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Computational Study on the Search for Non-Fullerene Acceptors, Examination of Interface Geometry, and Investigation of Electron Transfer Yutaka Imamura,* Marina Suganuma, and Masahiko Hada Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo 192-0397, Japan Downloaded via UNIV OF SOUTHERN INDIANA on July 17, 2019 at 04:07:51 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Extensive exploration of new non-fullerene acceptor materials in organic photovoltaics has led to enhancements in their power conversion efficiency. However, a comprehensive search for new non-fullerene acceptors with a detailed investigation of non-fullerene organic photovoltaic interface geometries has not been performed. In this study, we theoretically searched for new non-fullerene acceptors, modeled the interface of a non-fullerene acceptor and polymer, and estimated electron transfer rates for charge transfer and charge recombination processes via the Marcus formula. By examining more than 1850 candidate materials, promising acceptors were found. The theoretical investigation of the interface geometry revealed that steric hindrance restricts the possible interface geometries. Examination of the electron transfer rates suggested that the charge transfer process is more dominant than the charge recombination one, which is advantageous for high power conversion efficiency.

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INTRODUCTION Organic photovoltaics (OPVs) are attractive alternatives to inorganic solar cells because of their flexibility and low-cost solution processing.1,2 There have been many attempts to enhance the photovoltaic characteristics, such as the opencircuit voltage (VOC), short-circuit current density (JSC), and fill factor (FF).3 Power conversion efficiencies (PCEs) have reached more than 14%4−10 for OPVs with non-fullerene electron acceptors, although high PCEs were previously obtained for electron-donating materials such as semiconducting polymers and electron-acceptor materials such as fullerene derivatives. Non-fullerene electron acceptors are promising because of their high PCEs and cost-effectiveness. Typical nonfullerene units, such as perylenediimide11 derivatives and 3,9bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2′,3′-d′]-sindaceno[1,2-b:5,6-b′]dithiophene (ITIC)4−10 derivatives, have been used. In particular, ITIC is one of the most promising non-fullerene acceptors due to its record-high PCE.9,10 Extensive experimental studies4−10 on ITIC have been performed; however, there are only limited theoretical studies on ITIC12 and other non-fullerene acceptors,13 although many theoretical studies14−23 regarding polymers (donor) and fullerene (acceptor) have been reported. To further increase the practical PCE, (1) new non-fullerene acceptors should be theoretically explored and (2) the interfaces between donor/non-fullerene acceptor materials should be designed to promote the charge separation. Regarding (1), some studies have been conducted. 13 © XXXX American Chemical Society

Regarding (2), detailed information on the interface and electron transfer processes has been rarely reported with one exception.12 In this study, we first searched new acceptors, including ITIC constituent units, and constructed interface models for ITIC/PTzBT,24 promising acceptor candidates/ PTzBT, and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM)/PTzBT. Then, we analyzed the electron transfer rate for charge transfer and charge recombination, using Marcus theory.25 This study offers fruitful design insights for a new acceptor and its interface for electron transfer processes.

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THEORETICAL CALCULATIONS Generative Model. Acceptors were automatically generated by our program using several other programs.26−28 The generated acceptors were theoretically synthesized from donor, acceptor, and spacer unit libraries as shown in Figure 1 and were given in a simplified molecular-input line-entry system. To discover more promising acceptors, indacenodithiophene (IDT) and indacenodithieno[3,2-b]thiophene (IDTT), which is a moiety of ITIC, were adopted as the donor unit. Then, 26 acceptor units, including one in ITIC, were prepared. Donor and acceptor units that are given in red squares correspond to the units of ITIC. As a spacer unit, thiophene was used. The initial geometries of the acceptors were generated by RDKit28 Received: March 28, 2019 Revised: June 15, 2019 Published: June 26, 2019 A

DOI: 10.1021/acs.jpcc.9b02933 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Libraries of (a) donor, (b) acceptor, and (c) spacer units used for automatic generation of OPV acceptors.

by adding hydrogens. These acceptors were optimized by the PM7 semiempirical method in MOPAC27 and using the density functional theory (DFT) method in Gaussian.26 The PBE0 exchange−correlation functional29 and 6-31G*30 were used in DFT calculations. The PBE0 functional provides reasonable orbital energies, which are suitable for estimating photovoltaic parameters.19 In total, 1864 molecules composed of 932 acceptor−donor−acceptor types and 932 acceptor− spacer−donor−spacer−acceptor type acceptors were examined. Estimation of Photovoltaic Characteristics. We estimated the PCEs using photovoltaic characteristics, such as the open-circuit voltage, VOC, and short-circuit current density, JSC. According to previous studies,3,16,19 the optical absorption was assumed to occur in the energy range over Δεdonor gap , which is the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a donor, and JSC can be evaluated by numerically integrating in the energy range from Δεdonor gap to the edge of the short wavelength light (280 nm) as follows Gap EQE(ε) = 0.65 × θ(ε − Δεdonor )

JSC =

be larger than any experimental values at all Eloss values, because the best photovoltaic performance should be estimated for searching new OPV material candidates. Of course, depending on a purpose, a different parameter set, which suits specific experimental conditions, can be chosen as well. The determined f function in this study is shown as a red curve in Figure 2. 1 f (E loss) = 0.85 × ÅÄÅ −(E loss − 0.4) ÑÉÑ expÅÅÅ 0.03 ÑÑÑ + 1 (5) ÅÇ ÑÖ The above function was selected because the function was flexible enough to be optimized. The revised EQE, including the Eloss-dependent functional f(Eloss), can be obtained as follows

(1)

light (ε) d ε ∫ EQE(ε) × Φsolar AM

(2)

1.5

donor donor donor Δεgap = εLUMO − εHOMO light Φsolar AM1.5

Figure 2. EQE with respect to Eloss. The dots were obtained from ref 32. The red curve corresponds to eq 6.

(3)

EQE′(ε) = f (E loss) × θ(ε − Δϵdonor gap )

31

where is the air mass 1.5 solar spectrum. The external quantum efficiency (EQE) was set to 0.65 as in previous studies.19 Although this approximation is crude, JSC was appropriately estimated in previous studies using this method.3,13,15,16,19 However, as mentioned in another study,32 EQE depends on the energy loss, Eloss, which is the energy difference between VOC and the optical energy gap of a semiconductor.

′ = JSC

1.5

(7)

The open-circuit voltage can be simply estimated as an energy difference between the LUMO of an acceptor and the HOMO of a polymer (donor) with an energy loss of 0.3 eV, as used in the Scharber’s model3 acceptor donor eVOC = εLUMO − εHOMO − 0.3 eV

E loss = Δϵdonor gap − qVOC =ΔϵLUMO + Eother

light (ε ) d ε ∫ EQE′(ε) × Φsolar AM

(6)

(8)

Although FF depends on the manufacturing process of photovoltaic devices, it was set to 0.7, which is considered to be an optimal value. Finally, using VOC, JSC, and FF, PCE can be estimated as

(4)

Eloss can be rewritten as ΔϵLUMO + Eother, where ΔϵLUMO is the LUMO energy difference between the donor and acceptor, and Eother includes the other energy loss and was set to 0.3 eV.3 The experimentally measured EQE32 with respect to Eloss is shown in Figure 2 and depends on respective combinations of poly(3hexylthiophene) and acceptors. To describe the EQE − Eloss dependence, we introduced a function form, which has been used for fermi distribution function. Several parameter sets were examined and determined so that the EQE curve should

′ FF PCE′ = VOC JSC

(9)

For reference, the conventional PCE is also estimated via PCE = VOC JSC FF

(10)

In the previous formulation, EQE is expressed as θ(ε − Δεdonor gap ) and depends on the HOMO−LUMO gap of the B


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Figure 3. PCEs estimated using eq 10 (original Scharber’s model) for A-IDTT-A, A-IDT-A, A-Th-IDTT-Th-A, and A-Th-IDT-Th-A.

Figure 4. PCEs estimated using eq 9 (modified Scharber’s model) for A-IDTT-A, A-IDT-A, A-Th-IDTT-Th-A, and A-Th-IDT-Th-A.

using electron coupling H12, change in the Gibbs energy ΔG0, and reorganization energy λ.

donor, whereas the current formulation depends on the orbital energies of not only the donor but also the acceptor. The LUMO energies of acceptors are shifted by −0.524 eV, which is the orbital energy difference between the experimental and theoretical LUMO energies of ITIC calc_corr calc εLUMO,acceptor = εLUMO,acceptor + Δε

(11)

calc expt Δε = εLUMO,ITIC − εLUMO,ITIC

(12)

k=

|H12|2 ℏ

ij (λ + ΔG0)2 yz π zz expjjj− z j λTkB 4λTkB z{ k

(13)

The electron couplings for charge transfer and charge recombination were estimated as follows V−

PTzBT was adopted as a donor. The HOMO and LUMO energies of PTzBT were −5.2 and −3.2 eV, respectively. Interface Model and Electron Transfer Rate. For determining interface models, all of the planar geometries in the model were optimized by DFT using the hybrid exchange− correlation functional ωB97XD33 and the 6-31G**30 basis set. Since the interface geometry should be optimized with the van der Waals interaction, ωB97XD/6-31G** was adopted instead of PBE0/6-31G*, which was used for estimating orbital energies of more than 1850 candidates with a reasonable computational cost. All calculations were performed in Gaussian.26 The electron transfer rates for charge transfer and charge recombination were estimated using the Marcus formula25

H12 =

( S2 ) × (ε1 + ε2) 1 − S2

(14)

where V and S represent the off-diagonal Fock matrix elements and overlap integral between the LUMO of isolated ITIC, acceptor candidates, and LUMO/HOMO of the isolated PTzBT dimer; ε is the corresponding orbital energy. The temperature, T, was set to 300 K, and kB is the Boltzmann constant.

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RESULTS AND DISCUSSION Search for New Acceptors. We generated acceptor candidates, which are categorized into four types: A-IDTT-A, A-IDT-A, A-Th-IDTT-Th-A, and A-Th-IDT-Th-A. Th and A

C


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Figure 5. JSC (triangle), VOC (circle), and PCE (circle) estimated using eqs 7−9 for A-IDTT-A, A-IDT-A, A-Th-IDTT-Th-A, and A-Th-IDT-Th-A.

Figure 6. Optimized geometries of the ITIC and PTzBT model from two different angles at the displacements of (a) 0 Å, (b) 13.5 Å, and (c) 27.5 Å (dimer).

PCE of approximately 13%. It is noted that IDTT + indanone is essentially equivalent to ITIC. Acceptors, NOz and NTz, are known to exhibit a high PCE.34 To investigate in more detail, PCEs were decomposed into VOC and JSC as shown in Figure 5. VOC increases as the acceptor LUMO energy becomes higher, which is reasonable because the donor HOMO is fixed at −5.2 eV and the acceptor LUMO energy increases. Under the condition that the donor HOMO−LUMO gap of PTzBT is fixed, JSC is at a maximum for the PTzBT polymer when the acceptor LUMO level is low enough for charge transfer. When Eloss is close to 0.4 eV, i.e., the LUMO−LUMO gap is close to 0.1 eV, JSC begins to decrease. Since PCE is estimated by multiplying JSC and VOC, the maximum appears at approximately −3.55 eV. This behavior indicates that the trade-off relation between VOC and JSC should be considered to obtain high PCEs. For the indanone unit, JSC is around a maximum; however, VOC can be improved, whereas VOC and JSC are around a maximum for NOz and diazine. The experimental value of PCE for ITIC was estimated to be 7.1% (JSC = 11.7 mA/cm2,VOC = 0.97 V, FF = 0.61), which is lower than the value of 9.52% obtained in this study. This difference is because the parameters in PCE formulations, such as FF and EQE, are ideal (i.e., best efficiency). For example, FF was set to 0.61, and EQE was defined as follows

stand for thiophene and acceptor, respectively. We examined the conventional PCEs estimated by eq 10 as shown in Figure 3. The estimated PCEs ranged from 0% to approximately 15%. As confirmed, many acceptors have PCEs higher than 14%, which is not consistent with the experimental fact that the observed PCEs in organic photovoltaics are less than 14% with a few exceptions.9,10 Examination of the orbital levels of the acceptors with high PCEs reveals that the donor LUMOs are lower than the acceptor LUMOs. This indicates that the charge transfer process from the donor to acceptor was not considered in the original Scharber’s model of PCEs and that the estimated PCEs need to be improved. Then, PCEs were estimated by the modified version of the Scharber’s model, eq 9, which is expressed in terms of ΔϵLUMOdependent Eloss. By incorporating the dependence of Eloss in the Scharber’s model, the LUMO levels of donors and acceptors are implicitly considered; therefore, the PCE estimation is expected to be improved. As shown in Figure 4, the PCEs of the acceptors were, in fact, lowered by eq 9 based on the energy levels of the donor’s and acceptor’s LUMOs. To analyze the change of PCEs by eq 9 in more detail, the relation between the acceptor’s LUMO levels and PCEs is illustrated in Figure S1; as easily confirmed, the suppression of the PCEs starts around the LUMO level of −3.85 eV. The acceptors containing indanone, naphthobisoxadiazole (NOz), naphthobisthiadiazole (NTz), and diazine units exhibit a maximum D


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The Journal of Physical Chemistry C f (E loss) = 0.75 ×

1 ÄÅ −(E − 0.4) ÉÑ ÅÅ loss Ñ expÅÅ 0.03 ÑÑÑ + 1 ÅÇ ÑÖ

Table 1. Adsorption Energies for ITIC/PTzBT (15)

PCE was estimated to be 7.32% (JSC = 10.91 mA/cm2, VOC = 1.10 V). Interface Model. We constructed interface models for ITIC/PTzBT. The polymer, PTzBT, which is basically planar because of the infinite polymer chain, was modeled as a dimer with a methyl group as the alkyl group. The PTzBT dimer was optimized under the constraint that the PTzBT dimer was planar. The constraint is not exactly right because the PTzBT polymer is expected to be distorted. However, since the PTzBT polymer has a conjugated plane, the planar part should exist. Thus, the present interface model can offer essential information about the interaction between PTzBT and ITIC. For the ITIC/PTzBT interface, ITIC was located on the PTzBT dimer model for edge-on, end-on, and face-on orientations with a fixed PTzBT dimer geometry. After optimization, only the face-on conformation was obtained as a stable one, as shown in Figure 6a. Then, we shifted ITIC from the stable geometry (0.0 Å) by 0.5 Å along the long axis with respect to the PTzBT dimer and estimated the total energies without geometry optimization. The adsorption energies are given in Figure 7 and Table S1. The potential

displacement (Å)

adsorption energy (kcal/mol)

−23.0 −13.5 −9.5 0.0 3.5 13.5 17.0 27.5 32.5 39.0

24.10 39.89 42.87 54.03 54.19 54.16 54.03 42.86 34.19 24.18

of the ITIC/PTzBT interface involves instability of the distortion but is preferred. The distance between conjugation planes is approximately 3.4 Å. The HOMO and LUMO are distributed on ITIC and the PTzBT dimer, respectively, which reflects the intrinsic characteristics of the donor/acceptor. For comparison, the interface model with a nonplanar-type acceptor, PCBM, was also examined. For the PCBM/PTzBT interface, the initial geometries were generated so that PCBM was located on sites 1−8 of the PTzBT dimer model, as shown in Figure 8. The adsorption energies are approximately −13 kcal/mol, as shown in Figure 9 and Table S2. The changes in adsorption energies are significantly smaller than those of ITIC/PTzBT. PCBM basically does not prefer special sites of PTzBT because of the lack of steric hinderance. Then, we examined the interface geometry for promising acceptor candidates, such as IDTT + NOz and IDTT + diazine, which were obtained in the above section. The optimized geometries are shown in Figures S2 and S3, and the adsorption energies of the conformations at the displacements of 0.0, 3.5, 13.5, and 17.0 Å are shown in Table 2. Their geometries are very similar to that of ITIC, although the adsorption energies are slightly smaller: ∼52 and ∼49 kcal/mol for IDTT + NOz and IDTT + diazine. This result indicates that the interface geometry depends on the planar geometry of IDTT and is less affected by the choice of acceptor units in the promising acceptor candidates because the IDTT derivatives are planar and interact with the polymer via van der Waals interactions. Electron Transfer for Charge Transfer and Charge Recombination. To examine the promising candidates in more detail, the photogeneration mechanism consisting of photoadsorption, exciton formation, charge transfer, charge separation, and charge collection should be investigated. In particular, the charge transfer and charge recombination processes are key for a high PCE. Therefore, the electron transfer rates for charge transfer and charge recombination were estimated by the Marcus formula25 using electron couplings, changes in the Gibbs energy, and reorganization energies. The HOMO and LUMO energies of PTzBT were −5.2 and −3.2 eV, and those of ITIC were −5.4 and −3.8 eV. Although the corresponding theoretical HOMO and LUMO energies are available, the experimental values were used here because DFT orbital energies strongly depend on the choice of the exchange−correlation functional,35,36 and PTzBT was modeled as a dimer. The changes in Gibbs energy for charge transfer and charge recombination were set to −0.6 and −1.4 eV, respectively, in the case of ITIC/PTzBT. The reorganization energy λ was set to 0.6 eV, which is essentially similar to those in previous studies.22 As confirmed in Table 3, the

Figure 7. Potential curve (black squares) of the ITIC and PTzBT model (dimer). Red circles correspond to the energies with geometrical relaxation of ITIC.

curve (black squares in Figure 7) is almost symmetric, which is consistent with the symmetry of the PTzBT dimer. As confirmed in Table S1, the conformations at the displacements of −23.0, −13.5, −9.5, 0.0, 3.5, 13.5, 17.0, 27.5, 32.5, and 39.0 Å are stable, whereas the other conformations are very unstable because of steric hindrance between the methyl from the polymer model and the aryl groups from ITIC. This indicates that the steric hindrance strongly influences the stability of the interface geometry. After the optimization of ITIC of the above stable configurations, adsorption energies were obtained as shown in Figure 7 and Table 1. Figure 6a−c illustrates the interface geometries at the displacements of 0, 13.5 and 27.5 Å. The optimized geometries at the displacements of 0 and 13.5 Å are very similar for Figure 6a,b, while that at the displacement of 27.5 Å is slightly different from the others because the ITIC molecule reaches the edge of the PTzBT model. However, the basic interface geometry does not depend on the displacements. The adsorption energies changed from 24 to 54 kcal/ mol, depending on the conformations. The conformations at the displacements of 0.0, 3.5, 13.5, and 17.0 Å are especially stable. The alkyl groups of ITIC are distorted so that ITIC interacts with the PTzBT dimer. The distortion energy, which is defined here as the total energy difference between an isolated ITIC and ITIC on PTzBT at the displacement of 0.0 Å, was estimated to be 8.11 kcal/mol. Therefore, the formation E


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Figure 8. (a) Dimer model of PtzBT with the adsorption sites of PCBM and (b) a schematic of the adsorption geometry of the PCBM/PTzBT model.

of ITIC, probably because the interface geometries are similar. Thus, charge transfer is preferred over charge recombination. Therefore, ITIC and promising acceptor candidates are promising acceptors for OPVs.

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CONCLUSIONS Using a computational approach, we generated new nonfullerene acceptors, including IDT and IDTT units in ITIC, and also modeled the interface of the non-fullerene acceptor and polymer and estimated the electron transfer rates for charge transfer and charge recombination processes using the Marcus formula. The new acceptors of IDTT + NOz, NTz, and diazine units are the most promising out of more than 1850 candidate materials. ITIC and the new acceptors have a similar interface geometry, in which charge transfer is more dominant than charge recombination. This indicates that the promising acceptor candidates with an interface geometry parallel to the plane of the polymer (donor) should be designed with specific HOMO and LUMO energies, which are advantageous for charge transfer.

Figure 9. Potential curve of the PCBM and PTzBT model (dimer).

Table 2. Adsorption Energies for IDTT with NOz and Diazine Units on PTzBT adsorption energy (kcal/mol) displacement (Å)

IDTT + NOz

IDTT + diazine

0.0 3.5 13.5 17.0

51.69 52.11 52.10 51.70

49.08 49.12 49.09 49.11

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ASSOCIATED CONTENT

* Supporting Information

electron couplings of charge transfer are slightly larger than those of the charge recombination although the behavior of the electron couplings for charge transfer and charge recombination is very similar. Using the electron couplings, the electron transfer rates were estimated by the Marcus formula. As shown in Table 3, the electron transfer rate for charge transfer is larger than that for charge recombination at least by 1 order of magnitude. The charge transfer process is more dominant than the charge recombination process by 4 orders of magnitude. Because the electron couplings are similar for both processes, the difference is due to the change in Gibbs free energy. Next, we examined the IDTT + NOz and diazine + PTzBT interfaces, whose changes in Gibbs energy for charge transfer were set to −0.45 and −0.32 eV, respectively, and those for charge recombination were −1.55 and −1.68 eV, respectively. The reorganization energy, λ, was set to 0.6 eV. As confirmed in Table 3, the electron transfer rates do not differ from those

S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.9b02933.

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Adsorption energies for ITIC/PTzBT at displacements without geometry relaxation of ITIC (Table S1); adsorption energies for PCBM/PTzBT (Table S2); PCEs with respect to acceptor’s LUMO energies using eqs 9 and 10 (Figure S1); optimized geometry of IDTT with the NOz unit and PTzBT model (Figure S2); optimized geometry of IDTT with the diazine unit and PTzBT model (Fgure S3) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

Table 3. Electron Couplings and Electron Transfer Rates for ITIC, IDTT + NOz, and IDTT + Diazine electron transfer rate (s−1)

electron coupling (eV) charge transfer ITIC IDTT + NOz IDTT + diazine

0.0 Å 0.018 0.001 0.052

3.5 Å

13.5 Å

0.010 0.001 0.046 0.045 0.013 0.012 electron coupling (eV)

17.0 Å

0.0 Å

3.5 Å

0.018 0.000 0.053

6.96 × 10 3.94 × 109 1.56 × 1013 12

13.5 Å

17.0 Å

2.16 × 10 1.06 × 10 3.14 × 1013 3.03 × 1013 11 9.16 × 10 8.15 × 1011 electron transfer rate (s−1) 12

10

7.22 × 1012 2.56 × 104 1.61 × 1013

charge recombination

0.0 Å

3.5 Å

13.5 Å

17.0 Å

0.0 Å

3.5 Å

13.5 Å

17.0 Å

ITIC IDTT + NOz IDTT + diazine

0.014 0.000 0.042

0.008 0.036 0.010

0.000 0.036 0.010

0.015 0.001 0.042

1.50 × 108 1.37 × 103 2.18 × 105

4.81 × 107 1.32 × 107 1.26 × 104

8.89 × 103 1.28 × 107 1.13 × 104

1.55 × 108 6.04 × 103 2.25 × 105

F


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The Journal of Physical Chemistry C ORCID

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Yutaka Imamura: 0000-0002-9527-6813 Masahiko Hada: 0000-0003-2752-2442 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Itaru Osaka and Prof. Akinori Saeki for fruitful discussion. The calculations were performed at the Research Center for Computational Science, Okazaki, Japan, and using the supercomputer system at the Research Institute for Information Technology at Kyushu University. This study was supported in part by a Grant-in-Aid for Scientific Research on Innovative Areas “Coordination Asymmetry” from the Japan Society for the Promotion of Science (JSPS) JP17H05380 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. We would like to thank Editage (www.editage.jp) for English language editing.

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