Small Organic Molecules for Efficient Singlet Fission: Role of Silicon

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Small Organic Molecules for Efficient Singlet Fission: Role of Silicon Substitution Kalishankar Bhattacharyya, Saied Md Pratik, and Ayan Datta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06960 • Publication Date (Web): 23 Oct 2015 Downloaded from http://pubs.acs.org on October 25, 2015

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The Journal of Physical Chemistry

Small Organic Molecules for Efficient Singlet Fission: Role of Silicon Substitution Kalishankar Bhattacharyya, Saied Md Pratik 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

Abstract Singlet fission (SF) has emerged as an important mechanism for enhancing the efficiency of organic solar cells. In search for new molecules for SF, silicon substituted oligoacenes are shown to be excellent candidates. Here we show that monosilicon substitution in central ring of anthracene is found to be the smallest closed shell molecule predicting to exhibit SF. The crystal structure of 10-cyano-9-silaanthracene (10-CN-9-SA) shows the molecules in slipped parallel stacked orientations with a small intermolecular distances (dcenter-center= 4.13 Å). We have performed calculations using the Marcus electron transfer theory to calculate SF rate in a chromophoric pair. Our calculation indicates that lowest energy CT state mediates as a real intermediate in a SF pathway maximizing SF rate. Short intermolecular contacts and lowlying charge transfer (CT) states lead to an anticipated triplet yield of ~ 200 % in the SF process for these crystal. An indirect one-electron integral mechanism through a CT state predominates over the direct two-electron integral mechanism for this extremely efficient SF. Introduction Singlet fission (SF), a multichromophoric process by which intially excited state of a molecule interacts with its closed neighbours producing two excited triplets, is a new pathway that can accelerates solar cell application. The triplets are paired up into an overall singlet state.1-2 As shown in Scheme 1, this process is spin-allowed and can therefore be extremely fast. The prospect of generating two excitons from an initial single exciton is extremely attractive to increase the solar energy conversion efficiency.3 Based on the SF principle, one can find a way to increase the Shockley-Queisser limit of photovoltaic's ideal efficiency from ~32% to ~46%.4 SF initially observed for anthracene is now realized as the 1

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predominating decay process in tetracene and pentacene crystals.5 Subsequently, efficient SF has been observed in zeaxanthin aggregates, 1,3-diphenylisobenzofuran, TIPS-pentacene and rubrene.6-9 Notwithstanding the few molecules mentioned above, the list is remarkably short particularly in light of the technological importance for SF. Though in principle, one might design polymers based on existing molecules to facilitate inter/intrachain SF, it is important to explore new set of molecules which in their aggregated form exhibit good SF yields. In this context, first-principles calculations emerge as a powerful tool to design new libraries of molecules. Li and co-workers have recently studied the effects of heteroatom substitution on tetracene and pentacene on their stability and SF.10 However, it is desirable to predict small organic molecules as highly accurate excited state calculations are essential to estimate SF yield so as to motive their experimental synthesis and measurements.11 Recently, Zeng et al. have shown heteroatom substitution strategy by replacement of four C atoms in benzene, naphthalene and azulene by a pair of B and N each make them suitable candidates for SF.12

Figure 1: Mechanism of SF: The initial excited monomer (S1) can split into two triplets in the dimer via direct two-electron excitation or through an indirect charge-transfer (CT) mediated two consecutive one-electron excitations. V2e, VLL and VHL represent the relevant interchromophore coupling. A set of general rules have been proposed for favorable condition for SF namely, (i) the energy separation between the ground state (S0) and first excited state (S1) and the second triplet excited state (T2) has to be more than twice the separation between S0 and the first triplet excited state (T1): E(S1) ≥ 2E(T1) and E(T2) ≥ 2E(T1).13 (ii) Favourable packing between the chromophores to maximize coupling between the correlated two triplet pairs and to minimize intermolecular deactivation through excimers or e-h separation.14-15 In fact, even if a new set of molecules (in monomeric form) are shown to satisfy the first condition, the 2


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second condition is even more stringent as strong interchromophore coupling would be detrimental since it will lead to exiton splitting which may in turn result in violation of the first condition in dimers or aggregates.16 Also, one of the most preferred mode of packing of alternant aromatic hydrocarbons (viz. benzene, naphthalene, pyrene, perylene and coronene etc.) namely, the parallel π-stacked arrangment (H-aggregate) leads to a radiationless S1à S0 decay channel (Kasha’s rule).17 The recent progress in synthesis of organosilicon compounds particularly silaaromatic molecules like monosilabenzene, monosilanaphthalene and monosilaanthracane by Tokitoh et al. have generated exciting set of small aromatic molecules.18-19 Crystal structure, optical spectroscopy and calculations show that replacement of few carbon by silicon atoms in (4n+2)π molecule generates new orbital energy level without effecting overall aromaticity of the system.20 Based on the incoherent hopping model, we have shown that silaaromatic molecules have excellent FET characteristics which arises primarily due to the emergence of new electronic and vibronic states otherwise absent in the conventional polyaromatic hydrocarbons (PAH).21-22 In this present article, we show that silicon substitution in PAH significantly reduces the S0– T1 gap relative to the S0–S1 gap thereby allowing smaller fused hydrocarbon to satisfy the primary condition for SF. Based on calculations of the coupling matrix between the various unique dimer configurations of 10-cyano-9-silaanthracene retrieved from its predicted cystal structure, we predict to exhibit an excellent triplet yield (ΦT) of ~ 200%. To the best of our knowledge, 10-cyano-9-silaanthracene is the smallest closed shell molecule to date that satisfies the conditions for SF. Computational Details : Geometry optimization of the oligoacenes and their various monosilicon substituted analogues were performed at the B3LYP/6-31+G(d,p) level.23-25 Well known hybrid DFT functional B3LYP has been found satisfactory for geometry optimization in singlet fission community and double-ζ quality atomic basis are considered to be reliable.10,12 No symmetry constraints were applied during optimization. After that harmonic frequency calculations were performed to ensure the absence of vibrational instabilities in optimized structure. Time Dependent DFT calculations with 10 states were performed using the B3LYP, CAMB3LYP26 and ωB97XD27 levels for the optimizied monomers to calculate the vertical S0-S1 and S0-T1 gaps. Although hybrid functional B3LYP are known to underestimate the energies of charge-transfer states. However this error can be overcome using long range corrected CAM-B3LYP and dispersion corrected ωB97XD. Based on energy condition calculated S1 3



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and T1 were used to evaluate thermodynamic feasibility of SF. The initial coordinates of the crystal of 10-CN-9-SA were retrieved from the crystal of 10-CNA on which a carbon atom was replaced by Silicon at the 9-position.

Periodic DFT calculations for crystal was

performed using plane wave DFT-D3 calculation as implemented in VASP code28 which is known to account for weak dispersion interaction in molecular solids.29 The core-valence interactions were taken into account by projected augmented wave (PAW) approach along with generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) functional.30 The k-point mesh and energy cut off were chosen to be 2×2×8 and 500 eV respectively. Ultrasoft pseudopotential were taken in ionic core during crystal structure optimization. The binding energies of the various dimeric configurations within the crystal were corrected for Basis Set Superposition Error (BSSE) by using the counterpoise correction (CP).31 We calculated the ground state energy for 10-CN-9SA at various level of spin configuration. Table S1 shows the energies of the 10-CN-9SA for Restricted singlet (RB3LYP), Restricted open shell singlet (UB3LYP, BS) and Unrestricted triplet (UB3LYP) calculations. All the calculation have been performed at 6-31+G(d,p) basis set functions. However it is shown that closed shell singlet is more stable than triplet state (See Table S1). The relative positions of the charge-transfer states for the relevant dimers were obtained from TD-DFT calculations at the CAM-B3LYP level and they were identified from inspection of their natural transition orbitals (NTO) and increased transition dipole moment along intermolecular axes. The one-electron coupling (VHL and VLL) were calculated through the ADF suite of programs at the B3LYP/TZ2P level.32 All geometry optimization and TD-DFT calculations are performed using Gaussian G09 software.33 The two-electron coupling (V2e) was computed directly from the Slater-Condon rules based on the expansion of the frontier orbitals in terms of the 6-31+G(d,p) basis functions as written in equ.(3) for which 1/r is obtained from the interatomic orbital distances for a specific dimer geometry. Results and Discussions As shown in Figure 2, in case of both unsubstituted and their mono-silicon derivatives, the smallest monocyclic and bicyclic systems namely benzene and naphthalene have their S0-S1 excitation energies smaller than twice the S0-T1 gap.

4


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Figure 2: S1 and 2T1 excitation energies (relative to S0) at B3LYP/6-31+G(d,p) level (in eV) for monosilicon substituted linearly fused oligoacenes (n=1-5). The inset shows the same for unsubstituted oligoacenes. The left panel shows the structures of the molecules considered. Red and black lines indicate 2T1 and S1. n represents the no. of fused benzene ring. With an increase in the number of linearly fused aromatic rings both the S0-S1 and S0-T1 gaps decrease albiet with different slopes. This results in a crossover between the relative energies of the two excitations. In agreement with previous computational and experimental reports, within the oligoacene family, only for tetracene and onwards, the condition for SF satisfied.15 Our computed ∆ESF(ES1- 2ET1) = 0.37 eV for pentacene is in excellent agreement with the experimental ∆ESF = 0.57 eV.34-36 Our calculations also correctly predict a weakly allowed ∆ESF = 0.05 eV for an individual tetracene molecule which is again in good agreement with a experimental ∆ESF of 0.10 eV.37-38 Therefore, we expect that the present B3LYP/6-31+G(d,p) calculations are suitable for rapid screening of new molecules for fulfilling the primary condition for SF at least in their gas-phase. Previous calculations by Li10, Michl11 and Ratner39 have also shown the suitablity of the hybrid B3LYP functional in predicting the molecular vertical S0-S1 and S0-T1 gaps accurately even for heteroatom substitution within the aromatic framework. Nevertheless, it is important to note that strong interchromophore interactions for the crystalline phase of tetracene results in a red-shifted S0-S1 excitation (Davydov’s splitting) leading to a mild uphill ∆ESF of -0.18 eV.38 On monosilicon substitution within the oligoacenes, the crossover occurs even for a small nuclearity systems like 9-Silaanthracene and onwards.40 The calculated ∆ESF for 9Silaanthracene (9-SA), 5-Silatetracene (5-ST) and 5-Silapentacene (5-SP) are 0.70 eV, 0.34 eV and 0.46 eV respectively. Clearly, presence of a single silicon atom results in a significant reduction of the S0-S1 and S0-T1 gaps. The S0-S1 transitions for 9-SA, 5-ST and 5-SP are (ES05



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S1=2.65

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eV, f=0.077, HOMO → LUMO; ES0-T1=0.97 eV), (ES0-S1=2.05 eV, f=0.057, HOMO

→ LUMO; ES0-T1=0.85 eV) and (ES0-S1=1.61 eV, f=0.043, HOMO → LUMO; ES0-T1=0.49 eV) respectively. These are significantly red-shifted compared to (ES0-S1=3.21 eV, f=0.058, HOMO → LUMO; ES0-T1=1.8 eV), (ES0-S1=2.44 eV, f=0.050, HOMO → LUMO; ES0-T1=1.19 eV) and (ES0-S1=1.91 eV, f=0.041, HOMO → LUMO; ES0-T1=0.77 eV) for anthracene, tetracene and pentacene. The S0-S1excitation energies are tabulated in Table 1.

Table 1: S0-S1 excitation energies for the systems discussed in the present work at B3LYP/631+G(d,p) level.

Molecule

Excited State

Energy (eV)

Configuration

Oscillator Strength

anthracene 9-silaanthracene tetracene 5-silatetracene pentacene 5-silapentacene

S1 S1 S1 S1 S1 S1

3.21 2.65 2.44 2.05 1.91 1.61

HOMO-LUMO HOMO-LUMO HOMO-LUMO HOMO-LUMO HOMO-LUMO HOMO-LUMO

0.058 0.077 0.050 0.057 0.041 0.043

The relevant occupied molecular orbital (OMO) and unoccupied molecular orbital (UMO) are shown in Supp. Info. File (Fig. S1). Interestingly, eventhough the basis of the oneelectron excitations namely the OMO and UMO remain invariant on a single silicon atom substitution in the ring, the OMO-UMO gap reduces. Electron releasing and inductive effect of Si substituted oligoacene raises the energy of HOMO and, decreases the HOMO-LUMO gap. Such lowering of the gap in cyclic molecules on heavy atom substitution (M=Si, Ge) is well-known.41

Table 2:Singlet fission gap, ∆ESF (in eV) for substituted 9-SA at B3LYP/6-31+G(d,p) level of theory. X

NO2

∆ESF 0.31

F

Cl

Br

CF3

CN

0.20

0.14

0.11

0.99

0.05

6


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As discussed above, 9-SA is predicted to be smallest system to satisfy the primary condition for SF. The calculated structural parameters at the B3LYP/6-31(d) level for the silaaromatic ring are in excellent agreement with the available single-crystal data for 2,4,6tris(bis(trimethylsilyl)methylphenyl (Tbt) substituted 9-SA.42 The presence of a bulky group therefore, has inconsequential effect on the planarity of the ring and hence its electronic/optical properties. Nevertheless, a ∆ESF = 0.70 eV is far greater than desired as an excessive exoergicity should lead to loss due to heating and other non-resonant (slower) processes. Therefore, the S0-S1 and S0-T1 gaps were further tuned in 9-SA by various electron acceptor (A) substituents. Table 2 reports the calculated ∆ESF for a series of substituted 9-SA at the B3LYP/6-31+G(d,p) level. Presence of highly electronegative groups in the 10 position of 9-SA increase ∆ESF in the order: -Br < -Cl < -F

Small Organic Molecules for Efficient Singlet Fission: Role of Silicon

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