhancement of the triplet yield at increasingly higher concentrations of the thiadiazole indicates very efficient singlet fission with a triplet yield up to 189 ± 5%.

Molecular packing-dependent exciton dynamics in functionalized anthradithiophene derivatives: From solutions to crystals

Understanding the impact of inter-molecular orientation on the optical properties of organic semiconductors is important for designing next-generation organic (opto)electronic and photonic devices. However, fundamental aspects of how various features of molecular packing in crystalline systems determine the nature and dynamics of excitons have been a subject of debate. Toward this end, we present a systematic study of how various molecular crystal packing motifs affect the optical properties of a class of high-performance organic semiconductors: functionalized derivatives of fluorinated anthradithiophene. The absorptive and emissive species present in three such derivatives (exhibiting "brickwork," "twisted-columnar," and "sandwich-herringbone" motifs, controlled by the side group R) were analyzed both in solution and in single crystals, using various modalities of optical and photoluminescence spectroscopy, revealing the nature of these excited states. In solution, in the emission band, two states were identified: a Franck-Condon state present at all concentrations and an excimer that emerged at higher concentrations. In single crystal systems, together with ab initio calculations, it was found in the absorptive band that Frenkel and Charge Transfer (CT) excitons mixed due to nonvanishing CT integrals in all derivatives, but the amount of admixture and exciton delocalization depended on the packing, with the "sandwich-herringbone" packing motif least conducive to delocalization. Three emissive species in the crystal phase were also identified: Frenkel excitons, entangled triplet pairs ¹(TT) (which are precursors to forming free triplet states via singlet fission), and self-trapped excitons (STEs, similar in origin to excimers present in concentrated solution). The "twisted-columnar" packing motif was most conducive to the formation of Frenkel excitons delocalized over 4-7 molecules depending on the temperature. These delocalized Frenkel states were dominant across the full temperature range (78 K-293 K), though at lower temperatures, the entangled triplet states and STEs were present. In the derivative with the "brickwork" packing, all three emissive species were observed across the full temperature range and, most notably, the ¹(TT) state was present at room temperature. Finally, the derivative with the "sandwich-herringbone" packing exhibited localized Frenkel excitons and had a strong propensity for self-trapped exciton formation even at higher temperatures. In this derivative, no formation of the ¹(TT) state was observed. The temperature-dependent dynamics of these emissive states are reported, as well as their origin in fundamental inter-molecular interactions.

Singlet fission for quantum information and quantum computing: the parallel JDE model

Singlet fission is a photoconversion process that generates a doubly excited, maximally spin entangled pair state. This state has applications to quantum information and computing that are only beginning to be realized. In this article, we construct and analyze a spin-exciton hamiltonian to describe the dynamics of the two-triplet state. We find the selection rules that connect the doubly excited, spin-singlet state to the manifold of quintet states and comment on the mechanism and conditions for the transition into formally independent triplets. For adjacent dimers that are oriented and immobilized in an inert host, singlet fission can be strongly state-selective. We make predictions for electron paramagnetic resonance experiments and analyze experimental data from recent literature. Our results give conditions for which magnetic resonance pulses can drive transitions between optically polarized magnetic sublevels of the two-exciton states, making it possible to realize quantum gates at room temperature in these systems.

Change in Tetracene Polymorphism Facilitates Triplet Transfer in Singlet Fission-Sensitized Silicon Solar Cells

Singlet fission in tetracene generates two triplet excitons per absorbed photon. If these triplet excitons can be effectively transferred into silicon (Si), then additional photocurrent can be generated from photons above the bandgap of Si. This could alleviate the thermalization loss and increase the efficiency of conventional Si solar cells. Here, we show that a change in the polymorphism of tetracene deposited on Si due to air exposure facilitates triplet transfer from tetracene into Si. Magnetic field-dependent photocurrent measurements confirm that triplet excitons contribute to the photocurrent. The decay of tetracene delayed photoluminescence was used to determine a transfer efficiency of ∼36% into Si. Our study suggests that control over the morphology of tetracene during the deposition will be of great importance to boost the triplet transfer yield further.