Decay of the Lowest Triplet State in Singlet Fission Molecular

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Decay of the Lowest Triplet State in Singlet Fission Molecular Materials: A Case Study on Quinoidal Bithiophenes Rui-Hong Duan, Qian Peng, Xingxing Shen, Guangchao Han, Yuan Guo, Yan Zeng, and Yuanping Yi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b11646 • Publication Date (Web): 31 Jan 2018 Downloaded from http://pubs.acs.org on February 2, 2018

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The Journal of Physical Chemistry

Decay of the Lowest Triplet State in Singlet Fission Molecular Materials: A Case Study on Quinoidal Bithiophenes Ruihong Duan,†, ‡ Qian Peng,†, ‡ Xingxing Shen,§ Guangchao Han,†, ‡ Yuan Guo,†, ‡ Yan Zeng,†, // Yuanping Yi,*,†, ‡

†

CAS Key Laboratory of Organic Solids, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China ‡

§

Hebei Normal University of Science & Technology, Qinhuangdao City, Hebei Province, 066004, China

//

*

University of Chinese Academy Sciences, Beijing, 100049, China

School of Science, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China.

Corresponding authors. E-mail: [email protected].

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ABSTRACT Singlet fission, a process that two triplet excitons are generated by fission of one singlet exciton, has attracted considerable interest for its potential to break the Shockley-Quiesser theoretical limit for single-junction organic photovoltaic devices. In order to make full use of the resultant triplet excitons to improve the power conversion efficiency, triplet excitons must have long enough lifetimes to diffuse to the donor/acceptor interface and then dissociate into charge carriers. Thus the triplet decay dynamics are important for exploiting singlet fission in organic solar cells. In this work, we have theoretically investigated the decay of the lowest triplet excited state (T1) for quinoidal bithiophene derivatives, one kind of promising singlet fission molecular materials. Our results point to that the rates for radiative phosphorescence and nonradiative intersystem crossing are quite low under the Franck-Condon approximation. Interestingly, the energy barriers from the T1 minima to the T1/S0 minimum energy crossing points are just ca. 49~63 meV; furthermore, the spin-orbit couplings between T1 and S0 at the crossing points are very strong. This indicates that the singlet fission generated T1 excitons will decay rapidly to the ground state through the crossing points. Therefore, to fully utilize the potential of singlet fission, efforts should be made to suppress the triplet decay via the T1/S0 crossing points.

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I. INTRODUCTION Singlet fission (SF) is a multi-exciton generation process, in which one singlet exciton is split into two triplet excitons.1,2 If the resulting triplet excitons can separate effectively into free charge carriers, absorption of one photon can produce two charge carrier pairs and double photocurrent by applying efficient SF materials in organic solar cells (OSCs). It offers the potential for the power conversion efficiencies (PCEs) of single-junction OSCs to exceed the Shockley-Quiesser limit3 and rekindles intensive research interests.4 Up to now, efficient singlet fission has been found only in a limited number of systems, including oligoacenes,5-16 carotenoids,17 1,3-diphenylisobenzofuran (DPIBF),18 and quinoidal thiophene compounds.19 Among them, pentacene,5,6 tetracene,7 zeaxanthin,17 and DPIBF18 were reported to have triplet yields approaching 200%. It is noteworthy that tetracyanoquinodimethane bithiophene (QOT2) was demonstrated to be an intramolecular singlet fission material with a high triplet yield of 176%.19 Despite of vast experimental and theoretical investigations on singlet fission, applications of SF in OSC devices are much less studied. Due to the high SF efficiencies and good hole mobilities, pentacene and its derivatives are often used as model SF materials in device studies.20-29 In elaborately designed pentacene/C60 solar cells, the external quantum efficiency of photocarrier generation is over 100% at certain absorption wavelengths, but the PCE is only 1.8%.20,21 The main reasons are the low open circuit voltage and the absorbed light only above the pentacene singlet excitation energy of 1.8 eV.20 For the OSC devices using PbS/PbSe nanocrystals as

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electron acceptors and pentacene/TIPS-pentacene as both donor and SF materials, the PCEs reach 4.8% due to the infrared absorption of PbS/PbSe.24 In fact, the contribution of SF process to the PCE is minor in these devices.22-24 Besides oligoacenes, several thienoquinoid (ThQ) compounds were also studied in devices, with PDIF-CN2 and C60 as acceptors.30 For ThQ/PDIF-CN2 solar cells, the singlet fission character of the ThQ donor is verified by the negative magnetic-field dependence of photocurrent and SF-generated triplet excitons are the main source of photocurrent; however, the photocurrent is very low and the largest PCE is only 0.011%. The low efficiency could be attributed to the high crystallinity of PDIF-CN2 and poor contact between ThQs and PDIF-CN2. On the other hand, fast decay of the lowest triplet state (T1) into the ground state (S0) may be another important reason due to the very low excitation energies of the T1 states, e.g., 0.48~0.90 eV estimated by density functional theory (DFT) calculations.30 High SF efficiency is a necessary condition for SF based solar cell. Furthermore, in order to improve the PCE through SF for a practical device, triplet excitons must be effectively collected and dissociated.27,31 Usually, the T1 energies of SF materials are low to meet the energy requirement: the singlet excitation energy is twice higher than the triplet excitation energy E(S1) > 2E(T1). The T1 states of pure organic molecules are usually thought to have a long lifetime because the decay to S0 is spin-forbidden. However, according to the energy gap law32, the intrinsic low energy of T1 would accelerate its decay to S0, especially when T1 and S0 have opportunity to cross. Thus it is highly desirable to study the triplet dynamics following SF.

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In this work, we have theoretically investigated the decay pathways of the T1 state of three quinoid bithiophene (QBT) compounds (see Chart 1), which hold S1 excitation energies twice higher than T1 excitation energies and are candidates of promising SF materials.33 As expected, our calculations point to that the radiative decay rates of T1 are negligibly small while the non-radiative decay rates are on the modest magnitude of 104~106 s-1 under the Franck-Condon approximation. On the other hand, these compounds show very small energy barriers (49~63 meV) from the T1-geometry to the T1/S0 minimal energy crossing point (MECP) and strong spin-orbit couplings (> 6 cm-1) at the MECP, indicating that T1 excitons can decay rapidly into the ground state through the crossing point. Therefore, in order to fully utilize the potential of singlet fission for organic solar cells based on quinoidal bithiophene compounds, efforts should be made to suppress the decay of T1 into S0, in particular, the decay channel through the T1/S0 crossing point.

Chart 1. Chemical structures of the studied compounds.

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II. COMPUTATIONAL DETAILS Geometry optimizations and frequency analyses for the three QBT compounds were carried out by density functional theory (DFT) for the ground state (S0) and the first triplet excited state (T1) and by time-dependent DFT (TDDFT) for the first singlet excited state (S1) and the second triplet excited state (T2). In order to estimate the influence of functionals, two hybrid functionals with different percentages of Hartree-Fork exchange, B3LYP34 (20%) and M062X35 (54%) were adopted along with the 6-31G** basis set. Besides optimizations of the equilibrium geometries, potential energy curves were calculated for each state by relaxed scan along the torsion angle between two double bond connected thiophene rings (S1-C1-C2-S2, see Chart 1). In addition, natural transition orbitals (NTOs)36 based on the S0 geometries were obtained by TDDFT to illustrate the transition characters of all the excited states. All the above calculations were accomplished by Gaussian 09, Revision D.01.37 The T1/S0 minimum energy crossing points were optimized at the DFT-B3LYP/6-31G** level by using the sobMECP program38,39 in combination with the Gaussian 09 package. In order to investigate intersystem crossing between different spin states, we calculated spin-orbit couplings between S0 and T1, S1 and T1, S1 and T2. Besides, the oscillator strengths for the transition from T1 to S0 were computed to study the phosphorescence process. These calculations were accomplished with the B3LYP functional and 6-31G** basis set by the BDF package.40-43 Since TDDFT would largely underestimate the T1 energies at some geometries, the singlet (S1 and S2) and

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triplet (T1 and T2) excited states were evaluated by TD-DFT and TDA-TDDFT, respectively. The detailed comparison is given in Figure S1 of the Supporting Information.

III. RESULTS AND DISCUSSION

The molecular geometries of the S0, S1, T1 and T2 states for the three compounds were fully optimized with the B3LYP and M062X functionals. The two functionals give very similar geometries. The S0 geometries display planar backbones. Based on the S0 geometries, TDDFT calculations were performed to analyze the transition characters of excited states. As seen from the natural transition orbitals calculated with B3LYP in Figure 1, all the transitions from S0 to S1, T1, and T2 for QBT and QBTT-Me occur on the whole conjugated backbones. For QBTT-Ph, introduction of the phenyl substituents lead to a bit electron-transfer character from the phenyl groups to the QBTT backbone in the excited states. Interestingly, for the transitions from S0 to S1 or T1, the C1-C2 bond exhibits a bonding pattern in the hole NTO but an anti-bonding pattern in the electron NTO; this is expected to weaken the C1-C2 bond in S1 and T1 with respect to S0. For the transition from S0 to T2, the electron and hole NTOs have similar electronic density on the C1-C2 bond, so the C1-C2 bond in T2 would keep similar to that in the ground state. The M062X NTOs are shown in Figure S2, which are similar to the B3LYP NTOs but more localized. In spite of a little difference between the B3LYP and M062X NTOs, the changes in the electronic density upon excitation are almost the same on the C1-C2 bond. In addition, the

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transition natures are hardly changed with the different equilibrium geometries of excited states (Figure S3). T1

S1

T2

Electron QBT

77.1%

23.6%

78.9%

20.2%

Hole

Electron QBTT-Me Hole

Electron QBTT-Ph 93.0%

5.7%

Hole

Figure 1. TDDFT-B3LYP/6-31G** calculated natural transition orbitals of S0 → S1, T1 and T2 vertical excitations for the studied compounds. The changes of electron density distribution upon electronic excitation transition will result in relaxation of the excited-state geometries. Here, the C1-C2 bond and S1-C1-C2-S2 torsion angle between two thiophene rings (see Chart 1) are the key geometrical parameters; their values in the equilibrium S0, S1, T1, and T2 geometries are shown in Figure 2 and Table S1. Although the calculated results are somewhat different, the B3LYP and M062X functionals provide same trends both for different molecules and for different electronic states. At the ground state, the C1-C2 bond is a double bond with the length of ca. 1.375 Å by B3LYP and 1.36 Å by M062X for these

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quinoidal molecules. From the S0 to T2 geometry, the C1-C2 bond is slightly elongated and the increment is gradually enhanced from QBT, QBTT-Me, to QBTT-Ph. For the S1 and T1 states, the C1-C2 bond becomes anti-bonding and stretches more significantly, reaching ca. 1.41 Å at the S1 geometries and even ca. 1.45 Å at the T1 geometries for all the compounds. The molecular backbones for the three compounds are almost planar at the S0, S1, and T2 states. In contrast, owing to the much elongated and thereby weakened C1-C2 bonds, the molecular backbones in the T1 geometries become obviously twisted (see Figure S4). For instance, QBT displays a twist angle of 10.2° by B3LYP and of 14.4° by M062X (the S1-C1-C2-S2 torsion angle corresponds to 169.8° and 165.6°, respectively). The T1 geometries of the two QBTT compounds are more twisted; in particular, the twist in QBTT-Me can reach 30.9° by B3LYP and 26.0° by M062X. S0

T1

S1

Bond Length/Å

(a) B3LYP

T2

(b) B3LYP

1.45

180

1.40

160

1.35

140

1.30 1.45

120

(c) M062X

(d) M062X

180

1.40

160

1.35

140

1.30

Tosion Angle/Degree

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


120 QBT

QBTT-Me

QBTT-Ph

QBT

QBTT-Me

QBTT-Ph

Figure 2. C1-C2 bond lengths and S1-C1-C2-S2 torsion angles at the optimized S0, T1, S1 and T2 geometries for the studied compounds. 9



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The adiabatic excitation energies for S1, T1 and T2 are listed in Table 1 (vertical values see Table S2). Although the M062X excitation energies are higher than the B3LYP ones due to larger percent of Hartree-Fock exchange, the two functionals give very similar trends. Compared with T2, the S1 energy is a bit higher for QBT but lower for QBTT-Ph. For QBTT-Me, B3LYP and M062X give inverse energy order between S1 and T2. Nevertheless, for each molecule, the S1 and T2 energies are quite close and twice higher than the T1 energy by at least 0.1 eV, no matter which functional is used. This is favorable for singlet fission in these compounds.1 In addition, even though the intersystem crossing from S1 to T2 can compete with the singlet fission process, multiplication of T1 excitons could be efficient via triplet fission of T2 excitons.

Table 1. Adiabatic excitation energies (in eV) of T1, S1 and T2 for the studied compounds. E(T1) E(S1) E(T2) ΔE1a ΔE2b QBT 0.751 2.287 2.103 0.785 0.602 B3LYP QBTT-Me 0.957 2.209 2.169 0.296 0.255 QBTT-Ph 0.917 1.956 1.987 0.121 0.152 QBT 0.834 2.510 2.461 0.843 0.794 M062X QBTT-Me 1.130 2.462 2.543 0.203 0.283 QBTT-Ph 1.105 2.313 2.517 0.102 0.306 a b c ΔE1 = E(S1) - E(T1)×2, ΔE2 = E(T2) - E(T1)×2, ΔE3 = E(S1) – E(T2)

ΔE3c 0.183 0.041 -0.031 0.049 -0.080 -0.203

In order to utilize triplet excitons to produce charge carrier in organic solar cell, the excitons need to be able to diffuse to the donor/acceptor interface before decay into the ground state. The decay of T1 excitons into S0 can occur through three pathways (see Figure 3): radiative phosphorescence and nonradiative intersystem

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crossing (ISC) under the Franck-Condon approximation, and nonradiative ISC via the T1/S0 crossing point.44 Because the spin-orbit couplings between different spin states are small, the first two decay pathways are usually slow for pure organic molecules; the last pathway can be ultrafast if the crossing point is easy to reach.45

Figure 3. Decay pathways from the lowest triplet excited state (T1) to the ground state (S0): ❶ phosphorescence, ❷ intersystem crossing under the Franck-Condon approximation; ❸ intersystem crossing via the T1/S0 crossing point. Firstly, we deal with phosphorescence and direct intersystem crossing, which can be treated as vertical transition in the Franck-Condon region. According to Einstein’s spontaneous radiative relation,46 the phosphorescence rate kp is proportional to the oscialltor strength 𝑓𝑇1 →𝑆0 and square of the vertical emission energy ΔEvert. 𝑘𝑝 =

2 𝑓𝑇1 →𝑆0 ∆𝐸𝑣𝑒𝑟𝑡

(1)

1.499

In eq. 1, kp is in the unit of s-1, ΔEvert is in the unit of cm-1, and 𝑓𝑇1 →𝑆0 is dimensionless. The oscillator strengths and the vertical emission energies of T1 were calculated by using the T1 geometries. The related data are listed in Table 2. The oscillator strengths for all the three compounds are very small and the corresponding phosphorescence rates are on 10-4 to 10-2 s-1 order of magnitudes. This can be explained by a deep look into the oscialltor strength 𝑓𝑇1 →𝑆0 : 11



2

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(2)

𝑓𝑇1 →𝑆0 = 3 |𝜇 𝑇1 →𝑆0 | ∆𝐸𝑣𝑒𝑟𝑡

𝑓𝑇1 →𝑆0 is proportional to the square of the transition dipole moment 𝜇 𝑇1 →𝑆0 between T1 and S0. Since transition between T1 and S0 is spin-forbidden, generally 𝜇 𝑇1 →𝑆0 is zero. When spin-orbit coupling is considered as perturbation, the transition dipole moment between T1 and S0 can be written as: 𝜇 𝑇1 →𝑆0

= ∑𝑖>1

𝐻𝑇𝑆𝑂 ∙𝜇 1 →𝑆0 𝑇1 →𝑇𝑖 𝐸𝑇𝑖 −𝐸𝑆0

+ ∑𝑗>0

𝐻𝑇𝑆𝑂 ∙𝜇 1 →𝑆𝑗 𝑆𝑗→𝑆0 𝐸𝑆𝑗 −𝐸𝑇1

(3)

Generally, the energy differences between the ground state and the triplet excited states are large. For the SF molecular systems, the S1 energy is twice higher than the T1 energy, indicating the energy differences between T1 and the singlet exicited states are large as well. Therefore, both terms in eq. 2 are small, and the transition dipole moments and oscillator strengths for the T1→S0 transition are small for SF materials. The intersystem crossing rate from T1 to S0 in the Franck-Condon region can be estimated by the semi-classical Marcus theory,47 𝑘𝐼𝑆𝐶 = 𝐸𝑎 =

|𝐻𝑇𝑆𝑂 |2 1 →𝑆0 ℏ

(−∆𝐸𝑇1 →𝑆0 +𝜆) 4𝜆

𝜋

√𝜆𝑘

𝐵𝑇

2

=

𝐸

𝑒𝑥𝑝⁡(− 𝑘 𝑎𝑇)

(4)

𝐵

2 ∆𝐸𝑣𝑒𝑟𝑡

(5)

4𝜆

Here, Ea is the activation energy of this non-radiative process; λ, the reorganization energy for the T1→S0 transition; ∆𝐸𝑇1 →𝑆0 , the T1 adiabatic excitation energy; ћ, the reduced Planck constant; kB, the Boltzmann constant; T, the temperature (300 K). As seen in Table 2, the the spin-orbit coupling (SOC) at the T1 geometry is 1.4, 4.3, and 3.3 cm-1 for QBT, QBTT-Me, and QBTT-Ph, respectively. At the planar S0 geometry, the SOC is zero due to symmetry forbidden between Ag of S0 and Bu of T1. Among the three compouds, the more twist in the T1 geometry, the stronger SOC. The 12


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reorganization energy for the T1→S0 transition can be calculated as the energy difference of the ground state between the T1 and S0 geometries. From QBT to QBTT-Me and QBTT-Ph, the reorganization energy is increased from 0.294 eV to 0.382 and 0.315 eV, respectively. The increase for the two QBTT compounds can be mainly ascribed to the larger twist of the T1 geometry relative to the planar S0 geometry (see Figure 2), further confirmed by the results of normal mode analyses. As seen in Figure 4, compared to QBT, the reorganization energies of the low-frequency normal modes, especially of the rotation around the central C1-C2 bond (see Figure S5), are significantly enhanced for QBTT-Me and QBTT-Ph due to very large electron-vibration coupling constants (see Figure S6). On the contratry, the reorganization energies from the high-frequency stretching vibrations are somewhat reduced due to more delocalized excitation onto the fused thiophene moieties and even onto the phenyl groups for QBTT-Ph. After entering the obtained parameters of excitation energies, SOCs and reorganization energies into eqs 4 and 5, the intersystem crossing rates are calculated to be 9.27105, 1.81106, and 7.32104 s-1 for QBT, QBTT-Me, and QBTT-Ph, respectively (see Table 2). Table 2. Oscillator strengths f and vertical emission energies Evert, phosphorescence rates kp, spin-orbit couplings Hso, reorganization energies λ, activation energies Ea, and rates for the nonradiative intersystem crossing under the Franck-Condon approximation kisc for the T1→S0 transition. f QBT 1.39E-11 QBTT-Me 6.05E-09 QBTT-Ph 2.62E-09

Evert eV 0.457 0.575 0.602

Hso cm-1

kp s-1 1.26E-04 8.69E-02 4.12E-02

1.4 4.3 3.3

λ eV

Ea eV

0.294 0.382 0.315

0.178 0.216 0.288

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kisc s-1 9.27E+05 1.81E+06 7.32E+04


1500

QBT

1000 -1

Reorganization Energy (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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500 0

QBTT-Me

1000 500 0

QBTT-Ph 1000 500 0 0

400 800 1200 -1 Vibration Frequency (cm )

1600

Figure 4. Reorganization energy of each normal mode calculated with the B3LYP functional for QBT, QBTT-Me and QBTT-Ph. The reorganization energies in the frequencies of >1700 cm-1 are vanishingly small and not illustrated here.

To further consider the quantum tunneling effect of high-frequency molecular vibrations, we have also calculated the ISC rates in the Franck-Condon region by using the Marcus-Levich-Jortner (MLJ) formula48 (see Supporting Information for the computational details). As expected, the MLJ rates are about two order of magnitude higher than the Marcus rates, reaching 4.30107, 2.44108, and 7.97107 s-1 for QBT, QBTT-Me, and QBTT-Ph, respectively. It should be noticed that the increase of the MLJ rates is attributed not only to the consideration of the quantum effect of electron-vibration couplings, but also to the overestimation of reorganization energies by the normal mode analysis method. The total reorganization energies obtained by normal mode analysis are about 10% larger than those calculated by the adiabatic potential energy surface method (see Table S3). Based on the reorganization energies

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calculated by normal mode analysis, the Marcus rates will be increased by about one order of magnitude. Although these nonradiative rates are much faster than the phosphorescence process, they are still very low relative to the ultrafast charge separation process (on the time scale of ps or even sub-ps) in high-efficiency organic solar cells. 49 As analyzed above, for the S0→T1 transition, the central C1-C2 double bond is excited; the optimized T1 geometries are twisted and have much longer C1-C2 bonds with respect to the S0 geometries. So compared with the T1 state, the torsion potential around the C1-C2 bond is expected to be larger for the ground state; the potential energy curves of the S0 and T1 states may cross when the molecule is twisted along the central bond. The potential energy curves of S0, T1, S1 and T2 along the torsion angle S1-C1-C2-S2 have been obtained by constraint optimizations; the B3LYP and M062X results are similar and shown in Figure 5 and S6, respectively. As expected, the potential energy curves of S0 and T2 are relatively steep, especially for S0. In contrast, the potential energy curves are much smooth for S1 and T1, even flat for T1. The crossing point between the potential energy curves of S0 and T1 is located at ca. 110° torsion angle for QBT, which is larger than those for the two QBTT compounds (ca. 100°); this can be ascribed to the smaller energy difference between S0 and T1 for QBT.

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S0

3

T1

S1

T2 QBT

2 1 0

Energy/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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QBTT-Me 2 1 0 QBTT-Ph 2 1 0 90

100 110 120 130 140 150 160 170 180

Torsion Angle/degree Figure 5. Potential energy curves of S0, T1, S1 and T2 along the S1-C1-C2-S2 torsion angle for the studied compounds obtained by using the B3LYP functional.

Based on the partial optimized S0 geometries, the spin-orbit couplings between different spin states were calculated; the results are shown in Figure 6. When the molecules are changed from planar to perpendicular structures, the SOCs between S1 and T1 remain zero due to the same nature of electronic transition, which is consistent with the El-Sayed rules.50 At the optimized S0 geometries with planar backbones, the S0-T1 and S1-T2 SOCs are fully symmetry forbidden for QBT and QBTT-Me or nearly symmetry forbidden for QBTT-Ph. However, these SOCs increase rapidly when the molecules are twisted around the C1–C2 bond. For the perpendicular structures, the SOCs reach ca. 6 cm-1 (S1-T2) and 14 cm-1 (S0-T1) for QBT and ca. 12 cm-1 (S1-T2 and S0-T1) for both QBTT compounds. More importantly, the S0-T1 SOCs become very strong at the S0/T1 crossing points of the potential energy curves, which will facilitate 16


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intersystem crossing decay of T1 via the crossing points considering the small energy barrier from the T1 minima to the crossing points.

QBT

12 8

-1

4

SOC/cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 12

QBTT-Me

8 4 0 12

QBTT-Ph

8 4 0 90

100

110

120

130

140

150

160

170

180

Torsion Angle/degree Figure 6. Spin-orbit couplings for S0-T1, S1-T1, and S1-T2 intersystem crossing processes based on the partial optimized S0 geometries as a function of the S1-C1-C2-S2 torsion angle. In order to accurately obtain the geometries and S0-T1 SOCs at the crossing points and energy barriers from the equilibrium geometries to the crossing points, we optimized the S0/T1 minimum energy crossing points (MECPs). The backbone torsion angle at the MECP is 130.1° for QBT, showing a twist smaller than those for QBTT-Me (116.8°) and QBTT-Ph (114.9°). This is in good agreement with the results obtained by relaxed potential energy surface scan. Compared with the T1 minima, the backbone twists are increased by ca. 30°~40° at the MECPs (See Table 3). However, the energy differences between MECP and T1 can be as small as just 49~63 meV due

17



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to the flat torsion potential of T1. What’s more, the spin-orbit couplings between S0 and T1 are significantly enhanced at the MECPs relative to the T1 minima, exceeding 6 cm-1 for all the compounds. According to the Landau-Zener theory, the T1→S0 transition probability at the crossing point can be estimated as:51-54 𝜋|𝐻𝑇𝑆𝑂 | 1 →𝑆0

𝑃𝐿𝑍 = 1 − exp [− 2ℏ𝑣|𝐹

2

]⁡

(6)

𝑇1 −𝐹𝑆0 |

Here, v is the velocity of the system along the reaction coordinate; 𝐹𝑇1 and 𝐹𝑆0 , the energy derivatives along the coordinates of T1 and S0, respectively. It is obvious that the larger SOC, the higher transition probability. Since the torsion potential curves of T1 are nearly flat, the 𝐹𝑇1 values will be vanishingly small; also, the 𝐹𝑆0 values are minimized considering the low excitation energies of T1 and highly twisted MECP-geometries. Owing to the small values of |𝐹𝑇1 − 𝐹𝑆0 | and the strong SOCs, the T1→S0 transition probabilities will be very high for the studied systems. Thus the MECP results confirm that the T1/S0 intersystem crossing via the crossing point can constitute an important T1 decay pathway. To obtain accurate ISC rates via the T1/S0 crossing points, much complicated quantum dynamic simulations should be carried out in the future work. Table 3. Backbone torsion angles, S0-T1 spin-orbit couplings (Hso) at the S0, T1 and T1/S0 MECP geometries, and energy barriers from T1 to MECP.

QBT QBTT-Me QBTT-Ph

Torsion Angle/° T1 MECP T1-MECP 169.8 130.1 39.7 149.1 116.8 32.2 153.9 114.9 39.0

S0 0.0 0.0 0.6

Hso/cm-1 T1 MECP 1.4 6.1 4.3 6.9 3.3 6.4

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ΔE/meV T1→MECP 63 49 52

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IV. CONCLUSIONS We have studied the triplet decay channels of one kind of potential singlet fission molecular materials, quinoidal bithiophene derivatives. Our results show that the radiative phosphorescence rates are on the 10-4~10-2 s-1 order of magnitudes and the nonradiative intersystem crossing rates are on the 104~106 s-1 order of magnitudes under the Frank-Condon approximation. On the other hand, since the central C-C double bond is excited and much elongated at the T1 state, the T1 geometry is twisted and the torsion potential energy around the bond is very small. As the molecule is more twisted, the potential energy curves of S0 and T1 will cross and the T1/S0 MECPs lie only 49~63 meV above the T1 minima. In addition, when the molecular twist is increased from a planar structure, the spin-orbit coupling between S0 and T1 is activated and increased greatly. Consequently, triplet excitons can decay rapidly to the ground state via the T1/S0 crossing points. At the same time, our results underline that enhancing molecular planarity through steric hindrance or conformation lock would be an effective way to suppress triplet decay through the T1/S0 crossing point and thus fully utilize singlet fission to improve the photocarrier generation efficiency for organic solar cells based on quinoidal compounds.

ASSOCIATED CONTENT Supporting information Relative energies of the S0, T1, T2 states calculated by using different methods based on the constraint optimized S0 geometries as a function of the torsion angle; Natural

19



transition orbitals of the S1, S2, T1 and T2 excitations calculated by using the M062X functional based on the ground state equilibrium geometries; Illustration of S0, T1, S0/T1 MECP, S1 and T2 geometries optimized with the B3LYP functional; Potential energy curves of S0, T1, S1 and T2 along the S1-C1-C2-S2 torsion angle obtained by using the M062X functional; Optimized torsion angles and bond lengths at the S0, S1, T1, and T2 states; Vertical excitation energies of the T1, S1 and T2 states calculated by using the B3LYP and M062X functionals; Huang-Rhys factor of each normal mode for QBT, QBTT-Me, and QBTT-Ph; ISC rates in Franck-Condon region calculated according to the Marcus and MLJ formulas; Illustration of the low-frequency vibration modes with large reorganization energies; Computational details for the ISC rates in the Franck-Condon region calculated by the MLJ formula.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Y.Y.) Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The work was supported by the National Basic Research Program of the Ministry of Science and Technology of China (973) (Grant No 2014CB643506), the National Natural Science Foundation of China (Grant No 91333117), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No XDB12020200). 20


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TOC Graphic

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Decay of the Lowest Triplet State in Singlet Fission Molecular

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