Packing Guidelines for Optimizing Singlet Fission Matrix Elements in Noncovalent Dimers

A framework for multiexcitonic logic

Exciton science sits at the intersection of chemical, optical and spin-based implementations of information processing, but using excitons to conduct logical operations remains relatively unexplored. Excitons encoding information could be read optically (photoexcitation-photoemission) or electrically (charge recombination-separation), travel through materials via exciton energy transfer, and interact with one another in stimuli-responsive molecular excitonic devices. Excitonic logic offers the potential to mediate electrical, optical and chemical information. Additionally, high-spin triplet and quintet (multi)excitons offer access to well defined spin states of relevance to magnetic field effects, classical spintronics and spin-based quantum information science. In this Roadmap, we propose a framework for developing excitonic computing based on singlet fission (SF) and triplet-triplet annihilation (TTA). Various molecular components capable of modulating SF/TTA for logical operations are suggested, including molecular photo-switching and multi-colour photoexcitation. We then outline a pathway for constructing excitonic logic devices, considering aspects of circuit assembly, logical operation synchronization, and exciton transport and amplification. Promising future directions and challenges are identified, and the potential for realizing excitonic computing in the near future is discussed.

Structural Disorder at the Edges of Rubrene Crystals Enhances Singlet Fission

Materials that undergo singlet fission are of interest for their use in light-harvesting, photocatalysis, and quantum information science, but their ability to undergo fission can be sensitive to local variations in molecular packing. Herein we employ transient absorption microscopy, molecular dynamics simulations, and electronic structure calculations to interrogate how structures found at the edges of orthorhombic rubrene crystals impact singlet fission. Within a micrometer-scale spatial region at the edges of rubrene crystals, we find that the rate of singlet fission increases nearly 4-fold. This observation is consistent with formation of a region at crystal edges with reduced order that accelerates singlet fission by disrupting the symmetry found in rubrene's orthorhombic crystal structure. Our work demonstrates that structural distortions of singlet fission materials can be used to control fission in time and in space, potentially offering a means of controlling this process in light harvesting and quantum information applications.

Modulating singlet fission through interchromophoric rotation

Singlet fission (SF) is a spin-allowed, exciton-multiplying phenomenon that can be utilized to improve the efficiency of organic solar cells. It is well-understood that SF is sensitive to the local crystal morphology and an appropriately balanced coupling is essential to facilitate efficient SF. In this study, we show how the interchromophoric rotation selectively modulates the interaction between the monomer frontier molecular orbitals, promoting both fast and exothermal SF. We evaluate the effective electronic coupling for SF (V_SF), the square of which is proportional to the SF rate, and the effective energies of the Frenkel exciton (FE/S₁S₀) and triplet pair exciton (TT) in a terrylene dimer model. Optimal interplanar rotation of the chromophoric moieties in slip-stacked arrangements pulls the effective energy of the TT state below that of the FE state. Consequently, SF is favored over competing pathways such as excimer formation, thereby enhancing the overall triplet yield. This work represents a step towards improvising the molecular design guidelines for SF and understanding the importance of interchromophoric rotation over the conventional slip-stacked arrangements for achieving favorable intermolecular electronic coupling towards efficient SF.

Molecular rotational conformation controls the rate of singlet fission and triplet decay in pentacene dimers

Three pentacene dimers have been synthesized to investigate the effect of molecular rotation and rotational conformations on singlet fission (SF). In all three dimers, the pentacene units are linked by a 1,4-diethynylphenylene spacer that provides almost unimpeded rotational freedom between the pentacene- and phenylene-subunits in the parent dimer. Substituents on the phenylene spacer add varying degrees of steric hindrance that restricts both the rotation and the equilibrium distribution of different conformers; the less restricted conformers exhibit faster SF and more rapid subsequent triplet-pair recombination. Furthermore, the rotational conformers have small shifts in their absorption spectra and this feature has been used to selectively excite different conformers and study the resulting SF. Femtosecond transient absorption studies at 100 K reveal that the same dimer can have orders of magnitude faster SF in a strongly coupled conformer compared to a more weakly coupled one. Measurements in polystyrene further show that the SF rate is nearly independent of viscosity whereas the triplet pair lifetime is considerably longer in a high viscosity medium. The results provide insight into design criteria for maintaining high initial SF rate while suppressing triplet recombination in intramolecular singlet fission.

In this study we show that one molecule can have vastly different singlet fission and triplet recombination rates depending on its rotational freedom and the relative orientation of the pentacene moieties.

Identifying Hidden Intracell Symmetries in Molecular Crystals and Their Impact for Multiexciton Generation

Organic molecular crystals are appealing for next-generation optoelectronic applications due to their multiexciton generation processes that can increase the efficiency of photovoltaic devices. However, a general understanding of how crystal structures affect these processes is lacking, requiring computationally demanding calculations for each material. Here we present an approach to understand and classify organic crystals and elucidate multiexciton processes. We show that organic crystals that are composed of two sublattices are well-approximated by effective fictitious systems of higher translational symmetry. Within this framework, we derive hidden selection rules in crystal pentacene and predict that the bulk polymorph supports fast Coulomb-mediated singlet fission with a transition rate about 2 orders of magnitude faster than that of the thin-film polymorph, a result confirmed with many-body perturbation theory calculations. Our approach is based on density-functional theory calculations and provides design principles for the experimental and computational discovery of new materials with tailored excitonic properties.

Evaluating the Electronic Structure of Coexisting Excitonic and Multiexcitonic States in Periodic Systems: Significance for Singlet Fission

Singlet fission (SF) in organic molecular solids is an example of a process that is challenging to describe with the most common electronic structure approaches. It involves optically bright singlet excited states delocalized over many molecules, which could be efficiently treated by density functional theory, and multiexcitonic localized states that have to be studied with wavefunction methods, usually with small clusters considering their expensive computational costs. In this work, we propose a methodology to combine multiconfigurational wavefunction calculations with reduced Hamiltonian to investigate the electronic structure of large clusters or fully periodic systems. The method is applied to the prototypical SF materials tetracene and pentacene. The results allow one to study how states of different natures (excitonic, charge-transfer, and multiexcitonic) coexist and are contaminated by their couplings in large or periodic systems. Novel insights are therefore possible. For example, because the excitonic bands are relatively broad with respect to the multiexcitonic states, there are limited regions of the crystal momentum space where the transition between the two is more likely.

Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer

In this work, we study singlet fission in tetracene para-dimers, covalently linked by a phenyl group. In contrast to most previous studies, we account for the full quantum dynamics of the combined excitonic and vibrational system. For our simulations, we choose a numerically unbiased representation of the molecule's wave function, enabling us to compare with experiments, exhibiting good agreement. Having access to the full wave function allows us to study in detail the post-quench dynamics of the excitons. Here, one of our main findings is the identification of a time scale t₀ ≈ 35 fs dominated by coherent dynamics. It is within this time scale that the larger fraction of the singlet fission yield is generated. We also report on a reduced number of phononic modes that play a crucial role in the energy transfer between excitonic and vibrational systems. Notably, the oscillation frequency of these modes coincides with the observed electronic coherence time t₀. We extend our investigations by also studying the dependency of the dynamics on the excitonic energy levels that, for instance, can be experimentally tuned by means of the solvent polarity. Here, our findings indicate that the singlet fission yield can be doubled, while the electronic coherence time t₀ is mainly unaffected.

Structure Dependence of Kinetic and Thermodynamic Parameters in Singlet Fission Processes

Singlet fission-whereby one absorbed photon generates two coupled triplet excitons-is a key process for increasing the efficiency of optoelectronic devices by overcoming the Shockley-Queisser limit. A crucial parameter is the rate of dissociation of the coupled triplets, as this limits the number of free triplets subsequently available for harvesting and ultimately the overall efficiency of the device. Here we present an analysis of the thermodynamic and kinetic parameters for this process in parallel and herringbone dimers measured by electron paramagnetic resonance spectroscopy in coevaporated films of pentacene in p-terphenyl. The rate of dissociation is higher for parallel dimers than for their herringbone counterparts, as is the rate of recombination to the ground state. DFT calculations, which provide the magnitude of the electronic coupling as well as the distribution of molecular orbitals for each geometry, suggest that weaker triplet coupling in the parallel dimer is the driving force for faster dissociation. Conversely, localization of the molecular orbitals and a stronger triplet-triplet interaction result in slower dissociation and recombination. The identification and understanding of how the intermolecular geometry promotes efficient triplet dissociation provide the basis for control of triplet coupling and thereby the optimization of one important parameter of device performance.

Orientational Dependence of Cofacial Porphyrin-Quinone Electronic Interactions within the Strong Coupling Regime

We examine the relative magnitudes of electronic coupling H_DA in two face-to-face rigid and diastereomeric (porphinato)zinc(II)-quinone (PZn-Q) assemblies, 1β-ZnA and 1β-ZnB, in which the six quinonyl carbon atoms lie in virtually identical arrangements relative to the PZn plane at sub-van der Waals donor-acceptor (D-A) interplanar separations. Steady-state and time-resolved transient optical data and computational studies show that minor differences in relative D-A cofacial orientation give rise to disparate H_DA magnitudes for both photoinduced charge separation (CS) and thermal charge recombination (CR). Time-dependent density functional theory (TDDFT) computations illuminate the nature of direct charge transfer states and the electronic structural factors that give rise to these differential H_DAs. These data show more extensive mixing of locally excited (LE) and CS states in 1β-ZnA relative to 1β-ZnB and that these H_DA differences track the magnitudes of electronic coupling matrix elements determined from steady-state electronic spectral data and thermal CR rate constants measured via pump-probe spectroscopy. Collectively, this work shows that electron transfer dynamics may be manipulated in cofacial D-A systems, even at sub-van der Waals contact, provided that conformational rigidity precludes structural fluctuations that modulate D-A interactions on the charge transfer time scale.

Structure and photophysics of indigoids for singlet fission: Cibalackrot

We report an investigation of structure and photophysics of thin layers of cibalackrot, a sturdy dye derived from indigo by double annulation at the central double bond. Evaporated layers contain up to three phases, two crystalline and one amorphous. Relative amounts of all three have been determined by a combination of X-ray diffraction and FT-IR reflectance spectroscopy. Initially, excited singlet state rapidly produces a high yield of a transient intermediate whose spectral properties are compatible with charge-transfer nature. This intermediate more slowly converts to a significant yield of triplet, which, however, does not exceed 100% and may well be produced by intersystem crossing rather than singlet fission. The yields were determined by transient absorption spectroscopy and corrected for effects of partial sample alignment by a simple generally applicable procedure. Formation of excimers was also observed. In order to obtain guidance for improving molecular packing by a minor structural modification, calculations by a simplified frontier orbital method were used to find all local maxima of singlet fission rate as a function of geometry of a molecular pair. The method was tested at 48 maxima by comparison with the ab initio Frenkel-Davydov exciton model.

Singlet Fission Rate: Optimized Packing of a Molecular Pair. Ethylene as a Model

A procedure is described for unbiased identification of all π-electron chromophore pair geometry choices that locally maximize the rate of conversion of a singlet exciton into a singlet biexciton (triplet pair), using a simplified version of the diabatic frontier orbital model of singlet fission (SF). The resulting approximate optimal geometries provide insight and are expected to represent useful starting points for searches by more advanced methods. The general procedure is illustrated on a pair of ethylenes as the simplest model of a π-electron system, but it is applicable to pairs of much larger molecules, with dozens of non-hydrogen atoms, and not necessarily planar. We first examine the value of |T^A|², the square of the electronic matrix element for SF with initial excitation fully localized on partner A, on a grid of several billion geometries within the six-dimensional space of physically realizable possibilities. Several of the optimized pair geometries are somewhat unexpected, but all are found to follow the qualitative guidance proposed earlier. In the neighborhood of each local maximum of |T^A|², consideration of mixing with charge-transfer configurations and of excitonic interaction between partners A and B determines the SF energy balance and yields squared matrix elements |T*|² and |T**|² for the lower and upper excitonic states S* and S**, respectively. Assuming Boltzmann populations of these states, the geometry is further optimized to maximize k, the sum of the SF rates obtained from Marcus theory, and this reorders the suitable geometries substantially. At 87 pair geometries, the |T*|² and |T**|² values are compared with those obtained from high-level ab initio nonorthogonal configuration interaction calculations and found to follow the same trend. Finally, the biexciton binding energy at the optimized geometries is calculated. Altogether, 13 significant local maxima of SF rate for a pair of ethylenes are identified in the physically relevant part of space that avoids molecular interpenetration in the hard-sphere approximation. The three best geometries are twist-stacked, slip-stacked, and L-shaped. The maxima occur at the (five-dimensional) surfaces of seven six-dimensional "parent" regions of space centered at physically inaccessible geometries at which the calculated SF rate is very large but the two ethylenes interpenetrate. The results are displayed in interactive graphics. The computer code ("Simple") written for these calculations is flexible in that it permits a choice of performing the search for local maxima in six dimensions on |T^A|², |T*|², or k. It is available as freeware at https://cloud.uochb.cas.cz/simple .

Optimal arrangements of 1,3-diphenylisobenzofuran molecule pairs for fast singlet fission

A simplified version of the frontier orbital model has been applied to pairs of C₂, C_2v, C_s, and C₁ symmetry 1,3-diphenylisobenzofuran rotamers to determine their best packing for fast singlet fission (SF). For each rotamer the square of the electronic matrix element for SF was calculated at 2.2 × 10⁹ pair geometries and a few thousand most significant physically accessible local maxima were identified in the six-dimensional space of mutual arrangements. At these pair geometries, SF energy balance was evaluated, relative SF rate constants were approximated using Marcus theory, and the SF rate constant k_SF was maximized by further optimization of the geometry of the molecular pair. The process resulted in 142, 67, 214, and 291 unique geometries for the C₂, C_2v, C_s, and C₁ symmetry molecular pairs, respectively, predicted to be superior to the C₂ symmetrized known crystal pair structure. These optimized pair geometries and their triplet biexciton binding energies are reported as targets for crystal engineering and/or covalent dimer synthesis, and as possible starting points for high-level pair geometry optimizations.

Resolving population dynamics and interactions of multiple triplet excitons one molecule at a time

Resolving the population dynamics of multiple triplet excitons on time scales comparable to their lifetimes is a key challenge for multiexciton harvesting strategies, such as singlet fission. We show that this information can be obtained from fluorescence quenching dynamics and stochastic kinetic modeling simulations of single nanoparticles comprising self-assembled aggregated chains of poly(3-hexylthiophene) (P3HT). These multichromophoric structures exhibit the elusive J-aggregate type excitonic coupling leading to delocalized intrachain excitons that undergo facile triplet formation mediated by interchain charge transfer states. We propose that P3HT J-aggregates can serve as a useful testbed for elucidating the presence of multiple triplets and understanding factors governing their interactions over a broad range of time scales. Stochastic kinetic modeling is then used to simulate discrete population dynamics and estimate higher order rate constants associated with triplet-triplet and singlet-triplet annihilation. Together with the quasi-CW nature of the experiment, the model reveals the expected amounts of triplets at equilibrium per molecule. Our approach is also amenable to a variety of other systems, e.g., singlet fission active molecular arrays, and can potentially inform design and optimization strategies to improve triplet harvesting yields.

Population dynamics of multiple triplet excitons revealed from time-dependent fluorescence quenching of single conjugated polymer chains

The advent of multiple exciton harvesting schemes and prolonging exciton lifetimes to improve performance attributes of solar cells based on conjugated organic materials presents some interesting challenges that must be overcome in order to realize the full potential of these strategies. This is especially important for applications involving multi-chromophoric conjugated polymers where interactions between multiple spin-forbidden triplet excitons can be significant and are mediated by chain conformation. We use single molecule spectroscopic techniques to investigate interactions between multiple triplet excitons and emissive singlets by monitoring time-dependent fluorescence quenching on time scales commensurate with the triplet lifetime. Structurally related conjugated polymers differing by heteroatom substitution were targeted and we use a stochastic photodynamic model to numerically simulate the evolution of multi-exciton populations following photoexcitation. Single chains of poly(3-hexylthiophene) (P3HT) exhibit longer-lived triplet dynamics and larger steady-state triplet occupancies compared to those of poly(3-hexylselenophene) (P3HS), which has a larger reported triplet yield. Triplet populations evolve and relax much faster in P3HS which only becomes evident when considering all kinetic factors governing exciton population dynamics. Overall, we uncover new guidelines for effectively managing multi-exciton populations and interactions in conjugated polymers and improving their light harvesting efficiency.

Dehydrative π-extension to nanographenes with zig-zag edges

Zig-zag nanographenes are promising candidates for the applications in organic electronics due to the electronic properties induced by their periphery. However, the synthetic access to these compounds remains virtually unexplored. There is a lack in efficient and mild strategies origins in the reduced stability, increased reactivity, and low solubility of these compounds. Herein we report a facile access to pristine zig-zag nanographenes, utilizing an acid-promoted intramolecular reductive cyclization of arylaldehydes, and demonstrate a three-step route to nanographenes constituted of angularly fused tetracenes or pentacenes. The mild conditions are scalable to gram quantities and give insoluble nanostructures in close to quantitative yields. The strategy allows the synthesis of elusive low bandgap nanographenes, with values as low as 1.62 eV. Compared to their linear homologues, the structures have an increased stability in the solid-state, even though computational analyses show distinct diradical character. The structures were confirmed by X-ray diffraction or scanning tunneling microscopy.

Striking the right balance of intermolecular coupling for high-efficiency singlet fission

Singlet fission is a process that splits collective excitations, or excitons, into two with unity efficiency. This exciton splitting process, unique to molecular photophysics, has the potential to considerably improve the efficiency of optoelectronic devices through more efficient light harvesting. While the first step of singlet fission has been characterized in great detail, subsequent steps critical to achieving overall highly-efficient singlet-to-triplet conversion are only just beginning to become well understood. One of the most elementary suggestions, which has yet to be tested, is that an appropriately balanced coupling is necessary to ensure overall highly efficient singlet fission; that is, the coupling needs to be strong enough so that the first step is fast and efficient, yet weak enough to ensure the independent behavior of the resultant triplets. In this work, we show how high overall singlet-to-triplet conversion efficiencies can be achieved in singlet fission by ensuring that the triplets comprising the triplet pair behave as independently as possible. We show that side chain sterics govern local packing in amorphous pentacene derivative nanoparticles, and that this in turn controls both the rate at which triplet pairs form and the rate at which they decay. We show how compact side chains and stronger couplings promote a triplet pair that effectively couples to the ground state, whereas bulkier side chains promote a triplet pair that appears more like two independent and long-lived triplet excitations. Our results show that the triplet pair is not emissive, that its decay is best viewed as internal conversion rather than triplet-triplet annihilation, and perhaps most critically that, in contrast to a number of recent suggestions, the triplets comprising the initially formed triplet pair cannot be considered independently. This work represents a significant step toward better understanding intermediates in singlet fission, and how molecular packing and couplings govern overall triplet yields.

Theoretical Studies of Singlet Fission: Searching for Materials and Exploring Mechanisms

In this Review article, a survey is given for theoretical studies in the subject of singlet fission. Singlet fission converts one singlet exciton to two triplet excitons. With the doubled number of excitons and the longer lifetime of the triplets, singlet fission provides an avenue to improve the photoelectric conversion efficiency in organic photovoltaic devices. It has been a subject of intense research in the past decade. Theoretical studies play an essential role in understanding singlet fission. This article presents a Review of theoretical studies in singlet fission since 2006, the year when the research interest in this subject was reignited. Both electronic structure and dynamics studies are covered. Electronic structure studies provide guidelines for designing singlet fission chromophores and insights into the couplings between single- and multi-excitonic states. The latter provides fundamental knowledge for engineering interchromophore conformations to enhance the fission efficiency. Dynamics studies reveal the importance of vibronic couplings in singlet fission.