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Computationally Driven Design Principles for Singlet Fission in Organic Chromophores Kalishankar Bhattacharyya, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11039 • Publication Date (Web): 03 May 2019 Downloaded from http://pubs.acs.org on May 3, 2019

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The Journal of Physical Chemistry

Computationally Driven Design Principles for Singlet Fission in Organic Chromophores Kalishankar Bhattacharyya, and Ayan Datta* School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur – 700032, Kolkata, West Bengal, India Email: [email protected]

Abstract Singlet fission is a new mechanistic pathway to overcome the Schokley-Quisser limit by generating twice the number of triplet exciton per singly absorbed photons in selected materials. The first step of the Singlet fission (SF) is initiated by the capture of sunlight by chromophores in the visible region, which is the prime factor for subsequent transferring the excited energies to the neighboring chromophores. The key electronic properties of organic chromophores for singlet fission is dictated by the interplay of the electronic states involved in this process. Separation of two triplet exciton from the correlated triplet pair strongly depends on the molecular structure and their packing motif either though a covalent or noncovalent packing orientation that controls the efficiency of SF. In this feature article, we discuss the singlet fission mechanism considering the thermodynamic condition, their correlation to the molecular structure and finally, their effects on the triplet yield generation from the firstprinciples computation. The discussion ranges from the single molecule to dimeric pair of crystalline states in the context of technological importance and design principle rules for singlet fission. Finally, we end this article with a brief overview of the experimental findings of our proposed chromophores in terms of applicability in singlet fission.

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I.

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Introduction

Absorption of ultraviolet, visible or even near-infrared to infrared radiation causes conversion of photon energy into electro-chemical energy. In comparison to the high energy radiations, the advantage of visible light lies in its large abundance in the solar spectrum in the earth. For practical purposes, absorption of solar light i.e. photons generate excited electrons from the materials which converted into charges. This is the extremely fascinating phenomena and valuable in terms of renewable sources which could be exploited for meeting the requirements of energy.1-2 Therefore, both academia and industry have increased their attention towards renewable resources which might provide sustainable energy for our needs.1,

3-5

Excited

electrons from the ground state of photovoltaic materials (PV) are excited by absorption of the photon which eventually get converted to bound electron-hole pair (commonly known as exciton).6-7 In order to get electrical work from these PV materials, the electron-hole pair must be separated at a different electrode. Solar energy which is the most efficient renewable sources if harvested properly can reduce the consummation of reserve fossil fuel. So, designing a solar photo-voltaic materials is of the utmost importance nowadays.3, 8-13 Fundamental challenge in this field is the designing of the efficient solar-materials and investigate the underlying mechanism for harvesting visible light.14 Silicon solar cell and other heterojunction made from inorganic materials currently dominate the semiconductor market because the maximum power conversion efficiencies are high and comparable to maximum thermodynamic limit for single junction solar cell imposed by the Shockley -Quiesser theoretical limit (33%).15-17 In order to provide cost-effective energy, several materials are being explored for alternatives to silicon PV materials.18-24 Amongst them, organic materials based photo-voltaic solar cells are particularly attractive in terms of cost-effectiveness and processing techniques. Organic chromophores have gained significant interest in the 2 ACS Paragon Plus Environment

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optoelectronics due to their unique and tunable electronic properties, and low production costs in opposition to the conventional inorganic based semiconducting materials. Interestingly, a pair of organic chromophores in close packing orientation exhibit completely different photophysical properties that are not found in either single molecules or in pure materials.25-26 Due to interaction with light, fundamental and potentially beneficial photophysical reactions occur which are eventually involved in energy transfer, electron transfer mediated reaction.2731

Development of organic chromophore based photo-voltaic materials for solar energy

conversion is a hot research area with potential applications in many field of chemistry and biology including photo-voltaics, photocatalysis,32-35 organic lasers,36-38 molecular machine,3940

and bio-imaging.41-43 There have been several application of organic semiconductor in many

field i.e. organic light emitting diodes (OLEDs), organic thin film transistors (OTFTs), solar cells, etc.44-49 Nevertheless at the present moment, efficiency of the organic semiconductor are still lower compared to the inorganic semiconductor, however, significant effort have been devoted to increasing efficiency and trying to find commercial products from the organic semiconductor. In a conventional solar cell, the excited photon energy in excess of the band gap of the semiconductor is lost due to thermal dissipation. Another plausible method, known as multiple exciton generation (MEG), employs the excess photonic energy to generate an additional electron-hole pair instead of thermalization.50 Singlet fission (SF) is such a multiple exciton generation process that can be found in some organic compounds and act as an alternative route to avoid the thermalization. The first report of singlet fission process was reported in anthracene in 1968,51 but interest toward this phenomenon has grown very rapidly when Hanna and Nozik demonstrated multiple exciton generation (MEG) in organic chromophores through singlet exciton fission as a path to increase the thermodynamic upper limit for power conversion efficiency i.e. the Shockley-Queisser limit in single junction solar cells (∼33%), connecting the research on singlet fission to its potential application in



photovoltaics.52 Theoretical and computational investigations have played a decisive role in understanding of SF and guide the design principle of materials for SF.53-58 Also, computational studies have been exploited to unveil the SF mechanism, critically assess the electronic states, and overall singlet fission rates and dynamics.59-64 Computationally guided electronic-structure properties correlation would be helpful to deduce the organic chromophores for SF. However, it has been challenging to find out the new molecules and their architecture for singlet fission, plausible mechanistic pathway, and suitability as an efficient singlet fission sensitizers. This paucity of SF materials needs computationally assisted systematic efforts to properly figure out the design rules of materials and mechanism involved in the SF pathways. In this feature article, we demonstrate recent investigations in singlet fission and significant advancements in theoretical and computational modeling to design new materials for SF applications. The major focus of this article is to highlight the aspects of the singlet fission and to obtain an in-depth understanding of the theoretical mechanism of SF.

II.

Fundamental Aspect of Singlet Fission

Singlet fission is found in some organic compounds where an excited singlet state eventually generates two triplet excitons out of only one single excited photon. Although it converts from the singlet to triplet states manifold yet, singlet fission is a spin-allowed process because of the two generated triplets are coupled as an overall singlet.57, 65 Therefore, singlet fission occurs very ultrafast time scale region competing other radiative/non-radiative process starting from the excited S1 states of chromophores.66-67 A set of general rules have been proposed by Michl et al. to identify the efficient singlet fission materials.53, 68 However, the list of singlet fission sensitizers is remarkably small due to requirement of proper adjustment of the excited state energy level. Hence, ordering of electronic energy level of excited singlet and triplet states of the monomer are prime importance in the singlet fission. In particular, the first singlet excited 4 ACS Paragon Plus Environment

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state energies (S1) must arise at twice of the first triplet excited energies (T1) i.e. S1 ≥ 2T1. Second condition employs that second triplet state energies (T2) should be higher than the twice of T1 excitation energies to overcome the triplet-triplet annihilation process and upconversion process.69-71 The photophysical event for SF that gives basic insights for the mechanism associated with two consecutive steps is described in Equation 1, where S0, S1 and T1 are the ground state, first excited singlet state, and first triplet state of the chromophore, respectively. The first step is associated with the initially excited states (S0S1) and multi-exciton state (1TT). The second step transforms the multi-exciton state to the correlated triplet states. S0S1 ⇌ 1(TT) ⇌ T1 + T1

(1)

In singlet fission mechanism, the formation of coupled triplet pair 1(TT) has been drawn maximum attention due to its electronic nature as well as formation from the initially singlet excited state.72-73 Most of the theoretical and experimental investigations have focused on the mechanistic pathway of the formation of 1(TT) states and its spatial separation into two individual triplet exciton. Till date, the accepted mechanism of the singlet fission is the generation of correlated triplet pair 1(TT) from the initial excitation (S1), followed by the separation into two decoupled triplet states. Recently, Scholes and co-worker reported that SF is a three-step kinetic process where the electronically correlated triplet pair 1(TT) lost its electronic coherence but remains bound by spin coherence.74-75 Inevitably, disappearance of the electronic coherence between the triplet pair in correlated states subsequently affect the charge or energy transfer process in SF systems.75 Nevertheless, loss of spin coherence on a longer time scale eventually effects a minor role on the electronic properties of individual triplet pairs. S0S1 ⇌ 1(TT) ⇌ 1(T…T) ⇌ T1 + T1 5 ACS Paragon Plus Environment

(2)


Although a lot of singlet fission research accounts for the correlated triplet pair mechanism, very limited information regarding the electronic structure of the correlated triplet states involved in singlet fission has been elucidated. On what time scale the 1(TT) is evolving into the 1(T…T) pair and how the vibronic coupling in crystalline solids affect the overall dynamical nature remains yet unanswered. Besides, the role of electronic delocalization and entropic contributions to the separation of triplet pairs are also important parameters in the context of singlet fission. In particular, Chan and co-worker first reported that entropy factor plays a crucial role for the separation of correlated triplet pair into two triplet excitons.57 On the basis of three state kinetic model, Kolomeisky et. al illustrated the contribution of entropy in triggering the eventual separation form localized correlated triplet pairs in tetracene.76 A recent couple of review article demonstrated the evolution of correlated triplet pairs and separation into two triplet pairs in details and interested readers might look into these articles.63, 77-78 As possible mechanism of singlet fission is that the initially excited states gets converted to the multiexciton states either directly or via charge-transfer mediated pathways. Michl and coworkers reported the singlet fission mechanistic pathways based on the few state model in diabatic framework.53 Though these simplified model qualitatively predicts the singlet fission phenomena, still for a quantitative prediction one should consider the correlated many-electron wave-functions, a more appropriate methodology for singlet fission description as pointed out by Head-Gordon and co-workers.79-81 In adiabatic framework, there are three possible mechanistic pathway for singlet fission, (i) direct transition from singlet exciton (S1) to multiexciton states (1TT) without involvement of charge-transfer states (CT) (ii) chargetransfer mediated transition from S1 to 1(TT) where CT might act as superexchange pathways, or (iii) real charge transfer mediated S1 to 1(TT). It is important to note that the low lying singlet exciton contains charge transfer characteristic in respective adiabatic wave-functions and interestingly in some systems lowest energy singlet states is ascribed as CT states.82 Relatively 6 ACS Paragon Plus Environment

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low-energy CT states favours the coupling with S1 and 1(TT) states resulting in a most favourable CT mediated pathway for singlet fission. In contrast for some intra-molecular dimer of pentacene, the direct transition from S1 to 1(TT) of the singlet fission has been attributed to the higher lying CT states.59 Sometimes excimer formation makes the CT level isoenergtic with S1 and 1(TT) which favours the strong coupling between the S1 and 1(TT) states. While, significant reduction of CT energy level compared to triplet pair states, excimer might act as a trap states in these cases. Meanwhile, none of the example support the existence of real chargetransfer intermediate mediated singlet fission and hence, real CT-state mediated singlet fission pathways are ruled out. Krylov and co-worker have carried out detailed computational investigation on the excimer formation and their role in singlet fission mechanism.80 Due to the formation of excimer in tetracene derivative they exhibit faster formation of 1(TT) pair but significantly reduced rate of separation of triplet pairs. In contrast, the π-stacked orientation of tetracene dimer hinders singlet fission which is attributed to exciton being a trap state.73

Figure 1. Schematic Representation of Singlet Fission mechanistic pathways. S1, 1ME and T1 represents the first excited singlet, multi-exciton states and first triplet states, respectively. CT denotes the charge transfer states. Electronic configuration are depicted in box along the corresponding electronic states.



Over the discussion of singlet fission mechanism as shown in Figure1, the accurate description of electronic states and probable mechanistic pathway intends to get to the heart of the problem, but finding a chromophore for singlet fission sensitizer is still obscure. In this article, we had provided the design rules of singlet fission molecules based on the singlet fission energetic conditions and criteria. Paci et al. have nicely interpreted the design of singlet fission sensitizer and classified two kind of molecules might be feasible candidate for singlet fission.68 Large alternant hydrocarbons with long conjugation length are well suited for singlet fission. This is because, absence of odd-member ring in these type of hydrocarbon increases the stability of the molecules and enhances the direct HOMO-LUMO excitations (single-electron excitations) in S1 and T1 energy level. Another set of molecules are the open shell S0 ground state chromophores (biradical) where the disjoint radical pair breaks the degeneracy between the S0 and T1 states by stabilizing the S0 states and T1 while S1 and S2 becomes destabilized. As a result, the primary condition i.e. E(S1) ≥ 2 E(T1) are satisfied for the a large number of diradical system.83-85 Although these energetic criteria are a pre-requisite for singlet fission but a large exoergicity leads the energy losses due to vibrational effect which is responsible for the overall decrement of singlet fission efficiency. Interestingly, less exoergicity or even slight endothermicity is relatively favourable for efficient singlet fission.73 III.

Effect of Heteroatom Substitution in Polyaromatic Hydrocarbon

Functionalization of polyaromatic hydrocarbons through heteroatom doping or chemical group substitution is an efficient strategy to circumvent the photo-degradation of PAH.86-88 In presence of air, acene based molecules quickly degrade into the photo-oxidized products. Based on the energy level matching condition, electrons from the lowest unoccupied molecular orbital (LUMO) of PAH are transferred to the triplet oxygen producing highly reactive oxygen species (ROS). Previous theoretical and experimental investigations also revealed that the energy level of LUMO and HOMO decreases during chemical modification and hence hinder the electron 8 ACS Paragon Plus Environment

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transfer to the triplet oxygen.89-94 Indeed, the degree of singlet oxygen sensitization is also reduced due to the lowering of triplet excited energies of chemically substituted PAHs. Subsequently, heteroatom substitution also influences the optical, electronic energy level, and photo-stabilities of PAH.95-97 It was reported that nitrogen/ sulfur doped acene chromophore act as an efficient organic field effect transistor due to the solubilities, and high photo-stabilities etc.98-101 In this article, we outline the effect of heteroatom (silicon) substitution in polyaromatic hydrocarbon which significantly affects the electronic properties and excited state energy level position in polyaromatic hydrocarbons and might activate as a singlet fission sensitizer.85, 102-104

Figure 2. Excited state energy level ordering of linearly fused monosilicon substituted oligoacenes (n=1-5). Red and black line indicates the 2T1 and S1 energy level. The inset also shows same energy level ordering for the unsubstitued oligoacenes. The left panel shows the monosilicon substituted oligoacenes. Reprinted with permission from ref 104. Copyright 2015, American Chemical Society. The first singlet excitation energies (S1-S0) of smallest alternant polycyclic hydrocarbons i.e. benzene and naphthalene are much lower than twice of the first triplet excitation energies 2(T1S0). However, the energy level of S1 and T1 states decrease with an increase in the number of 9 ACS Paragon Plus Environment


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fused benzene moieties. To clarify the role of silicon substitution and excited state energy level, the calculated energy level of substituted acene molecules with their pristine molecules (n=1-5) are also shown in Figure2. Clearly, the ability to reduce the energy level position directly correlates with an increase of the conjugation length of higher acene series chromophores. Previous experimental and computational investigation demonstrated that the criteria of SF is fully satisfied in pentacene whereas SF is mildly endothermic in tetracene moieties.62, 71-72, 105113

The silicon substituted benzene and naphthalene follows the same trend as shown in Figure2

but, interestingly the crossover occurred for 9-silaanathracene and onward. In comparison with the un-substituted anthracene, tetracene and pentacene, the computed ΔESF for 9-silaanthracene (9-SA), 5-silatetracene (5-ST), and 5 silapentacene (5-SP) are 0.70 eV, 0.34 eV, and 0.63 eV, respectively. To make the SF process exothermic, the 2T1 energy level should be lower than the S1 energy level to eventually facilitate the efficient generation of triplet states in chromophores. So, it was concluded that the singlet fission process becomes exoergic from 9-silaanthracene based on the first-principle calculations. However, the question arises why silicon substitution alters the energy level from anthracene. Substitution of silicon in the acene series significantly affects the HOMO-LUMO gap and their orbital energies.104 As shown in Table1, optically bright first excitation energies (S1) for 9-SA, 5-ST and 5-SP arise at 2.65 eV, 2.05 eV, and 1.61 eV, respectively. Table 1: First excited singlet state energies and singlet fission gap (ΔESF) of the systems considered here. Reprinted with permission from ref 104. Copyright 2015, American Chemical Society.

Molecule anthracene 9-silaanthracene tetracene 5-silatetracene

Excited State S1 S1 S1 S1

Energy (eV) 3.21 2.65 2.44 2.05

Configuration HOMO-LUMO HOMO-LUMO HOMO-LUMO HOMO-LUMO 10

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Oscillator Strength 0.058 0.077 0.050 0.057

ΔESF ( eV) -0.39 0.70 0.04 0.34

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pentacene 5-silapentacene

S1 S1

1.91 1.61

HOMO-LUMO HOMO-LUMO

0.37 0.63

0.041 0.043

The computed absorption spectra of these molecules are in the visible region with significant oscillator strength. It is important to note that, the presence of silicon does not alter the single electron excitation i.e. HOMO-LUMO transition in comparison to the anthracene, tetracene, and pentacene. Therefore, 9-SA is the smallest alternant hydrocarbons to exhibit the singlet fission phenomena based on our computation. However, the large exoergicity (ΔESF = 0.70 eV) in 9SA might reduce the excess energies as heat or other competitive relaxation decay process which will compete with SF and eventually decreases the overall SF efficiencies.113-115 Hence, further tuning of S1 and T1 energy level in 9-SA were performed by substitution of various electron withdrawing groups as shown in Table2. Therefore, substitution in the 10 positions of 9-SA, ΔESF decreases in the order -Br > -Cl > -F > -CF3 which can be ascribed to the inductive effect. In fact, a strong inductive effect of the trifluoromethyl group increases ΔESF which can be explained due to the destabilization of frontier molecular orbital energies. In contrast, substitution –CN group could counterbalance the inductive effect with the mesomeric effect (-R effect) and demonstrate as efficient SF materials due to reasonable ΔESF values. Hence, 10cyano-9-SA is an efficient SF chromophore with ΔESF = 0.05 eV.

Table 2: Singlet Fission energetic gap, ΔESF (in eV) for substituted 9-silaanthracene. Reprinted with permission from ref 104. Copyright 2015, American Chemical Society.

H Si

X

NO2

∆ESF 0.31

F

Cl

Br

CF3

CN

0.20

0.14

0.11

0.99

0.05

X

IV.

Polymorphism Dependent Singlet Fission 11 ACS Paragon Plus Environment


The optimal arrangement of chromophores in the crystal structure is an important criterion for triplet exciton formation either direct or mediated pathways. Michl and co-workers suggested that slip-stacked orientation of chromophores in the direction of transition dipole moment would be a more favourable than an exact face-to-face π-stacked orientation of chromophores.116-118 Hence, favourable slipped stacked π•••π orientation would maximize the electronic couplings resulting in a high triplet yield.60, 119-121 Not only slip-stacked packing but also other effects like heteroatom or functional group substitution, the addition of donor-acceptor group in chromophores can also facilitate SF. Indeed, such small changes in the crystal structure can reorder the packing orientation and distances between stacked chromophores. Nevertheless, it brings new opportunities to design the various kind of packing orientation between the adjacent chromophores eventually triggers the coupling pathways in the more elegant way. Fine tuning of molecular architecture through polymorphism can alter the optoelectronic properties of organic chromophores at room temperature.122-124 Several previous reports have suggested that polymorphism can potentially regulate the charge mobilities of the organic semiconductor in organic field effect transistors.125-128 Different packing motifs of tetracene crystalline structure significantly influences on the mechanistic pathway of SF.122, 129 Indeed, different packing motif in 1,3-diphenylisobenzofuran and 1,6-diphenyl-1,3,5-hexatriene modulates the electronic states and electronic coupling which makes them promising singlet fission chromophores.130 In a similar fashion, TIPS-pentacene also has different polymorphic structures and dimeric pairs from these polymorphic phases based on the different intermolecular distances would alter the excited state dynamics of SF significantly.55,

131-136

Therefore, it is important to investigate how

polymorphism can alter singlet fission efficiency and can be harnessed as a new tool to design SF pair for efficient triplet yield generation.


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Figure 3. Molecular structures of anthracene derivatives (I-VI). Reprinted with permission from ref 142. Copyright 2015, American Chemical Society. Based on the first-principle screening of SF, we have investigated the excited state S1 and T1 energy level for a set of molecules as shown in Figure3. Substitution of acetylene (-CH≡C-R) and triisopropylsilyethnyl (TIPS) in 9, 10-position of anthracene substantially alters the excited state energy level ordering of these molecules which can be explained from the frontier molecular orbital analysis. It is observed that the HOMO-LUMO gap in I decreased by 0.29 eV compared to anthracene moieties as shown in Figure 4. In comparison to the monosubstituted I, the frontier orbital energies of 9,10-disubstituted II decreases significantly by 0.29 eV in LUMO and marginally stabilized by 0.01 eV in HOMO. For –CH3 substitution in acetylenic groups for III decreases the HOMO-LUMO gap by an increment of HOMO position. Replacement of – SiCH3 groups in –CH3 position for IV significantly stabilizes HOMO-LUMO orbital, which is decreased by 0.56 eV and 0.47 eV in comparison to III, and in fact has the lowest HOMO and LUMO energies among these five molecules.



Figure 4. Frontier orbital energies (HOMO, LUMO) and their position of the system considered in Figure 3. Reprinted with permission from ref 142. Copyright 2017, American Chemical Society. The same trend is also followed in V where TIPS group is substituted at the same position. Therefore, the reduction of frontier orbital energies is in the order I>II>III>IV≈V which can be explained solely from the increased conjugation length in the following order. −C≡C−Si(CH3)3 and −TIPS groups are alike and hence amplify the effect of conjugation in IV and V in a similar way. For larger polyaromatic hydrocarbons, overall valance bond resonance structure was perturbed due to contribution coming from the edge specific atomic orbitals. Hence, TIPS group have a little effect in the conjugation of pentacene and tetracene, however substantially affect it for anthracene and therefore, leads to significant changes in excited S1/T1 level. It is important to note that the condition for triplet pair formation, ΔESF = (S1-2T1) should be fulfilled to make 14 ACS Paragon Plus Environment

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the process exoergic. Among the five molecules, only III-V are suitable for SF sensitizer. However, experimental crystal structure information is not available for III and IV whereas two polymorphic structure have present for V.137-138 It is already reported that V (TIPS-Anthracene) has worked as an efficient organic field effect transistor with excellent charge mobilities.139 Therefore, TIPS-Anthracene can be an excellent candidate for SF. First singlet excitation energies (S1) of TIPS-Ant arises at 2.78 eV with significant oscillator strength which is consistent with the experimental absorbance spectra (2.98 eV) based on our existing computational method.140 Interestingly, the S1 state is composed from the HOMO to LUMO transition and generates a locally exciton states (LE) which is highly favorable for multi-exciton generation (ME) with the neighboring chromophores.

Figure 5. Optimized unit cell and radial distribution function, g(r) of (a) PI and (b) PII polymorphs. Reprinted with permission from ref 142. Copyright 2017, American Chemical Society.



Experimentally TIPS-Ant gives an excimer like photoluminescence emission spectra around 540 nm in solution phase and shows fluorescence quantum yield around ~0.94. However, the quantum yield is substantially quenched in the solid phase which is attributed to the excited energy being transferred to the other radiative process.141 Large fall of quantum yield in the solid state compared to the solution is a prime-facie signature for singlet fission in these materials. From crystal structure pattern, it has shown that two types of the polymorphic structure with different packing orientation arise in TIPS-Ant. Although, overlay structure between them confirm that basic molecular parameter i.e. bond distances, angles, and dihedrals remains the same in both of them and supports the absence of any conformational polymorphism.142

Figure 6. Various molecular packing structures based on the radial distribution pattern of PI and PII. Center-to-center distances are shown in parentheses. Reprinted with permission from ref 142. Copyright 2017, American Chemical Society.


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Figure5 depicts herringbone pattern in both polymorphic crystals. In PI, both face-to-edge and slipped stacked orientation are present whereas only face-to-face orientation arises in PII. Intermolecular distances between the neighboring chromophores in dimeric pairs also effects both polymorphic structures as evident from the radial distribution functions. The weak van der Waals interactions between the chromophores as well as long-range interaction through TIPS moieties effect the overall stability in these crystals which are also corroborated with computed cohesive energy calculations per each molecular unit. As shown in Figure5 most populated dimeric pair for PI are exhibits at 10.22 Å followed by at 7.81, 8.01, and 9.81 Å as seen from RDF plot. Similarly, only two dimeric pair arises for PII at 8.00 and 10.07 Å, respectively. Out of four dimeric pairs of PI, two are V-shaped orientation and other two are slipped parallel and T shaped orientation, respectively (See Figure6). However, two V-shaped conformations contribute mostly where TIPS group interacts predominantly with the central anthracene rings. Shortest C−H•••π distances arise at 2.94−3.00 Å and 3.38−3.42 Å in PI-A and PI-B, and shortest C−C•••π distances arise at 5.11 Å and 5.25 Å, respectively. In PII crystal, one dimeric pair arises at V-shaped orientation and another one comes in the slipped-parallel packing as depicted form the RDF plot. C−H•••π distances and C−C•••π distances of these dimers are also in similar distances with previous dimer pair of PI. Weak inter-molecular interactions acting in the dimer stabilizes the packing which is consistent with computed BSSE corrected binding energies.142 Such a morphology controlled by intermolecular C−H•••π or C−C•••π interactions plays an important role in packing arrangements which in turn exhibits an excellent SF mechanism.143-144 V.

How Dimeric Pair Affects Singlet Fission Rates: Computational Approach

Finding an optimal packing of the organic chromophores is an important parameter for maximizing the electronic couplings in singlet fission. Theoretically covalent/non-covalent dimeric pairs are the smallest systems to investigate singlet fission in comparison to the crystalline solids. Relative orientations, centre-to-centre distances, and presence of linkers 17 ACS Paragon Plus Environment


connected to the monomers in the dimeric structures would be fascinating tools to explore the singlet fission. Experimental studies on tetracene, pentacene dimer in solution demonstrated that singlet fission rate varies depending on linkers connected between the monomer pairs.145148

It is true that initial delocalized excited states (S1) and localized 1(TT) both are confined into

the dimer pair which helps to estimate the energetics and rate of singlet fission. However, it would be difficult to establish the model for crystalline moieties because delocalized singlet exciton (S1) might proceed along with competing processes in line with singlet fission. Therefore, designing efficient singlet fission chromophores, especially a construction of the dimer model is essential to establish the mechanistic pathways. From the radial distribution function plot of 10-cyano-9-silaanthracene crystal, the largest contribution of dimeric pair arises at center-to-center distances of 4.13 Å followed by the smallest contribution from center−center distance ≥ 8.00 Å. As can be seen from the Figure7, the relative orientation of dimer at 4.13 Å looks like slipped stacked packing whereas dimeric pair at 8.03 Å is V-shaped orientation. It is important to point out that VHL and VLL completely vanish for perfect stacked dimer geometries due to the cancellation of transition dipole moment hence, slipped stacked pattern would be an efficient orientation for maximizing the singlet fission yield.149-150


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Figure 7. (a) Optimized unit cell structure of 10-CN-9-SA and (b) radial distribution pattern of 3×3×3 supercell of 10-CN-9-SA. (c) Configuration I and II represents the most available dimeric pair of 10-CN-9-SA. Reprinted with permission from ref 104. Copyright 2017, American Chemical Society. Based on the singlet fission mechanism as shown in Figure1, relevant rate for singlet fission pathways were evaluated from the Marcus equation.56, 151-152

ki 

2 | Vi |2 h

1 4 k BT

exp[

(  E ) ] 4 k BT

(2)

Where, λ, kB, and T are the molecular reorganization energy, Boltzmann constant and temperature (300 K), respectively. Electronic couplings (Vi) in meV unit denotes the VLL, VHL, and V2e involved in the singlet fission pathways. Based on Slater-Condon rules, coupling parameter VHL and VLL are determined through off-diagonal elements of the Fock matrix.153 The one-electron coupling is larger for both dimeric pair which affects mediating states namely the charge transfer states both I and II.104 Similarly in the polymorphic phases i.e. PI-B and PII-F have the maximum electronic coupling and hence maximizes the singlet fission rate. Indeed, slipped parallel stacking orientation of PI-C and PII-E also have larger electronic couplings which can be understood based on the symmetry breaking therefore enhance the electron-hole transfer pathways.142 VI.

Experimental Evidence of Singlet Fission in Anthracene Derivative

Based on the observation of delayed fluorescence occurring from the triplet-triplet annihilation, the characteristics of singlet fission was first reported in anthracene crystals about five decades ago.154 Singh and co-workers first reported a dark intermediate state which is formed as two correlated triplet pairs that could eventually dissociate into free triplet excitons or converted to the lowest singlet exciton states. Since S1 energy level (3.13 eV) is lowered by 0.53 eV compared to the 2T1 energy level (3.66 eV), singlet fission is endoergic in anthracene.51, 155 19 ACS Paragon Plus Environment


However, triplet state population in anthracene has occurred through direct excitation with a low-intensity laser (1.79 eV) which nicely corroborated with the energy level position of T1.70, 156-157

Burg et al. investigated the temperature dependence singlet fission of pure and doped

anthracene crystals to explain the additional thermal energy are required to form the correlated triplet pair.158-159 Later, they also investigated the magnetic field dependence fluorescence of anthracene crystals and established the kinetic rate model based on Merrifield’s theory.160 Nevertheless, the triplet quantum yield of anthracene crystal still is very low due to the endoergic behavior of singlet fission. Ghosh et al investigated the singlet fission properties of 9,10-bis(phenylethynyl)anthracene (BPEA) derivative upon photo-excitation in aggregates.161 Visible light emission of BPEA in solution is completely quenched in solid states upon aggregation which supports strong intermolecular interactions arises in BPEA crystals. Therefore, quenching of BPEA in solid states creates a new channel for deactivation of singlet excited states. Small spin-orbit coupling in BPEA does not allow the triplet relaxation in solution phase. Simultaneously, the rotation of substituents in 9,10 positions of anthracene obscured the exact role of packing in BPEA in solution. However, aggregation in solid states triggered excited state planarization of BPEA and eventually makes the molecular packing efficient for SF. Strong molecular packing increases the coupling between the monomeric pair thereby causes the quenching in BPEA. Based on the transient absorption spectroscopy, it was found that excited state dynamics of BPEA get completely altered compared to solution phase.


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Figure 8. (A) Left panel represents transient absorption spectra of BPEA nano-aggregate at different delay times with 390 nm at 10μJ. (B) Right panel shows the Temporal profiles along with fitted data recorded at 650, 508, and 475 nm, respectively. Reprinted with permission from ref 161. Copyright 2018, American Chemical Society. The absorption spectra in the region of 550-750 nm solely arise from the excitonic nature of the S1 states as shown in Figure8. Interestingly, absorption spectra rapidly decreases around ~4 ps which attributed to the exciton-exciton annihilation occurred in the molecular solids. After few ps, exciton-exciton annihilations again causes the ground state to repopulate upto 100 ps which are clearly shown from the ground state bleaching spectra. Thereafter, the transient species formed in the region of 100 ps does not decay up to 1ns timescale. This transient spectral characteristics in BPEA clearly indicates that the ground state population is excited by the singlet exciton which is the common scenario in singlet fission mechanism in crystalline solids and aggregates. It is important to note that strong intermolecular interactions in solid phase favor the singlet fission which was absent in the solution phase. Although singlet fission in anthracene is endoergic in nature, however, substitution at the 9, 10 position as well as favorable coupling between the pair alters the energy level and therefore eventually fulfills the energetic condition of singlet fission. Schmidt and co-worker found that substitution of 9,10 21 ACS Paragon Plus Environment


position of anthracene by TIPS group also exhibits singlet fission which is an excellent agreement with our previous first-principle computations.162 Indeed, the non-radiative decay rate of TIPS-anthracene is approximately ~106 s-1 again indicating singlet fission. Observed SF rate constant of TIPS-Anthracene in dilute solution is ~108 s-1 similar to the TIPS-tetracene supports the occurrence of singlet fission along with triplet-triplet annihilation. Recently Wasielewski and co-workers reported that efficient SF occurs in the two polymorphic phases of crystalline BPEA (C2/c and Pbcn). The electronic coupling is highly sensitive towards the packing distances of various conformations of the respective polymorphic structure. Calculations reveal that distances between the slipped-stacked packing of the C2/c polymorph of BPEA significantly influenced the interchromophore coupling resulting in high triplet yield.163

VII.

Summary and Outlook

In this article, a common strategy described is that fine-tuning of the excited state energy level by heteroatom substitution in acenes and precise orientation of chromophoric pair can lead an exciting singlet fission materials for photovoltaic devices. Rapid progress in computational methodology has guided to scrutinize the target structures for singlet fission, resulting in potential SF materials for enhancing the power-conversion efficiencies. In particular, theoretical and computational investigation have a profound role to envisage singlet fission phenomena, for example, by selecting the new molecules with relevant characteristics of electronic states, identifying the mechanistic pathway, and finally directing to rationalize with the experimental observation. A major limitation in this field of singlet fission is the lack of suitable candidates which might be able to exhibit the fission. Therefore, the first principle computation would be a decisive factor to identify the singlet fission sensitizer from the computational perspective, as is


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described herein. A further step ahead, ab initio computation of excited states of molecular crystals have helped to rationalize the singlet fission in the condensed system, which would be better approximation than the local dimeric model. Till date, the investigation of singlet fission has been reported based on the intermolecular chromophore system whereas examples of intramolecular singlet fission (iSF) are scarce.135, 164-166 Therefore, computational modeling will be necessary to identify the novel chemical structures e.g. polymeric structures and covalent dimers for iSF. In fact, singlet fission is less investigated in polymer and there are only a few recent reports.143,

166

The advantage of intra-molecular singlet fission being its

insensitivity to local orientations of molecular packing which are highly sensitive towards the singlet fission yields. The effect of spacers and the vibronic coupling between the various states and role of charge transfer with S0/S1/1TT are issues that will be subject of significant interest to the community of singlet fission.

AUTHOR INFORMATION Corresponding Author Corresponding Author: [email protected]. Phone: +91-33-24734971. Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT KB thanks IACS for Research Fellowship. AD thanks DST, BRNS and TATA Steel for partial funding. We thank CRAY supercomputer and IBM P7 cluster for computational facilities.



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Kalishankar Bhattacharyya is a PhD scholar in the School of Chemical Sciences at Indian Association for the Cultivation of Science, Kolkata, India. He obtained M.Sc. degree (2013) from Visvabharati University, West Bengal, India. His research focuses on the computational investigation of photophysical properties of organic chromophores for solar cell application, singlet fission, high level multi-reference computation and excited state dynamics of bioorganic chromophores.

Ayan Datta is currently a Professor in the School of Chemical Sciences in Indian Association for the Cultivation of Science (IACS), Kolkata, India. He obtained his PhD from JNCASR-Bangalore in 2007 and worked as a Postdoctoral fellow in University of North Texas (UNT). His research interests span over computational study in molecules and materials and studying emerging properties under strong and weak perturbations in nature using relevant models and methods at various length and time-scales. The group has studied systems like silicene, phosphorene, non-statistical dynamics in organic molecular reactivity, homogeneous and heterogeneous catalysis, singlet fission in organic chromophores and dynamics and structures of unnatural DNA bases. Our primary goal is to provide a qualitative and predictable understanding for experiments. Therefore to gain a qualitative picture, we are always eager to work very closely with experimentalists to refine, reframe and even refute existing models in chemistry. 34 ACS Paragon Plus Environment

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