The electronic structures and optical properties of fullerene derivatives for organic solar cells: The number and size effects of fullerene-cage

Accepted Manuscript The electronic structures and optical properties of fullerene derivatives for organic solar cells: The number and size effects of fullerene-cage Yang Zhang, Cai-Rong Zhang, Li-Hua Yuan, Mei-Ling Zhang, Yu-Hong Chen, ZiJiang Liu, Hong-Shan Chen PII:

S0254-0584(17)30811-8

DOI:

10.1016/j.matchemphys.2017.10.029

Reference:

MAC 20068

To appear in:

Materials Chemistry and Physics

Received Date: 12 December 2016 Revised Date:

28 September 2017

Accepted Date: 7 October 2017

Please cite this article as: Y. Zhang, C.-R. Zhang, L.-H. Yuan, M.-L. Zhang, Y.-H. Chen, Z.-J. Liu, H.S. Chen, The electronic structures and optical properties of fullerene derivatives for organic solar cells: The number and size effects of fullerene-cage, Materials Chemistry and Physics (2017), doi: 10.1016/ j.matchemphys.2017.10.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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ACCEPTED MANUSCRIPT

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The electronic structures and optical properties of fullerene derivatives for organic solar cells: the number and size effects of fullerene-cage Yang Zhanga, Cai-Rong Zhanga,b*, Li-Hua Yuana, Mei-Ling Zhanga, Yu-Hong Chena,b,

School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050,

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a

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Zi-Jiang Liuc, Hong-Shan Chend

China;

State Key Laboratory of Advanced Processing and Recycling of Non-ferrous Metals, Lanzhou University of Technology，Lanzhou, Gansu 730050, China;

d

Department of Physics, Lanzhou City University, Lanzhou 730070, China;

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c

College of Physics and Electronic Engineering, Northwest Normal University,

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Lanzhou, Gansu 730070, China.

*Corresponding author. Tel.: +86 0931 2973780, Fax: +86 0931 2976040

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b

E-mail address: [email protected] (C.R. Zhang).

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ACCEPTED MANUSCRIPT Abstract: As electronic acceptor materials in heterojunction, fullerene derivatives (FDs) can significantly affect the power conversion efficiency of organic solar cells (OSCs). Here, in order to investigate the number and size effects of fullerene-cage in

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FDs for OSCs, the geometries, electronic structures and related properties, as well as photovoltaic parameters of several FDs, including MP, PCBM, BP, TP and PC71BM, were analyzed based upon density functional theory (DFT) and time dependent DFT

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calculations. The results indicate that the fullerene-size is more important than the

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number of fullerene-unit to affect the local geometrical parameters, energy level alignments, hyper-polarizabilities, and optical absorptions in visible region. Furthermore, the lowest unoccupied molecular orbital (LUMO) energies are almost same for these FDs, and the orbital energies near frontier molecular orbitals for BP

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and TP exhibit two- and three-fold quasi-degenerate, respectively. The transition configurations and molecular orbitals reveal the absorption bands in visible region of MP, PCBM, PC71BM and TP are local excitations, and that of BP are charge transfer

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excitations. The similar open-circuit voltages and fill factors of OSCs based upon

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P3HT/MP, P3HT/PCBM, P3HT/BP, P3HT/TP, and P3HT/PC71BM blend films result from the similar LUMO energy levels of these FDs.

Keywords: fullerene derivatives, electronic structures, excited states, optical properties, organic solar cells

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1. Introduction Organic solar cells (OSCs) have great importance in the development of new generation solar cells due to its light weight, easy fabrication, flexibility, renewable

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materials, low cost, environmental-friendly characters, and so on [1-3]. Up to now, different architecture of OSCs, including layer by layer, bulk heterojunction (BHJ), and tandem configurations, had been presented. Whatever the architecture applied to

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fabricate OSCs, the organic blend of electron donor/acceptor (D/A) materials, also

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called active layer sometimes, plays the key role in the conversion from photon to electricity.

The power conversion efficiency (PCE) of OSCs at early stage was quite low. For instance, the PCE of OSCs based on fullerene was about 0.04% in 1993 [4]. To

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improve the PCE, many efforts have been done. Since the exciton utilization in bi-layer heterojunction OSCs is limited due to the insufficient exciton diffusion length relative to the active layer thickness [5], the development of BHJ OSCs solved this

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issue through the enhancement of exciton dissociation at D/A interfaces, and achieved

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7.13% of PCE [6]. One of the other routes for improving PCE would be the architecture variation, such as the development of invert device to fabricate tandem OSCs [7-9].

The fundamental issue to improve PCE of OSCs is to investigate the work

mechanisms. Up to now, it was recognized that the qualitative work mechanism of OSCs can be described as followings [2, 3, 10-12]: (i) the D/A blend heterojunction absorb sunlight photons with wavelength in its absorption band and then forms 3

ACCEPTED MANUSCRIPT excitons (bounded electron-hole pairs); (ii) then the excitons will diffuse to the D/A interface where the excitons dissociation lead to charge-separated states, and the driving forces for exciton dissociations, overcoming the exciton binding energies

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(EBE), originate from the energy level offsets for the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LUMO) between donor and acceptor [1, 13], respectively; (iii) the charge transfer (CT) complex, also called

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as CT state (CTS) under this condition, will be formed after the exciton dissociation at

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D/A interface, but the electron and hole pairs still under the influence of the Coulomb interaction; (iv) the CTS can separate into free charge carriers under the action of internal electric field provided by the work function difference of electrodes; (v) the free charge carriers will transport in corresponding organic materials, and the

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electrons and holes are collected by cathode and anode, respectively. Apparently, to increase the PCE of OSCs, the novel electronic acceptor and donor materials should be developed, with the expected properties, including broad and strong optical

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absorption in the visible and near infrared region, higher charge carrier mobility and

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suitable electron energy levels [1, 14]. The electron acceptor materials in OSCs can be classified as fullerene derivatives

(FDs) and non-fullerene conjugated systems [15]. The FDs are widely used electron acceptor materials in OSCs since the ultrafast photo-induced charge transfer (CT) was reported in MEH-PPV/C60 photovoltaic devices [16]. In recent years, a lot of FDs were reported for further improving the PCE of OSCs [17]. The commonly used electron acceptor in OSCs is [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), and 4

ACCEPTED MANUSCRIPT the 6.82% PCE was achieved by the OSCs based on P3HT/PCBM [18]. Phenyl C71 butyric acid methyl ester (PC71BM) replaced PCBM under the same test conditions for OSCs, and then about 50% higher current densities were obtained [19],

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highlighting the fullerene-cage size effects. Many other novel electron acceptor and donor materials have been designed and synthesized to improve PCE of OSCs, such as PBDD-FF4T/PC71BM (9.2% PCE) [20] and PTTBTz/ICBA (5.352% PCE) [21]. To

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date, the PCE of OSCs have achieved the threshold of commercial application (over

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than 10%) [22-25].

FDs with multi-fullerene C60 units were synthesized, and demonstrated that their photovoltaic properties are better than mono-fullerene derivative [26-28]. The typical example of FDs as electron acceptor includes MP (a mono-PCBM derivative), BP (a

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bis-PCBM derivative with a dumb-belled structure), and TP (a trimer-PCBM derivative). The OSCs were fabricated using P3HT as electron donor and the FDs MP, PCBM, BP and TP as electron acceptors, respectively, and the BP exhibited the best

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PCE value of 3.70%, even better than PCBM (3.22%) under the same experimental

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conditions [29].

In this work, in order to investigate the number and size effects of fullerene-cage in

FDs for OSCs, the geometries, energy level alignments, dipole moments, polarizabilities,

hyper-polarizabilities,

excitation

properties,

and

photovoltaic

parameters of MP, PCBM, BP, TP, and PC71BM were analyzed based upon density functional theory (DFT) and time dependent DFT (TDDFT) calculations. The chemical structures of FDs in this study are presented in Scheme S1 in Supplemental 5

ACCEPTED MANUSCRIPT Materials (SM). The results are helpful to understand different performance of OSCs based upon P3HT/MP, P3HT/PCBM, P3HT/BP, P3HT/TP, and P3HT/PC71BM blend films, but also favorable to design novel molecules for electronic acceptor materials in

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heterojunction of OSCs.

2. Computational details

Based upon DFT and TDDFT methods, the geometries, electronic structures,

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polarizabilities, hyperpolarizabilities and excitation properties of fullerene derivatives

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MP, PCBM, PC71BM, BP and TP were calculated without symmetry constraints using Gaussian 09 package [30]. The long-range corrected Coulomb-attenuating functional CAM-B3LYP [31] was adopted in the calculations for geometries, electronic structures, polarizabilities and hyperpolarizabilities.

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The basis sets can affect the accuracy of calculated results. For the calculations of polarizability and hyperpolarizability, in principle, the larger basis sets should be used to describe polarization effect. To check the basis sets effects, we carried out the

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examination of 6-31G(d,p) and 6-31+G(d,p) basis sets for the MP properties. The

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polarizability anisotropy invariant ∆α calculated with 6-31G(d,p) and 6-31+G(d,p) are 123.3 and 130.7 a.u., respectively, corresponding relative error about 5.7%. However, the computational CPU time for adding diffuse basis sets increases drmatically, from 3660 to 8340 minutes on our computing cluster. So the huge compuational costs hinder the application of diffuse function into basis sets for larger system, such as TP. On the other hand, it was demonstrated that 6-31G(d,p) basis sets were sufficient for calculating the excitation properties and electron density of organic molecules [32, 6

ACCEPTED MANUSCRIPT 33]. Hence, considering the accuracy and computational time, 6-31G(d,p) basis sets were adopted in the calculations of this work. To understand the absorption spectra details of FDs in this work which were

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measured in solution [29, 34], the excitation properties were calculated using TDDFT methods with solvent effects. Both the functional in TDDFT and solvent model can affect the accuracy of calculated results for excitation [35]. On the basis of polarizable

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continuum model (PCM) [36, 37] using the integral equation formalism model within

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the solvent reaction field, the SMD solvation model [38], which is based on the polarized continuous quantum mechanical charge density of the solute, was applied to take into account of solvent effects. It was found that CAM-B3LYP functional is superior to B3LYP and PBE0 functionals for the investigation of excitation properties

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for PC71BM [39]. To further check the reliability of CAM-B3LYP functional, we performed TDDFT calculations with CAM-B3LYP and B3LYP functionals for MP which was selected as representative system. The calculated maximum of absorption

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wavelength λmax with CAM-B3LYP and B3LYP functionals are 500 and 603 nm,

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respectively, corresponding experimental absorption maximum at about 495 nm [29]. Apparently, the calculations with the CAM-B3LYP functional generate more accurate excitation energies. Therefore, the CAM-B3LYP functional was adopted in TDDFT calculations to investigate the excitation properties of other FDs in this work.

3. Results and discussion 3.1. Molecular structures The optimized geometrical structures of MP, PCBM, PC71BM, BP and TP are 7

ACCEPTED MANUSCRIPT presented in Figure 1. In order to understand molecular structures conveniently, the optimized Cartesian coordinates of atoms in these FDs are given in SM. In this work, the moiety constructed by aromatic ring phenyl and butyric acid methyl ester (named

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as BM) is abbreviated as PBM. The geometries of MP and PCBM indicate that introducing methyl moiety into BM group generates negligible effects on the corresponding geometrical parameters. The spatial orientations between phenyl ring

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and BM in these FDs are similar to that of the “α type” chiral isomer for PC71BM [40].

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The total energy of PCBM with this spatial orientation is about 0.33 eV lower than that of the reported isomer [41] in which the BM moiety is rotated about 90° relative to the configuration in this work, and thus the PBM unit is nearer to C60 cage than that of the configuration in this work. To address the local geometrical structures between

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PBM moieties and fullerene cages, we defined three bonds and two angles which are labeled in Figure 2. Bond1 and bond2 in figure 2 are bridge bonds which link the PBM moiety and the adjacent edge between six-C rings (denoted as C6-6) in C60/70.

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The selected bond lengths, bond angles and dihedral angles of MP, PCBM, PC71BM,

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BP and TP are listed in Table S1 of SM. The data in table S1 indicate that the local geometrical parameters of fullerene derivatives based upon C60 are almost same, whereas the corresponding geometrical parameters are slightly different from PCBM and PC71BM. For instance, the bond1, bond2, and bond3 for fullerene derivatives based upon C60 are 1.509, 1.507, and 1.594 Å, respectively, while the corresponding values of PC71BM are 1.505, 1.508, and 1.602 Å, respectively. Also, the bond length of bond3 in PCBM agree well with that of B3LYP/6-31G(d) (1.600 Å [41], calculated 8

ACCEPTED MANUSCRIPT with Gaussian03 package) and B3LYP-D3/def2-SVP (1.616 Å [42], calculated with ORCA package) results. The geometrical analysis for these fullerene derivatives supports that the fullerene size (C60 versus C70) effects on local geometrical

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parameters are more significant than that of fullerene cage numbers (the fullerene cage numbers of MP, BP, and TP are 1, 2, and 3, respectively). The different geometrical parameters of these FDs result from the difference in chemical bond

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properties which is closely related to the orbital hybridization.

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3.2. Energy level alignment

Energy level alignment can affect the dynamics of exciton dissociation and electron-hole recombination at the organic heterojunction interface between electron donor and acceptor materials, and then affect the efficiency of OSCs. Figure 3 gives

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the selected molecular orbital (MO) energies, the HOMO and LUMO gaps (Eg) for MP, PCBM, PC71BM, BP and TP. It can be found that the HOMO and LUMO energies, as well as Eg of the different FDs based upon C60 are almost same, about

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-6.70, -2.00, and 4.70 eV, respectively. The negligible difference of calculated frontier

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orbital energies for the FDs based upon C60 agrees with the experimental LUMO energies measured using electrochemical cyclic voltammetry, where the LUMO energy differences among MP, BP, TP, and PCBM are smaller than 0.04 eV [29]. The experimental results of PCBM, mPCBM (a mono-[C60]fullerene derivative bearing a hydroxyl group [28]), and dPBCM (a [C60]fullerene dimer derivative with a hydroxyl group in the middle of the dumb-belled structure [28]) can also support this. However, the HOMO energy of PC71BM is higher about 0.20 eV than that of PCBM, and their 9

ACCEPTED MANUSCRIPT LUMO energies are almost same, resulting into a reduction of Eg. The orbital energies of these FDs underline that the fullerene size (C60 versus C70) effects on energy level alignment are more significant than that of fullerene cage numbers. Also, on the basis

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of the single-particle approximation, HOMO and LUMO energies can be adopted to approximate the oxidization and reduction potential, respectively. The similar HOMO (LUMO) energy of the FDs based upon C60 in this work means their oxidization

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(reduction) potential could be similar. The experimental reduction potential of MP, BP,

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TP, and PCBM support this [29]. Whereas, compared with the FDs based upon C60, in terms of Koopmans’ theorem, the higher HOMO energy of PC71BM induces the smaller value of oxidized potential. Furthermore, the same frontier MO energies of BP and TP also indicate the moieties between PCBM generate negligible effects on

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energy level alignment. Therefore, the orbital energies near frontier MOs for BP and TP are two- and three-fold quasi-degenerate, respectively, suggesting lack of effective interactions between PCBM units in BP and TP.

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3.3 Dipole moment, polarizability and hyper-polarizability

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Dipole moment can describe the intrinsic properties of molecule. Polarizability and hyper-polarizability characterize the ability of molecules to response the applied external electric field [43]. These quantities can determine many physical and chemical properties, such as nonlinear optical (NLO) properties and chemical activity. The tensor components of polarizability are defined as the second order derivatives of the total energy E with respect to the uniform external electric field F [43-45]: =

( )

, = , ,

(1) 10

ACCEPTED MANUSCRIPT The tensor components of polarizability αxx, αyy, αzz are interpreted as the main semi-axes of the molecular polarizability ellipsoid [44]. The definition for isotropic polarizability (mean polarizability) is the following formula [39, 43, 44, 46], +

+

(2)

The polarizability anisotropy invariant is ∆α =

#

"" ! $$

%

#( $$ !

and the hyper-polarizability β [47] is

β x = β xxx + β xyy + β xzz β y = β yyy + β yzz + β xxy β z = β xxz + β yyz + β zzz

&

/%

(3)

(4)

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β = β x2 + β y2 + β z2

)

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! ""

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α=

(5) (6) (7)

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where the βijk are the tensor components of hyperpolarizability ( = , , ). The calculated isotropic polarizability α, the polarizability anisotropy invariant ∆α,

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dipole moment D, and the hyper-polarizability β of MP, PCBM, PC71BM, BP and TP are listed in table 1, and the calculated tensor components of polarizabilities and

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hyper-polarizabilities for these fullerene derivatives are given in table S2 in SM. The experimental isotropic polarizabilities of C60 and C70 are 517±54 a.u. [48]

and

589±95 a.u. [49], respectively. Therefore, the isotropic polarizabilities of these FDs are larger than that of the corresponding pristine fullerenes since the introduced moieties which attached on fullerene cage break the fullerene’s symmetry and modify their electronic structures. The polarizability of MP is slightly larger than that of PCBM, indicating the role of terminal moiety. The ∆α is determined by the anisotropy 11

ACCEPTED MANUSCRIPT of molecular structure and electron density. The ∆α and α values of PC71BM are about 41 and 109 a.u. larger than that of PCBM, respectively, because the symmetry reduction of fullerene cage by enlarging the fullerene cage from C60 to C70 enhances

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electron delocalization, resulting into an increase of polarizabilty [50]. The calcualted ∆α of PCBM is very close to that of HSE/6-31G(d) result (about 616.9 a.u. [44]). The ∆α and α values of PCBM in this work are slightly larger than that of B3LYP/3-21G*

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results (∆α=96.90 a.u. and α=577.70 a.u. [46]) due to the different computational

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methods. Similarly, the ∆α and α values of PC71BM are less than that of B3LYP/6-31G(d,p) results (∆α=233.16 a.u. and α=789.07 a.u. [40]). TP has the largest values of α and ∆α due to its trinity character of moelcuar structure. Furthermore, it can be found that the α values of MP, BP, and TP almost linearly depend on the

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number of fullerene cage. One possible reason for larger values of α may be the lower compactness structure which is responsible for the larger α of [70]PCBM isomers [40]. Another possible reason would be, due to the negligible effects of the moieties which

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connect PCBM units on electronic structures, the increase of PCBM units enhance the

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electron delocalization, and thus result into strong response for the external field. The hyper-polarizability of PC71BM is significantly larger than those of MP, BP, TP and PCBM, emphasizing the importance of cage size effects. The hyper-polarziability of BP is the smallest due to the symmetry induced by its dumbbell structure. The difference of hyper-polarizability between MP and PCBM highlights the terminal moiety effect. The dipole moment of PC71BM is slight larger than those of MP, PCBM, and TP due to the ellipsoid character of C70, while the smallest dipole moment 12

ACCEPTED MANUSCRIPT of BP can be understood from the cancel effect of two PCBM units. The smaller molecular diople moment can reduce the inter-molulecar interaction, then affect packing-mode

of

morphology,

and

further

influence

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charge-transport/exciton-diffusion properties. Overall, the size of fullerene cage is more important than the number of fullerene cage to affect hyper-polarizability, whereas the number of fullerene cage generate more signifcant effects on α, and the

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smallest dipole moment and hyper-plolarizability of BP mean the effects of molecuar

3.4 Excitation properties

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structure and fragment orientation.

The UV-Vis absorption properties are very important to exposure the excitation properties of electronic acceptor/donor materials in heterojunction of OSCs. The

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simulated absorption spectra of MP, PCBM, PC71BM, BP and TP are presented in Figure 4. The experimental absorption spectra are well reproduced by calculations. For instance, the lowest singlet excitation energies of calculated results for PCBM, BP,

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and TP are 2.48 eV, corresponding experimental values 2.49, 2.53, and 2.55 eV [29],

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respectively. Also, the calculated absorption λmax of PC71BM are 462 and 363 nm, agreeing well with that of experiment (462 and 372 nm [34]). Both the experiment [29] and calculations indicate that, the absorption bands with lower excitation energy in the visible region is enhanced from MP/PCBM to BP and then to TP, supporting that the covalent linkage of fullerene derivatives could significantly influence the absorption performance [28]. This is resulted from their electronic structures and PCBM units. Also, the calculations (see figure 4) and experiment [34] demonstrated 13

ACCEPTED MANUSCRIPT that the absorption coefficient of PC71BM in visible region is significantly higher than that of fullerene derivatives based on C60, since C70 fullerene cage break the Ih symmetry of C60, and then some prohibited transitions in C60 become to the permitted

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transitions in C70 under the given excitation energy region, leading to the better light harvesting capability of PC71BM. This is also approved by experimental works [13, 51].

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To analyze the details of excitation properties, table 2 lists the calculated electronic

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transition configurations with coefficients larger than 10%, excitation energies (in eV) and wavelengths (in nm, λ>400 nm), oscillator strengths ( f>0.001 ) for singlet excited states of MP, PCBM, PC71BM, BP and TP. The more detailed data are given in Table S3 in SM. In terms of the data in tables 2 and S3, it can be found that the energy level

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alignments of excited states for MP, PCBM, BP and TP are almost same, and the excited states of BP and TP are doublet and triplet degenerated, respectively. This again underlines their similar electronic structures and the absence of effective

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interaction between PCBM units in BP and TP. The corresponding MOs related to

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transitions are checked in order to understand the transition character. The isodensity plots of the HOMO and LUMO of these fullerene derivatives are presented in figure 5, and the isodensity plots of more MOs are available in figures S1 and S2 in SM. Figure 5 indicates that both the HOMO and LUMO of these fullerene derivatives are mainly located on fullerene cages, and the little contribution of HOMO come from the atomic orbital of the bridge carbon which links the C60/70 and side chain. The character of these frontier MOs agree well with other work in references [39, 41, 46, 52, 53]. For 14

ACCEPTED MANUSCRIPT MP and PCBM, the absorption band at about 500 nm is dominated by π-π* local excitations since the HOMO and LUMO involved in transitions are mainly localized in fullerene cage, and the absorption bands from 408 to 422 nm are also local

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excitations due to the character of MOs related to the main transition configurations. PC71BM exhibits more abundant absorption bands with larger oscillator strength than that of MP, PCBM, BP and TP because of the reduced symmetry of C70. The

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PC71BM’s MOs involved in transitions also suggest the local excitation character. The

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transitions at about 500 and 408-422 nm for BP and TP are quite different. The character of MOs related to transitions for TP exhibits local excitation, whereas the relocation of MOs for BP between initial and final states in transitions suggests the CT character. CT excitations can generate intra-molecular CT excitons, but also

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charge density variations, and further induce current density in terms of charge

r r r ∂ρ dV , where J , S, ρ , t, V are current density, conservation law ( ∫∫ J ⋅ dS = − ∫∫∫ S V ∂t

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surface area, charge density, time, and volume, respectively). Furthermore, it should be noticed that, for these fullerene derivatives, PBM moieties don’t have any

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contribution to the MOs involved in transitions of visible absorption bands. Therefore, it can be inferred that PBM moiety doesn’t directly take part in photoelectric conversion process, but in improving the solubility of the fullerene derivatives to affect morphology in processing, and in adjusting the HOMO and LUMO levels to influence electron/hole dynamics at heterojunction interfaces. It should be mentioned that the experimental absorption spectra of MP, PCBM, BP, and TP reported absorption bands at about 690 nm (1.80 eV) with small absorption 15

ACCEPTED MANUSCRIPT coefficient. This type absorption peak was called as mono-adduct of C60 peak by Francois Diederich et.al because the peak was not observed from bis-adduct of C60 in their work [54]. The UV-vis absorption spectra of PCBM, mPCBM, and dPCBM also

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reported a small peak at about 700 nm, which was assigned as the feature of [6,6]-addition on C60 [28]. However, it is regretted that these experiments didn’t further check the origin of the absorption peak at about 700 nm. On the other hand,

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the singlet absorption λmax in CAM-B3LYP functional results for MP, PCBM, BP and

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TP with the lowest excitation energy are at about 500 nm, and thus the corresponding excitation energies are 0.68 eV higher than that of experiment at about 690 nm. The B3LYP functional results for MP generate same tendency. In order to check the origin for this absorption, the triplet TDDFT calculations were performed for these fullerene

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derivatives. The first triplet excitation energies calculated with CAM-B3LYP functional for MP, PCBM, BP and TP are about 1.57 eV, and the corresponding value of PC71BM is about 1.31 eV. The energy differences for MP, PCBM, BP and TP

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between the calculated excitation energies of the first triplet excited states and the

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experimental small absorption peak at about 690 nm are about 0.23 eV. Considering the performance of TDDFT calculations in this kind of spin flip transition [55, 56], the calculated results are reasonable. Therefore, the experimental small absorption peaks at about 690 nm for MP, PCBM, BP and TP may come from the triplet excitations. The analysis of transition configurations and MOs suggest that the first triplet transitions for MP, PCBM, PC71BM and TP are local excitations, while that of BP is CT excitation. 16

ACCEPTED MANUSCRIPT The

EBE

is

an

important

physical

quality

to

determine

the

charge-separation/exciton-dissociation in solar cells [57]. The EBE for an isolated system can be obtained as the difference between the electronic and optical gap [58].

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The Eg is the electronic gap, while the optical gap comes from the first singlet excitation energy [57, 59]. In terms of calculated Eg and the optical gap, the EBE of MP, PCBM, BP and TP are 2.22 eV, while the EBE of PC71BM is 2.12 eV,

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highlighting the size effects of fullerene cage on EBE. The smaller EBE is favorable

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for exciton dissociation in heterojunction, and it also benefits to CT from the excited molecules to the adjacent molecules with lower energy states. So, the smallest EBE of PC71BM is favorable to the candidate as the electronic acceptor for OSCs. 3.5 Photovoltaic parameters

PCE =

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The PCE of OPVs is determined by the following formula VOC × J SC × FF Pin

(8)

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where Voc is the open-circuit voltage, Jsc is the short-circuit current density, FF is the fill factor, and Pin is the incident light power density. The Voc can be calculated using

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the equation as follow [60, 61]:

q()*+ + ∆)) = ,-.-/ − 12.-3

(9)

here ∆V is the sum of the voltage losses in OSCs, HOMOD is the donor HOMO level and LUMOA is the acceptor LUMO level, q is electric charge. Apparently, if MP, PCBM, BP, TP and PC71BM are applied as electron acceptor and the same electron donor material is adopted to fabricate OSCs, the VOC must be very similar since the LUMO of these fullerene derivatives are almost same. The experimental VOC of OPVs 17

ACCEPTED MANUSCRIPT based upon P3HT/PC71BM is about 0.60 V (weight ratio w/w 1:1) [62], and the VOC of OPVs fabricated with P3HT/MP, P3HT/PCBM, P3HT/BP, and P3HT/TP are 0.57, 0.58, 0.56 and 0.56 V, respectively [29]. Therefore, both the theoretical and

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experimental VOC suggest that the fullerene cage and size in these fullerene derivatives as electron acceptor materials for OSCs generate negligible effects on VOC.

The short-circuit current density JSC can be determined using the following

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formula[63, 64], J SC = q ∫η (λ )η EDηCTηCC S (λ )dλ

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(10)

Where q, η(λ), ηED, ηCT, ηCC, S(λ) are charge, light absorption efficiency, exciton-diffusion efficiency, CT efficiency, charge-collection efficiency, and the number of photons given by the solar spectrum over all frequencies, respectively. The

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experimental JSC for P3HT/MP, P3HT/BP, P3HT/TP, and P3HT/PCBM blend films are 8.61, 10.34, 6.93, and 8.45 mA·cm-2, respectively [29]. According to absorption spectra of these fullerene derivatives in visible region, the order of η(λ) is

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PC71BM>TP>BP>MP≈PCBM. However, apart from the intrinsic properties of

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molecules in heterojunction of OSCs, the parameters ηED and ηCT can be determined by packing model of morphology, and the ηCC depends on the interaction at interface between active layer and substrate. So, the parameters ηED, ηCT, ηCC are beyond the single molecular scheme. The better performance of BP was attributed to the aggregation of fullerenes through covalent bonds [29]. The FF can be approximated as [65-67] FF =

voc − ln(voc + 0.72) voc + 1

(11) 18

ACCEPTED MANUSCRIPT where voc is the dimensionless voltage, which can be calculated using the following equation [68], voc =

qVOC nk BT

(12)

RI PT

where kB, T, and q are Boltzmann constant, temperature, and the elementary charge respectively, n is the ideality factor of the diode. In terms of equations (11) and (12), FF is mainly determined by VOC. Therefore, the FF of OSCs based on P3HT/MP,

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P3HT/PCBM, P3HT/BP, P3HT/TP, and P3HT/PC71BM might be very similar due to their similar VOC. The experimental results of FF for P3HT/MP, P3HT/BP, P3HT/TP,

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and P3HT/PCBM blend films are 55.8%, 63.9%, 63.4%, and 65.7%, respectively [29], supporting the tendency deduced from equations (8) and (9).

4. Conclusion

In this work, in order to investigate the number and size effects of fullerene-cage of

TE D

FDs applied as electronic acceptor materials in OSCs, the geometries, energy level alignments, dipole moments, polarizabilities, hyper-polarizabilities, excitation

EP

properties, and photovoltaic parameters of MP, PCBM, BP, TP, and PC71BM were analyzed based upon DFT and TDDFT calculations. On the basis of the calculated

AC C

results that agree the available experimental work, it can be found that, 1) The geometries of these FDs exhibit that the fullerene size effects on local geometrical parameters are more significant than that of fullerene cage numbers, though molecular geometries are mainly determined by local interaction. 2) The orbital energies of these FDs indicate that the fullerene cage size effects on energy level alignment are more important than that of fullerene cage numbers. Furthermore, the orbital energies near frontier MOs for BP and TP are two- and 19

ACCEPTED MANUSCRIPT three-fold quasi-degenerate, respectively, due to the absence of effective interactions among PCBM units in BP and TP. 3) The size of fullerene cage is also more important than the number of fullerene

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cage to affect hyper-polarizability, whereas the number of fullerene cage generates more significant effects on isotropic polarizability, and the α values of MP, BP, and TP almost linearly depend on the number of fullerene cage.

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4) The size of fullerene cage has more remarkable effects than the number of

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fullerene cage on the absorption coefficients and EBE. The enhancement of optical absorption in the visible region from MP to PCBM, BP and then to TP result from electronic structures and the PCBM units. The transition configurations and MOs suggest the absorption bands in visible region of MP,

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PCBM, PC71BM and TP are local excitations, and that of BP are CT excitations. Furthermore, the experimental small absorption peaks at about 690 nm for MP, PCBM, BP and TP may come from the triplet excitations.

EP

5) The similar VOC and FF of OPVs based upon P3HT/MP, P3HT/PCBM, P3HT/BP,

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P3HT/TP, and P3HT/PC71BM blend films result from the similar LUMO energy levels of the FDs.

Acknowledgement This work was supported by the National Natural Science Foundation of China (Grant No. 11164016). The authors were grateful to the high-performance computing platform of Lanzhou University of Technology. The authors were also appreciative of 20

ACCEPTED MANUSCRIPT National Supercomputing Center in Shenzhen.

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9857-9865.

30

ACCEPTED MANUSCRIPT

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Table 1. The calculated isotropic polarizability α, the polarizability anisotropy invariant ∆α, dipole moment D, and the average hyper-polarizability β of MP, PCBM, PC71BM, BP and TP. The unit of D is Debye.The other quantities are given in atomic units (a.u.). MP PCBM PC71BM BP TP α 645 595 704 1229 1813 ∆α 119 123 164 222 267 D 1.414 1.363 1.516 0.723 1.416 β 83 62 349 22 69

31

ACCEPTED MANUSCRIPT Table 2. The calculated electronic transition configurations with coefficients (>than 10%), excitation energies (in eV) and wavelengths (in nm, λ>400 nm), oscillator strengths ( f>0.001 ) for singlet excited states of MP, PCBM, PC71BM, BP and TP.

BP

S1

H→L(91%)

500/2.48

0.0040

S9

H-4→L+1(56%);H-2→L+2(29%)

422/2.94

0.0016

S10

H-3→L+2(53%);H-4→L+1(18%);H→L+2(14%)

410/3.02

0.0023

S11

H→L+2(52%);H-1→L+1(24%);H-3→L+2(14%)

408/3.04

0.0025

S1

H→L+1(49%);H→L(22%);H-2→L(13%)

520/2.38

0.0092

S2

H→L(67%);H→L+1(19%)

491/2.53

0.0379

S3

H→L+2(71%);H-1→L(13%)

462/2.69

0.0509

S4

H-1→L(80%);H→L+2(10%)

455/2.73

0.0119

S5

H-2→L(56%);H-1→L+2(22%)

445/2.79

0.0272

S6

H-1→L+1(62%);H-2→L+2(11%)

S7

SC

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f

442/2.81

0.0805

H-2→L+1(30%);H-1→L+2(29%);H→L+1(16%)

439/2.83

0.0515

S8

H-3→L+1(43%);H→L+3(19%);H-2→L+2(16%)

430/2.89

0.0024

S9

H-2→L+1(41%);H-1→L+2(23%);H-2→L(21%)

426/2.91

0.0052

S11

H-3→L(80%)

411/3.02

S12

H-4→L(55%)

402/3.08

0.0022 0.0025

S1

H→L(91%)

500/2.48

0.0040

S9

H-2→L+2(29%);H-4→L+1(56%)

422/2.94

0.0016

S10

H-3→L+2(53%);H-4→L+1(18%);H→L+2(14%)

410/3.02

0.0023

S11

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PCBM

E(nm/eV)

H→L+2(52%);H-1→L+1(25%);H-3→L+2(14%)

408/3.04

0.0024

S1 S2 S17 S18

H-1→L+1(38%);H→L(27%);H→L+1(22%) H-1→L(48%);H→L+1(30%);H→L(12%) H-8→L+2(24%);H-9→L+2(21%);H-4→L+4(15%) H-9→L+3(24%);H-8→L+3(21%);H-5→L+5(13%); H-5→L+4(10%) H-7→L+4(20%);H-6→L+5(20%) H-7→L+5(24%);H-6→L+4(24%) H-1→L+5(25%);H→L+4(25%);H-2→L+2(13%); H-3→L+3(12%)

500/2.48 500/2.48 422/2.94 422/2.94

0.0031 0.0048 0.0019 0.0012

410/3.02 410/3.02 408/3.04

0.0014 0.0031 0.0050

S1

H-2→L(90%)

500/2.48

0.0036

S2

H-1→L+1(90%)

500/2.48

0.0042

S3

H→L+2(91%)

500/2.48

0.0040

S25

H-14→L+3(56%);H-8→L+6(29%)

422/2.94

0.0014

S26

H-12→L+5(55%);H-6→L+8(29%)

422/2.94

0.0015

S27

H-13→L+4(55%);H-7→L+7(29%)

422/2.94

0.0017

S28

H-11→L+6(49%);H-14→L+3(17%);H-2→L+6(13%)

410/3.02

0.0012

S29

H-10→L+7(50%);H-13→L+4(17%);H-1→L+7(13%)

410/3.02

0.0032

S30

H-9→L+8(53%);H-12→L+5(18%);H→L+8(14%)

410/3.02

0.0023

S31

H-1→L+7(48%);H-4→L+4(23%);H-10→L+7(13%)

408/3.04

0.0028

S32

H-2→L+6(32%);H→L+8(18%);H-5→L+3(15%)

408/3.04

0.0050

AC C

S19 S20 S21

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PC71BM

transition configurations

EP

MP

states

TP

32

ACCEPTED MANUSCRIPT Figure captions Figure 1. The optimized geometrical structures of MP, PCBM, PC71BM, BP and TP. The hydrogen atoms are omitted for clarity. The PBM moieties in BP and TP are also labeled (The color of circles denotes C, H, O with gray, light gray, red, respectively).

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Figure 2. The definition of selected bonds and angles in PCBM moiety (the Hydrogen and other atoms in fullerene cage are omitted for clarity)

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Figure 3. The calculated molecular orbital energies and HOMO-LUMO gaps (in eV) at the CAM-B3LYP/6-31G(d,p) level in chloroform solution. The orbital energies of BP and TP are two- and three-fold quasi-degenerate, respectively. Therefore, the more orbital energies of BP and TP are not further labeled in the figure.

M AN U

Figure 4. The absorption spectra of MP, PCBM, PC71BM, BP and TP. (a) the absorption spectra of these five fullerene derivatives; (b) the absorption spectra of MP, PCBM, BP and TP. The 0.15 eV of half width at half-maximum is applied for simulating absorption spectra.

AC C

EP

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Figure 5. Isodensity plots (isodensity contour =0.02 a.u.) of the frontier molecular orbitals of MP, PCBM, PC71BM, BP and TP.

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ACCEPTED MANUSCRIPT PCBM

M AN U

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BP

PC71BM

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MP

AC C

EP

TE D

TP

Figure 1.

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RI PT

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AC C

EP

TE D

Figure 2.

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AC C

EP

TE D

Figure 3.

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ACCEPTED MANUSCRIPT b

AC C

EP

TE D

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Figure 4.

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a

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ACCEPTED MANUSCRIPT Molecule

HOMO

LUMO

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MP

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PCBM

AC C

EP

BP

TE D

PC71BM

TP

Figure 5.

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ACCEPTED MANUSCRIPT The geometrical characters of MP, PCBM, PC71BM, BP and TP are calculated. The energy level alignments of MP, PCBM, PC71BM, BP and TP are compared. The dipole moments, polarizabilities and hyperpolarizabilities are studied.

RI PT

The excitation properties of MP, PCBM, PC71BM, BP and TP are analyzed.

AC C

EP

TE D

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The photovoltaic performance of MP, PCBM, PC71BM, BP and TP are discussed.