Achieving Small Exciton Binding Energies in Small Molecule

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Energy Conversion and Storage; Plasmonics and Optoelectronics

Achieving Small Exciton Binding Energies in Small Molecule Acceptors for Organic Solar Cells: Effect of Molecular Packing Lingyun Zhu, Zeyi Tu, Yuanping Yi, and Zhixiang Wei J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b02161 • Publication Date (Web): 12 Aug 2019 Downloaded from pubs.acs.org on August 13, 2019

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The Journal of Physical Chemistry Letters

Achieving Small Exciton Binding Energies in Small Molecule Acceptors for Organic Solar Cells: Effect of Molecular Packing Lingyun Zhu1, Zeyi Tu2,Yuanping Yi2,*, Zhixiang Wei1,*

1

CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, CAS Center for Excellence in Nanoscience, National Center for Nanoscience and Technology, Beijing 100190, China 2

Beijing National Laboratory for Molecular Sciences, CAS Key Laboratory of Organic Solids, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China

*

E-mails: [email protected] (Y.Y.); [email protected] (Z.W.)

1

ACS Paragon Plus Environment

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ABSTRACT Because of strong exciton binding energy (Eb), exciton dissociation process and extra energy losses are present in organic solar cells relative to inorganic and perovskite solar cells. Here, we calculated the Eb of a series of small molecule acceptors in solid crystals by a self-consistent quantum mechanics/embedded charge approach. The results show that the Eb are substantially reduced from the gas phase to solid state due to electronic polarization (mainly from the induction effect of charges). Moreover, in contrast to little changes in the gas phase, the Eb in the solid state can vary significantly, indicating important molecular packing effect. Remarkably, an extremely weak Eb of 0.04 eV is achieved in a three-dimensional packing crystal, which is comparable to the Eb of organo-lead tri-halide perovskites. This work underlines the importance of threedimensional molecular packing on achieving small Eb and would be helpful to reduce energy losses in organic solar cells.

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Owing to great efforts on materials design and device optimization, the power conversion efficiencies (PCEs) of organic solar cells (OSCs) based on nonfullerene (NF) small molecule acceptors (SMAs) have exceeded 16% for single-junction devices1-3 and 17% for tandem devices,4 which much surpass the best fullerene-based OSCs.5-6 However, compared with inorganic solar cells and perovskite solar cells, the PCEs of OSCs remain relatively low due to large losses in open-circuit voltages.7-10 Because of strong binding energies between electron and hole, excitons are created by photon absorption in organic photoactive materials. To dissociate excitons into free charge carriers, the active layers of OSCs consist of two types of components: electron donor (D) and acceptor (A) materials, which can thus provide necessary energy offsets to overcome the exciton binding energies (𝐸𝑏 ) and to make electron and hole separate at the D-A interfaces. For this reason, extra energy losses are brought about in OSCs.11 If the 𝐸𝑏 of organic materials can be reduced to the same magnitude as inorganic and perovskite materials, then excitons generated in organic photoactive materials will be dissociated by thermal energy without any driving forces and even single-component OSCs can be realized.12 Previous studies have shown that the electronic and charge transport properties of organic semiconductors are deeply affected by molecular packing structures in the solid state.13-18 Likewise, we expect that molecular arrangements can play an important role in regulating the 𝐸𝑏 of organic photoactive materials. In the past, most studies focused on the 𝐸𝑏 of homogeneous conjugated polymers and oligoacenes.19-28 However, different from these commonly studied systems, high-efficiency NF SMAs exhibit 3



anisotropic A-D-A structures, and the electronic and excitonic properties tend to be more affected by molecular packing structures. To date, it is still lack of understanding of the impact of molecular arrangements on the 𝐸𝑏 of organic materials. Recently, we investigated the 𝐸𝑏 of a series of NF SMAs and the results pointed out that the driving forces for hole transfer (dissociation of the acceptor excitons) are linearly correlated to the 𝐸𝑏 of acceptors.29 In these calculations, the electronic polarization effect of the surrounding environment on 𝐸𝑏 was considered by using the polarizable continuum model (PCM) incorporating a dielectric constant. Unfortunately, this method cannot convey the molecular arrangements regulated intermolecular interactions. In this contribution, a self-consistent quantum mechanics/embedded charge (QM/EC) method was applied to investigate the molecular packing effect on the 𝐸𝑏 of A-D-A SMAs in the solid state. For this method, the atomic charges of both the central active molecule and the surrounding environmental molecules are updated and get converged by iterative and successive QM/EC computations, so the electronic polarization effect can be considered explicitly and in a polarizable way. The self-consistent QM/EC approach proved to be able to provide reliable assessments of molecular energy levels and excitation energies of organic semiconductors and light-emitting materials.30-33 Here, to directly elucidate the molecular packing effect on 𝐸𝑏 , we take the crystal structures from the Cambridge Structural Database for seven representative A-D-A SMAs with similar architectures, i.e., 4TIC,34 6TIC-4F,35 ITIC,36 COi7IC,37 IDIC4Cl,38 ITN-C9,39 and ITzN-C9.39 The chemical and crystal structures are shown in Figure S1 and S2, and the important molecular packing patterns are summarized in 4


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Figure 1. In the ITIC and COi7IC crystals, one-dimensional stacking structures are observed, but the intermolecular stacking modes are totally different. The backbones of two adjacent ITIC molecules present a crossed edge-to-face orientation, whereas the adjacent COi7IC molecules are parallel and connected in a head-to-tail way by - interaction between the terminal acceptor groups. In the case of IDIC-4Cl, ITN-C9 and ITzN-C9, the crystals display two-dimensional brickwork arrangements through two kinds of - interactions between the terminal acceptor groups with different degrees of overlap. Interestingly, in both the 4TIC and 6TIC-4F crystals, the molecular backbones are crosswise arranged and form three-dimensional packing structures via three or two kinds of - interactions between the terminal acceptor groups. (a)

(b)

ITIC

COi7IC

(c)

(d)

IDIC-4Cl

ITzN-C9

(e)

(f)

4TIC

6TIC-4F

Figure 1. Molecular packing patterns of the studied systems (for the sake of clarity, both alkyl chains and phenyl groups are omitted). The electron-donationg central units and electron-withdrawing terminal groups are in green and orange, respectively. The molecular packing patterns of ITN-C9 are similar to IDIC-4Cl and not given here.

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Exciton binding energy is defined as the difference between the fundamental transport gap and the optical gap, 𝐸𝑏 = 𝐸𝑔𝑡 − 𝐸𝑔𝑜

(1)

Here, the optical gap (𝐸𝑔𝑜 ) is the excitation energy of the first singlet (optically allowed) excited state (S1). The fundamental transport gap (𝐸𝑔𝑡 ) can be computed according to the following equation, 𝐸𝑔𝑡 = IP − EA

(2)

where the ionization potential (IP) and electron affinity (EA) can be calculated as the energy difference between the ionic state and the neutral ground state (S0), IP = 𝐸+ − 𝐸0

(3)

𝐸𝐴 = 𝐸0 − 𝐸−

(4)

where 𝐸0 is the total potential energy of the S0 state; 𝐸+ and 𝐸− denote the total potential energies of the system with an excess positive and negative charge, respectively. Experimentally, the 𝐸𝑔𝑜 can be determined by the absorption edge or more exactly at the intersection between the absorption and emission spectra.40-41 The IP and EA can be measured by ultraviolet photoelectron spectroscopy and inverse photoemission spectroscopy, respectively,42 but these measurements are absent in most cases. Alternatively, the IP and EA values are usually measured by the electrochemical cyclic voltammetry. Nevertheless, as the exciton binding energy is dependent on several energy quantities, it is a big challenge to achieve accurate estimates by the different levels of measurements.

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Here, the total energies and electronic properties were calculated by density functional theory (DFT) for the S0 and ionic states and by time-dependent DFT (TDDFT) for the S1 state using the long-range corrected (LRC) functional B97XD43 and the def2-SVP basis set. Moreover, the range separation parameter (ω) of the LRC functional was optimized by a gap-tuning procedure to obtain a more reliable description of the electronic properties for the studied A-D-A NF acceptors.44-47 For the gas phase, the calculations were performed on isolated molecules, whose geometries were extracted from the experimental crystal structures without further optimization. To take account of the electronic polarization effect on the S0, S1, and ionic states in the solid phase, we carried out self-consistent QM/EC calculations on sphere clusters extracted from the experimental crystals (Figure S3). As seen in Figure S4, the selfconsistent procedure consists of iterative QM/EC single-point computations, in which each molecule in the clusters is successively regarded as the QM part in the presence of atom-centered point charges representing the other molecules.30-33 The initial atomic charges of each molecule are fitted to reproduce the electrostatic potentials (ESPs) derived from the DFT/TDDFT calculations in the gas phase by the Merz-SinghKollman scheme;48 afterwards, they are continuously updated according to the QM/EC calculated ESPs. The iteration will be continued until the total energy change between two adjacent QM/EC calculations for the central active molecule is less than 10-5 Hartree. In the calculations, the cluster radius is set to 100 Å (ca. 2000 molecules, see Table S1), which is large enough to account for the long-range Coulomb interaction (Figure S5a). In addition, owing to the huge magnitude of computational cost, the 7



iterative procedure only includes the molecules (ca. 300 in total) within a distance of 50 or 60 Å to the centroid of the active molecule. Notably, the test calculations show that the results of IP, EA, 𝐸𝑔𝑜 and 𝐸𝑏 are already converged at such cutoff distance (Figure S5b). All the calculations were carried out with the Gaussian 09 package.49 The calculated IP, EA, 𝐸𝑔𝑜 , and 𝐸𝑏 in the gas phase and solid state are shown in Figure 2. In the gas phase, the IP and EA values are in the range of 6.31 ~ 6.76 eV and 2.25 ~ 2.65 eV, respectively. For COi7IC and the compounds with the donor unit of IDT or IDTT, the IP and EA values show almost the same evolution trends with the change of molecular structures; IDIC-4Cl exhibits the largest values for both IP and EA due to the strong electron-withdrawing effect of chlorine substituents, whereas ITIC and ITzN-C9 have the smallest ones. Consequently, these compounds have similar 𝐸𝑔𝑡 (3.98 ~ 4.16 eV). After replacing benzene in the IDT and IDTT units with thieno[3,2b]thiophene, the electorn delocalizaiton gets more effcient. This is beneficial to achieve a decreased IP and an increased EA in 4TIC and 6TIC-4F, thus the 𝐸𝑔𝑡 of 4TIC and 6TIC-4F are reduced to ca. 3.8 eV. The changes in 𝐸𝑔𝑜 correspond well to 𝐸𝑔𝑡 , and the 𝐸𝑔𝑜 is in the range of 2.17~2.27 eV for COi7IC and the IDT and IDTT based compounds and decreased to ca. 2.0 eV for 4TIC and 6TIC-4F. As a whole, the 𝐸𝑏 is only slightly changed among all the compounds and calculated to be ca. 1.8 eV for 4TIC, 6TIC-4F, and ITN-C9 and ca. 1.9 eV for the other compounds. The large binding energies imply that excitons are impossible to separate in the gas phase.

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Energy (eV)

7 6 5

(a)

gas:

IP

EA

Eog

solid:

IP

EA

Eog

4 3 2 ITIC

COi7IC

IDIC-4Cl ITzN-C9

ITN-C9

4TIC

6TIC-4F

ITN-C9

4TIC

6TIC-4F

2.0 1.5

Eb (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


gas solid

(b) 1.0 0.5 0.0 ITIC

COi7IC

IDIC-4Cl ITzN-C9

Figure 2. (a) Calculated ionization potential IP, electron affinity EA, optical gap 𝐸𝑔𝑜 , and (b) exciton binding energy 𝐸𝑏 in the gas phase and the solid state.

Upon going from the isolated molecules to the solid crystals, the S0 and S1 states as well as the ionic states get more stabilized (Figure 3a). For each compound, the stablization energies (negative energy difference bewteen the gas phase and the solid state) are very close for the S0 and S1 states, but much stronger for the ionic states, especially for the anionic state. Consequently, the 𝐸𝑔𝑜 values are hardly changed from the gas phase to the solid state; however, the decrease in IP and increase in EA are very significant, leading to a reduction in 𝐸𝑔𝑡 as large as 1.3~1.8 eV (Figure 2a and Table S2). Thereby, the 𝐸𝑏 values in the solid state are much decreased with respect to those in the gas phase (Figure 2b). Among the studied crystals, ITN-C9 and ITzN-C9 exhibit the largest 𝐸𝑏 of 0.49 and 0.43 eV, respectively. For ITIC, COi7IC, and IDIC-4Cl, the 𝐸𝑏 is ca. 0.25 eV. Remarkably, the crystals with three-dimensional moleuclar packing 9



structures present the weakest 𝐸𝑏 , as small as 0.16 eV for 6TIC-4F and even only 0.04 eV for 4TIC. It should be noted that in constrast to the small change of 0.1 eV in the gas phase for the 𝐸𝑏 among the different studied systems, the 𝐸𝑏 in the solid crystals can vary relatively much significantly. This result underlines the critical importance of molecular packing structures on the electronic polarization effect. As the driving forces for exciton dissociation is linearly correlated to 𝐸𝑏 ,29 the calculated 𝐸𝑏 values here are consistent with the small driving forces for hole transfer observed in the highefficiency OSCs using A-D-A small molecule acceptors.50-56 Moreover, the 𝐸𝑏 of the 4TIC crystal is as small as those of the organic-inorganic tri-halide perovskites,57-59 implying that excitons can be seperated without any driving force at room temperature.

0

E (eV)

(a) cation anion S0

-1

S1

-2 1

P+ (eV)

(b) 0

total electrostatic induction

-1 1

(c) P- (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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0

total electrostatic induction

-1 ITIC

COi7IC IDIC-4Cl ITzN-C9 ITN-C9

4TIC

6TIC-4F

Figure 3. (a) Energy difference between the gas phase and the solid state for the ground state (S0), the first singlet exctied state (S1), and the cationic and anionic states; (b,c) Polarization energies and the corresponding electrostatic and induction components for the positive (b) and negative (c) charges. 10


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As discussed above, the changes in the S1 excitation energies is negligibly small from the gas phase to the solid state (Table S2), which can be ascribed to the similar ESPs of the S0 and S1 states (Figure 4). Therefore, in the following, we concentrate on the electronic polarization effect of the positive and negative charge carriers to gain a further understanding of the 𝐸𝑏 in the solid crystals. According to the Lyons relation,60 the polarization energy for a positive or negative charge carrier is calculated as the difference of IP or EA between the solid state and the gas phase, 𝑃+ = IP(solid) − IP(gas)

(5)

𝑃− = EA(gas) − EA(solid)

(6)

Since the nuclear relaxation of the molecule and the lattice due to the presence of the charge is small, the polarization energy can be divided into two main parts,61-62 𝑃 = 𝑃𝑒𝑙𝑠𝑡 + 𝑃𝑖𝑛𝑑

(7)

where 𝑃𝑒𝑙𝑠𝑡 represents the electrostatic term that comes from the Coulomb interaction of permanent charges (as derived from the gas phase electron density) between the central molecule and the surrounding environment. This term can be either repulsive or attractive depending on the molecular packing structures and intramolecular charge distribution. 𝑃𝑖𝑛𝑑 denotes the induction term that arises from the induced charge redistribution of the central molecule and the surrounding molecules. The induction effect will lead to stabilization of the charged molecule compared to the vacuum state since the charge always has an attractive interaction with the charge redistribution induced dipoles of the surrounding molecules.

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ITIC

COi7IC

0.1 e

IDIC-4Cl

ITzN-C9

ITN-C9

-0.1 e 4TIC

6TIC-4F S0

S1

cation

anion

Figure 4. Electrostatic potentials of the ground state (S0) and the first excited state (S1), and the cationic and anionic states.

As seen in Figure 3b and 3c, the electrostatic contributions to polarization energies are opposite for the positive and negative charge carriers. For the ITIC, COi7IC, IDIC4Cl, 4TIC, and 6TIC-4F systems, electrostatic interactions will stabilize the negative charge but destabilize the positive charge due to the electron-deficient nature of the ESPs, and the 𝑃𝑒𝑙𝑠𝑡 for the negative and positive charges are comparable due to their similar distribution on the charged molecule. In particular, the ESP surfaces get highly electron-deficient upon chlorine or fluorine substitution for IDIC-4Cl and 6TIC-4F, and the absolute 𝑃𝑒𝑙𝑠𝑡 of both the positive and negative charges can be as large as 0.4 eV 12


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for IDIC-4Cl and even 0.7 eV for 6TIC-4F. On the contrary, the ESP surfaces become weakly electron-rich upon fusing the end-groups with one more benzene for ITzN-C9 and ITN-C9; accordingly, in general, the positive charges are stabilized while the negative charges are destabilized very slightly by electrostatic interactions. As expected, the induced dipoles of all the surrounding molecules point outward [toward] the central molecule with an excess positive [negative] charge (Figure S6). Both the positive and negative charges are hence stabilized by the induction effect. Moreover, the induced dipoles are quite large for all the studied systems and reach 4 D for the molecules along the π-π stacking direction, making the 𝑃𝑖𝑛𝑑 stronger than the 𝑃𝑒𝑙𝑠𝑡 for all the studied compounds. Meanwhile, because of different intermolecular distances and orientations, the 𝑃𝑖𝑛𝑑 can vary from -0.59 to -0.88 eV for the positive charge and from -0.76 to -0.93 eV for the negative charge. Upon adding up the electrostatic and induction contributions, the polarization energies for the positive and negative charges are similar for ITzN-C9 and ITN-C9, but for the other compounds the 𝑃− are obviously stronger than the 𝑃+ , especially for IDIC-4Cl and 6TIC-4F. In order to reveal the relationship between the 𝐸𝑏 in the solid state and the polarization energies of the charge carriers, Figure 5 displays the plot of the 𝐸𝑏 vs the total polarization energies of the positive and negative charges. By and large, the 𝐸𝑏 exhibit a negative correlation with the absolute total polarization energies (|𝑃+ + 𝑃− |). For ITN-C9 and ITzN-C9, the relatively large 𝐸𝑏 can be attributed to the small |𝑃+ + 𝑃− |. In contrast, the reduced 𝐸𝑏 of 4TIC is mainly ascribed to the enhanced |𝑃+ + 𝑃− |. In addition, since the electrostatic interactions for the positive and negative 13



charges are comparable and cancel out each other, the reduction of 𝐸𝑏 from the gas phase to the solid state is dominated by the induction effect of the charge carriers.

0.5

ITN-C9 ITzN-C9

0.4

Eb (eV)

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0.3

ITIC IDIC-4Cl

0.2

COi7IC 6TIC-4F

0.1

4TIC

0.0 1.3

1.4

1.5

1.6

1.7

1.8

-(P++P-) (eV) Figure 5. Plot of the exciton binding energies 𝐸𝑏 in the solid state vs the total polarization energies of the positive and negative charges 𝑃+ + 𝑃− .

Finally, we would compare the calculated results with the available experimental measurements (Figure S7). In the experiments, the IP and EA were measured by electrochemical method and the 𝐸𝑔𝑜 were determined by the absorption spectra from thin films. Compared with the experimental data, the EA are underestimated while the IP and 𝐸𝑔𝑜 are overestimated by our calculations. On the one hand, this can be due to different molecular packing structures in the crystals and the films. On the other hand, the exciton and charge carriers are assumed to be localized on one single molecule in the calculations. To consider the electronic delocalization effect, we did calculations on the dimers with nearest-neighbored molecules in the experimental crystals (Figure S8). Indeed, the EA are increased while the IP and 𝐸𝑔𝑜 are decreased by some degrees for 14


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the dimers with respect to the single molecules in the gas phase (Table S2 and S3). More interestingly, the obtained 𝐸𝑏 are reduced for the dimers, especially in the case of 4TIC. This makes a further confirmation of weak 𝐸𝑏 presented in the 4TIC crystal. In summary, we have investigated the effect of electronic polarization on exciton binding energies seven representative A-D-A organic photovoltaic acceptors in the solid crystals by a self-consistent QM/EC approach. Because of strong electronic polarization, the exciton binding energies are substantially reduced in the solid crystals with respect to the gas phase and smaller than 0.5 eV. Moreover, in contrast to small changes of the exciton binding energies in the gas phase among the studied molecules, the binding energies in the solid phase can vary much due to the different molecular packing structures. Especially, the systems with three-dimensional molecular packing patterns exhibit very weak binding energies, as small as 0.16 eV for 6TIC-4F and even 0.04 eV for 4TIC. This implies that excitons generated in the 4TIC crystal can be seperated directly by thermal energy without any driving force and it is important to develop three-dimensional packing for reducing exciton binding energies. In addition, our calculations point out that the polarization effect is negligible for the electronic excitation energies and hence the exciton binding energies in the solid state show a good negative correlation with the total polarization energies of the positive and negative charges. Notably, the electrostatic interactions of the positively and negatively charged molecules with the surrounding molecules are opposite and comparable, thus just cancelling out each other. Therefore, the reduction of binding energies from the gas phase to the solid state is dominated by the induction effect of the charge carriers. 15



This work underlines the importance of molecular arrangements on tuning the exciton binding energies and sheds some light on the efficient exciton dissociation processes under small driving forces observed in organic solar cells. We hope our calculated results will stimulate experiments to further accurately characterize the exciton binding energies and splitting dynamics in nonfullerene organic photovoltaic materials and demonstrate the effect of different molecular packing structures.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Computational details for optimization of density functional and convergence test of cluster size; chemical and crystal structures as well as extracted dimer configurations of the nonfullerene acceptors; the setup of model clusters, iteration workflow, and test of convergence behavior with the cluster radius for QM/EC calculations; induced dipoles in the surrounding molecules for the positive and negative charges; ionization potential, electron affinity, and optical gap measured by experiments from the thin films and calculated based on the model dimers.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Y.Y.); [email protected] (Z.W.) 16


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ORCID Lingyun Zhu: 0000-0001-7391-1866 Yuanping Yi: 0000-0002-0052-9364 Zhixiang Wei: 0000-0001-6188-3634 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was financially supported by National Natural Science Foundation of China (Grant Nos. 21773040, 91833305), the Ministry of Science and Technology of China (Grant No. 2017YFA0204502), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDB12020200). The calculations have been done in the Computing Cluster of the National Center for Nanoscience and Technology.

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Achieving Small Exciton Binding Energies in Small Molecule

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