Mapping the Relation between Stacking Geometries and Singlet Fission Yield in a Class of Organic Crystals

Functionality optimization for effective singlet fission coupling screening in the full-dimensional molecular and intermolecular coordinate space

In computational chemistry, accurately predicting molecular configurations that exhibit specific properties remains a critical challenge. Its intricacies become especially evident in the study of molecular aggregates, where the light-induced functionality is tied to highly structure-dependent electronic couplings between molecules. Here, we present an efficient strategy for the targeted screening of the structural space employing a "functionality optimization" technique, in which a chosen descriptor, constrained by the ground state energy expression, is optimized. The chosen algorithmic differentiation (AD) framework allows one to automatically obtain gradients without its tedious implementation. We demonstrate the effectiveness of the approach by identifying perylene bisimide (PBI) dimer motifs with enhanced effective SF coupling. Our findings reveal that certain structural modifications of the PBI monomer, such as helical twisting and bending as well as slipped-rotated packing arrangements, can significantly increase the effective SF coupling.

Electronic Couplings for Triplet-Triplet Annihilation Upconversion in Crystal Rubrene

Triplet-triplet annihilation photon upconversion (TTA-UC) is a process able to repackage two low-frequency photons into light of higher energy. This transformation is typically orchestrated by the electronic degrees of freedom within organic compounds possessing suitable singlet and triplet energies and electronic couplings. In this work, we propose a computational protocol for the assessment of electronic couplings crucial to TTA-UC in molecular materials and apply it to the study of crystal rubrene. Our methodology integrates sophisticated yet computationally affordable approaches to quantify couplings in singlet and triplet energy transfer, the binding of triplet pairs, and the fusion to the singlet exciton. Of particular significance is the role played by charge-transfer states along the b-axis of rubrene crystal, acting as both partial quenchers of singlet energy transfer and mediators of triplet fusion. Our calculations identify the π-stacking direction as holding notable triplet energy transfer couplings, consistent with the experimentally observed anisotropic exciton diffusion. Finally, we have characterized the impact of thermally induced structural distortions, revealing their key role in the viability of triplet fusion and singlet fission. We posit that our approaches are transferable to a broad spectrum of organic molecular materials, offering a feasible means to quantify electronic couplings.

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.

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.

Molecular Design and Crystal Chemistry of Polyfluorinated Naphthalene-bis-phenylhydrazimides with Superior Thermal and Polymorphic Stability and High Solution Processability

Naphthalene tetracarboxylic diimides (NDIs) are highly promising air-stable n-type molecular semiconductor candidates for flexible and cost-effective organic solar cells and thermoelectrics. Nonetheless, thermal and polymorphic stabilities of environmentally stable NDIs in the low-to-medium temperature regime (<300 °C) remain challenging properties. Structural, thermal, spectroscopic, and computational features of polyfluorinated NDI-based molecular solids (with up to 14 F atoms per NDI molecule) are discussed upon increasing the fluorination level. Slip-stacked arrangement of the NDI cores with suitable π-π stacking and systematically short interplanar distances (<3.2 Å) are found. All these materials exhibit superior thermal stability (up to 260 °C or above) and thermal expansion coefficients indicating a response compatible with flexible polymeric substrates. Optical bandgaps increase from 2.78 to 2.93 eV with fluorination, while LUMO energy levels decrease down to -4.37 eV, as shown per DFT calculations. The compounds exhibit excellent solubility of 30 mg mL^-1 in 1,4-dioxane and DMF.

True molecular conformation and structure determination by three-dimensional electron diffraction of PAH by-products potentially useful for electronic applications

The true molecular conformation and the crystal structure of benzo[e]dinaphtho[2,3-a;1',2',3',4'-ghi]fluoranthene, 7,14-diphenylnaphtho[1,2,3,4-cde]bisanthene and 7,16-diphenylnaphtho[1,2,3,4-cde]helianthrene were determined ab initio by 3D electron diffraction. All three molecules are remarkable polycyclic aromatic hydrocarbons. The molecular conformation of two of these compounds could not be determined via classical spectroscopic methods due to the large size of the molecule and the occurrence of multiple and reciprocally connected aromatic rings. The molecular structure of the third molecule was previously considered provisional. These compounds were isolated as by-products in the synthesis of similar products and were at the same time nanocrystalline and available only in very limited amounts. 3D electron diffraction data, taken from submicrometric single crystals, allowed for direct ab initio structure solution and the unbiased determination of the internal molecular conformation. Detailed synthetic routes and spectroscopic analyses are also discussed. Based on many-body perturbation theory simulations, benzo[e]dinaphtho[2,3-a;1',2',3',4'-ghi]fluoranthene may be a promising candidate for triplet-triplet annihilation and 7,14-diphenylnaphtho[1,2,3,4-cde]bisanthene may be a promising candidate for intermolecular singlet fission in the solid state.

Self-Assembling Behaviour of Perylene, Perylene Diimide, and Thionated Perylene Diimide Deciphered through Non-Covalent Interactions

The π-conjugated supramolecular polymers (SMP) have gained vast popularity in materials chemistry and biomedicine due to their spectacular self-assembling behaviour. A detailed account of the electronic structure and bonding through quantum theory of atoms-in-molecules, non-covalent interactions, and energy decomposition analysis (EDA) in the oligomers of perylene, perylene diimide (PDI), and thionated-PDI (t-PDI) is presented. The oligomers of all three molecules show a slip angle of θ≈62° thus forming H-aggregates. The stacking pattern in perylene oligomers prefers a slip-stacked brick-layer order, while the bulkier PDI and t-PDI prefer a parallel step-wise pattern in their oligomers. Successive addition of monomers leads to a consequent rise in the association energy, although to a much greater extent in PDI and t-PDI than in perylene. While the major contribution to this association energy comes from the dispersion interactions in all three systems, the steric interactions in t-PDI quench the cooperativity in its SMP formation. A detailed analysis of the non-covalent interactions reveals the presence of π-π, π-hole⋅⋅⋅O=C, and π-hole⋅⋅⋅S=C electrostatic interactions playing a crucial role in the self-assembly process, which can be further implemented on developing force field-based methods for understanding the self-assembling mechanism in higher degree of oligomers.

Steering the multiexciton generation in slip-stacked perylene dye array via exciton coupling

Dye arrays from dimers up to larger oligomers constitute the functional units of natural light harvesting systems as well as organic photonic and photovoltaic materials. Whilst in the past decades many photophysical studies were devoted to molecular dimers for deriving structure-property relationship to unravel the design principles for ideal optoelectronic materials, they fail to accomplish the subsequent processes of charge carrier generation or the detachment of two triplet species in singlet fission (SF). Here, we present a slip-stacked perylene bisimide trimer, which constitutes a bridge between hitherto studied dimer and solid-state materials, to investigate SF mechanisms. This work showcases multiple pathways towards the multiexciton state through direct or excimer-mediated mechanisms by depending upon interchromophoric interaction. These results suggest the comprehensive role of the exciton coupling, exciton delocalization, and excimer state to facilitate the SF process. In this regard, our observations expand the fundamental understanding the structure-property relationship in dye arrays.

Understanding structure-property relationship of dye arrays is of great importance for designing organic photonic and photovoltaic materials. Here, authors present a slip-stacked perylene bisimide array as a model system to investigate singlet fission mechanisms by depending upon interchromophoric interaction.

Effect of nanoscale confinement on ultrafast dynamics of singlet fission in TIPS-pentacene

Singlet fission (SF) is a phenomenon for the generation of a pair of triplet excitons from a singlet excited molecule interacting with another adjacent molecule in its ground electronic state. By increasing the effective number of charge carriers and reducing thermal dissipation of excess energy, SF is promised to enhance light-harvesting efficiency for photovoltaic applications. While SF has been extensively studied in thin films and crystals, the same has not been explored much within a confined medium. Here, we report the ultrafast SF dynamics of triisopropylsilylethynyl pentacene (TIPS-Pn) in micellar nanocavity of varying sizes (prepared from TX-100, CTAB, and SDS surfactants). The nanoparticle with a smaller size contains weakly coupled chromophores and is shown to be more efficient for SF followed by triplet generation as compared to the nanoparticles of larger size which contain strongly coupled chromophores and are less efficient due to the presence of singlet exciton traps. Through these studies, we delineate how a subtle interplay between short-range and long-range interaction among chromophores confined within nanoparticles, fine-tuned by the curvature of the micellar interface but irrespective of the nature of the micelle (cationic or anionic or neutral), play a crucial role in SF through and generation of triplets.

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.

Environmental effects on the singlet fission phenomenon: a model Hamiltonian-based study

In the screening of compounds for singlet fission, the relative energies of the constitutive units are decisive to fulfil the thermodynamic rules. From a model Hamiltonian constructed on the local spin states of an active chromophore and its environment, it is suggested that embedding greatly influences the energy differences of the active monomer spin states. Even in the absence of charge transfer, the field generated by a singlet environment produces an increase of the [E(S₁) - E(S₀)]/[E(T₁) - E(S₀)] critical ratio by up to 6% as compared to the one of a free chromophore. Besides, variations are observed when the intimate electronic structure of the singlet environment is modified. This propensity towards singlet fission is even more pronounced (10%) when the environment is switched to the triplet state. Finally, the embedding is likely to reverse the spin state ordering in the limit of vanishing atomic orbital overlaps. Despite its simplicity, the model stresses the importance of the environment spin nature in the quest for singlet fission candidates, and more generally in spectroscopy analysis.

Enhancing Singlet Fission Coupling with Nonbonding Orbitals

Singlet fission (SF) is a process where a singlet exciton is split into a pair of triplet excitons. The increase in the excitonic generation can be exploited to enhance the efficiency of solar cells. Molecules with conjugated π bonds are commonly developed for optoelectronic applications including SF, due to their low energy gaps. The electronic coupling for SF in such well-stacked π-conjugated molecule pairs can be rather limited due to the orthogonal π and π* orbital overlaps that are involved in the coupling elements, leading to a large cancellation in the coupling. In the present work, we show that such limits can be removed by involving triplet states of different origins, such as those with nonbonding n orbitals. We demonstrate such an effect for formaldehyde and methylenimine dimers, with a low-lying n-π* triplet state (T₁) in addition to the π-π* triplet (T₂). We show that the coupling can be enhanced by 40 times or more for the formaldehyde dimer, and 15 times or more for the methylenimine dimer, with the T₁-T₂ state as the end product of SF. With 1759 randomly oriented pairs of formaldehyde derived from a molecular dynamics simulation, the coupling from a singlet exciton to this T₁-T₂ state is, on an average, almost two times larger than that for a regular T₁-T₁ state. We investigated a few families that have been shown to be prospective candidates for SF, using our proposed strategy. However, our unfavorable results indicate that there are clear difficulties in fulfilling the E_S1 ≳ E_T1 + E_T2 energy criterion. Nevertheless, our results provide a new molecular design concept for better SF (and triplet-triplet annihilation, TTA) materials that allows future development.

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.

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.

Singlet Fission Dynamics of Colloidal Nanoparticles of a Perylenediimide Derivative in Solutions

Singlet fission (SF) is an intriguing process in which a singlet exciton produces two triplet excitons in molecular aggregates. Perylenediimide (PDI) derivatives are promising materials for SF-based photovoltaics, and the SF process in PDI aggregates is important to investigate for their applications. In this work, we studied the entire SF process occurring in the colloidal nanoparticles of a PDI derivative in solutions by using time-resolved fluorescence and transient absorption (TA) experiments. PE-PDI was found to form the colloidal nanoparticles of H- and J-aggregates in polar solvents. The TA signals of PE-PDI aggregates in solutions were selectively measured by wavelength-dependent excitation. The TA signals were analyzed by using a global fitting analysis, and all kinetic parameters involved in the entire SF process were determined. Our current investigation has confirmed that fast SF occurs on the surface of the colloidal nanoparticles of PDI aggregates via the charge transfer mediated mechanism, giving a high quantum yield of triplet excitons.

Singlet Fission in Thin Solid Films of Bis(thienyl)diketopyrrolopyrroles

The singlet fission (SF) process discovered in bis(thienyl)diketopyrrolopyrroles (TDPPs) can boost their potential for photovoltaics (PV). The crystal structures of TDPP analogs carrying n-hexyl, n-butyl, or 2-(adamant-1-yl)ethyl substituents are similar, but contain increasingly slipped stacked neighbor molecules. The observed SF rate constants, k_SF , (7±4), (9±3) and (5.6±1.9) ns^-1 for thin films of the three compounds, respectively, are roughly equal, but the triplet quantum yields vary strongly: (120±40), (160±40) and (70±16), respectively. The recent molecular pair model reproduces the near equality of all three k_SF at the crystal geometries and identifies all possible pair arrangements in which SF is predicted to be faster, by up to two orders of magnitude. However, it is also clear that the presently non-existent ability to predict the rates of processes competing with SF is pivotal for providing a guide for efforts to optimize the materials for PV.

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.

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.

Energetics and optimal molecular packing for singlet fission in BN-doped perylenes: electronic adiabatic state basis screening

Singlet fission has the potential to increase the efficiency of photovoltaic devices, but the design of suitable chromophores is notoriously difficult. Both the electronic properties of the monomer and the packing motif in the crystal have a big impact on the singlet fission efficiency. Using perylene as an example, it is shown that doping with boron and nitrogen not only helps to align the energy levels but also shifts the stacking position that is optimal for singlet fission. Among all perylene derivatives doped with one or two BN groups, we identify the most suitable isomer for singlet fission with the help of TD-DFT and CASPT2 calculations. The optimal relative disposition of the two monomer units in a cofacially stacked homodimer is explored using two semiempirical models for the singlet fission rate: The first one is the well-known diabatic frontier orbital model, while the second treats singlet fission as a non-adiabatic transition and approximates the rate as the length squared of the non-adiabatic coupling vector between eigenfunctions of the diabatic Hamiltonian.

Modulating the Electronic and Solid-State Structure of Organic Semiconductors by Site-Specific Substitution: The Case of Tetrafluoropentacenes

The properties as well as solid-state structures, singlet fission, and organic field-effect transistor (OFET) performance of three tetrafluoropentacenes (1,4,8,11: 10, 1,4,9,10: 11, 2,3,9,10: 12) are compared herein. The novel compounds 10 and 11 were synthesized in high purity from the corresponding 6,13-etheno-bridged precursors by reaction with dimethyl 1,2,4,5-tetrazine-3,6-dicarboxylate at elevated temperatures. Although most of the molecular properties of the compounds are similar, their chemical reactivity and crystal structures differ considerably. Isomer 10 undergoes the orbital symmetry forbidden thermal [4+4] dimerization, whereas 11 and 12 are much less reactive. The isomers 11 and 12 crystallize in a herringbone motif, but 10 prefers π-π stacking. Although the energy of the first electric dipole-allowed optical transition varies only within 370 cm-1 (0.05 eV) for the neutral compounds, this amounts to roughly 1600 cm-1 (0.20 eV) for radical cations and 1300 cm-1 (0.16 eV) for dications. Transient spectroscopy of films of 11 and 12 reveals singlet-fission time constants (91±11, 73±3 fs, respectively) that are shorter than for pentacene (112±9 fs). OFET devices constructed from 11 and 12 show close to ideal thin-film transistor (TFT) characteristics with electron mobilities of 2×10-3 and 6×10-2  cm2  V-1  s-1 , respectively.

Lessons from intramolecular singlet fission with covalently bound chromophores

Molecular dimers, oligomers, and polymers are versatile components in photophysical and optoelectronic architectures that could impact a variety of applications. We present a perspective on such systems in the field of singlet fission, which effectively multiplies excitons and produces a unique excited state species, the triplet pair. The choice of chromophore and the nature of the attachment between units, both geometrical and chemical, play a defining role in the dynamical scheme that evolves upon photoexcitation. Specific final outcomes (e.g., separated and uncorrelated triplet pairs) are being sought through rational design of covalently bound chromophore architectures built with guidance from recent fundamental studies that correlate structure with excited state population flow kinetics.

Topology of quantum coherence networks in singlet fission: mapping exciton states into real space and the dislocation induced three dimensional manifolds

An understanding of the global structure of quantum coherence networks in coupled multistate systems is of great importance for the development of emerging quantum technologies such as quantum control and quantum materials design. Here, we study the topology of a quantum coherence network of a typical singlet exciton fission system by mapping the exciton states into crystal structures in real space. The defects in crystals could lead to changes in the topological structures, and also fission dynamics. In particular, we demonstrate that the dislocation induced three dimensional manifold, which differs from its lower dimensional counterparts globally, could generate exotic global structures, such as chiral spirals, and modulate singlet fission substantially. The findings may shed light on the new possibilities of engineering effective structures for fission materials.

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 .

Exploiting Excited-State Aromaticity To Design Highly Stable Singlet Fission Materials

Singlet fission, the process of forming two triplet excitons from one singlet exciton, is a characteristic reserved for only a handful of organic molecules due to the atypical energetic requirement for low energy excited triplet states. The predominant strategy for achieving such a trait is by increasing ground state diradical character; however, this greatly reduces ambient stability. Herein, we exploit Baird's rule of excited state aromaticity to manipulate the singlet-triplet energy gap and create novel singlet fission candidates. We achieve this through the inclusion of a [4n] 5-membered heterocycle, whose electronic resonance promotes aromaticity in the triplet state, stabilizing its energy relative to the singlet excited state. Using this theory, we design a family of derivatives of indolonaphthyridine thiophene (INDT) with highly tunable excited state energies. Not only do we access novel singlet fission materials, they also exhibit excellent ambient stability, imparted due to the delocalized nature of the triplet excited state. Spin-coated films retained up to 85% activity after several weeks of exposure to oxygen and light, while analogous films of TIPS-pentacene showed full degradation after 4 days, showcasing the excellent stability of this class of singlet fission scaffold. Extension of our theoretical analysis to almost ten thousand candidates reveals an unprecedented degree of tunability and several thousand potential fission-capable candidates, while clearly demonstrating the relationship between triplet aromaticity and singlet-triplet energy gap, confirming this novel strategy for manipulating the exchange energy in organic materials.

Substituent effects on energetics and crystal morphology modulate singlet fission in 9,10-bis(phenylethynyl)anthracenes

Singlet fission (SF) converts a singlet exciton into two triplet excitons in two or more electronically coupled organic chromophores, which may then be used to increase solar cell efficiency. Many known SF chromophores are unsuitable for device applications due to chemical instability or low triplet state energies. The results described here show that efficient SF occurs in derivatives of 9,10-bis(phenylethynyl)anthracene (BPEA), which is a highly robust and tunable chromophore. Fluoro and methoxy substituents at the 4- and 4'-positions of the BPEA phenyl groups control the intermolecular packing in the crystal structure, which alters the interchromophore electronic coupling, while also changing the SF energetics. The lowest excited singlet state (S₁) energy of 4,4'-difluoro-BPEA is higher than that of BPEA so that the increased thermodynamic favorability of SF results in a (16 ± 2 ps)^-1 SF rate and a 180% ± 16% triplet yield, which is about an order of magnitude faster than BPEA with a comparable triplet yield. By contrast, 4-fluoro-4'-methoxy-BPEA and 4,4'-dimethoxy-BPEA have slower SF rates, (90 ± 20 ps)^-1 and (120 ± 10 ps)^-1, and lower triplet yields, (110 ± 4)% and (168 ± 7)%, respectively, than 4,4'-difluoro-BPEA. These differences are attributed to changes in the crystal structure controlling interchromophore electronic coupling as well as SF energetics in these polycrystalline solids.

Quantum master equation approach to singlet fission dynamics in pentacene ring-shaped aggregate models

The quantum master equation approach is applied to the singlet fission (SF) dynamics of pentacene ring-shaped aggregate models to clarify the Frenkel excitonic (FE) coupling effects on the SF rate and correlated-triplet pair (TT) yield as well as their dependences on the aggregate structure and size. Interestingly, the smallest ring model, a ring-shaped trimer, is found to exhibit a significantly smaller SF rate and a slightly smaller TT yield than those of the dimer model with the same intermonomer interaction and to show remarkable variations in the SF dynamics with increasing the FE coupling. With increasing the size of the aggregates with FE coupling, it is found that the SF rate rapidly increases, attains the maximum at 17-mer (∼3 times enhancement compared to the non-FE-coupling case), and then decreases, approaching a stationary value around 25-mer, while the almost stationary TT yield at 25-mer remains 16% smaller than that in the non-FE-coupling case. These features are found to be in qualitative agreement with those in the corresponding linear aggregates, although the aggregate size gives a maximum SF rate, and the values of the maximum SF rate as well as of the converged TT yield are different between the ring-shaped and linear aggregates. These results are interpreted based on the relative relaxation factors between the adiabatic exciton states as well as on the vibronic coupling effects. The present results contribute to a deeper understanding of the aggregate structure and size dependences of SF dynamics and to constructing the design guidelines for highly efficient SF aggregates.

Singlet/triplet exciton dissociation and charge recombination in donor-acceptor ThQs-C60 /PDIxCN2 complexes

The donor-acceptor interface plays a critically important role in determining the power conversion efficiency of organic solar cells via controlling charge separation (CS) and recombination (CR) processes. Here, we combine the electronic structure calculations with electron transfer rate theory to clarify the CS and CR processes in ThQs-C₆₀ /PDIxCN₂ donor-acceptor complexes. The results reveal that in ThQs-PDIxCN₂ the CS comes from both the dissociations of photo-induced singlet exciton and singlet fission-induced triplet exciton with a high efficiency, whereas in ThQs-C₆₀ only the singlet exciton dissociation can take place because the triplet exciton lies below the charge-transfer exciton. However, very high CR rates in ThQs-PDIxCN₂ obliterate the benefit of fast CS, inversely leading to the ThQ-C₆₀ complex with a better cell efficiency. The present results are consistent with experimental observation and may furnish a possible patten to improve the overall conversion efficiency. © 2018 Wiley Periodicals, Inc.

Triplet Pair States in Singlet Fission

This account aims at providing an understanding of singlet fission, i.e., the photophysical process of a singlet state ( S₁) splitting into two triplet states (2 × T₁) in molecular chromophores. Since its discovery 50 years ago, the field of singlet fission has enjoyed rapid expansion in the past 8 years. However, there have been lingering confusion and debates on the nature of the all-important triplet pair intermediate states and the definition of singlet fission rates. Here we clarify the confusion from both theoretical and experimental perspectives. We distinguish the triplet pair state that maintains electronic coherence between the two constituent triplets, ¹(TT), from one which does not, ¹(T···T). Only the rate of formation of ¹(T···T) is defined as that of singlet fission. We present distinct experimental evidence for ¹(TT), whose formation may occur via incoherent and/or vibronic coherent mechanisms. We discuss the challenges in treating singlet fission beyond the dimer approximation, in understanding the often neglected roles of delocalization on singlet fission rates, and in realizing the much lauded goal of increasing solar energy conversion efficiencies with singlet fission chromophores.

Synergetic Effects of Triplet-Triplet Annihilation and Directional Triplet Exciton Migration in Organic Crystals for Photon Upconversion

In condensed solids, triplet exciton migration and succeeding triplet-triplet annihilation (TTA) are major bottleneck processes for efficient photon upconversion (UC) using sunlight excitation. We theoretically investigated the reaction times of TTA and the triplet-triplet energy transfer (TTET) as the elementary processes of triplet exciton migration in organic crystals of two molecular species: 9,10-diphenylanthracene (DPA) and its double-strapped alkyl  derivative (C7-sDPA) as the models of a recently reported crystalline system of TTA-UC by Kamada et al. The reaction times calculated based on Marcus theory clarified that the dimensionality of TTET and synergetic effects of TTA and TTET are responsible for the high UC quantum yield as well as their triplet lifetimes.

Intramolecular Singlet Fission: Insights from Quantum Dynamical Simulations

We investigate the dynamics of intramolecular singlet fission in a dimer consisting of two pentacene-based chromophores covalently bonded to a phenylene spacer using an approach that combines high-level ab initio multireference perturbation theory methods and quantum dynamical simulations. The results show that the population of the multiexcitonic state, corresponding to the first step of singlet fission, is facilitated by the existence of higher-lying doubly excited and charge transfer states that participate in a superexchange-like way. The important role played by high-frequency ring-breathing molecular vibrations in the process is also discussed.

Quantum Master Equation Approach to Singlet Fission Dynamics in Pentacene Linear Aggregate Models: Size Dependences of Excitonic Coupling Effects

The singlet fission (SF) dynamics of pentacene linear aggregate models are investigated using the quantum master equation method by focusing on the Frenkel excitonic (FE) coupling effects on the SF rate and double triplet (TT) yield as well as on their aggregate size dependences. It is found that for the dimer model, unrealistically large FE couplings are needed to provide significant effects on the SF dynamics, while for the larger aggregate models a realistic FE coupling causes significant variations in the SF dynamics: as increasing the aggregate size, the SF rate rapidly increases, attains the maximum at 8-mer (~3 times enhancement as compared to the non-FE-coupling case) and then decreases, approaching a stationary value after 12-mer, although the stationary TT yield at 20-mer remains slightly smaller than that in the non-FE-coupling case. These features are explained based on the relative relaxation factors between the adiabatic exciton states. The present results contribute to constructing the design guidelines for highly efficient SF aggregates. © 2018 Wiley Periodicals, Inc.

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 Modeling of Singlet Fission

Singlet fission is a photophysical reaction in which a singlet excited electronic state splits into two spin-triplet states. Singlet fission was discovered more than 50 years ago, but the interest in this process has gained a lot of momentum in the past decade due to its potential as a way to boost solar cell efficiencies. This review presents and discusses the most recent advances with respect to the theoretical and computational studies on the singlet fission phenomenon. The work revisits important aspects regarding electronic states involved in the process, the evaluation of fission rates and interstate couplings, the study of the excited state dynamics in singlet fission, and the advances in the design and characterization of singlet fission compounds and materials such as molecular dimers, polymers, or extended structures. Finally, the review tries to pinpoint some aspects that need further improvement and proposes future lines of research for theoretical and computational chemists and physicists in order to further push the understanding and applicability of singlet fission.

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.