Polymorphism Controlled Singlet Fission in TIPS-Anthracene: Role of

Article pubs.acs.org/JPCC

Polymorphism Controlled Singlet Fission in TIPS-Anthracene: Role of Stacking Orientation Kalishankar Bhattacharyya and Ayan Datta* Department of Spectroscopy, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur, 700032 Kolkata, West Bengal, India S Supporting Information *

ABSTRACT: Generation of multiple triplet excitons from one singlet exciton (singlet fission, SF) has been reported in several organic molecules recently. The overall SF yield in such molecular materials, however, is controlled by polymorphism in organic semiconductors through noncovalent interactions like van der Waals and weak electrostatic interactions. In this article, we demonstrate how SF is strongly perturbed by even small variations in molecular packing for polymorphic crystals of triisopropylsilyethnyl-anthracene derivatives, TIPS-Ant (PI and PII). Based on quantum chemical calculations, SF dynamics have been computed for both PI and PII polymorphs. PI and PII differ in their intermolecular π···π stacking patterns, which eventually control their electronic properties. Using the incoherent hopping model for the crystals, we computed SF rate through the Marcus electron transfer theory. For both PI and PII, the direct two-electron pathway predominates over the charge-transfer (CT) mediated mechanism. PII has higher triplet yield (∼196%) compared to PI (∼178%). Both time-dependent DFT as well as Weller equation reveal that the charge transfer (CT) state is a high energy state, and hence, CT mediated SF barely influences triplet yield. Interplay of the local excitation (LE), multiple excitation (ME), and correlated triplet (T1T1) energy levels controlled the overall exciton dynamics/diffusion in TIPS-Ant polymorphs. Polymorphism is shown to be a key factor for the rational design of optimal SF in polyaromatic hydrocarbons (PAH).

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shown SF with high triplet yield.8 Baldo et al. have reported ∼200% triplet yield arising from a SF process in pentacene− fullerene hybrid solar cells.9 Nevertheless, from a technological viewpoint, this list is still confined to only a few organic molecules. Therefore, designing new materials and understanding their structure−properties relationship is of utmost importance. Paci et al. theoretically proposed sets of organic molecule, which might show efficient SF.18 Zeng and coworkers have suggested that a small molecule like azaborine formed by replacement of four C atoms in azulene by a pair of B and N can be a good candidate for SF.19 In our previous study, we have shown that substitution of −CN group in 9silaanthracene (structure VI, Figure 1) makes it an excellent candidate for multiexciton generation particularly because the crystal packing allows good intermolecular contacts.20 In the visible region, excited state energy level matching is a fundamental criteria to design SF materials. To undergo SF after initial excitation by photon, the molecule should satisfy the two energy conditions, namely, E(S1) ≥ 2E(T1) and E(T2) > 2E(T1), in which E(S1) is the energy of the first excited singlet state, while E(T1) and E(T2) are the energy levels of the two low-lying triplet states. The first condition implies that the

INTRODUCTION Singlet fission (SF) is a multiexciton generation (MEG) pathway wherein a pair of triplet exciton is formed between two neighboring chromophores starting from a singlet excitation on a molecule.1,2 This spin allowed SF process opens a new avenue for increasing the solar energy conversion efficiency for third generation solar cell.3,4 Production of two correlated triplet states from one single exciton attracts significant attention due to its ability to harness the higher energy photons into a photovoltaic cell rather than losing this excess energy for low band gap semiconductors. Based on the SF principle, the Shockley−Queisser limit for single junction solar cell can be enhanced from ∼32% to ∼46%.5 Also, since the process is extremely fast, triplet excitons have higher lifetime thereby making the diffusion length longer in donor− acceptor interfaces. This reduces the probability for charge recombination in photovoltaic materials.6,7 Research in this emerging area is being actively pursued by several groups both theoretically and experimentally due to potential application of SF in optoelectronic device.8−10 SF was first observed for anthracene crystal wherein quenching of fluorescence by multiple exciton generation was reported.1 Subsequently, different organic crystals such as acene derivative (pentacene, tetracene, and hexacene),11−131,3diphenylisobenzofuran,14 perylene derivative,15 rubrene,16 carotenoids,17 conjugated polymer, and biradicaloids have © XXXX American Chemical Society

Received: October 5, 2016 Revised: January 6, 2017 Published: January 6, 2017 A

DOI: 10.1021/acs.jpcc.6b10075 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

between singlet fission efficiency and solid state packing for SF active molecules. In the present article, we have shown that triisopropylsilyethnyl-anthracene (TIPS-Ant) derivatives are promising new materials for SF. Substitution of various functional groups on anthracene effectively tunes the energy level of singlet and triplet excitons. Based on the solid state DFT calculations, we investigate the relative stability for the polymorphs of TIPS-Ant (PI and PII) and elucidate how diverse molecular packing affects SF. This is in agreement with previous charge transport studies for TIPS-Ant derivatives, which indicate π-stacking orientation dependent hole mobilities.34 We also compute direct two-electron interchromophore coupling at various dimeric configuration to estimate the SF rates. Efficient πstacking between the molecules in PII polymorph leads to higher SF yield, and therefore, PII crystal is indicated to be the most suitable candidate for experimental realization.

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COMPUTATIONAL DETAILS Geometry optimization of ground state structure of all the anthracene derivatives were performed at the B3LYP/631G(d,p) level.35−37 Vibrational frequency was computed to ensure that there is no structural instability in the optimized structures. Excited state calculations were performed through time-dependent DFT using the same basis set. Further, extended basis set calculations with the triple-ζ basis were performed to compute the vertical excitation energy. In agreement with previous reports, it is observed that the method provides a reasonable comparison with experimental results and provides a balance between computational resource and accuracy.38 To calculate vertical S0−S1 and S0−T1 gaps in each molecule, time-dependent DFT with 15 states have been performed using B3LYP, PBE0, 39 CAM-B3LYP,40 and ωB97XD41 versions of DFT. Various benchmark studies have shown that long-range corrected hybrid functional CAMB3LYP and dispersion corrected ωB97XD are approximate for accurate description of singlet excitation.42 Moreover, exchange-correlation PBE0 functional has been found to produce reasonably good results describing the absorption and emission spectra for optical properties of the TIPS-Ant derivatives.38 TIPS-Ant molecule has 52 atoms and the crystals of PI and PII have 416 atoms in their unit cells. Initial coordinates for the PI and PII crystals were retrieved from the experimental crystallographic information files (CIF).43,44 The ionization potential, electron affinities, and reorganization energies were calculated at the B3LYP/6-311+G(d,p) level of theory. Based on the harmonic approximation, reorganization energy was evaluated by normal-mode analyses using Franck−Condon method.45 Periodic DFT calculations for crystals were performed using the plane wave DFT-D346 method as implemented in the VASP code.47 Inclusion of core−valence interactions were accounted by projector augmented wave (PAW), and the Perdew−Burke−Ernzerh of (PBE) exchangecorrelation functional was used within generalized gradient approximation (GGA).39 Ionic core were described by the ultrasoft pseudopotentials. During the crystal structure optimization, kinetic energy cut off and k-point mesh were chosen to be 500 eV and 2 × 2 × 2, respectively. The binding energy of various dimeric pair taken from the crystal structure (PI and PII) were corrected for Basis Set Superposition Error (BSSE) using the counter-poise correction (CP) method. Position of the charge transfer states for the exciton migration in relevant dimers were accounted through TD-DFT at the

Figure 1. Molecular structures of anthracene derivatives (I−V) considered for the present study. VI = 10-cyano-9-silaanthracene previously explored as a promising SF material.20

production of two triplet states should be exergonic, while the second one rules out triplet−triplet annihilation. In fact, triplet excitons can potentially annihilate themselves to form higher energy singlets, triplets, or quintets, and therefore, it is imperative that the triplet excitons diffuse apart just after SF (in few ps).21 Favorable spatial orientation and electronic coupling between adjacent chromophore are shown to accelerate energy transfer rate during singlet fission.22 Recently, Zhang et al. have shown that very large exergonicity would cause reduction in SF efficiency due to other competitive exciton relaxation processes.23 Bardeen and co-workers have shown that photophysical events such as relaxation and decoherence can affect dynamics of SF during single crystal to polycrystalline phase transition.24 Recent studies show that SF may occur either through direct or mediated pathways depending on the electronic coupling and relevant low-lying charge-transfer states.25 Therefore, favorable packing like the slipped stacked π···π orientation would facilitate good electronic coupling. However, within a crystal structure additional effects like heteroatom substitution, presence of donor−acceptor moieties and functional groups also play an important role.26,27 Such remote perturbations can alter π−π distances and reduce efficient overlap between two adjacent chromophores. However, a positive aspect of this is the opportunity to access variety of different packing patterns in polymorphs of a given small organic molecule. Assisted by supramolecular structure variations, polymorphism can potentially regulate the electronic properties in conjugated organic chromophores at ambient room temperature.28,29 In the context of organic semiconductors, polymorphism strongly influences charge transport properties of thin film field-effect transistor devices (OFET).30,31 Singlet exciton fission is highly sensitive to the morphological patterns appearing from different packing motifs within polycrystalline thin films of tetracene.32 Similar to the tetracene, TIPS-pentacene also exists in polymorphic phases, and intermolecular distance between various pairs of dimer are known to significantly impact excited state dynamics for SF.33 Therefore, polymorphism provides a valuable and novel platform for studying the relationship B


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The Journal of Physical Chemistry C CAM-B3LYP level and also verified through the natural transition orbital (NTO) analyses. All geometry optimizations and TD-DFT calculations were performed using the Gaussian G09 suite of programs.48 Transfer integrals (VHL and VLL) of various molecular dimers were calculated by using the fragment orbital approach as implemented in the ADF package at the B3LYP/TZ2P level.49 Based on the expansion of frontier orbitals in terms of the 6-311+G(d,p) basis set, the twoelectron integral (V2e) was directly computed from the Slater− Condon rules for which 1/r is measured from the interatomic orbital distances for a specific dimer configuration.

Table 1. Excitation Energies (in eV) for I−V at B3LYP/631G(d,p) Level of Theory with Respect to Ground State (S0)

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molecule

S1(eV)

2T1 (eV)

T2 (eV)

ΔESF(eV)

I II III IV V

3.05 2.84 2.80 2.71 2.72

3.20 2.80 2.80 2.70 2.72

3.25 3.20 3.22 3.17 3.19

−0.15 0.04 0.00 0.01 0.00

comparison with other levels of theory), which should facilitate coherence between them and maximize SF efficiency. TIPS-Ant is, therefore, predicted to be an excellent molecule for experimentalists to pursue SF detection. It is important to note that though all the five molecules in Table 1 satisfy the first SF condition based on initial computational screening, only four of them (II−V) are suitable since, E(T2) ≈ 2E(T1) for I. Out of these four molecules, packing patterns are known for only V as experimental crystallographic information is unavailable for II−IV. Encouragingly, TIPS-anthracene (V) has been used as an n-type organic semiconductors having excellent field effect mobility (μ(hole) ≈ 3.7 cm2 V−1 s−1) and attractive solubility.51 Introduction of two bulky TIPS group in V makes it twisted, which increases its fluorescence lifetime and assists exciton dissociation between two adjacent neighboring chromophores.52 The computed ΔESF of TIPS-Ant meets the basic energy conditions of the SF at B3LYP/6-31G(d,p) level. We further benchmarked ΔESF of TIPS-Ant including diffuse function in triple −ζ basis set and range separated hybrid functional (Table 2). As shown in Table 2, excitation/emission energies of TIPSAnt computed using various versions of DFT broadly agree with the experimental results. The best agreement is observed for the PBE0 functional, which is known to account for the local excitation (LE) state accurately in TIPS-Ant.38 To shed light into the optical transitions, we analyzed the low lying singlet excited states in TIPS-Ant. The lowest singlet excited state of the TIPS-Ant is the 11BU state at 2.78 eV, which is in excellent agreement with experimental absorption peak at 2.92 eV. In TIPS-Ant, S1 state is a local excitation (LE) assigning the π−π* transition. This transition is mostly dominated by the HOMO (ag) to LUMO (bu) excitation. The π orbital is mostly composed of the anthracene core along with the CC bond from the −TIPS group. The next lying singlet state, S2 (11AU), lies at 3.74 eV, which is composed of transitions from HOMO (bg) to LUMO+1 (bu) and HOMO−1 (ag) to LUMO (au). The subsequent higher levels (S3, S4, etc.) have rather low oscillator strengths. From the Table 3, one can see that the S1 transition has the highest oscillator strength and, therefore, is optically allowed to contribute toward the absorption spectrum. Hence, photoexcitation to the S1 state is required to attain singlet fission within two neighboring TIPS-Ant molecules in crystals. We also investigated the higher lying optically active states, and only one such state (91BU, f = 0.310) lies at 6.62 eV. Nevertheless, it is important to note that this state might contribute toward triggering a transition from Sn → S1 to further increase SF (bright fission).53 Role of Intermolecular Interactions on SF Efficiency in TIPS-Ant. Aggregation of TIPS-Ant has been well studied in both solution and solid state.54 In dilute solution, it shows a broad and excimer-like emission around 504 nm, which is well matched with the computed results. Fluorescence quantum

RESULTS AND DISCUSSION Molecular Level Computational Screening for SF. We examined the singlet and triplet exciton energy levels for molecules I−VI as shown in Figure 1. Heteroatom substitution and functionalization of the acenes to tune S1−S0 and S0−T1 gaps is the common and efficient strategy for generating new libraries of SF molecules.13,18,27 Recently, we have designed anthracene derivatives by substituting Si-atoms in the core and functionalized it with cyano group and found that frontier orbital energy level and excited state properties of 10-cyano-9silaanthracene are significantly influenced.20 Herein, we systemically explore the effect of substitution by acetylene (−CHC−R) and TIPS group in the 9,10-position of anthracene. The frontier molecular orbitals and their energies are illustrated in Figure S1. Introduction of acetylene group in anthracene reduces the HOMO−LUMO gap from 3.59 eV (exptl: 3.45 eV) in pristine anthracene to 3.30 eV in I. Substitution of the second −CHCH group in II leads to a further reduced HOMO−LUMO gap (3.01 eV) for which the HOMO level is marginally stabilized (−5.23 to −5.24 eV), but the LUMO energy level decreases significantly (−1.94 to −2.23 eV). Presence of −CH3 groups in the acetylenic units hardly affects its HOMO−LUMO gap (ΔEHL(III) = 2.98 eV). Replacing −CH3 with −SiH3 groups in IV also does not alter the gap significantly (ΔEHL(IV) = 2.89 eV). This trend is also true when the −CCSiH3 group is replaced by the TIPS group in the 9,10-position (V) for which ΔEHL(V) = 2.90 eV. Therefore, the reduction of the HOMO−LUMO gap in TIPSAnt (V) with respect to anthracene arises entirely due to the increased conjugation from two acetylene molecules in 9 and 10 positions, and the −CCSi(CH3)3 groups (−TIPS) are electronically benign. However, as the size of the polyaromatic molecule increases, the contribution from the edge specific atomic orbitals reduces to the overall valence bond resonance structure. Thus, the introduction of TIPS group in anthracene leads to a significant change in S1/T1 energy levels, while the effect is smaller for the higher analogues like TIPS-pentacene and TIPS-tetracene.50 ΔESF = 2E(T1)−(S1) is the primary criterion for screening molecules for efficient SF yield. S0−S1, 2(S0−T1), and T2 excitation energies for I−V are tabulated in Table 1. In line with previous computational and experimental studies only tetracene and pentacene produce detectable SF yield, while large endoergonicity for anthracene rules it out completely.2 On substitution of −CHCH in I and II, both E(S1) and E(T1) decrease significantly (E(S1) = 3.27 eV, E(2T1) = 3.20 eV) thereby making them suitable for SF. For disubstituted −CH C−CH3 in III, E(S1) and E(2T1) behave similar to I and II. Interestingly for TIPS-Ant (V), E(S1) and E(2T1) are degenerate (at least in this level of theory, see Table 2 for C


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Table 2. Singlet Excitation Energy, Singlet Fission Gap (ΔESF), and Absorption and Emission Wavelengths with Their Oscillator Strength Using Different DFT Functionals with 6-31G(d,p) Basis Set (Also Computed with 6-311+G(d,p) Basis Set, Shown in Bold) functional B3LYP PBE0 CAM-B3LYP ωB97XD

S1−S0

ΔESF (eV)

absorption (nm)

emission (nm)

absorption (exptl)53

emission (exptl)53

2.72 2.66 2.78 2.72 2.99 2.93 3.00 2.94

0.00 0.08 0.30 0.24 0.95 0.81 0.68 0.58

457.1 (0.39) 465.9 (0.37) 446.6 (0.41) 454.7 (0.40) 415.3 (0.49) 423.6 (0.46) 414.1 (0.50) 421.2 (0.48)

517.0 (0.36) 526.7 (0.35) 503.5 (0.39) 512.4 (0.37) 471.72 (0.46) 481.42 (0.43) 470.7 (0.46) 479.4 (0.44)

441

504,473

Table 3. Transition Energies and Their Corresponding Oscillator Strengths (f) of the Low Lying Excited States Obtained from Various DFT Functionals with 6-31G(d,p) Basis Set state

character

PBE0

CAM-B3LYP

ωB97XD

B3LYP

11BU 11AU

ag → bu bg → bu ag → au bg → bu au → b u ag → bg ag → bu ag → bu bu → bu ag → bu ag → bu

2.78(0.408) 3.74(0.014)

2.98 (0.486) 3.88(0.017)

2.99(0.4934) 3.88(0.017)

2.99(0.486) 3.88(0.017)

4.17(0.001) 4.18(0.000)

4.63(0.001) 4.67(0.000)

4.66(0.001) 4.71(0.000)

4.63(0.000) 4.68(0.000)

4.19(0.100)

4.72(0.183)

4.77(0.180)

4.73(0.184)

4.51(0.000) 4.63(0.314)

5.02(0.000) 5.05(0.113)

5.07(0.000) 5.10(0.109)

5.02(0.000) 5.05(0.183)

21AU 11BG 21BU 11Ag 31BU

yield of TIPS-Ant in solution is ∼0.94, which decreases in the solid state and may be attributed to delayed fluorescence in molecular solid. TIPS-Ant has the ability to form two types of polymorph with unique packing. Comparison of the bond length, angles, and dihedrals confirm that these two polymorphs preserve their basic constituent molecular structure and do not exhibit conformational polymorphism (see Supporting Information for overlaid structures of TIPS-Ant in gas-phase and in two polymorphic phases).29 As seen in Figure 2, in both phases, TIPS-Ant orients in herringbone pattern, which is a rather common packing mode for organic aromatic

crystals.30 Polymorph I (PI) comprises a mixed packing arrangement of face-to-edge and slipped face-to-face stacking, while polymorph II (PII) exhibits mainly slipped face-to-face stacking. Figure 2 shows the relaxed crystal structure of each polymorph of TIPS-Ant. The initial coordinates of each polymorph for the crystal structure optimization were retrieved from the respective CIF files.43,44 PI has a orthorhombic space group Pca21 (CCSD ref code: ATARUI) with two molecule in the asymmetric unit, while PII has monoclinic space group P21/c (CCSD ref code: ATARUI01) with one molecules in asymmetric unit. The optimized lattice parameters of both PI and PII change by only ∼1% with respect to the experimental crystal structure. As clearly seen from radial distribution functions in PI and PII, there are significant differences in the intermolecular interaction patterns. Interestingly, these differences arise from weak intermolecular interactions and do not alter the overall stability of the polymorphs. Calculations at the plane wave DFT-D3 method reveal that the cohesive energy per asymmetric unit of PI and PII are −43.1 and −43.3 kcal/mol, respectively. Therefore, our computations nicely corroborate experimental observations that both PI and PII crystallize under ambient conditions. For detailed understanding the intermolecular interactions of dimeric pairs within each polymorph, we extended the unit cell in 3 × 3 × 3 supercells. We calculate the radial distribution function g(r) maintaining the center-tocenter distance of 16 Å as cutoff. As seen from the radial distribution functions (Figure 2), the most significant contributions for PI arises at 10.22 Å followed by the contact at 7.81, 8.01, and 9.81 Å. For PII, most populated dimeric pair arise at 8.00 and 10.07 Å, respectively. In PI, major overlap of monomer arises due to head-to-tail interactions with the central anthracene ring and TIPS groups

Figure 2. Optimized unit cell of polymorph and radial distribution function g(r) of (a) PI and (b) PII up to a center-to-center distance of 16 Å obtained from a 3 × 3 × 3 supercell. D


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E(S1+S0−) − E(S1S0) and ΔEHL = E(S1+S0−) − E(1TT)). The couplings between the electronic states are denoted as VLL, VHL, and V2e. VLL represents coupling between the initial excited state, S1S0, and the charge separated state (S1+S0−), while coupling between the S1+S0− state and singlet-pair of triplet states (1TT) is represented by VHL. V2e represents direct twoelectron coupling between the S1S0 and 1TT states. Based on the fragment orbital approach, one electron integral is depicted as off-diagonal elements in the Fock matrix. We computed the electronic matrix elements VLL and VHL at B3LYP/TZ2P level in the Amsterdam density functional (ADF) package. The direct two-electron integral (V2e) was computed using Slater− Condon rules described by Michl55 and Ratner56

along the ab-plane (Figure 3). PI has two pairs consisting of Vshaped dimers (PI-A: shortest C−H···π distances = 2.94−3.00

V2e =

Å, shortest C−C···π distances = 5.11 Å, dcenter‑to‑center = 7.81 Å. PI−B: shortest C−H···π distances = 3.38−3.42 Å, shortest C− C···π distances = 5.25 Å, dcenter‑to‑center = 8.01 Å), one slipped− parallel dimer (PI−C: shortest C−H···π distances = 4.39 Å, shortest C−C···π distances = 6.62 Å, dcenter‑to‑center = 9.81 Å), and one T-shaped dimer (PI-D: shortest C−H···π distances = 2.78 Å, shortest C−C···π distances = 3.80 Å, dcenter‑to‑center = 10.22 Å). However, in PII, π-stacking between monomers arises in the bc-plane. It consists of one V shaped dimer (PII-E: shortest C−H···π distances = 3.17 Å, shortest C−C···π distances = 4.13 Å, dcenter‑to‑center = 8 Å) and one slipped− parallel dimer (PII−F: shortest C−H···π distances = 3.41 Å, shortest C−C···π distances = 4.02 Å, dcenter‑to‑center = 10.07 Å). Such rich diversity in packing arrangements of PI and PII furnishes excellent systems to study intermolecular interactiondependent SF in TIPS-Ant. The role of weak van der Waals interactions in stabilizing the various packing configurations of PI and PII is also supported by BSSE corrected binding energy at ωB97xD/6-31G(d,p) level. Among PI and PII, the most stable dimmers are PI-A and PII-E with binding energies −11.5 and −11.2 kcal/mol, respectively (Table S1). Based on a semiclassical approach of the Marcus theory, we compute the one electron transfer rate as ⎡ −(λ + ΔE)2 ⎤ 2π 2 1 |Vi | exp⎢ ⎥ ℏ ⎣ 4λkBT ⎦ 4πλkBT

(2)

where aL and bL are the molecular orbital coefficients of LUMO and aH and bH are the molecular orbital coefficients of HOMO of monomeric pair within the relevant dimer. Using numerical method of Gaussian-expansion for molecular integrals, V2e were computed by expanding the frontier orbitals in Gaussian basis set. The calculated one-electron and two-electron couplings for all the unique dimers in PI and PII are tabulated in Table 4. PI−B and PII−F have the largest electronic coupling energies and therefore are best pairs to exhibits fast SF. Nevertheless, the slipped parallel orientations in PI−C and PIIE result in asymmetry in the electron−hole transfer pathway, which increases the overall effective couplings.32 One important inference from our computations is that V2e is larger in comparison to the VLL and VHL for most of the dimers. Absence of CT state within ∼1.00 eV of the first excited state as well as small energy separation of between the S1 and 2T1 states (ES1 ≈ 2ET1) might facilitate direct coupling between S1S0 and 1TT states. In order to further calibrate the couplings in PI and PII, we also computed the one electronic coupling using CT state mediated singlet fission proposed by the Damrauer57 and Berkelbach et al.58

Figure 3. Configurations PI-A, PI-B, PI-C, PI-D, PII-E, and PII-F exhibiting unique dimeric configurations in PI and PII. Center-tocenter distances are shown in parentheses.

ki =

2 (⟨aLbH|C|aLbL⟩ − ⟨aHbH|C|aHbL⟩) 3

Vmed ≈

3 2

(VHLVLL − VLHVHH) ΔECT

(3)

ΔECT represents the energy gap between the mediating CT state and single excited state and is taken as 600 meV.59,60 As can be seen from Table 4, largest Vmed is obtained for two dimeric pair of PII, namely, PII-E (1.89 meV) and PII−F (0.17 meV). For PI, molecular orientations of respective dimer pair significantly alter the Vmed couplings. As a consequence of asymmetric orientations of PI−B/PI-D in PI, Vmed is enhanced. The resulting one-electron couplings obtained by the superexchange mediated pathway are also in the same trends with our virtual charge transfer mediated pathway (see Table 4). We

(1)

where λ, kB, and T are the reorganization energy, Boltzmann constant, and temperature (300 K), respectively. ΔE represents the energy differences between the accessible states (ΔELL =

Table 4. Calculated One-Electron Coupling (VHL, VLL, VLH, and VHH, all in meV), Two-Electron Coupling (V2e in meV), Charge Transfer Mediated Coupling (Vmed in meV), and Effective SF Coupling (Veff in meV) of Unique Configuration of PI and PII polymorph

configuration

VHL

VLL

VLH

VHH

V2e

Vmed

Veff

PI

PI-A PI-B PI-C PI-D PII-E PII−F

−0.33 1.91 −1.16 −0.45 32.42 −11.80

−3.18 4.13 −1.48 −2.20 −28.34 −14.24

1.0 1.58 −0.41 1.84 11.02 −14.0

−0.18 0.59 −0.20 0.15 1.13 −5.74

0.02 75.42 17.62 41.60 80.00 130.00

0.003 0.015 0.004 0.02 1.89 0.17

0.02 75.43 17.62 41.62 81.89 130.17

PII

E


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Figure 4. (a) Animation of vibrational eigenvectors for reorganization of S0 to S1 and S0 to T1 superimposed on the respective optimized molecular structures. Significant vibrational modes contributing toward the reorganization energy for (b) S0 to T1 and (c) S0 to S1.

further estimated the overall effective coupling (Vtot ≈ V2e + Vmed) including contribution from either direct coupling (V2e) or charge transfer mediated coupling (Vmed). In both polymorphic systems, direct coupling is likely to predominate over the charge transfer mediated SF pathway. Based on normal mode calculations, we have been able to decipher the important modes that facilitate electron coupling between the states. We relaxed the optimized ground state (S0), S1, and T1 structure along normal mode (NM) to identify the key vibrational mode, which might influence the direct mixing. We further calculated mode specific reorganization energy of the normal mode based on the projection of optimized ground state structure onto the optimized S1 and T1 geometries. During relaxation of the S1/T1 geometries, the contribution of each vibrational mode toward to the reorganization energy were computed by NM method.45 Based on the harmonic approximation, reorganization energy is described as 3N − 6

λ=

∑ i=1

3N − 6

λi =

∑ i=1

3N − 6

hωiSi =

∑ i=1

⎛ Ki ⎞ 2 ⎜ ⎟ΔQ i ⎝2⎠

stabilizes this biradical character and slows down its oxidation. In Figure S2, we have shown the spin density in the triplet state TIPS-Ant, which clearly indicates its biradical character. This radical character in TIPS-Ant is a key feature for direct coupling between the locally excited state (S1S0) within the dimer with its multiply excited state, namely, the coupled triplet states (1T1T1). Such a coupling is, of course, spin-allowed since the 1 T1T1 state is effectively an open-shell singlet state for the dimer. We investigate the relative position of the CT state for each dimeric configuration to establish the direct coupling mechanism against the superexchange mediated by high-lying CT states. We estimated the CT state through TD-DFT calculations at CAM-B3LYP/6-311+G(d,p) levels for PI and PII. Although conventional TD-DFT has limitations to describe the CT states particularly for relatively large systems; however, the range separated hybrid CAM-B3LYP functional has been quite successful to determine the CT states in stacked geometries of organic chromophores.62 The computed excited state energies obtained by tuning range separated hybrid functional show excellent agreement with the previous result (Table S2).63 Our natural transition orbital (NTO) analyses also show that electron−hole pair with significant CT character lie at significantly higher energy with respect to the first excited state energy (Figure S3). We find that CT states remain at high energy irrespective of configuration of the dimer. It is therefore reasonable that the small energy separation (ES1 ≈ 2ET1) and the relatively large energy gap of CT states preclude SF via the indirect coupling. We also compute the lowest CT state including the Coulombic interaction of dimeric pair and ionization potential (IP) of the donor and electron affinity (EA) of the acceptor as follows:64

(4)

where λi is the contribution of the ith mode of the λ, ΔQi is the displacement vector along the normal mode between ground state and S1/T1 geometries, and Si is the Huang−Rhys factor, which measures the mode-specific charge phonon coupling to the electronic transition. Ki and ωi are the force constant and vibration frequency, respectively. Based on the higher Huang− Rhys (HR) factor and substantial reorganization energy changes along the relaxation pathway, we found out that ring breathing mode at 1307 cm−1 underwent the coupling between relevant states. This is in nice agreement with a previous report wherein the same ring breathing mode (1307 cm−1) dominates charge hopping in the Franck−Condon region for TIPS-Ant derivatives.61 As shown in Figure 4, simultaneous contraction of C−C bond and concomitant expansion of the other bonds due to the ring breathing mode (1307 cm−1) leads to a biradical character for the central ring in TIPS-Ant. Nevertheless, substitution of TIPS group with triple bond in 9,10-position in anthracene

ECT = IP D + EAA + Ecoul D + /A −

(5)

where IP is the ionization potential of donor and EAA is the electron affinity of acceptor anion. Coulomb energy can be calculated as follows: F


Article

The Journal of Physical Chemistry C d + /a − = Ecoul

∑ qa , qd

qaqd 4πε0εR a − d

unity. For PI, the variation of stacking geometries in dimer is shown to significantly alter the SF rate. The k2e of PI−B/PI-D are ∼15 times larger than PI-A/PI−C and dominate singlet fission yield. For PI and PII, the typical τSF is calculated to be 3.56 ps (PI: ⟨k2e⟩ ≈ 2.80 × 1011) and 13 ps (PII: ⟨k2e⟩ ≈ 7.87 × 1011) at 300 K. The time scale (τSF) for both the polymorphs is significantly faster than other competing decay processes, and therefore, they should favorably lead to greater triplet yield. This is also in agreement with available experimental evidence on TIPS-pentacene wherein formation of multiexciton state in picoseconds time-scale has been reported.33 Based on the present computations, one can derive an essential diagram for SF in TIPS-Ant crystals (see Figure 5).

(6)

where qa and qd are the partial charges obtained from the natural population analyses of donor and acceptor, respectively, and ε = 3.0 is considered as the static dielectric constant of the medium.65 Our calculated IP (6.33 eV) and EA (1.06 eV) for TIPS-Ant is in excellent agreement with reported literature.51 The ionization energy, electron affinity, and lowest CT state are listed in Table S2. Our calculated CT states from the Weller eq (eq 5) follow similar trends as computed from range-separated TDDFT calculations. Calculation at the ωB97xD have similar behavior as well (see Table S3). It is important to note that in absence of multireference methods, which are practically intractable for dimers of sizes as in PI and PII, we can not assign the exact position of the CT-state. Nevertheless, the overall agreement of our results with experimental evidence38 indicate that CT-states should not be dominant in the present case as the CT state lies at least ∼1.20 eV above the S1 state. Based on the Marcus-like nonadiabatic eq (eq 1), we evaluated the direct two−electron transfer rate, (k2e).56 Although CT state is higher in energy, one electron transfer rate might contribute to the SF rate albeit to a lesser extent. Imposing the steady state approximation between the S1S0 and S1+S0− to form correlated 1TT pair, one might estimate the one electron transfer rate (k1e). With experimentally reported charge recombination rate, kback ≈ 10−8 s−1 for crystalline TIPS substituted polyacene,66 we computed k1e involving kHL and kLL for all PI and PII dimeric pairs via k1e =

kLLkHL kHL + k back

Figure 5. Schematic illustration of exciton dynamics for singlet fission in a typical dimer for TIPS-Ant polymorphs (PI and PII).

(7)

Using this simple kinetic model, the quantum yield of the singlet fission (ΦSF) was evaluated as follows: k1e + k 2e ΦSF = k1e + k 2e + kF

Excitation by visible light (λmax = 441 nm, blue region) creates local excitation in a single molecule (S1S0 state). Due to excellent energy level matching between S0S1 and the 2T1 states, an efficient direct two-electron coupling furnishes the multiexciton state (ME: 1T1T1) at an ultrafast time-scale (∼10−20 ps). Due to thermal and lattice defect-induced decoherence, this ME state splits into two independent triplets. These uncorrelated triplet states diffuse/percolate within the crystal before eventually relaxing into the ground-state, S0S0. Due the rather high energy of the CT-state, SF mediated by this state can safely be ruled out.

(8)

The computed k2e and SF yields for various dimeric pairs in polymorphs PI and PII are reported in Table 5 (see Supporting Table 5. Direct Two-Electron Rate (k2e in s−1), Yield of SF (ΦSF), and Triplet Yield (ΦT) for PI and PII polymorph

configuration

PI

PI-A PI-B PI-C PI-D PII-E PII−F

PII

k2e 5.03 7.84 4.52 2.41 8.39 6.82

× × × × × ×

1010 1011 1010 1011 1011 1011

ΦSF

ΦT

0.82 0.98 0.80 0.95 0.98 0.98

178%

■

CONCLUSIONS In summary, we have demonstrated the singlet fission in TIPSAnt is highly favorable for both the polymorphs (PI and PII). Based on quantum chemical calculations, the frontier molecular orbital energies, reorganization energy, and transfer integrals are systemically studied for TIPS-Ant derivatives. The mechanism for SF is found to be the direct two-electron pathway and not the charge transfer (CT) state mediated pathway. Interestingly, even for the same molecular packing motif, small changes in molecular orientation are shown to significantly alter electronic coupling and hence the singlet fission rates. The present calculations elegantly demonstrate the paramount role of polymorphism in assisting singlet fission in TIPS-Ant. It is important to note that only few of the specific dimeric pairs show enhanced SF, while others have low yields. So, clever crystal engineering in terms of enriching the polymorphic phases by these favorable pairs has the potential

196%

Information). Based on the number-average pair of dimers within each polymorph, the triplet yield (ΦT) of PI and PII is calculated as twice of the average SF yield (ΦSF). It should be pointed out that triplet yield are sensitive to various competing process, such as radiative (R) and nonradiative (NR) decay and intersystem crossing (ISC). However, the time-scale of these processes are typically longer than singlet fission, and hence, we compute ΦSF by ignoring their contributions. As can be seen from Table 5, the largest SF rate is obtained for PII pair. For the two dimeric pairs of PII, namely, PII-E and PII−F, k2e are similar in magnitude and result in the triplet yield close to G


Article


(12) Lee, J.; Bruzek, M. J.; Thompson, N. J.; Sfeir, M. Y.; Anthony, J. E.; Baldo, M. A. Singlet exciton fission in a hexacene derivative. Adv. Mater. 2013, 25, 1445−1448. (13) Chen, Y.; Shen, L.; Li, X. Effects of heteroatoms of tetracene and pentacene derivatives on their stability and singlet fission. J. Phys. Chem. A 2014, 118, 5700−5708. (14) Johnson, J. C.; Nozik, A. J.; Michl, J. High triplet yield from singlet fission in a thin film of 1, 3-diphenylisobenzofuran. J. Am. Chem. Soc. 2010, 132, 16302−16303. (15) Ramanan, C.; Smeigh, A. L.; Anthony, J. E.; Marks, T. J.; Wasielewski, M. R. Competition between singlet fission and charge separation in solution-processed blend films of 6, 13-bis(triisopropylsilylethynyl) pentacene with sterically-encumbered perylene-3, 4:9, 10-bis(dicarboximide) s. J. Am. Chem. Soc. 2012, 134, 386−397. (16) Ma, L.; Zhang, K.; Kloc, C.; Sun, H.; Michel-Beyerle, M. E.; Gurzadyan, G. G. Singlet fission in rubrene single crystal: direct observation by femtosecond pump−probe spectroscopy. Phys. Chem. Chem. Phys. 2012, 14, 8307−8312. (17) Wang, C.; Tauber, M. J. High-yield singlet fission in a zeaxanthin aggregate observed by picosecond resonance Raman spectroscopy. J. Am. Chem. Soc. 2010, 132, 13988−13991. (18) Paci, I.; Johnson, J. C.; Chen, X.; Rana, G.; Popovic, D.; David, D. E.; Nozik, A. J.; Ratner, M. A.; Michl, J. Singlet fission for dyesensitized solar cells: Can a suitable sensitizer be found? J. Am. Chem. Soc. 2006, 128, 16546−16553. (19) Zeng, T.; Ananth, N.; Hoffmann, R. Seeking small molecules for singlet fission: a heteroatom substitution strategy. J. Am. Chem. Soc. 2014, 136, 12638−12647. (20) Bhattacharyya, K.; Pratik, S. M.; Datta, A. Small Organic Molecules for Efficient Singlet Fission: Role of Silicon Substitution. J. Phys. Chem. C 2015, 119, 25696−25702. (21) Chan, W.-L.; Ligges, M.; Jailaubekov, A.; Kaake, L.; Miaja-Avila, L.; Zhu, X.-Y. Observing the multiexciton state in singlet fission and ensuing ultrafast multielectron transfer. Science 2011, 334, 1541−1545. (22) Johnson, J. C.; Nozik, A. J.; Michl, J. The role of chromophore coupling in singlet fission. Acc. Chem. Res. 2013, 46, 1290−1299. (23) Zhang, Y.-d.; Wu, Y.; Xu, Y.; Wang, Q.; Liu, K.; Chen, J.-W.; Cao, J.-J.; Zhang, C.; Fu, H.; Zhang, H.-L. Excessive Exoergicity Reduces Singlet Exciton Fission Efficiency of Heteroacenes in Solutions. J. Am. Chem. Soc. 2016, 138, 6739−6745. (24) Piland, G. B.; Burdett, J. J.; Dillon, R. J.; Bardeen, C. J. Singlet fission: From coherences to kinetics. J. Phys. Chem. Lett. 2014, 5, 2312−2319. (25) Monahan, N.; Zhu, X.-Y. Charge transfer-mediated singlet fission. Annu. Rev. Phys. Chem. 2015, 66, 601−618. (26) Busby, E.; Xia, J.; Wu, Q.; Low, J. Z.; Song, R.; Miller, J. R.; Zhu, X.; Campos, L. M.; Sfeir, M. Y. A design strategy for intramolecular singlet fission mediated by charge-transfer states in donor−acceptor organic materials. Nat. Mater. 2015, 14, 426−433. (27) Deibel, C.; Strobel, T.; Dyakonov, V. Role of the Charge Transfer State in Organic Donor-Acceptor Solar Cells. Adv. Mater. 2010, 22, 4097−4111. (28) Tiago, M. L.; Northrup, J. E.; Louie, S. G. Ab initio calculation of the electronic and optical properties of solid pentacene. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 67, 115212. (29) Pratik, S. M.; Nijamudheen, A.; Bhattacharya, S.; Datta, A. Color Polymorphism: Understanding the Diverse Solid-State Packing and Color in Dimethyl-3, 6-dichloro-2, 5-dihydroxyterephthalate. Chem. Eur. J. 2014, 20, 3218−3224. (30) Chung, H.; Diao, Y. Polymorphism as an emerging design strategy for high performance organic electronics. J. Mater. Chem. C 2016, 4, 3915−3933. (31) Bhattacharyya, K.; Mukhopadhyay, T. K.; Datta, A. Controlling electronic effects and intermolecular packing in contorted polyaromatic hydrocarbons(c-PAHs): towards high mobility field effect transistors. Phys. Chem. Chem. Phys. 2016, 18, 14886−14893.

to enhance SF yield further upward. While such efforts are yet to be undertaken, rapid progress toward understanding of aggregation mechanism of organic molecules can certainly boost new experiments. Nucleation kinetics and nanocalorimetry of aggregation for 10−100 molecules should hold the key toward progress in designed crystallization for small molecules wherein theoretical studies would provide the new insights.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b10075. Cartesian coordinate for all the structures reported, TDDFT results, relaxed cell parameters, additional calculations, and complete ref 48 (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +91-33-24734971. ORCID

Ayan Datta: 0000-0001-6723-087X Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS A.D. thanks DST, BRNS, and INSA for partial funding. We thank CRAY supercomputer and IBM P7 cluster for computational facilities.

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REFERENCES

(1) Singh, S.; Jones, W.; Siebrand, W.; Stoicheff, B.; Schneider, W. Laser generation of excitons and fluorescence in anthracene crystals. J. Chem. Phys. 1965, 42, 330−342. (2) Smith, M. B.; Michl, J. Recent advances in singlet fission. Annu. Rev. Phys. Chem. 2013, 64, 361−386. (3) Congreve, D. N.; Lee, J.; Thompson, N. J.; Hontz, E.; Yost, S. R.; Reusswig, P. D.; Bahlke, M. E.; Reineke, S.; Van Voorhis, T.; Baldo, M. A. External quantum efficiency above 100% in a singlet-excitonfission−based organic photovoltaic cell. Science 2013, 340, 334−337. (4) Tayebjee, M. J.; Gray-Weale, A. A.; Schmidt, T. W. Thermodynamic limit of exciton fission solar cell efficiency. J. Phys. Chem. Lett. 2012, 3, 2749−2754. (5) Shockley, W.; Queisser, H. J. Detailed balance limit of efficiency of p−n junction solar cells. J. Appl. Phys. 1961, 32, 510−519. (6) Rao, A.; Wilson, M. W.; Hodgkiss, J. M.; Albert-Seifried, S.; Bassler, H.; Friend, R. H. Exciton fission and charge generation via triplet excitons in pentacene/C60 bilayers. J. Am. Chem. Soc. 2010, 132, 12698−12703. (7) Najafov, H.; Lee, B.; Zhou, Q.; Feldman, L. C.; Podzorov, V. Observation of long-range exciton diffusion in highly ordered organic semiconductors. Nat. Mater. 2010, 9, 938−943. (8) Akdag, A.; Havlas, Z. k.; Michl, J. Search for a small chromophore with efficient singlet fission: biradicaloid heterocycles. J. Am. Chem. Soc. 2012, 134, 14624−14631. (9) Lee, J.; Jadhav, P.; Baldo, M. High efficiency organic multilayer photodetectors based on singlet exciton fission. Appl. Phys. Lett. 2009, 95, 033301. (10) Burdett, J. J.; Müller, A. M.; Gosztola, D.; Bardeen, C. J. Excited state dynamics in solid and monomeric tetracene: The roles of superradiance and exciton fission. J. Chem. Phys. 2010, 133, 144506. (11) Zimmerman, P. M.; Musgrave, C. B.; Head-Gordon, M. A correlated electron view of singlet fission. Acc. Chem. Res. 2013, 46, 1339−1347. H


Article


(54) Parkhurst, R. R.; Swager, T. M. Synthesis and optical properties of phenylene-containing oligoacenes. J. Am. Chem. Soc. 2012, 134, 15351−15356. (55) Smith, M. B.; Michl, J. Singlet Fission. Chem. Rev. 2010, 110, 6891−6936. (56) Renaud, N.; Sherratt, P. A.; Ratner, M. A. Mapping the relation between stacking geometries and singlet fission yield in a class of organic crystals. J. Phys. Chem. Lett. 2013, 4, 1065−1069. (57) Alguire, E. C.; Subotnik, J. E.; Damrauer, N. H. Exploring NonCondon Effects in a Covalent Tetracene Dimer: How Important Are Vibrations in Determining the Electronic Coupling for Singlet Fission? J. Phys. Chem. A 2015, 119, 299−311. (58) Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R. Microscopic Theory of Singlet Exciton Fission. II. Application to Pentacene Dimers and the Role of Superexchange. J. Chem. Phys. 2013, 138, 114103. (59) Sebastian, L.; Weiser, G.; Bassler, H. Charge Transfer Transitions in Solid Tetracene and Pentacene Studied by Electroabsorption. Chem. Phys. 1981, 61, 125−135. (60) Seefeld, K. P.; Muller, H.; Bassler, H. Energy Transfer in Amorphous Anthracene -Tetracene Films. J. Lumin. 1978, 16, 395− 404. (61) Fuemmeler, E. G.; Sanders, S. N.; Pun, A. B.; Kumarasamy, E.; Zeng, T.; Miyata, K.; Steigerwald, M. L.; Zhu, X.-Y.; Sfeir, M. Y.; Campos, L. M. A Direct Mechanism of Ultrafast Intramolecular Singlet Fission in Pentacene Dimers. ACS Cent. Sci. 2016, 2, 316−324. (62) Manna, A. K.; Dunietz, B. D. Communication: Charge-transfer rate constants in zinc-porphyrin-porphyrin-derived dyads: A Fermi golden rule first-principles-based study. J. Chem. Phys. 2014, 141, 121102−121106. (63) Dreuw, A.; Head-Gordon, M. Single-reference ab initio methods for the calculation of excited states of large molecules. Chem. Rev. 2005, 105, 4009−4037. (64) Yi, Y.; Coropceanu, V.; Brédas, J.-L. A comparative theoretical study of exciton-dissociation and charge-recombination processes in oligothiophene/fullerene and oligothiophene/perylenediimide complexes for organic solar cells. J. Mater. Chem. 2011, 21, 1479−1486. (65) Hulea, I.; Fratini, S.; Xie, H.; Mulder, C.; Iossad, N.; Rastelli, G.; Ciuchi, S.; Morpurgo, A. Tunable Fröhlich polarons in organic singlecrystal transistors. Nat. Mater. 2006, 5, 982−986. (66) Walker, B. J.; Musser, A. J.; Beljonne, D.; Friend, R. H. Singlet exciton fission in solution. Nat. Chem. 2013, 5, 1019−1024.

(32) Arias, D. H.; Ryerson, J. L.; Cook, J. D.; Damrauer, N. H.; Johnson, J. C. Polymorphism influences singlet fission rates in tetracene thin films. Chem. Sci. 2016, 7, 1185−1191. (33) Wu, Y.; Liu, K.; Liu, H.; Zhang, Y.; Zhang, H.; Yao, J.; Fu, H. Impact of intermolecular distance on singlet fission in a series of TIPS pentacene compounds. J. Phys. Chem. Lett. 2014, 5, 3451−3455. (34) Park, J.-H.; Chung, D. S.; Park, J.-W.; Ahn, T.; Kong, H.; Jung, Y. K.; Lee, J.; Yi, M. H.; Park, C. E.; Kwon, S.-K. Soluble and easily crystallized anthracene derivatives: precursors of solution-processable semiconducting molecules. Org. Lett. 2007, 9, 2573−2576. (35) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5652. (36) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785. (37) Hariharan, P. C.; Pople, J. A. The influence of polarization functions on molecular orbital hydrogenation energies. Theor. Chim. Acta 1973, 28, 213−222. (38) Jun, Y. Time-Dependent Density Functional Theory Study of Low-Lying Absorption and Fluorescence Band Shapes for PhenyleneContaining Oligoacenes. J. Phys. Chem. A 2015, 119, 12706−12714. (39) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. (40) Yanai, T.; Tew, D. P.; Handy, N. C. A new hybrid exchange− correlation functional using the Coulomb-attenuating method(CAMB3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (41) Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom−atom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615−6620. (42) Sun, H.; Zhong, C.; Bredas, J.-L. Reliable Prediction with Tuned Range-Separated Functionals of the Singlet−Triplet Gap in Organic Emitters for Thermally Activated Delayed Fluorescence. J. Chem. Theory Comput. 2015, 11, 3851−3858. (43) Butler, I. R.; Callabero, A. G.; Kelly, G. A.; Amey, J. R.; Kraemer, T.; Thomas, D. A.; Light, M. E.; Gelbrich, T.; Coles, S. J. Ferrocenylsubstituted fluorescent anthracenes and anthraquinones. Tetrahedron Lett. 2004, 45, 467−472. (44) Khan, M. S.; Al-Mandhary, M. R.; Al-Suti, M. K.; Al-Battashi, F. R.; Al-Saadi, S.; Ahrens, B.; Bjernemose, J. K.; Mahon, M. F.; Raithby, P. R.; Younus, M. Synthesis, characterisation and optical spectroscopy of platinum(II) di-ynes and poly-ynes incorporating condensed aromatic spacers in the backbone. Dalton Trans. 2004, 2377−2385. (45) Reimers, J. R. A practical method for the use of curvilinear coordinates in calculations of normal-mode-projected displacements and Duschinsky rotation matrices for large molecules. J. Chem. Phys. 2001, 115, 9103−9109. (46) Grimme, S. Density functional theory with London dispersion corrections. WIREs Comput. Mol. Sci. 2011, 1, 211−228. (47) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169. (48) Frisch, M.; Trucks, G.; Schlegel, H. B.; Scuseria, G.; Robb, M.; Cheeseman, J.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G.; et al. Gaussian 09, revision D. 01; Gaussian. Inc.: Wallingford, CT, 2009. (49) te Velde, G. t.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. J. Comput. Chem. 2001, 22, 931−967. (50) Shen, L.; Chen, Y.; Li, X.; Li, C. Tuning of the stability and energy levels of singlet exciton fission relevant excited states of pentacenes by site-specific substitution. J. Mol. Graphics Modell. 2016, 66, 187−195. (51) Wang, L.; Li, P.; Xu, B.; Zhang, H.; Tian, W. The substituent effect on charge transport property of triisopropylsilylethynyl anthracene derivatives. Org. Electron. 2014, 15, 2476−2485. (52) Anthony, J. E. The larger acenes: versatile organic semiconductors. Angew. Chem., Int. Ed. 2008, 47, 452−483. (53) Casanova, D. Bright Fission: Singlet Fission into a Pair of Emitting States. J. Chem. Theory Comput. 2015, 11, 2642−2650. I


Polymorphism Controlled Singlet Fission in TIPS-Anthracene: Role of

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