Theoretical Strategy To Design Novel n-Type Copolymers Based on

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A Theoretical Strategy to Design Novel n-Type Copolymers Based on Anthracene Diimide and Pyrido[2,3-g]quinolone Diimide for Organic Solar Cells Zhiyong Fu, Wei Shen, Xiaoqin Tang, Min He, Rongxing He, and Ming Li J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b03731 • Publication Date (Web): 03 Jun 2015 Downloaded from http://pubs.acs.org on June 9, 2015

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The Journal of Physical Chemistry

A Theoretical Strategy to Design Novel n-Type Copolymers Based on Anthracene Diimide and Pyrido[2,3-g]quinolone Diimide for Organic Solar Cells Zhiyong Fu, Wei Shen, Xiaoqin Tang, Min He, Rongxing He and Ming Li∗ College of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China

∗

To whom correspondence should be addressed. E-mail: [email protected] 1

ACS Paragon Plus Environment


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Abstract The design and synthesis of efficient electron transporting materials have been a hot issue of research in the area of organic solar cells (OSCs), organic field-effect transistors (OFETs) and organic light-emitting diodes (OLEDs). This paper is focused on designing novel n-type donor-acceptor (D-A) copolymers as electron transporting materials for replacing the widely used fullerene acceptor materials in OSC applications. We first present a strategy which can remarkably improve the photovoltaic performances of D-A copolymer acceptors by means of adjusting the molecular

planarity

and

intensifying

the

electron-withdrawing

ability

of

electron-deficient unit. And then we further analyze the role played by the D-A copolymer acceptor in the light-absorbing performance of the active layer. Based on the reported two D-A copolymer acceptors (PNDIT and P(NDI2OD-T2)) which are composed of electron-deficient naphthalene diimide (NDI) unit and different electron-rich units of thiophene or bithiophene, replacement of NDI unit with anthracene diimide (ADI) unit and pyrido[2,3-g]quinoline diimide (PQD) unit can produce two types of copolymer acceptors (P2, P3 and P2a, P3a). From the calculated results, the introduction of ADI and PQD units to replace NDI unit can significantly improve the optoelectronic properties, light-absorbing efficiencies and intermolecular electron transport abilities of the copolymers as well as exciton separation efficiencies at donor/acceptor interface. Finally, this study would give us a theoretical guidance to design efficient D-A copolymer acceptors for replacing fullerene acceptors in organic solar cells.

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Keywords: D-A copolymer acceptor, Charge separation efficiency, Charge transfer rate

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1. Introduction For decades, with the mass exhausting of natural resources and the growing demand for environmental-friendly energies, much attention has been attached to the search of alternative energies.1,2 Solar energy, which is clean, unlimited, and readily available, has already been extensively studied among various renewable energy resources. Bulk heterojunction (BHJ) organic solar cells, the active layers of which typically consist of donor materials and acceptor materials, are becoming very attractive among the light-absorbing devices in recent years because of their advantages of low cost, light weight, easy processing and large-area capability.3,4 In the past decades, a mass of efforts5-8 have been put into designing and synthesizing new donor materials for improving the performances of OSCs. Significant progress in power conversion efficiencies (PCE) has reached ~9.2%8 for single heterojunction solar cells, however, the devices based on them have not yet entered the market for commercial applications (PCE > 10%). In comparison with considerable researches on the donors, much less attention has been focused on the acceptors, consequently, they

have

lagged

far

behind

their

counterparts

(donors).

PC61BM

([6,6]-Phenyl-C61-butyric acid methyl ester) is the most used acceptor in OSCs, nevertheless, the weak visible light-absorbing ability and low LUMO level are two unfavorable factors for PC61BM as excellent acceptor. Thus, the design and synthesis of efficient non-fullerene acceptors is a promising research field for replacing fullerene acceptors. As highly efficient donors, they should have the following characters: lower-lying

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HOMO level, strong and broad light absorption region, and high hole carrier mobility. However, up to now, there has not been a rigid design guideline for developing an ideal acceptor in OSCs. For an ideal acceptor, the requirements9,10 generally include: (1) suitable HOMO/LUMO levels relative to the donor to ensure the photo-excited electron transfer from the donor to the acceptor, moreover, large difference between the HOMO level of donor and the LUMO level of acceptor is desirable, which is favorable for increasing the Voc (open circuit voltage), (2) strong and wide light absorption band can better match the donor absorption band, which is beneficial to the improvement of light-absorbing efficiency of the active layer, (3) high electron affinity facilitates the exciton separation at the donor/acceptor interface, (4) high electron mobility, (5) good solubility, air stability and film-forming property. For PC61BM, as the most representative acceptor, one of its weak points is the poor light absorption in the visible region, which results in the mismatch of the donor light absorption band and then reduces the light-absorbing efficiency in the photoactive layer.11 In addition, the deep-lying LUMO level of the fullerene acceptor (PC61BM) will lead to a small Voc, because the Voc value is directly proportional to the difference between the HOMO level of the donor and the LUMO level of the acceptor. Therefore, for the sake of improving the performances of OSCs, in search of new efficient acceptors (such as having strong and broad light absorption in the visible and near-infrared region, high electron mobility and so on) are imperative. What strategies can be used to design an acceptor to satisfy the above-mentioned requirements of an ideal acceptor? This study remains on the road.

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It is well-known that an effective strategy in designing the copolymer donors with good performance in OSCs is to alternate a electron-rich unit and an electron-deficient unit in the same D-A polymer backbone.12 The D-A copolymer donors not only easily adjust their HOMO/LUMO levels and reduce the band gap for extending the light-absorption range, but also control their carrier (hole or electron) transport properties.13,14 Whether the design strategy of the D-A copolymer donors can be used to design the new efficient acceptors? In recent years, the aromatic diimide derivatives9,15,16 (such as naphthalene diimide and perylene diimide) are the promising n-type materials for fabricating OSCs and OFETs due to their excellent optoelectronic properties, good oxidative and thermal stability, large electron affinities and high electron mobilities. Interestingly, we found that these reported acceptors based on aromatic diimides all have the same D-A composition structure17-19 in OSCs. For instance, Zhou and co-workers17 designed a series of perylene diimide based copolymers as acceptors for organic solar cells, and Neher and co-workers18 studied the effect of aggregation morphology of a n-type copolymer P(NDI2OD-T2) on the optical property and carrier mobility. Recently, Jenekhe and his coworkers19 investigated the efficiency of organic solar cells with the NDI-based copolymers as acceptors. Those reports found that the D-A copolymer acceptors on the basis of aromatic diimide derivatives possess narrow band gaps and high electron carrier mobilities. A unique advantage of OSCs based on D-A copolymer donors and D-A copolymer acceptors is that they can be tailored to have complementary electronic and optical properties. And that is beneficial to maximize

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the frontier molecular orbital offsets and solar spectrum overlap when compared with the widely reported OSCs on the basis of D-A copolymer donors and fullerene acceptors. However, the solar cells generally exhibit low efficiencies (1% ~ 6%) with aromatic diimide derivatives as acceptor materials.19,20 For the sake of enhancing the performance of D-A copolymer acceptors, we first need to understand how the electronic, optical and charge transport properties of them can be fine-tuned. In this work, we aim to improve the light absorption properties (for better match with donor absorption band), light-absorbing efficiencies and intermolecular carrier mobilities of acceptor materials as well as the exciton separation ability at the donor/acceptor interface by the strategies: (1) improving the coplanarity between the electron-rich unit and electron-deficient unit in the D-A copolymer acceptor, (2) increasing the electron-withdrawing ability of electron-deficient unit of D-A copolymer acceptor. Based on the reported D-A copolymer acceptors18,19 (P1 and P1a), we here designed two groups of new D-A copolymer acceptors (P2-P3 and P2a-P3a, see Figure 1). Hereon, we first focus on how the molecular planarity and the electron-drawing ability of electron-deficient unit affect the HOMO/LUMO levels and the light absorption performance of the copolymer acceptors. Then we further study the effect of two above-mentioned factors on the exciton separation efficiency at donor/acceptor interface, and the intermolecular electron mobility of those acceptors. In conclusion, we also analyze the role of the D-A copolymer acceptor in the light absorption performance of the active layer. Our calculations make an attempt to offer a strategy for designing an efficient non-fullerene acceptor for organic solar

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cell applications.

2. Computational Details In the present work, the ground state geometries of the investigated copolymers were optimized by DFT21,22 (density functional theory). To simplify the calculations for saving the computational costs, all the alkyl branched chains (see Figure 1) of copolymers were replaced by methyl group, and the terminal groups of the repetitive units were saturated with hydrogen atoms, with little effect on the optoelectronic properties.7,23,24 For the sake of finding a suitable method, a series of hybrid functionals (B3LYP25, PBE0 and HSE06) at 6-31G** level were used to calculate the HOMO levels of P1 and P1a, where the calculated results were summarized in Table 1. As shown in Table 1, the calculated HOMO levels of P1 and P1a (trimer model) at HSE06/6-31G** level (-5.82 eV for P1, -5.33 eV for P1a) are in good agreement with the experimental data of P1 and P1a (-5.77 eV19 for P1, -5.36 eV26 for P1a). Similarly, the LUMO levels (see Figure 2) of P1 and P1a were taken from the KS (Kohn-Sham) LUMO eigenvalues in agreement well with the reported experimental data27(-3.83 eV for P1, -3.77 eV for P1a). The absorption spectra of P1 and P1a were computed by time-dependent DFT (TD-DFT) with a suite of hybrid functionals of B3LYP, PBE0 and HSE06 at the 6-31G** level based on the optimized ground state structures (trimer model) at HSE06/6-31G** level. As shown in Table 2, the electronic absorption peaks of the copolymers (P1 and P1a) with TD-DFT at PBE0/6-31G** level agree well with the experimental values.

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The intermolecular distance of adjacent molecular segments and the charge transfer integral were both performed at the M06-2X/6-31G** level.28,29 In this work, the spin-restricted DFT and the unrestricted DFT were used to optimize the ground state geometries and the ion-state geometries, respectively. The calculated vibrational frequencies of all the studied copolymers show that there was no imaginary frequency, which suggests that all the optimized structures are stable structures. The DFT and TD-DFT calculations were carried out by the Gaussian 09 program in the gas phase.30

3. Results and discussion 3.1. The ground state structural properties As we all known, the ground state geometries of the copolymers are directly related to the electronic and optical properties as well as the intermolecular π-π stacking and the charge-carrier mobility.31,32 Thus, it’s extremely essential to analyze the ground state structures of the copolymers. Herein, the ground-state structure properties of P1-P3 and P1a-P3a were deduced on the basis of investigating that of the corresponding monomers (M1-M3 and M1a-M3a, see Figure S1a and S1b). The optimized ground-state structures and selected structural parameters of all monomers (M1-M3 and M1a-M3a) are listed in Figure S1b and Table 3, respectively. It is well known that a semiconductor molecule possesses good planarity, which is conducive to improve the intrachain π conjugation and the interchain π-π stacking, and enhance the carrier mobility.33 As can be seen in Table 3, the calculated dihedral angle (φ) of M1 reaches 45.94°, implying that the molecular backbone of M1 has poor planarity. The poor planarity of M1 hinders the main-chain π conjugation and the

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interchain π-π stacking, and leads to low carrier mobility.19 Hereon, improving the planarity of molecular skeleton is one of the purposes of this work. In comparison of M2 with M1, the substitution of the ADI unit for the NDI unit can evidently reduce the dihedral angle between electron-rich unit and electron-deficient unit, which is conducive to strengthening the intramolecular π-conjugation and the intermolecular π-π stacking. The decrease of the dihedral angle is due to the fact that the steric hindrance between sulfur atom and hydrogen atom in M2 is far less than that of between the sulfur atom and the carbonyl group in M1. Moreover, the dihedral angle further reduces by change of the carbon atoms on the ADI unit in M2 to the nitrogen atoms in M3. According to the calculation results presented in Table 3, M2 and M3 have stronger conjugation effects and shorter bond lengths (L) in comparison with M1. Among the monomers of M1-M3, M3 has the best planarity, which implies that it may have stronger intrachain π-conjugation, larger interchain electronic coupling effect and higher carrier mobility in comparison to other monomers (M1 and M2). Hereon, we mainly analyze the variation of the bond lengths and the dihedral angles of M1-M3 because there is an analogous trend for M1a-M3a with that of M1-M3.

3.2. Frontier molecular orbitals For organic solar cells, one of the requirements for an ideal acceptor is that it has suitable HOMO/LUMO levels in comparison with that of donor aiming to guarantee photo-induced electron transfer from donor to acceptor.9 In addition, the HOMO/LUMO levels and energy gaps have a direct connection with the electronic and optical properties.34 Therefore, it is necessary to analyze the HOMO/LUMO

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levels and energy gaps of the copolymers here. For all the copolymers, the HOMO/LUMO levels were calculated on a trimer model by DFT at the HSE06/6-31G** level. As shown in Table 4, for P1-P3, the calculated HOMO levels are in the order P2 > P1 > P3, and the sequence of their LUMO levels is P1 > P2 > P3. The order of energy gaps (S0 → S1) for those copolymers is P1 > P3 > P2. For P1a-P3a, the change trend of HOMO/LUMO levels is as same as that of P1-P3. The energy gaps of P1a-P3a are in the sequence P1a > P2a > P3a. What is the effect on the electronic properties of the copolymers when the NDI unit is substituted for ADI unit and PQD unit? Hereon, we analyze the HOMO/LUMO levels and energy gaps of the copolymers (P1-P3, P1a-P3a) for expounding this problem. By the change of the NDI unit in P1 (P1a) to the ADI unit in P2 (P2a), the LUMO level and the energy gap are decreased, while the HOMO level is increased. This result (the decreased of LUMO level and energy gap) is due to the fact that the introduction of the ADI unit to replace NDI unit in copolymer, which can significantly enhance π-conjugation degree of the copolymer backbone. P2 (P2a) has a stronger main-chain π-conjugation compared with P1 (P1a) based on the following reasons: (1) the anthracene unit is more conducive to electron delocalization than that of naphthalene unit, (2) the substitution of the ADI unit for NDI unit in P1 can evidently decrease the dihedral angles between the electron-rich unit and electron-deficient unit (see Table 3). For P2 (P2a), a weaker electron-withdrawing ability of the electron-deficient unit than that of P1 (P1a) should have a direct impact on the increasing of HOMO level. In addition, by the change of

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the carbon atom on the ADI unit in P2 (P2a) to a more strongly electron-withdrawing nitrogen atom in P3 (P3a), which can lower the HOMO/LUMO energies markedly, and have a little influence on the energy gap. In conclusion, these results reveal that the improved molecular planarity and the increased electron-withdrawing ability of electron-deficient unit both can tune the HOMO/LUMO levels and energy gaps. An ideal conjugated polymer donor35 should have an appropriate HOMO energy (-5.4 eV) and a narrow band gap (1.5 eV). Then the LUMO energy of an ideal polymer donor would be around -3.9 eV. In order to guarantee the exciton dissociation at donor/acceptor interface and the electron effectively transfer from donor to acceptor, the LUMO level of donor material should be at least 0.3 eV higher than the LUMO level of acceptor material.3 With the ideal polymer donor as the donor of organic solar cell, the LUMO level of acceptor should be below -4.2 eV. What’s more, air instability of the acceptor can seriously suppress the electron transfer process because the susceptibility of the charge carriers is easy trapping under ambient conditions. Marks and co-workers found that the LUMO level should be below -4.0 eV32 relative to the vacuum level for air stable electron transporting semiconductors in OSCs and organic transistors. From Figure 2, based on the requirement above (LUMO level < -4.0 eV), the designed copolymers of P3 and P3a are air-stable acceptors in the surrounding environment. Likewise, P3 and P3a may be applied to the organic transistors. PC61BM is the most used acceptors in OSCs with the LUMO energy level of -4.3 eV.36,37 With the LUMO level of ideal donor, P3, P3a and PC61BM are suitable

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acceptors for OSCs. The cells may have larger Voc with P3 or P3a as acceptors than that of PC61BM on account of the energy difference between the HOMO of the donor and the LUMO of the acceptor in direct proportion to the Voc. From the molecular orbital plots (see Figure 3) of all the copolymers, the HOMOs are delocalized over the backbone with π character, while the LUMOs are π antibonding orbitals which are mainly localized on the electron-deficient units. As can be seen in Figure 3, the S0 → S1 (HOMO → LUMO) electronic transitions of these copolymers are intramolecular charge transfer, where the electrons transfer from the electron-rich unit to the electron-deficient unit.

3.3. Light Absorption For OSCs, we generally think that the light absorption property of the donor plays a crucial role on the Jsc.29,31 However, the absorption properties of the acceptors, especially the light absorption in the visible-near infrared region, also are very important for the Jsc of the OSCs.11 The Jsc can be expressed38 ∞

J sc = q ∫ Sun ( λ ) × η ( λ ) × ϕ IQE ( λ ) d λ 0

(1)

In this equation, Sun(λ) is the number of incident photons with wavelength λ per unit area, η(λ) is the light-absorbing efficiency of the photoactive layer (a phase-separated donor/acceptor blend layer), and ϕIQE (λ) stands for the internal quantum efficiency. From eq (1), one can see that Jsc is directly affected by the light-absorbing efficiency of the active layer. Hereon, the analysis of the light-absorbing efficiency of the acceptor is necessary because it is directly related to the light-absorbing efficiency of the active layer. The expression of light-absorbing efficiency can be written as:39

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η ( λ ) = 1 − 10 − f

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(2)

In this equation, f is the oscillator strength of the acceptor associated to a certain wavelength (λ). Hereon, we considered the η(λ) at the absorbing position of the lowest transition absorption peaks (S0 → S1) and the second absorption peaks for those copolymer acceptors. In general, in order to capture sunlight to the largest extent, the donor should exhibit a narrow band gap between 1.2 and 1.9 eV.40 However, for OSCs, the mismatch of the donor absorption band and the acceptor absorption band is not beneficial to the solar light harvest, which will result in low light-absorbing efficiency and low photoelectric conversion efficiency.11 For instance, Li and his coworkers11 found that the Jsc of the classical P3HT/PC61BM solar cell is limited by the mismatch of the P3HT visible absorption band and weak visible absorption of PC61BM. Furthermore, they found that Jsc of the P3HT/PC71BM ([6,6]-Phenyl-C71-butyric acid methyl ester) solar cell can be improved with PC71BM as the acceptor in comparison with P3HT/PC61BM cell. This is due to that PC71BM has stronger and wider light absorption in the visible region than that of PC61BM. In other words, the matching of the P3HT absorption band and PC71BM absorption band is better than that of P3HT and PC61BM. Therefore, an acceptor should have a strong and wide absorption spectrum in visible-near infrared region for matching the absorption band of donor to improve the performance of OSCs. Then we emphatically study the optical properties of these D-A copolymers (P1-P3, P1a-P3a). For all the copolymers, the light-absorbing parameters were calculated with

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TD-PBE0/6-31G** method on the basis of the optimized ground state structures at HSE06/6-31G** level. The excitation energy, oscillator strength, light absorption efficiency, electronic transition type and main configuration are listed in Table 5 (considering the first 25 excited states). As can be seen in Table 5, the calculated absorption peaks (594, 369 nm for P1, 723, 398 nm for P1a) reproduce the experimental data well (598, 34119 nm for P1, 697, 39126 nm for P1a). The absorption spectra of the investigated copolymers and fullerene acceptors are presented in Figure 4. In Figure 4, there are two noticeable absorption peaks (f > 0.2) of these copolymers (except P3) in the visible and near-infrared regions. From Figure 4a, one can see that the light absorption range of fullerene acceptors (PC61BM and PC71BM) are mainly located in the ultraviolet light region, which may result in low light-absorbing efficiency of the active layer (donor/fullerene acceptor blending layer) because of the mismatch of the donor absorption band and the absorption band of fullerene acceptors (In general, the light absorption range of donors are mainly located in the visible and near-infrared region.). Nevertheless, the simulated absorption spectra of the reported copolymer acceptors (P1 and P1a) have better light-absorbing abilities in the visible and near-infrared region in comparison to that of fullerene acceptors (Figure 4a). In OSCs, the substitution of P1 and P1a for the fullerene acceptors is likely to enhance the solar light harvest. Moreover, comparing the absorption spectrum of P1 (P1a) with that of newly designed copolymers P2-P3 (P2a-P3a) shows that the absorption peaks of the designed copolymers yield a significantly red shift. The positions of maximum absorption peak are 594, 680 and

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673 nm for P1 (f = 0.868), P2 (f = 1.410) and P3 (f = 2.018) in the visible region, respectively. The calculated light absorption efficiencies are 0.864 (P1), 0.946 (P2) and 0.990 (P3), respectively. For the second absorption peaks, the locations are 369 nm (f = 0.2150) and 374 nm (f = 2.067) for P1 and P2, respectively. The light-harvesting efficiencies are 0.390 (P1) and 0.993 (P2). For P1a-P3a, the positions of maximum absorption peak are 723, 779 and 802 nm for P1a (f = 1.883), P2a (f = 1.836) and P3a (f = 2.679) in the visible-near infrared region. The calculated light-absorbing efficiencies are 0.987 (P1a), 0.985 (P2a) and 0.998 (P3a), respectively. The second absorption peaks of P1a-P3a are respectively at 398 nm (f = 1.324), 427 nm (f = 3.341) and 419 nm (f = 2.665). The corresponding light-absorbing efficiencies are 0.953 (P1a), 0.999 (P2a) and 0.998 (P3a), respectively. The above-mentioned calculated results show that P2-P3 and P2a-P3a can yield a more intense and a broader light absorption in the visible and near-infrared region compared with that of P1 and P1a, which result in a better spectral overlap with the donor absorption spectrum. That could provide a more efficient light absorption of the active layer for enhancing Jsc in organic solar cell applications. Furthermore, the results demonstrate that the introduction of ADI unit and PQD unit to replace NDI unit can markedly enhance intramolecular π-conjugation and improve the light-absorbing efficiencies. From Table 5, one can see that the strong transition absorptions of all copolymers in the visible-near infrared range are corresponding to the electronic transitions from

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HOMO to LUMO, HOMO to LUMO+3, HOMO to LUMO+4, and so on. To better understand the electronic transition movement, the electron density difference diagrams of the electron transitions are listed in Figure 5. Moreover, in order to illuminate how the introduction of electron-deficient units of ADI and PQD into the place of NDI unit influences the intramolecular charge transfer characters of these copolymers, we calculate the electron transfer distance and the overlap between the regions of density depletion and increment.41 For the sake of calculating the two parameters, the total electron density of initial and final states, and their centroids should be calculated. The total density difference between the initial and final states (∑

∂α →β

) can be expressed as the sum of molecular orbital transitions incorporating

each participating excitation, α→β.31,41 ∂α → β =

Cα2 → β

∑ Cα

(ρ

α

2

− ρβ )

(3)

→β

Cα→β denotes the orthogonal coefficient of the TD-DFT equation. ρα and ρβ denote the

electron densities of each participating molecular orbital relevant to the transitions.

ρ r = ∑ η i ϕi ( r ) = ∑ ηi C j ,i χ i ( r ) 2

i

2

(4)

i

Where ηi represents the occupation number of orbital i, and χ denotes basis function. C

is the coefficient matrix, the element of ith row jth column is equivalent to the expansion coefficient of orbital j with respect to basis function χ. The electron density difference between the initial and final states is the linear combination of various electron transition models. All the calculated results could be carried out with cubman utility that provided by the Gaussian 09 and Multiwfn42 programs. Next, two functions ρ+(r) and ρ-(r) are used to define the increase and decrease of the density due to the 17



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electronic transition. The centroids of the spatial regions can de defined by ρ+(r) and ρ- (r), can be expressed as:41

C+ = ( x+ , y+ , z+ ) =

∫ r ρ ( r ) dr ∫ ρ ( r ) dr

(5)

∫ r ρ ( r ) dr ∫ ρ ( r ) dr

(6)

+

+

and C− = ( x− , y− , z− ) =

−

−

The charge transfer distance (l) can be written as:

l = C+ − C−

(7)

Based on the above-mentioned equations, the parameters of these acceptors are calculated and the calculation results are listed in Figure 5. Hereon, we mainly elaborate the influence of improving planarity of molecular backbone and increasing electron-withdrawing ability of electron-deficient unit on the electron transfer process by replacing NDI unit with ADI unit and PQD unit. As shown in Figure 5, for the S0 → S1 electronic transitions of all the copolymers are the transition of HOMO → LUMO, and the corresponding electron transfer direction is from the electron-rich units to electron-deficient units. In Figure 5, the calculated data show that the S0 → S1 electron transfer distances (l) are increased from P1a to P3a, the order is P1a (11.817 Å) < P2a (13.238 Å) < P3a (19.206 Å). For the second absorption transitions of

P1a-P3a, the electron transfer distances are in the sequence P1a (2.471 Å) < P2a (16.425 Å) < P3a (17.911 Å). In addition, the overlap (Λ) between the regions of density depletion and increment are also listed in Figure 5. For P1a-P3a, the extents of overlap (S0 → S1) decrease in the order P1a (0.5626) > P2a (0.5203) > P3a (0.2965).

18


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Likewise, the overlap extents of the second absorption transitions for P1a-P3a are in the sequence P1a (0.8860) > P2a (0.4198) > P3a (0.4005). By comparing the results of P1a and P2a, one can see that the improvement of molecular planarity can facilitate the charge separation and significantly increase the electron transfer distance. Moreover, the increased electron-withdrawing ability of the electron-deficient unit can further contribute to the enhancement of electron transfer distance and the charge separation by comparing the results of P2a and P3a. There is a similar tendency for these properties of P1-P3. Compared to that of the reported copolymers (P1 and P1a), the efficient electron movement of newly designed copolymers can ensure their efficient light absorption because of the light absorption efficiency in connection with the efficiency of electron density movement.31 In conclusion, from the above-mentioned analysis, the improved molecular planarity and the increase of electron-withdrawing ability of electron-deficient unit are both beneficial to the enhancement of light-harvesting efficiency of these copolymer acceptors.

3.4. The electron-harvesting ability of acceptors Generally, the working mechanism of photocurrent generation in an OSC consists of four main steps:43,44 (1) the donor of the active layer harvest the photons to generate excitons, (2) the excitons diffuse to the donor/acceptor interface, (3) the bound excitons dissociate at the donor/acceptor interface to form free charges (hole and electron), (4) free charge transport towards corresponding electrodes and collection by the electrodes. According to the conversion mechanism of light-to-electricity in OSCs, after photo-excitation in donors, the generated excitons

19



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are dissociated free charges at the donor/acceptor interface to realize the electron transfer from donor to acceptor. Therefore, the efficient electron transfer which from donor to acceptor evidently plays a crucial role in the process of photoelectric conversion. In OSCs, the high electron-affinity molecules as acceptors (like PC61BM) have proven to be an effective way for speedy exciton dissociation at the donor/acceptor interface.9,45,46 Thus, the electron affinities of acceptors are an important parameter to assess the ability of excition separation at the donor/acceptor interface. Hereon, it’s essential to investigate the electron affinities of the reported and designed copolymers in this work. The calculated vertical electron affinities (EAv) and adiabatic electron affinities (EAa) for all copolymers are listed in Table 6. For the acceptors, it is advantageous for the separation of excition at the donor/acceptor interface based on the high electron affinities (EAv/a) in organic solar cells. In addition, many papers34,47,48 have reported that the EAv is a positive correlation with molecular LUMO level. As shown in Table 6, the order of values of EAv/EAa is P1 < P2 < P3. Similarly, for P1a-P3a, the sequence of values of EAv/EAa is P1a < P2a < P3a. As for P1-P3 and P1a-P3a, the changed trends of EAv values are consistent with that of the variation of their LUMO levels (see Figure 2). Finally, these results manifest that: (1) the improved molecular planarity is conducive to the exciton separation at the donor/acceptor interface, (2) the increase of electron-withdrawing ability of electron-deficient unit for copolymers, which can further strengthen exciton dissociation ability at the donor/acceptor

20


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interface.

3.5. Performance of acceptor in the intermolecular electron transport In OSCs, the generated charges (hole and electron) will be transported along with the donor and acceptor to the respective electrodes in the back of the dissociation of the excitons at the donor/acceptor interface. A high electron mobility of acceptor material in electron transport process facilitates to enhance Jsc of organic solar cell devices by reducing the charge recombination.9 In general, there are two typical models for evaluating carrier (hole or electron) motion in materials, such as the incoherent hopping model and coherent band model.49 In room temperature, the charge transport of organic materials can be generally described as hopping process.50 For OSCs, the charge transfer rate (kCT) is an important parameter for evaluating the performance of carrier motion. Hereon, the charge transfer rate can be estimated by Marcus theory based on the eq (8):50,51

1  2  π  2 exp  −γ kCT = ν  4K T  h  γ K BT B    

)

(

(8)

Where KB is the Boltzmann constant, T is the temperature (298.15 K), γ is the reorganization energy, ν is the charge-transfer integral between the two adjacent molecular segments, and h is the reduced Planck’s constant. According to the eq (8), the parameters of ν and γ are direct correlation with the charge transfer rate. Therefore, the analyzing of these two parameters is very necessary here.

3.5.1. Charge-transfer Integral The charge transfer integral of the adjacent segments can be calculated by the Marcus-Hush model at room temperature.50 In this work, we just calculate the 21



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Page 22 of 56

electron transfer integral since the electron transfer integral (ν) is more important than the hole transfer integral for the acceptors. And the ν is calculated as:50

ν=

EL +1 − EL 2

(9)

EL and EL+1 are the energies of LUMO and LUMO+1 of the adjacent neutral optimized acceptor molecules, respectively. As is well-known, the way of the intermolecular stacking for polymers can significantly influence the charge transfer integral.50,52 However, the accurate prediction of intermolecular π-stacking ways for polymers are still a great challenge in theory. Up to now, many reports33,52,53 have shown that the face-to-face π-stacking with a large orbital overlap possesses a major contribution to the intermolecular charge transport for organic semiconductors, which is beneficial to enhance the electronic coupling. Hereon, we only comparatively investigate the intermolecular electron transport properties of these copolymers by considering the π-stacking ways in the direction of face-to-face between the adjacent molecules. The stacking model of adjacent molecules is listed in Figure S3. Herein, the calculated values of ν only make a qualitative comparison for the reported and designed copolymer acceptors. The newly designed copolymer acceptors (except P2a) have larger ν values compared with P1 and P1a (see Table 7). In particular, the ν values of P3 and P3a achieve 0.1170 and 0.0761 eV, respectively. This result reveals that the good molecular planarity which can enhance the intermolecular π stacking and electronic coupling.

3.5.2. Reorganization Energy Generally, the reorganization energies includes the inner reorganization energy and 22


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the external reorganization energy, with the inner reorganization resulting from the changes of molecule geometry when the electron transfer takes place, and the external reorganization energy arising from changes in the surrounding medium that couple with the charge transfer.43 When the medium contribution to the relaxation energy as the result of the solvent polarization effect is neglected (such as in the solid film), we usually only consider the inner reorganization energy.54,55 Many papers have reported that the charge transfer rate has a clear relation to the inner reorganization energy.56,57 Therefore, we mainly study the inner reorganization energy of the copolymers in this paper. The inner reorganization energy for electron (γ) can be defined by eq (10):57

γ =  E0− − E−  +  E−0 − E0 

(10)

Where E0 and E－ stand for the energies of neutral and anion segments in their lowest energy geometries, respectively. E－0 denotes the energy of neutral segment at anion －

state, and E0 is the energy of anion segment with the neutral optimized geometry. As can be seen in Table 7, the γ values of all the investigated copolymers (P1-P3, P1a-P3a)

based

on

a

trimer

model

are

smaller

than

that

of

tris(8-hydroxyquinolinato)aluminum(III)58 (Alq3, γ = 0.276 eV) which is a typical electron transport material. This means that their electron transfer rates may be higher than that of Alq3. As illustrated in Table 7, the values of γ are 0.163, 0.102 and 108 eV for P1-P3, 0.105, 0.086 and 0.90 eV for P1a-P3a, respectively. The γ values of newly designed copolymers are all smaller the corresponding reported copolymers (P1 and P1a). In comparison of P2 (P2a) with P1 (P1a), the result shows that the improved coplanarity

23



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of polymer backbone can markedly reduce the reorganization energy. In addition, the

γ values of P3 (P3a) are close to that of P2 (P2a). It indicates that the increase of the electron-withdrawing ability of electron-deficient unit has little effect on γ values. Therefore, the improved coplanarity of polymer backbone for the copolymers is an effective way to enhance the reorganization energy.

3.5.3. Electron mobility We only calculate the electron mobility (µ) here because the electron motion plays a major role in the acceptors according to the photoelectric conversion mechanism of OSCs. From the Einstein relation, the electron mobility can be calculated as:

µ=

eD K BT

(11)

Where KB is the Boltzmann constant, T represents the temperature (298.15 K), D is the charge diffusion constant, and e is the electronic charge. For a d-dimensional system, D is defined as the ratio between the mean-square displacement and the diffusion time.59 In a spatially isotropic system, D can be approximately defined by:60,61

1 x (t ) D = lim t →∞ 2d t

2

≈

1 2d

∑r k p 2

i

i

(12)

i

i

Where d and i represent the spatial dimension and a specific hopping pathway with ri being the electron hopping distance, respectively. Hereon, p = ki i

∑ ki

is the electron

hopping probability to the neighbor units. When only considering two adjacent molecular fragments (trimer model), D can be simply defined as:62,63

D =

1 kCT r 2 2 24


(13)

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Where kCT is the charge transfer rate, and r denotes intermolecular centre-to-centre distance (see Table 7 and Figure S2a-S2f). The electron mobility (µ) is expressed as:31,61

er 2 µ= kCT 2 K BT

(14)

The calculated transfer rates and electron mobilities of all the copolymers are listed in Table 7, respectively. As shown in Table 7, the orders of the charge transfer rates for P1-P3 and P1a-P3a are P1 < P2 < P3 and P2a < P1a < P3a, respectively. The calculated electron mobilities of P1-P3 and P1a-P3a are in the order P1 (2.005×10−4 cm2·v-1·s-1) < P2 (2.8516 cm2·v-1·s-1) < P3 (6.3093 cm2·v-1·s-1) and P2a (2.1651 cm2·v-1·s-1) < P1a (3.1638 cm2·v-1·s-1) < P3a (3.4935 cm2·v-1·s-1), respectively. Hereon,

one

can

see

that

the

calculated

electron

mobilities

of

P1

(2.005×10−4 cm2·v-1·s-1) and P1a (3.1638 cm2·v-1·s-1) are good agreement with the experimental data (2×10−4 cm2·v-1·s-1 for P119 and 0.85 cm2·v-1·s-1 for P1a64). Based on eq (14), the above-mentioned results (see Table 7) show that the electron mobilities of these copolymers are mainly determined by the charge transfer rates (kCT) instead of intermolecular centre-to-centre distance (r). As can be seen in Table 7, the charge transfer rate of P2a is smaller than P1a. From the eq (8), we find that the charge transfer rates of the copolymer acceptors (P1a and P2a) are mainly influenced by electron transfer integral (ν) in two parameters of ν and

γ. The ν value of P1a is larger than that of P2a, resulting in the smaller charge transfer rate of P2a than P1a. And then it makes the electron mobility of P1a larger than that of P1a. Compared with P1a, the ν value of P2a is smaller, due to the weak π-π stacking 25



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of adjacent segments (in Figure S3), which hinders the intermolecular electronic coupling. Likewise, the poor molecular coplanarity of P1 impedes the intermolecular electronic coupling, which makes the electron mobility of P1 (2.005×10-4 cm2⋅v-1⋅s-1) decreased by four orders of magnitude in comparison to other copolymers (P2, P3, P1a-P3a). The high electron mobility contributes to the charge separation at donor/acceptor interface, and effectively hinders the charge recombination. Among all the copolymers, P3/P3a possess the highest electron mobilities, and they can be the candidates for electron transporting materials of OFETs and acceptor materials of organic solar cells.

3.6. Light-absorbing properties of the donor/acceptor active layers As is well-known, Jsc is one of three key parameters (Voc, Jsc and FF) affected the PCE of organic solar cell device. It is very meaningful to analyze the light-absorbing performance (such as light absorption intensity and range) of the active layer because it is directly related to the Jsc of organic solar cell. Based on the eqs (1) and (2), one can see that the light absorption range and intensity of the active layer has a significant impact on the Jsc. The optical parameters (see Table 8) of these donor/acceptor active layers were calculated with TD-PBE0/6-31G** method on the basis of the optimized ground state structures at HSE06/6-31G** level. Hereon, we only investigated the donor/acceptor active layers of PSEHTT/P1 (reported by Jenekhe19), PSEHTT/P2 and PSEHTT/P3 in order to save the computational cost and time. For the donor copolymer (PSEHTT),

26


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the electronic absorption peak (602 nm, see Table 8) were computed at TD-PBE0/6-31G**//HSE06/6-31G** level with a dimer model agrees well with the experimental data (579 nm).65 In general, there are a mass of possible configurations in modeling any 3D organic conductor on account of the multitudinous of the donor/acceptor stacking ways. To date, many studies50,66 have reported that the face-to-face stacking model is beneficial to the improvement of the intermolecular electronic coupling. Moreover, the computational cost is quite large and time-consuming while considering all of the configurations. The aim of this work is only to qualitatively evaluate the light-absorbing performance of the active layers. As a result, we only take into account the ideal face-to-face model (in Figure S3) of donor/acceptor active layers in this work, which consists of an oligomer donor (dimer) and an oligomer acceptor (trimer). For these donor/acceptor active layers, the calculated excitation energies, oscillator strength, light absorption efficiencies, electronic transition types and main configurations are listed in Table 8 (considering the first 35 excited states). The absorption spectra of these active layers and the donor PSEHTT are presented in Figure 6. As can be seen in Table 8 and Figure 6, the designed donor/acceptor active layers (PSEHTT/P2 and PSEHTT/P3) have a red-shift and strong light absorption in comparison with that of PSEHTT/P1. This is due to the fact that P2 and P3 possess stronger and wider light absorption in the vision and near-infrared region compared with P1. Moreover, the PSEHTT/P2 and PSEHTT/P3 have stronger and wider light absorption by compare with the donor PSEHTT, while the maximum light absorption

27



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peak of PSEHTT/P1 is blue-shifted. These results reveal that the absorption properties of the acceptors are directly influence on the light-absorbing performance of the donor/acceptor active layers. As a consequence, the acceptors with excellent light-absorbing properties can markedly improve the light-absorbing performance of the donor/acceptor active layers. By the eq (2), the calculated light-absorbing efficiencies of PSEHTT/P1-PSEHTT/P3 are shown in Table 8. Compared with PSEHTT/P1, with much better light-harvesting performances of PSEHTT/P2 and PSEHTT/P3 in the vision region are beneficial to the improvement of Jsc. Finally, the results indicate that the introducing of the ADI unit and PQD unit to replace the NDI unit in the copolymers can observably improve light-harvesting performances of the active layers. And that could noticeably enhance Jsc of organic solar cells. Furthermore, the calculated total densities of states (TDOS) and projected densities of states (PDOS) (see Table 9) elaborate what fragments are involved in the electronic transition orbitals of the active layers. As shown in Table 8, the main electronic transitions of all donor/acceptor active layers in the visible region are corresponding to HOMO-2 to LUMO, HOMO to LUMO+3, HOMO-3 to LUMO and so on. According to Table 8 and 9, we can see that not only the donors take part in the electronic transition absorption of the active layers, but also the acceptors clearly involve in them. Therefore, the optical absorption performance of the acceptor is very important for the improvement of the light-absorbing performance of the donor/acceptor active layer in OSCs.

4. Conclusion 28


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In this work, to clarify the issue that how the improved molecular planarity and the increased electron-withdrawing ability of electron-deficient unit influence the electronic and optical properties, exciton separation efficiencies at donor/acceptor interface and carrier transport properties of the D-A copolymer acceptors, we studied and compared their HOMO/LUMO levels, light-absorbing efficiencies, electron affinities as well as electron mobilities for the reported and designed copolymer acceptors by the quantum chemical methods and Marcus theory. Based on the calculated results, by comparing of P2 with P1, it can be found that the improved coplanarity between electron-rich unit and electron-deficient unit of the copolymer not only extends the intramolecular π-conjugation, and yields a stronger and broader light absorption in the visible and near-infrared region, but also enhances the light-absorbing efficiency, exciton separation efficiency at donor/acceptor interface and electron mobility. Furthermore, by contrast of P3 with P2 (and P2a with P3a), increasing the electron-withdrawing ability of electron-deficient unit can further enhance the exciton separation efficiency at donor/acceptor interface, and the electron mobility among the interchains. Hereon, our calculations also demonstrate that the light absorption properties of the acceptors are very important for the light-absorbing performance of the active layers as similar as that of the donors. In our designed compounds, the copolymers (P3/P3a) have strong and wide light absorption, high light-absorption efficiencies and the best exciton separation abilities as well as the largest electron mobilities among all the copolymers, indicating that they show high potential as candidates for acceptor materials of organic solar cells. This study

29



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presents us with a designed guideline for designing efficient copolymer acceptors for organic solar cell applications.

ASSOCIATED CONTENT Supporting Information. The results (Figure S1-S3) are not provided in the main text. This material is available free of charge via the Internet at http://pubs.acs.org.

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Molecular Model of the P3HT/PCBM Interface. J. Phys. Chem. C 2011, 115, 2406-2415.

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Table 1. The HOMO energy levels (eV) obtained in the gas phase with B3LYP, PBE0 and HSE06 methods at 6-31G** basis set. Here, “M’’, “D’’ and “P’’ represent monomer, dimer and trimer, respectively. Oligomer B3LYP PBE0 HSE06 Exp. (HOMO) M1 -6.28 -6.56 -6.16 D1 -6.03 -6.30 -5.92 -5.77 P1 -5.95 -6.21 -5.82 M1a -5.65 -5.91 -5.54 D1a -5.49 -5.74 -5.40 -5.36 P1a -5.43 -5.68 -5.33

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Table 2. The absorption peaks (λ, in nm) and energy gaps (Eg,TD, in eV) of S0 → S1 obtained in the gas phase with B3LYP, PBE0 and HSE06 methods at 6-31G** basis set on the basis of the optimized geometries (trimer model) at HSE06/6-31G** level, respectively. B3LYP PBE0 HSE06 Method λa Oligomer Εg,TD λ Εg,TD λ Εg,TD λ

a

P1

1.97

P1a

1.58

629 367 783 419

2.09 1.71

594 369 723 398

1.95 1.52

Experimental values

41


636 392 814 425

598 341 697 391


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Table 3. The selected bond length L (Å) and dihedral angles φ (°) of all these monomers (see Figure S1a) calculated at HSE06/6-31G** level. M1

M1a

M2

L C2-C3

L 1.469

C4-C5

1.463 1.442

φ C1-C2-C3-C4 S1-C4-C5-C6

M2a

C2-C3

37.06 -19.95

1.458

C4-C5

C1-C2-C3-S1

M3a

1.453

1.448 1.441

2.86

2.17 -12.61

L 1.454 1.443

C1-C2 C5-C6

φ 45.94

M3

φ 16.90

S1-C4-C5-C6

-15.08 17.58

N1-C1-C2-C3 C4-C5-C6-S1

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Table 4. The calculated HOMO Eg,TD. All energies are in eV. Compounds P1 HOMO -5.82 LUMO -3.87 Eg,TD (S0 → S1) 2.09

and LUMO energy levels, and S0 → S1 energy gap P2 -5.54 -3.98 1.82

P3 -5.86 -4.25 1.84

P1a P2a -5.33 -5.25 -3.81 -3.93 1.71 1.59

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P3a -5.43 -4.20 1.55


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Table 5. Calculated excitation energy, oscillator strength (ƒ > 0.2), light absorption efficiency η(λ) and main configurations of all these copolymers. λexp denotes the experimental absportion peaks. Excitation energy f Main Transition η(λ) λexp (eV and nm) configuration (nm) P1 2.09 594 0.868 H→L (84%) 0.864 598 S0 → S1 3.36 369 0.215 H-6→L (15%) S0 → S17 0.390 341 H-7→L (10%) H-8→L (24%) P2 1.82 680 1.410 H→L (93%) S0 → S1 0.961 3.32 374 2.067 H→L+3 (67%) S0 → S24 0.991 S0 → S1 0.990 P3 1.84 673 2.018 H→L (93%) P1a 1.71 723 1.883 H→L (83%) S0 → S1 0.987 697 3.12 398 1.324 H→L+4 (68%) 0.953 391 S0 → S12 P2a 1.59 S0 → S1 779 1.836 H→L (87%) 0.985 2.90 427 3.341 H→L+3 (64%) S0 → S15 0.999 P3a 1.55 802 2.679 H→L (81%) S0 → S1 0.998 2.96 419 2.665 H-8→L (12%) S0 → S20 0.998 H→L+3 (38%) H→L+4 (22%)

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Table 6. EAv (vertical electron affinities) and EAa (adiabatic electron affinities) of all the copolymers. P1 P2 P3 P1a P2a P3a EAv 2.91 3.14 3.41 2.99 3.17 3.40 EAa 2.98 3.19 3.44 3.05 3.22 3.43

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Table 7. Computed transfer integrals ν (eV), inner reorganization energies γ (eV), electron transport rates kCT (×1013 s-1), intermolecular distances r (Å) and electron mobilities µ (cm2⋅v-1⋅s-1) of all the trimer models. ν kCT r (cala) r (expb) µ (cal) µ (exp) γ -4 -4 P1 0.0008 0.163 5.4511×10 4.35 4.20 2.005×10 2×10-4 P2 0.0766 0.103 11.259 3.61 2.8516 P3 0.1178 0.108 24.774 3.62 6.3093 P1a 0.0750 0.105 10.487 3.94 3.1638 0.85 3.93 P2a 0.0589 0.086 8.5960 3.60 2.1651 P3a 0.0761 0.090 13.493 3.65 3.4935 a b cal denotes calculated values, exp denotes experimental values.

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Table 8. Calculated excitation energies, oscillator strength (ƒ > 0.4), light absorption efficiencies η(λ) and main configurations of the donor (PSEHTT) and these active layer materials (PSEHTT/P1-PSEHTT/P3). Excitation energy f Main Transition η(λ) (eV and nm) configuration PSEHTT 2.06 602 3.82 H→L (93%) S0 → S1 2.87 432 0.52 H-1→L+1 (88%) S0 → S5 PSEHTT/P1 2.11 587 3.02 H-2→L (35%) S0 → S8 0.9990 H→L+3 (44%) H-3→L (9%) 2.15 577 1.12 H-3→L (35%) S0 → S9 0.9241 H-2→L (42%) H→L+3 (11%) S0 → S7 0.6020 PSEHTT/P2 1.81 685 0.40 H-2→L (75%) H-1→L+2 (13%) 2.05 603 3.32 H→L+3 (81%) S0 → S10 0.9995 PSEHTT/P3 2.06 602 3.64 H→L+3 (75%) S0 → S11 0.9998 H-3→L (13%) 2.09 594 0.66 H-3→L+1 (74%) S0 → S12 0.7822

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Table 9. The molecular orbital compositions (%) of donor segments and acceptor segments for all donor/acceptor active layers. Active layer Orbital Donor Acceptor H-3 6 94 H-2 96 4 PSEHTT/P1 H 99 1 L 0 100 L+3 100 0 H-2 7 93 H-1 98 2 PSEHTT/P2 H 99 1 L 1 99 L+2 1 99 L+3 99 1 H-3 21 79 H 97 3 PSEHTT/P3 L 2 98 L+1 1 99 L+3 99 1

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Figure Captions Figure 1. Molecular structures of the reported and designed copolymers. Figure 2. Schematic energy levels of the copolymers (P1-P3, P1a-P3a), ideal donor and PC61BM. Figure 3. HOMO and LUMO orbital diagrams for all copolymers. Figure 4. Simulated absorption spectra of all trimer models (P1-P3, P1a-P3a), and the experimental absorption spectra of PC61BM and PC71BM. Figure 5. Electron density difference plots of electronic transition for these copolymers (P1-P3, P1a-P3a). Figure 6. Simulated absorption spectra of these donor/acceptor active layers and the donor PSEHTT.

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Figure 1. Molecular structures of the reported and designed copolymers.

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Figure 2. Schematic energy levels of the copolymers (P1-P3, P1a-P3a), ideal donor and PC61BM.

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HOMO

Page 52 of 56

LUMO

P1

P2

P3

P1a

P2a

P3a

Figure 3. Electron density plots of HOMO and LUMO for all these copolymers (trimer model) computed at HSE06/6-31G** level.

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(a)

(b) Figure 4. Simulated absorption spectra of all the copolymers (P1-P3, P1a-P3a), and the experimental absorption spectra11 of PC61BM and PC71BM.

53



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P1 S0 → S1, l = 8.753, Λ = 0.5481

S0 → S17, l = 0.596, Λ = 0.9936

P2 S0 → S1, l = 10.257, Λ = 0.5442

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P3 S0 → S1, l =10.958, Λ = 0.3374

S0 → S25, l = 6.045 Λ = 0.8376

P1a S0 → S1, l = 11.817, Λ = 0.5626

P2a S0 → S1, l = 13.238, Λ = 0.5203

P3a S0 → S1, l = 19.206, Λ = 0.2965

S0 → S12, l = 2.471, Λ = 0.8860

S0 → S15, l = 16.425, Λ = 0.4198

S0 → S20, l = 17.911, Λ = 0.4005

Figuer 5. Electron density difference plots of electronic transition for the copolymers (trimer model). l is the electron transfer distance (Å), Λ denotes the overlap between the regions of density depletion and increment. Electron densities transfer from light green area to purple area.

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Figure 6. Simulated absorption spectra of these donor/acceptor active layers and the donor PSEHTT.

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Table of content Image The design of a series of non-fullerene D-A copolymer acceptors.

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Theoretical Strategy To Design Novel n-Type Copolymers Based on

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