Remote Functionalization through Symmetric or Asymmetric

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Spectroscopy and Excited States

Remote Functionalization through Symmetric or Asymmetric Substitutions Control the Pathway of Intermolecular Singlet Fission Arun K. Pal, Kalishankar Bhattacharyya, and Ayan Datta J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.9b00419 • Publication Date (Web): 12 Aug 2019 Downloaded from pubs.acs.org on August 13, 2019

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Journal of Chemical Theory and Computation

Remote Functionalization through Symmetric or Asymmetric Substitutions Control the Pathway of Intermolecular Singlet Fission Arun K. Pal, Kalishankar Bhattacharyya and Ayan Datta* School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A & 2B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, WB, India

ABSTRACT Singlet fission (SF) produces two coupled triplet excitons from a high energy singlet excitation. The mechanism of SF in a variety of phenyl (–Ph) substituted pentacene is systematically studied through both ab initio and density functional theory calculations. Two classes of substitution to pentacene are considered namely, symmetric configuration with four Ph groups (TPP) and an asymmetric configuration with two Ph groups (DPP). The position of the singlet and triplet states are determined by calibrating the active space through state average complete active space self-consistent field (SA-CASSCF) calculations. The SF rates are computed based on restricted active space with single and double spin flip wave functions (RAS-SF and RAS-2SF), which are analyzed based on different intermolecular π-stacking patterns of TPP and DPP. The contribution of charge transfer (CT) state near the multiexciton (ME) state plays a significant role for SF efficiency. The role of excimer formation is supportive for ME generation [J. Am. Chem. Soc. 2016, 138, 617] and hence it is critically studied. The ME generation in TPP is a slower process and occurs through an excimer-mediated path with a large coupling between the first singlet excited state and ME state. On the other hand, DPP exhibits a relatively faster SF rate through the formation of a ME state via low-lying CT state, especially the slip-stacked dimers. The present computation elegantly demonstrates the crucial role of functional group substitution in the structure of SF active molecules in determining the efficiency of fission dynamics.

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INTRODUCTION Polyaromatic acene derivatives as amorphous thin films or molecular crystals are extensively used for the application in solar cell devices where the generation of charge carriers occur under solar radiation.1-4 In recent times, the spin-conversion processes in tetracene and pentacene crystals have generated significant attention for upgrading the photo-voltaic efficiency in organic light emitting diodes (OLEDs), which exceed the Shockley-Queisser limit as in “third generation” photovoltaic devices (PD).2, 5-8 Two low lying coupled triplet pairs are formed from a single exciton in these chromophores. Therefore, both the triplet excitons yield a set of electron-hole (e–h) pair by absorbing one solar photon and increases the efficiency of charge carrier generation in OLEDs from 34% to 46%.9-10 But the timescale of this process needs to be rapid (picosecond or femtosecond time-scale) as it is occurs through multiexciton (ME) generation 2, 6,11 This phenomenological spin-conversion process is termed singlet fission (SF), as shown in scheme 1. In recent years, both experimental and theoretical investigation for designing new SF materials has led to an understanding of the pathways based on the electronic structure of the intermediate steps.12

Scheme 1. Mechanistic pathways in singlet fission process. LE: Locally excited state, CT: Charge transfer state, ME: Multiexciton state. In SF, the thermodynamic and kinetic conditions must be satisfied for a spontaneous process, i.e., (a) E(S1) ≥ 2E(T1) and (b) E(T2) ≥ 2E(T1), where E(S) and E(T) are the excitation energies of singlet and triplet states, respectively.6 The first condition ensures exoergicity while the latter one prevents the recombination of e–h pairs created from the spin-product during SF processes (triplet-triplet annihilation). For instance, pentacene in the solid state satisfies these 2 ACS Paragon Plus Environment

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conditions while tetracene barely fulfills, E(S1) ≈ 2E(T1).6 In a recent study, Zhang et al. have revealed that an excessive exoergicity might hamper SF in heteroacenes.13 In general, SF can occur through two pathways, namely, direct transfer to the singlet coupled triplet pairs or through a mediating charge-transfer (CT) state.14-16 The preference of one over the other is controlled by the nature of electronic coupling between the electronic states and CT excitation energy. Therefore, it is important to maximize SF efficiency through a favorable non-covalent interactions π…π stacking and hydrogen bonding between two chromophores.17 Numerous researches have been published in last five years where the authors revealed that the packing motif in the crystal structure of acenes plays a crucial role in SF.18-24 However, the arrangement of crystal packing over the SF rate is still a subject for debating. For instance, by adopting nonadiabatic molecular dynamics method on a broad range of pentacene dimers, Belijonne et al. proposed that the slip-stacking (SS) crystal arrangements are more efficient for SF.22 The authors conclude that the standard CT character in a photoexcitation is necessary for this fact. The same finding was proposed by Kolata et al. on perfluropentacene.20 On the other hand, Krylov et al. addressed that the intermolecular electronic coupling is also a remarkable factor and the efficiency of SF in herringbone (HB) motif cannot be ignored.23 Phenylated acenes are of great interest in this manner as they may contain cofacial π-stacking motif along with SS and HB crystal packing.25 Recently, Marom et al. carried out a systematic computational study on various packing pattern of phenyl substituted tetracenes and pentacenes.19 They analyzed the thermodynamic diving forces along with CT character and concluded that weak cofacial or SS intermolecular interactions are more advantageous for exothermicity in SF. Yost et al. have reported a detailed study on the ultrafast photoinduced SF dynamics of substituted acenes. 6,13diphenylpentacene and 6,13-di(biphenyl)-4-yl-pentacene with orthogonal π-stacking and displaced slipped stacking, respectively, show fission yield near unity even when the distance between two monomers is >5 Å.26 Based on experimental and theoretical studies, Kaur et al. have shown that the choice and position of substitutions to a chromophore can control the lifetime alongwith the resistance efficiency under photooxidative condition.27 Clearly, substituted pentacenes are of great interest to control SF efficiency. Several computational studies on SF have been reported on the intermolecular interaction based on pentacene dimer.6,

18, 28-29

Zimmerman and co-workers suggested that for pentacene 3

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dimer the intermediate 1(ME) state intersects the S1 state at smaller intermolecular distances using multireference Moller-Plesset perturbation theory (MRMP).30 The π-orbital overlap between the two adjacent chromophores occur via an excimer formation resulting an intersection between S1 and 1(ME) states.31 Restricted active space double spin-flip (RAS-2SF) method was utilized for this purpose, developed by Casanova and Gordon.32 Furthermore, Krylov et al. characterized the associated electronic states in SF of a pentacene dimer by describing the nonadiabatic coupling matrix (NAC) elements from the norm of reduced one-particle density matrix calculations.33 Therefore, it is interesting to compare and contrast the SF rates in substituted pentacene dimers by ab-initio multireference methods. Indeed, till now, most computational studies have been performed on unsubstituted pentacene dimers instead of functional group substitution on various position of the chromophore. In fact, it has been recently reported that altering the functional group position in pentacene derivatives significantly affect the excited state populations and controls the photo-degradation channels under photo-physical environment.34-36

(b)

(a)

Figure 1. Structures of (a) 5,6,7,8-tetraphenyl pentacene (TPP), and (b) 7,8-diphenyl pentacene (DPP). To address the question how the involved mechanism for ME generation in intermolecular SF and associated rates would change upon functional group substitution, we have studied the monomers and dimers of pentacenes with phenyl substitution at 5,6,7,8- and 7,8- positions. As shown in Figure 1, the structures are abbreviated as tetraphenyl pentacene (TPP) and diphenyl pentacene (DPP). The different types of crystal packing arrangements of TPP and DPP are considered. The SF screening study for the monomeric chromophores are 4 ACS Paragon Plus Environment

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performed by the time-dependent density functional (TD-DFT) level of theory. The bright (CT) and dark (ME) electronic states are captured by using various ab-initio methods, as discussed in the next section. The possible intermolecular electronic couplings with π-stacked dimers are computed. The relevant SF rates are also discussed through the inclusion of excimer formation in the dimer. Finally, an attempt is made to understand how the position of CT state affects the overall SF mechanistic pathways. COMPUTATIONAL DETAILS The ground state geometries of the investigated monomers and dimers are optimized with Gaussian09 (G09) program37 by adopting B3LYP functional and 6-31+G(d,p) Pople’s basis set. We also perform vibrational frequency analyses to confirm the absence of structural instabilities. The reference structure of TPP is retrieved from the available X-ray crystallographic data (CCDC code: 091042).38 The DPP molecule was optimized using the stable TPP geometry, by removing two phenyl groups from a shared acene ring. For the dimers, we optimized the position of the hydrogens to maintain the carbon framework at crystallographic geometry. The dispersion correction to B3LYP functional (B3LYP-D3BJ) has been incorporated in the calculation of binding energies alongwith basis set superposition error (BSSE) correction. The excited singlet and triplet states of the monomers are optimized with the same methods by using time-dependent (TD) formalism of density functional theory (DFT) framework. The vertical excited energies are computed with the 6-311++G(d,p) basis set using the 50-50 keyword as implemented in TDDFT section of G09.39 The essential requirement of ab-initio treatment with multireference perturbation theory (MRPT) and complete active space self-consistent field (CASSCF) for the calculations of vertical excited states of polyacenes has been extensively reported by Hirao et al40 and others.18, 41-43

In this work, we apply state-averaged CASSCF (SA-CASSCF)44 along with the extended

multiconfiguration quasidegenerate perturbation theory of second order (XMCQDPT2) to calculate the energies of low-lying singlet and triplet excited states.45 A double-ζ valance (DZV) basis set was used to reduce the computational cost.46 Three roots with equal weight are considered in SA-CASSCF(p,q) calculations, where p refers the active electrons and q states the active orbitals. Initially, we employ 4-electrons-in-4-orbitals (4e-4o) model to characterize the 5 ACS Paragon Plus Environment


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SF mechanism and then we sequentially extended the active space requirement to 6e-6o, 8e-8o, 10e-10o and 12e-12o. The orbitals in SA-CAS calculations are chosen by analyzing their energy levels because the degeneracy in frontier MO energies represents a greatest overlap between each other.47 For the excited state dimers, we use the 6e-6o model in SA-CAS calculations as a tradeoff of accuracy and computational tractability. The conventional shifting parameter of 0.02 Hartree was used in all XMCQDPT2 calculations to prevent the intruder state effects.48 The calculations for the monomers are carried out by the GAMESS program49-50 while for the dimers we use Firefly.45, 51 Restricted active space with a single spin flip (RAS-SF) calculations are also performed to calculate the excitation energies of monomers.32 RAS-SF calculations are done at a 2e-2o active space [RAS(2,2)-SF] alongwith a high-spin triplet reference and by employing 6-31G(d), 6-311G(d,p) and cc-pVDZ (H)/cc-pVTZ (C) basis sets. We evaluate the corrected energies by using a correlated excited state method, scaled opposite spin version of configuration interaction singles with a double correlation, SOS-CIS(D).52 We have used SOS-CIS(D) instead of CIS(D) as for CIS(D), the range is limited to a better explanation of the ground-state and excited states by the Slater (HF) determinant and CIS reference, respectively.53-54 Occasionally, the latter method gives also overestimated transition energies due to near degeneracy effect.55 Further, the excitation energies for the dimers are computed by using 4e-4o active space with a double spinflip [RAS(4,4)-2SF] and 6-31G(d) basis set, where a quintet reference state is considered.56 The coupling between the adiabatic states, ||γ|| and the key electronic energy gaps are characterized from the RAS(4,4)-2SF calculations. These calculations are performed using the Q-Chem computational package.57 The energy difference between two RAS-CI states (ΔE), energy drive due to SF (ESF) and ME stabilization energy (Eb) are calculated by the following equations:42, 5859

1 E  E  S1   E   ME   ,   ESF  E  S1   E  2T1  , 1 Eb  E  2T1   E   ME   .  


(1)

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Eb denotes the minimal amount of energy is needed to overcome the barrier for separating into two triplet states (2T1) from 1ME state.60-61 The 1ME state will be bound if the Eb is positive whereas negative Eb indicates fast 2T1 generation from an unbound 1ME state. The associated rates in SF process are evaluated via the following relations proposed by Krylov et al., which use the Fermi Golden Rule and linear free energy relationship,62 2

   1 k1  S1   ME      exp   ESF  ,    E  k2   ME   2T1   exp   Eb  ,   1

(2)

where   1 k BT and α is the constant from linear free energy relation. Finally, we carried out the attachment/detachment calculations for the dimers to locate the CT state, as implemented in QChem.63-64 RESULTS AND DISCUSSIONS Substitution of organic groups to the acene chain is an efficient approach for tuning the low-lying energy. Recently, Guldi and co-workers have reported the tuning of intramolecular SF pathway in substituted pentacene derivatives.65 Presently, we systematically study the influence on the SF rate for the substitution of phenyl ring in a symmetric and asymmetric fashion in pentacene. The structural information from crystallography is available for TPP.38 TPP behaves like a hole-transporting (p-type) semiconductor in thin-films with a field effect mobility of 10–3 cm2/V.s.38 The phenyl groups are oriented perpendicular with the plane of pentacene ring as shown in Figure 1. The conformational arrangement of the substituted four phenyl rings in the optimized structure agrees with the crystallographic structure.



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Figure 2. UV-Vis absorption and emission plots. Table 1: HOMO (EH) and LUMO (EL) energies at B3LYP level. The energy gaps (ΔE = EL – EH) are shown in bold. All energies are reported in eV.

6-311+G(d,p)a,d

–EH 4.96 4.93 -

Pentacene –EL ΔE 2.67 2.29 2.76 2.17 2.08

–EH 5.16 4.86 5.00

DPP –EL 2.93 2.71 3.08

ΔE 2.23 2.15 1.92

–EH 4.80 4.78 4.95

TPP –EL 2.59 2.67 3.07

ΔE 2.21 2.11 1.88

6-311++G(d,p)b Expt.c,d a Previously reported.27 b Our calculations. c Measured optical band gaps in o-dichlorobenzene (for pentacene) and CH Cl solutions (for 2 2 TPP and DPP).33, 66 d DPP: the phenyl groups are substituted at 9C and 10C of pentacene (at middle ring). The calculated and measured frontier MO energies are listed in Table 1. The values with 6-311+G(d,p) basis set and B3LYP functional are available from a previous study by Miller et al.27 Note that, in the experiment and previous calculation, the phenyl substitution in DPP was at the 9,10-position whereas it is 7,8-position in our case.66 However, the comparison has been made as the electronic structure of both the DPP chromophores are closely related. We use a larger basis set for our calculation which exhibit a better agreement with the experimentally observed data. For pentacene, the deviation is 4% with respect to the experiments while it is 10% for TPP and DPP. Introducing the phenyl groups in pentacene makes the structures more stabilized. Table 1 demonstrates that the HOMO–LUMO energy gaps decrease from pentacene to TPP. Strictly speaking this is not a case of delocalization between the aromatic moieties. Rather the perpendicular -Ph rings behave as electron withdrawing groups and exert negative inductive effect (–I). As shown in the Figure S1, the pentacene carbon atoms adjacent to the -Ph substituents become more electron deficient due to the electron density withdrawal from the 8 ACS Paragon Plus Environment

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pentacene ring, which in turn, stabilizes the frontier MOs and hence, the absorption gets redshifted. The UV-vis absorption and emission plots are shown in Figure 2. The presence of a greater number of phenyl rings in pentacene results a bathochromic shift in the absorption peak with a low intensity. Nevertheless, both DPP and TPP exhibit significant absorption peak in the visible region (390-750 nm). Therefore, either of the molecules satisfy the condition for solar light harvesting through SF. The thermodynamic conditions for an efficient SF in a molecule must be maintained namely E(S1) ≥ 2E(T1) and E(T2) ≥ 2E(T1). The energy gaps, E(S1 – 2T1) and E(T2 – 2T1) are summarized in Table 2. Though several SF studies on pentacene molecule have been performed previously, here we also compute the TDDFT energies to compare it with TPP and DPP. The calculated SF energy gaps of pentacene agree well with the experiment, as shown in Table 2. E(S1), E(T1) and E(T2) of DPP and TPP are found to significantly decrease in comparison to pentacene. SF energy gaps of both DPP and TPP are exoergic but slightly endoergic with respect to pentacene. The first excited state, S1 is the locally excited (LE) and bright state for all of them, in which the contribution of electronic transition is purely from the HOMO-to-LUMO excitation. The population in T1 state arises with about 74% contribution from HOMO-to-LUMO transition. The π-orbital is mostly delocalized in pentacene. The next singlet excited state, S2 (2.84 and 2.80 eV, for DPP and TPP, respectively) is dominated by the transition of an electron between HOMO–1 and LUMO+1. This transition is a dark one alongwith S3, S4, etc. Hence, S1(1Bu) is an optically allowed excited state and plays a significant role in visible light absorption. Table 2 illustrates that the energy level of the T2 state is significantly higher than the twice of T1 state. This finding ensures that there are no opportunities of an electron to return at S0 state, which helps to avoid the triplet-triplet annihilation process. The quintet state in TPP and DPP is also significantly higher in energy than singlet ground state. Therefore, the preliminary TDDFT screening supports the potential for DPP and TPP to exhibit SF characteristics.



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Table 2. Vertical transition energies (eV) with TD-B3LYP method and 6-311++G(d,p) basis set. The oscillator strengths (a.u.) are shown in parenthesis. Molecule E(S1) E(2T1) E(T2) Pentacenea 1.88 (0.04) 1.20 (0.00) 1.89 (0.00) DPP 1.84 (0.06) 1.18 (0.00) 1.85 (0.00) TPP 1.80 (0.09) 1.14 (0.00) 1.81 (0.00) aExperiment27, 30: 2T – S = – 0.58 eV, 2T – T = > – 0.30 eV. 1 1 1 2

E(S1 – 2T1) 0.68 0.66 0.66

E(T2 – 2T1) 0.69 0.67 0.67

Still, two adjacent chromophores are required to get a bright SF with a photoexcitation to the S1 state. One organic chromophore excites to its first singlet state due to photoexcitation and shares a percentage of energy with the adjacent ground-state chromophore. The total Hamiltonian contains in this process depends upon two parts, a Hamiltonian that defines the relaxed part and the other describe the interaction part. The process starts with the S1 eigenstate of a relaxed chromophore and then allow the interaction Hamiltonian to generate two independent excited triplet state via ME formation. However, a solution of single chromophore with elongated fluorescence lifetime and high concentration of ground-state structure might qualify for SF.2, 67 The experimental and previous ab-initio calculations on low-lying singlet and triplet excited states of pentacene are provided in Table S1 of Supporting Information. The calculated values with SA-CAS(12,12)/MCQDPT2 theory are in line with the experiment. There is only 0.4% error in S1 energy from MCQDPT2 whereas it increases while one uses MRMP with same active space strategy.18, 30 The ME states, arise due to doubly excitation and therefore, cannot be captured by a single reference excitation like TDDFT and CIS, but can be studied with a multireference SA-CASSCF calculation.33,

68-69

Therefore, we utilized the SA-CASSCF with

MCQDPT2 for a more quantitative calculation on excited states. Figure 3 demonstrates the XMCQDPT2 excitation energies of TPP and DPP molecule and the values are listed in Table S2. The wave functions in SA-CASSCF calculations were constructed using the equal weightage of ground and excited electronic states, where C1 point group was considered. SI contains more discussions on SA-CAS calculations. Identifying a computationally tractable and sufficiently complete active space in SA-CASSCF calculations is an important aspect of any MR calculations. As seen from Figure 3, the results from SA-CAS(n,n) to (m,m) where m > n become stabilized at n = 6 and 8 for TPP and DPP, respectively. This indicates that the multi-particle 10 ACS Paragon Plus Environment

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excitations out of lower shells are important. Usually, it is expected that the energetically lowlying singlet excited state of each SF chromophore is well defined by HOMO-to-LUMO electronic transition and the occupancy of electron in the MO of much lower energy than HOMO is treated as rigid core.70 Usually, the contribution of HOMO-LUMO transition is intense at S1 state but it can be in energetically higher singlet state only if the internal conversion to S1 state is slower than the SF rate.24, 71 Therefore, the active space requirement of greater than 8e-8o is not effective for sustaining the SF environments, at least for such similar cases.

Figure 3. Calculated excitation energies (eV) from SA-CASSCF/XMCQDPT2/DZV level of theory. It is important to note that we have denoted the first excited singlet state as S1 in TDDFT whereas it is denoted as S2a in ab-initio section. The reason is that within an adiabatic framework, the second singlet excited electronic state (S2a) arises in the Franck-Condon region, which is optically allowed and a locally excited (LE) state. In the energy level diagram, the appearance of a dark electronic state (dipole forbidden) at around 0.2 eV lower from the optically allowed state results in a doubly excited state with singlet character, (S1a). This picture is consistent at all choices of active space in SA-CAS calculations. The exoergicity of SF process can be determined by demonstrating the energy gaps between S1a and twice of first triplet excited state, 2T1. For TPP, the calculation with 8e-8o active space dimension shows that the S1a state is 0.1 eV higher than 2T1 state. For DPP, though the SA-CAS(4,4) calculations show that S1a is 0.2 eV higher than 2T1 but increasing the CAS dimension makes it mildly endothermic [ΔE(S1a – 2T1) = – 0.15 eV at SA-CAS(8,8)] . The calculations with a TZP basis set and 4e-4o active space are also carried out for the DPP monomer as listed in Table S2. The TZP energies are similar to the calculated results from DZP basis set. 11 ACS Paragon Plus Environment


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Table 3: RAS(2,2)-SF and SOS-CIS(D) transition energies of the monomers. The energies are reported in eV. TPP

DPP

Basis sets

Methods

6-31G(d)

RAS(2,2)-SF SOS-CIS(D) Correction

T1 1.28 1.10 0.18

S1 3.55 2.51 1.04

T1 1.30 1.12 0.18

S1 3.60 2.58 1.02

6-311G(d,p)


1.27 1.09 0.18

3.43 2.38 1.05

1.28 1.11 0.17

3.49 2.46 1.03

C: cc-pVTZ H: cc-pVDZ


1.26 1.05 0.21

3.36 2.25 1.11

1.27 1.07 0.20

3.40 2.32 1.08

Further, the low-lying singlet and triplet transition energies are calculated using the correlated method, SOS-CIS(D) and dynamically uncorrelated RAS-SF theory, presented in Table 3. The energies are calculated with different basis set requirement. XMCQDPT2 energy levels are nearly degenerate with the SOS-CIS(D) calculations, as shown in Table S2 and Table 3. The results obtained from RAS-SF method are blue-shifted with respect to the XMCQDPT2 and SOS-CIS(D) energies. The corrections in RAS-SF energies are listed in Table 3. The RASSF triplet vertical energies carry an error of about 0.2 eV whereas the error is much higher in case of singlet excites state (~1 eV). This observation confirms that the dynamical correlation plays an important role. The corrected energies with split valance double-ζ and triple-ζ basis sets are similar. However, a difference of about 0.03 eV (for T1) and 0.1 eV (for S1) arises in Dunning correlated-consistent (cc) formalism because the Dunning basis sets were optimized against correlated calculations, whereas Pople sets were optimized for Hartree-Fock calculations. In case of dimers, to avoid massive computational cost, we adhere on the 6-31G(d) basis set for the RAS-2SF calculations.


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Figure 4. Plot of radial distribution function (RDF), g(r) versus center-to-center (r) distance of 20 Å with a cutoff from 3×3×3 TPP supercells. TPP pairs are shown next to the RDF plot and DPP pairs are shown in below. Center-to-center distances of the DPP pairs are shown below the distant arrows. The various intermolecular interaction patterns for the TPP dimers were taken from the radial distribution function retrieved from the crystal structure. We extended the X-ray crystallographic unit cell to a 3×3×3 supercell for a better understanding of the intermolecular packing pattern. The radial distribution plot is shown in Figure 4, drawn by keeping a center-tocenter distance cutoff of 20Å. Most populated dimeric pairs are seen with a contact distance of 9.01Å (TPP-PI) and 8.10Å (TPP-PII). TPP-PI, a V-shaped dimer from classical herringbone pattern, involves with a short C–C π distance of 4.92Å while in PII it is a slipped parallel dimer with shortest C–C π-stacking distance of 7.01Å. Therefore, we consider these two dimers of TPP for intermolecular SF calculations. The investigated DPP dimers are modeled from the TPP dimers, as experimental crystal data is unavailable. The different pattern of π-stacking in a molecular crystal can tune the intermolecular interaction and hence the SF energy gaps, which led us to investigate all possible stacking pattern in DPP. There are four possibilities if one 13 ACS Paragon Plus Environment


selects the alternative position for phenyl group substitution in both DPP chromophores. DPP-PI and PII are constructed from the HB dimer of TPP, whereas DPP-PIII and PIV are built from SS dimer of TPP. The face-to-face antiparallel pattern in DPP-PII and DPP-PIV are designated as cofacial molecular arrangement. Such an arrangement in packing pattern of DPP makes it an interesting system for comparing SF efficiency. The optimized dimers are illustrated in Figure 4 alongwith their respective center-to-center distances. The connection between molecular pairs and molecular crystals arises from the validity of the point-dipole approximation to describe electronic properties in organic crystals held by weak dipolar interactions.72 Since, the excitations arise from π-type orbitals, they are localized on the molecules (monomers). But, the packing of the monomers in a dimer and in a crystal is largely governed by weak dispersion forces and hence, the splitting in a dimer are rather small. The excitations are formally termed as Frenkel type in which the electron-hole pairs are localized in between the molecular pairs. So, we believe that the model of dimers for understanding excitations in molecular crystal is quite robust. The binding energy (BE) can define the reinforcement of intermolecular interaction in dimers.73 Therefore, we calculated the BE of all pairs at B3LYP-D3BJ/6-31+G(d,p) level by incorporating BSSE correction. The binding energies of TPP-PI and TPP-PII are evaluated as – 12.6 and –15.8 kcal mol–1, respectively. The larger BE in TPP-PII indicates that the intermolecular interaction between two chromophores is quite strong and therefore, might be strengthen the interaction in excited state structures.28,

70, 74-76

The BSSE corrected binding

energies for all the DPP pairs (~ –8 kcal mol–1) are similar but are lower than the TPP pairs. However, DPP-PI and DPP-PIII have relatively higher BE as tabulated in Table S3 of SI.


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Table 4: Calculated and corrected RAS(4,4)-2SF excitation energies (eV) for the dimers with 631G(d) basis set. Oscillator strengths (f) are shown in parentheses. States

TPP P1

PII

T1

1.28 (0.00)

1.27 (0.00)

S1a

2.57 (0.00)

2.55 (0.00)

S2a

3.58 (0.11)

3.60 (0.01)

Charactera

DPP

Charactera

PI

PII

PIII

PIV

1.27 (0.00)

1.28 (0.00)

1.28 (0.00)

1.28 (0.00)

ME

2.57 (0.00)

2.58 (0.00)

2.57 (0.00)

2.57 (0.00)

ME

LE

3.65 (0.66)

3.67 (0.49)

3.67 (0.76)

3.67 (0.77)

LE + CT

3.60 3.62 3.68 3.69 3.68 3.68 LE + CT (0.69) (0.79) (0.10) (0.24) (0.01) (0.01) a ME: Multiexciton State, LE: Locally excited state, CT: Charge transfer state. S3a

LE

Table S4 lists the XMCQDPT2 transition energies for the dimers with 6e-6o active space requirement. The arrangement between the energies of ME and LE states again satisfy the SF requirement, as in monomers. The excitation energies calculated from RAS(4,4)-2SF method are shown in Table 4. The RAS-2SF calculated energies of the optically allowed state, S2a, are around 1 eV higher with respect to the XMCQDPT2 energies. This confirms that the XMCQDPT2 calculations provide a reliable account of dynamical correlation effects. Nevertheless, the contribution of CT configurations to the LE and ME states can be calculated from the RAS-2SF wave functions.60 The weightage of the adiabatic wave functions was evaluated from the corresponding configuration amplitudes because RAS-2SF considers all possible configurations with equal footing within an adiabatic frame. The maximum weightage of ME character to the S1a state for both TPP and DPP pairs confirms the existence of intermolecular SF. In TPP pairs, the S2a state carries a major contribution (90%) of LE configuration and a very small amount (10%) of CT percentage. The CT configurations become significant predominantly for the higher singlet excited state (S3a) for TPP. For DPP-PI and DPPPII, the contribution of CT character to S2a state is around 45% while it is around 35% for the other DPP pairs. Table 4 also shows that the oscillator strengths of S2a states in DPP pairs are significantly larger which confirms the presence of locally excited state with some CT character. Therefore, the differences between the symmetric and asymmetric dimeric pairs make an interesting switchover in the mechanism of optical excitation. Furthermore, the CT states are captured by the attachment-detachment density plots, as shown in Figure S3 of SI. Though the 15 ACS Paragon Plus Environment


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CT states are considerably higher in energy for a CT-mediated SF but the fact is in agreement with previous observations.18, 74, 77-79 Table 5: SF electronic quantities (ΔE, ESF and Eb), NAC parameter ||γ||, and associated SF rates of the dimers. The energies are reported in eV. ΔE

ESF

Eb

||γ||2 × 10–4

log (k1)

log (k2)

PI PII

1.01 1.05

1.02 1.06

– 0.01 – 0.01

0.22 0.83

13.2 13.0

0.08 0.08

DPP PI PII PIII PIV

1.08 1.10 1.09 1.10

1.10 1.11 1.11 1.11

– 0.03 – 0.02 – 0.01 – 0.01

0.22 0.10 0.06 0.05

14.1 14.5 14.6 14.7

0.25 0.17 0.08 0.08

TPP

The key electronic energies (ΔE, ESF and Eb) are evaluated from Eq. (1) and listed in Table 5. The rates of formation of multiexciton state and separated triplet pairs are designated as, k1 and k2, respectively. The relevant electronic coupling between the S2a (LE or LE + CT) and S1a (1ME) states are also tabulated in Table 5. Krylov and co-workers introduced NAC (nonadiabatic coupling) for calculating the coupling parameter based on the many-electron wave functions.33 However, multiexciton states could be described as coupled triplet states. Hence, 1ME

state is an example of a strongly correlated state in which two triplet states are localized on

separate moieties or molecules (xSF). The SF rates are calculated using Eq. (2), where we use α = 0.5 to consider the admixture of the CT states.58, 80 ESF for TPP-PII is more exoergic than that of its PI, whereas they are nearly equal for all DPP-Pairs. The electronic couplings are almost same in case of the TPP-PI and first two DPP-Pairs, while it decreases for the other DPP pairs in comparison to TPP-PII. The ΔE values suggest that the 1ME states are more stabilized in case of DPP pairs. Therefore, in DPP pairs, the rate of the formation of correlated triplet pair is faster with respect to TPP pairs. The rate (k2) is faster for DPP-PI and DPP-PII because of lower energetic barrier (Eb) for separation of two triplet states. Though the substituted phenyl groups are not significantly contributing to the frontier MO configurations, but they can affect the SF rates. Figure 4 and Table 5 explain that with 16 ACS Paragon Plus Environment

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decreasing the distance between the stacked DPP chromophores the rate of ME generation increases. The substituted phenyl groups in the cofacial SS dimer of DPP can interact with the backbone of another whereas in HB dimer the phenyl groups are tried to separate (spatially) the pentacene backbone, results in a weak coupling between the contributing MOs. Recently, Marom et al. referred that the degree of singlet exciton transport and thermodynamic diving force (ES – 2ET) are the important factors for SF tuning in phenylated acene crystals. In a feasible SF process, the electron is mainly populated to the chromophores those are strongly coupled with a chromophore where the hole is present.19, 81 They concluded that the crystal packings with SS and weak cofacial motif are efficient for SF as they hold the highest degree of singlet exciton CT character and thermodynamic diving force. Hence, the possible π-stacking interactions and exoergicity in SF of DPP dimers provide an indication to the experimentalists for synthesis and SF characterization.

Figure 5: Potential energy surface (PES) plot of the ground state and first excited singlet state (S2a) of TPP-PII and DPP-P(III/IV) pairs. Inset shows that minima at center-to-center distance of ~6.5Å to the PES for S2a. Furthermore, Miller et al. have recently proposed that the SF rates are significantly controlled by the position of the CT state in the energy level diagram.80 Therefore, we studied the SF rate in the excited state dimers of DPP-PIII and DPP-PIV, and compared to the excimer formation in TPP-PII. The excimer structures for TPP-PII and DPP-PIII/PIV are obtained from their first singlet excited state based on the geometry scan by TDDFT, where we vary the centerto-center distances between 4.5Å and 13.5Å with an interval of 0.5Å. The potential energy curves are shown in Figure 5 and it suggest that the center-to-center distance ~6.5Å of π-stacked structure belongs to the minima at the potential energy surface for S2a. The shape of the curves agrees with a previous excimer formation calculation on acene system by Gao et al.82 The 17 ACS Paragon Plus Environment


structural orientations of the excimer geometries are shown in Figure S4 of SI. These excimer geometries are further used in a similar way as described above to evaluate the NAC parameter. We choose the slipped parallel pairs as they possess no spatial overlap at a shorter contact distance. The calculated energies and NAC values are collected in Table S5 of SI. We have followed the same protocol as discussed by Korovina et al.58 For both excimeric and nonexcimeric forms, the ΔE indicates that the stability of 1ME state is relatively higher in case of DPP. However, the NAC values of the DPP-excimers are much larger than their non-excimeric structure, but the parameter is similar for TPP, which validates the excimer formation in TPP. Consequently, the rate of 1ME formation (k1) slightly increases for TPP excimer but the rates for DPP excimers significantly decreases. Furthermore, in comparison to the non-excimeric forms, the energetic barrier (Eb) of TPP excimer for separating into two triplet states from 1ME state decreases by about 40 meV while for DPP (PIII) excimer, it decreases by about 10 meV. This implies that the excimer in TPP is less stable than two independent triplets. Therefore, the second step of SF in TPP excimer is faster than DPP excimer. The observations support that the possibility of formation of correlated triplet pair is via formation of excimer state in TPP. An excimer intermediate is formed during SF for symmetrically substituted pentacene dimers (TPP), and therefore, this is an excimer-mediated model. The excimer formation in asymmetrically substituted pentacene dimers (DPP) produce a comparatively long-lived correlated triplet pair. Hence, SF occurs in DPP through the superexchange pathway. The variation of intermolecular distance based on symmetrically and asymmetrically substituted pentacenes dictates the role of CT mediated in SF mechanism. Finally, the underlying message of the article is that very small tweaking of intermolecular orientations typically arising due to crystallization conditions in experiments can result is remarkable change in the mechanism of Singlet-Fission. CONCLUSIONS Singlet fission (SF) is favorable for both TPP and DPP pairs. The role of symmetric and asymmetric substitution to pentacene is demonstrated by adopting a suitable ab-initio framework. 18 ACS Paragon Plus Environment

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A systematic approach towards calibration of the active space requirements is utilized in SACASSCF calculations to make a correlation between SF excitation energies in the molecules. SA-CAS calculation with 8-electron-in-8-orbital provides accurate estimates for the present SF study. The alternation for the SF rate in the symmetric (TPP) and asymmetric (DPP) pairs is controlled by the CT contribution near to the 1(ME). The CT state of TPP is much higher while the contribution of CT configuration is significantly for the ME state for DPP. The SF process in symmetrically substituted pentacene dimers (TPP) occurs via the formation of excimer and designated as an excimer-mediated process. The presence of mediated CT state is found in the SF pathway of asymmetrically substituted pentacene (DPP) and referred as superexchange SF process. The efficiency of SF in slip-stacked cofacial DPP dimer is relatively intense than others and hence, predicted to be an excellent stacking motif in crystal packing to pursue experimental realization. The present study demonstrates that even small and even ‘innocently’ appearing structural breaking can cause significant changes in the rate and overall mechanism of singlet fission in molecular crystals. SUPPORTING INFORMATION Calculated

excited

energies

of

TPP

and

DPP

monomers

and

dimers

at

SA-

CASSCF/XMCQDPT2/DZV level, BSSE energies, optimized coordinates of the investigated systems alongwith attachment/detachment density plots in dimers, excimer structures and full references of G09 and Q-Chem. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] ACKNOWLEDGEMENTS AKP

thanks

SERB

for

the

National

Postdoctoral

Fellowship

(NPDF

File

No.

PDF/2018/000129). AKP is also thankful to Prof. Alex A. Granovsky for the helpful discussions about the XMCQDPT2 calculations using Firefly. KSB thanks IACS for Institute senior 19 ACS Paragon Plus Environment


Research Associate fellowship. AD is grateful to DST and TATA Steel for funding. We thank IACS supercomputing center for providing high performance computational facilities. We are grateful to the two anonymous reviews for their contributing comments to this work. REFERENCES 1. Chason, M.; Brazis, P. W.; Zhang, J.; Kalyanasundaram, K.; Gamota, D. R., Printed Organic Semiconducting Devices. Proc. IEEE 2005, 93, 1348-1356. 2. Smith, M. B.; Michl, J., Singlet Fission. Chem. Rev. 2010, 110, 6891-6936. 3. Dimitrakopoulos, C. D.; Mascaro, D. J., Organic Thin-Film Transistors: A Review of Recent Advances. IBM J. Res. Dev. 2001, 45, 11-27. 4. Bhattacharyya, K.; Datta, A., Polymorphism Controlled Singlet Fission in Tips-Anthracene: Role of Stacking Orientation. J. Phys. Chem. C 2017, 121, 1412-1420. 5. Picciolo, L.; Murata, H.; Kafafi, Z., Organic Light-Emitting Devices with Saturated Red Emission Using 6, 13-Diphenylpentacene. Appl. Phys. Lett. 2001, 78, 2378-2380. 6. Casanova, D., Theoretical Modeling of Singlet Fission. Chem. Rev. 2018, 118, 7164-7207. 7. Berkelbach, T. C.; Hybertsen, M. S.; Reichman, D. R., Microscopic Theory of Singlet Exciton Fission. Iii. Crystalline Pentacene. J. Chem. Phys. 2014, 141, 074705. 8. Zirzlmeier, J.; Lehnherr, D.; Coto, P. B.; Chernick, E. T.; Casillas, R.; Basel, B. S.; Thoss, M.; Tykwinski, R. R.; Guldi, D. M., Singlet Fission in Pentacene Dimers. Proc. Natl. Acad. Sci. 2015, 201422436. 9. Nagata, R.; Nakanotani, H.; Potscavage Jr, W. J.; Adachi, C., Exploiting Singlet Fission in Organic Light‐Emitting Diodes. J. Adv. Mater. 2018, 30, 1801484. 10. Wilson, M. W.; Rao, A.; Ehrler, B.; Friend, R. H., Singlet Exciton Fission in Polycrystalline Pentacene: From Photophysics toward Devices. Acc. Chem. Res. 2013, 46, 1330-1338. 11. Kim, H.; Zimmerman, P. M., Coupled Double Triplet State in Singlet Fission. Phys. Chem. Chem. Phys. 2018, 20, 30083-30094. 12. Bhattacharyya, K.; Datta, A., Computationally Driven Design Principles for Singlet Fission in Organic Chromophores. J. Phys. Chem. C 2019. 13. 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. 14. Monahan, N.; Zhu, X.-Y., Charge Transfer–Mediated Singlet Fission. Annu. Rev. Phys. Chem 2015, 66, 601-618. 15. Casanova, D., Bright Fission: Singlet Fission into a Pair of Emitting States. J. Chem. Theory Comput. 2015, 11, 2642-2650. 16. Mauck, C. M.; Hartnett, P. E.; Margulies, E. A.; Ma, L.; Miller, C. E.; Schatz, G. C.; Marks, T. J.; Wasielewski, M. R., Singlet Fission Via an Excimer-Like Intermediate in 3, 6-Bis (Thiophen-2-Yl) Diketopyrrolopyrrole Derivatives. J. Am. Chem. Soc. 2016, 138, 11749-11761. 17. 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. 18. Zeng, T.; Hoffmann, R.; Ananth, N., The Low-Lying Electronic States of Pentacene and Their Roles in Singlet Fission. J. Am. Chem. Soc. 2014, 136, 5755-5764. 19. Wang, X.; Liu, X.; Tom, R.; Cook, C.; Schatschneider, B.; Marom, N., Phenylated Acene Derivatives as Candidates for Intermolecular Singlet Fission. J. Phys. Chem. C 2019, 123, 5890-5899. 20. Kolata, K.; Breuer, T.; Witte, G.; Chatterjee, S., Molecular Packing Determines Singlet Exciton Fission in Organic Semiconductors. ACS Nano 2014, 8, 7377-7383. 20 ACS Paragon Plus Environment

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Remote Functionalization through Symmetric or Asymmetric

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