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J. Phys. Chem. C 2008, 112, 19158–19161
First Principle Calculations of the Electronic Properties of the Fullerene Derivative as an Electron Acceptor in Organic Solar Cells Zhuxia Zhang,†,‡ Peide Han,†,‡ Xuguang Liu,†,§ Junfu Zhao,†,‡ Husheng Jia,†,‡ Fangui Zeng,| and Bingshe Xu*,†,‡ Key Laboratory of Interface Science and Engineering in AdVanced Materials (Taiyuan UniVersity of Technology), Ministry of Education, Taiyuan 030024, P.R. China, College of Materials Science and Engineering, Taiyuan UniVersity of Technology, Taiyuan 030024, P.R. China, College of Chemistry and Chemical Engineering, Taiyuan UniVersity of Technology, Taiyuan 030024, P.R. China, and College of Mining Engineering, Taiyuan UniVersity of Technology, Taiyuan 030024, P.R. China ReceiVed: August 14, 2008
The electronic parameters of fullerenes are essential for their potentials used as active layers in organic solar cells. Two isomeric forms of the C60 ([5,6] fulleroid and [6,6] methanofullerene), named [60] PCBM (phenylC61-butyric acid methyl ester) clusters, were calculated using the B3LYP method with the 6-31G(d) basis set. It has been found that the contraction of C6-6 double bonds is favorable for addition. The first adiabatic electron affinity (AEA) for [60] PCBM is similar to that for C60. The energy gaps between the highestoccupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) of [60] PCBM have been reduced compared with C60. PCBM derivatives show an increased level of LUMO of fullerenes. From the natural charge populations, it has been found that adding a PCBM unit onto the C60 cages does not change the charge populations remarkably; attaching a PCBM has no effect on the electronic structures of C60. The results of theoretical calculation suppose that PCBM is not involved in the process of photoelectric conversion, but it plays a key role in adjusting the level of HOMO-LUMO for increasing photoelectric conversion efficiencies. 1. Introduction Organic solar cells are of the so-called polymer/fullerene bulk heterojunction (BHJ) type.1–3 The state-of-the-art in the field of organic photovoltaics is currently represented by BHJ solar cells based on poly(3-hexylthiophene) (P3HT) and the fullerene derivative [6,6]-phenyl-C61-butyric acid methyl ester (PCBM), with reproducible efficiencies approaching 5%.4–6 This lack of n-type semiconductors has, to a degree, impaired progress toward solution-processed organic complementary circuits. To this end, a primary challenge is to discover or to develop some air-stable n-type semiconductors with better solubility. Due to their high electron affinity and ability to transport charges effectively, fullerenes have been considered as ubiquitous acceptors. However, without a better soluble property, fullerenes are incompatible with solution-based processing. To improve solubility, a normal way is to prepare derivatives by adding some soluble functional groups onto fullerenes. Although chemical functionalization of fullerenes can improve the solubility in various organic solvents and enhance the processability, it simultaneously gives rise to the change of the specific electron properties based on a highly delocalized state on the surface of fullerene, which is a fully p-conjugated nanomolecule. As it has been suggested somewhere,7 introducing a functional group onto fullerene should result in a conversion of the sp2 carbon into an sp3 one, which directly * Corresponding author. Tel/Fax: +86-0351-6010311. E-mail: xubs@ tyut.edu.cn. † Key Laboratory of Interface Science and Engineering in Advanced Materials. ‡ College of Materials Science and Engineering. § College of Chemistry and Chemical Engineering. | College of Mining Engineering.
interferes with p-conjugation of the fullerene sphere. More recently, it has been noted that placing electron-donating substituents on the phenyl ring of PCBM can raise the LUMO of PCBM, which allows further optimization of the open-circuit voltage (Voc) of polymer/[60]fullerene organic solar cells.8 However, an emerging question is whether the [60] PCBM and C60 differ in their reactivity. In addition to the challenge of addressing this issue, it is of fundamental importance to determine the impact induced by attaching a functional group onto fullerene. Thus, it is worth investigating the effects on the geometric and electronic structures of fullerenes after introducing some functional groups. A further motivation for testing new soluble C60 derivatives is to develop a fundamental relationship between the structure and the property, so that a design guideline can be obtained for improving the performance of fullerene derivatives used as acceptors in the solar cells. In this paper, the effects of functionalized units on the chemical and physical properties of fullerenes have been studied. To clarify the geometrical and electronic features of [60] PCBM, theoretical calculations were carried out. Considering that the system of substituted fullerene derivatives is relatively large and has a restriction for using the ab initio accurately, density functional theory (DFT) techniques were applied for the geometry optimizations at B3LYP9 levels by using the Gaussian 03 program.10 2. Computational Details All isomers were optimized at the B3LYP/6-31G(d) level of density functional theory. Due to the large size of the structures, frequency calculations were carried out at B3LYP/STO-3G. Structure, stability, the energy gaps between the HOMO and
10.1021/jp8089825 CCC: $40.75 2008 American Chemical Society Published on Web 11/07/2008
Electronic Properties of the Fullerene Derivative
J. Phys. Chem. C, Vol. 112, No. 48, 2008 19159
Figure 1. B3LYP/6-31G(d) optimized molecular structures (in Å). M1 and M2 are the addition products across the [6,6]-junction, F1 and F2 are the addition products across the [5,6]-junction. M2 and F2 are obtained by rotating the phenyl 90° relative to the C60 unit.
LUMO, the first adiabatic electron affinity (AEA), and the natural atomic charges have been calculated to aid further experimental investigations. All calculations were carried out with the Gaussian 03 program. 3. Results and Discussion 3.1. Stability and Geometric Structure. Covalent attachment of a Cs symmetrical PCBM moiety to C60 can afford two different isomeric products, the addition to the [6,6]-junction bond ([6,6] refers to the bond at the junction of a six-membered ring with another six-membered ring) and the [5,6]-junction bond of C60. The optimized results indicate the addition of PCBM across the [6,6]-junction produces a closed methanofullerene (Figure 1, M1) and across the [5,6]-junction results in an enlarged fullerene (an open fulleroid) (Figure 1, F1). The phenyl is perpendicular to the surface of C60 in both M1 and F1. As shown in Figure 1, there are two other isomers M2 and F2 obtained by rotating the phenyl 90° relative to the C60 unit, in which the phenyl is parallel to the surface of C60. All structures have been constrained to Cs-symmetry in the calculations. At the B3LYP/6-31G(d) theoretical level (by symmetry Ih), there are only two types of C-C bonds for C60 with corresponding distances of 1.453 Å at the [5,6] ring junctions (labeled as C5-6) and 1.395 Å at the [6,6] ring junctions (labeled as C6-6), respectively. Both C6-6 and C5-6 bonds particularly refer substituted C-C bonds in this paper. The C6-6 bond length between the two sp3 carbons of C60 is about 1.600 Å in M1, which is in good agreement with that of the [6,6] closed isomers, 1.57-1.61 Å, in the crystal structures of methanofullerene derivatives of C60, reported in the literature,11–13 and longer than a normal Csp3-Csp3 single bond. However, in F1, the C5-6 bond length is about 2.148 Å, which is clearly longer than that of the [6,6] closed isomer. From Figure 1, it can be seen that the four bonds (highlighted in black) by connecting the PCBM group and the carbon cage pop out from the C60 cage. Compared with the original bond lengths in C60, the four bonds are elongated about 3.7%, while all the other bond lengths of the derivations are only less than 1% from their parent C60 cage. Therefore, the influence of adding the PCBM group on the C60 cage is mainly localized in the region of four bonds near the C6-6 and C5-6 bonds. The bridge angle is about 89.2° at the sp2 carbon in the [5,6] open unit and about 62.2° at the sp3 carbon in the [6,6] closed unit. In the cases of M2 and F2, as the phenyl is rotated to be parallel to the surface of C60, the steric hindrance between PCBM and C60 has been reduced. Thus, the PCBM unit is nearer to C60 compared with M1 and F1. Meanwhile, the variation of fullerene derivatives, as illustrated in Figure 1, is mainly focused on the region around the connections between the PCBM group
TABLE 1: Symmetry, Total Energies ET (a.u.), HOMO-LUMO ∆Eg (eV), Computed Binding Energies (Ebin, kcal/mol)a, Lowest Vibrational Frequencies (ω1/cm-1), and AEA (kcal/mol) for C60 and Its Derivatives Ebin AEA symm ET (a.u.) ∆Eg (eV) (kcal/mol)a ω1b (cm-1) (kcal/mol) C60 M1 M2 F1 F2
Ih Cs Cs Cs Cs
-2286.17 -2902.29 -2902.32 -2902.27 -2902.31
2.76 2.55 2.56 2.65 2.64
s 52.22 33.60 65.78 43.75
271.36 -67.46 3.26 -19.39 -68.93
48.28 46.27 44.90 46.19 45.80
a On the basis of eq (C60 + PCBMf[60]PCBM + H2.) B3LYP/STO-3G.
b
At
and the C60 cage. Due to the larger stereoelectronic interaction, the distances of C6-6 and C5-6 bonds in M2 and F2 are slightly longer than those in M1 and F1. However, a steric interaction is negligible to other regions of C60 since they are far away from PCBM. The bond lengths are almost kept as constant on the surface of C60 except for those bonds near to the C6-6 or C5-6 bonds. Usually, 1,2-additions are observed across a [6,6]-ring junction, which possesses a higher electron density than the [5,6]ring junction. The driving force of addition reactions to C60 mainly depends on the relief of strain energy stemming from the curved surface of fullerene and the deviation from the planarity of the C60 double bonds. This is confirmable that the energies of [6,6] closed isomers M1 and M2 are 13.56 and 10.15 kcal/mol, respectively, which are thermodynamically stable compared with those obtained from [5,6] open derivatives F1 and F2. M2 is the most stable isomer with the lowest total energy of -2902.32 a.u., which is lower than that of M1, F1, and F2 with a relative difference value of 18.83, 31.38, and 6.28 kcal/ mol, respectively, and it is a minimum on the potential energy surface with zero imaginary frequency (NImag ) 0). The calculated HOMO-LUMO energy gaps of M1, M2, F1, and F2 are 2.54, 2.56, 2.64, and 2.65 eV, respectively. Generally, fulleroid is a kinetically controlled product as it has a larger energy gap, whereas methanofullerene is a thermodynamic product. Most of the [5, 6] open derivatives undergo a conversion into the thermodynamically stable [6,6] derivatives through a thermal,14 an electrochemical,15 or a photochemical process.16 From the above discussion, it can be concluded that the most stable derivative of monofunctionalized fullerene PCBM, for the design of donor-acceptor arrays, is unequivocally the [6,6] closed fullerene. The DFT optimized results are in agreement with the photostability data obtained from experiment.6 Table 1 gives symmetry, total energy, HOMO-LUMO energy gap, binding energy, the lowest vibrational frequencies, and the first AEA for C60, M1, M2, F1, and F2, respectively.
19160 J. Phys. Chem. C, Vol. 112, No. 48, 2008
Figure 2. Kohn-Sham HOMO and LUMO levels of the C60, methanofullerene, and fulloid as predicted at the B3LYP/6-31G(d) level.
3.2. Adiabatic Electron Affinity. There is a conversion of sp2 into sp3 carbon when introducing a functional group onto fullerene, and this probably affects p-conjunction of the fullerene sphere. The fullerene core in these [6,6] closed isomers is affected by a loss of 2π-electrons, compared to pristine C60. Converting the fullerene core into such a 58π-electron system subsequently leads to an alteration of the electron accepting properties of the fullerene derivatives. In this study, the first AEA for the derivatives was computed using the B3LYP/631G(d) to examine the electron accepting ability. By adding one electron to the neutral molecule and taking the difference between their total energies of equilibrium geometry, the evaluation of the first AEA can be given by
EAEA)E[60] PCBM-E[60] PCBM-1 From the above formula, the first AEA calculated for methanofullerene M1 is 46.27 kcal/mol, which is smaller than that for parent C60 (48.28 kcal/mol). Meanwhile, with a similar tendency, the first AEA was calculated for four isomer ranges from 44.90 to 46.27 kcal/mol. This suggests that the addition of PCBM onto C60 will alter its electron-accepting ability, but this effect is little and almost negligible. 3.3. Computed Binding Energy. The stability of neutral [60] PCBM clusters with respect to their constituent parts can be estimated by their binding energy, which can be calculated by
Ebin)E([60]PCBM) + E(H2)-E(PCBM)-E(C60) The Ebin values for M1, M2, F1, and F2 range among 33.60-65.78 kcal/mol, indicating that four derivatives have a significantly endothermic nature for the formation. Due to the steric effect of bulky substituents, the addition position is somewhat strained, thus C60 is destabilized after chemical modification by PCBM. This result also can be validated by a narrower HOMO-LUMO energy gap and the bond length as
Zhang et al. well as the torsion of PCBM. For example, the C-C bond length is about 1.509 Å in a normal cyclopropane (the B3LYP/631G(d) value), while the bond lengths in cyclopropane of [60] PCBM are remarkably elongated (shown in Figure 1). On the other hand, PCBM is the farthest from C60 and has the largest torsion angle of 107.11° for M1. The above results indicate that there is apparently a weak interaction between PCBM and C60. 3.4. Energy Gap. The energy gap of the C60 cage is 2.76 eV; however, the values have been reduced to 2.55-2.65 eV for [60] PCBM isomers. They are all kinetically relatively stable species with a HOMO-LUMO energy gap >1.0 eV. It can be concluded that PCBM derivatives are not only solution processable due to the solubilization property of the side chain but also changeable in the level of LUMO for fullerenes. Figure 2 shows Kohn-Sham HOMO and LUMO levels of C60, methanofullerene, and fulloid as predicted at the B3LYP/6-31G(d) level. As shown in Figure 2, with PCBM addition, the LUMO levels of the four isomers for [60] PCBM are indeed raised with respect to C60. As indicated in the literature,8 raising the LUMO level of the acceptor can increase the open circuit voltage of BHJ solar cells. Therefore, PCBM not only improves the compatibility of polymer/fullerene but also raises the LUMO level of fullerenes for excellent photovoltaic performance. Figure 3 displays the calculated isosurfaces of the HOMO and LUMO for C60 and its derivatives. The isosurfaces for the LUMO of C60 and the HOMO of PCBM indicate that the C6-6 position on the C60 surface matches the R-carbon atom attached to the benzene ring in PCBM due to their orbital symmetry, so that the monoaddition sites will be positioned at both the C6-6 bond and the R-carbon. A majority of the HOMOs (as shown in Figure 3) of all isomers are located on the cages. Similarly, a majority of the LUMOs are located on the cage spheroid with a small amount on the PCBM within the interacting distances. This further suggests there are some weak interactions between the cage and PCBM. More importantly, it is worth noting that the PCBM group has almost no contribution to the HOMO and LUMO of the derivatives. From the natural populations, there is nearly no electron transfer from PCBM to C60. Therefore, it can be proposed that PCBM is not involved in the process of photoelectric conversion but plays a key role for adjusting the level of HOMO-LUMO to improve the efficiency of the photoelectric conversion. 4. Conclusions A series of the parameters of [60] PCBM derivatives were calculated using the B3LYP method with the 6-31G(d) basis
Figure 3. Isosurfaces of (a) the HOMO and (b) the LUMO for C60 and its derivatives (the isovalue is 0.02 a.u.). The red and green represent the negative and positive parts of the wave functions, respectively.
Electronic Properties of the Fullerene Derivative set. It has been found that adding the PCBM group to the C60 cage on the C6-6 position gives the derivatives with the most stable structures. Among them, the fulleroid is a kinetically controlled product with a larger energy gap, and methanofullerene is a thermodynamic product. [60] PCBM derivatives inherit the properties of the parent fullerene. In particular, the electronic properties of C60 derivatives are similar to those of C60 adducts. However, C60 is destabilized after the chemical modification of PCBM on the C6-6 bond because of the steric effect of bulky substituents. The narrower energy gap also indicates destabilization. The PCBM as a functional group plays an important role not only for improving the compatibility of the polymer/fullerene but also for raising the LUMO level of fullerenes for an excellent photovoltaic performance. Acknowledgment. This research was financially supported by State Basic Research Development Program of China (973 program) (Grant No. 2004CB217808), the National Natural Science Foundation of China (Grant No. 20676086, 90306014, 20671068), and the Natural Science Foundation of Shanxi Province (Grant No. 20050018 and 2006011053). Also many thanks to the Key Laboratory of Coal Science & Technology (Taiyuan University of Technology), Ministry of Education, for the software.
J. Phys. Chem. C, Vol. 112, No. 48, 2008 19161 References and Notes (1) Shaheen, S. E.; Brabec, C. J.; Sariciftci, N. S.; Padinger, F.; Fromherz, T.; Hummelen, J. C. Appl. Phys. Lett. 2001, 78, 841. (2) Schilinsky, P.; Waldauf, C.; Brabec, C. J. Appl. Phys. Lett. 2002, 81, 3885. (3) Padinger, F.; Rittberger, R. S.; Sariciftci, N. S. AdV. Funct. Mater. 2003, 13, 85. (4) Ma, W.; Yang, C.; Gong, X.; Lee, K.; Heeger, A. J. Funct. Mater. 2005, 15, 1617. (5) Li, G.; Shrotriya, V.; Huang, J.; Yao, Y.; Moriarty, T.; Emery, K.; et al. Nat. Mater. 2005, 4, 864. (6) Hummelen, J. C.; Knight, B. W.; LePeq, F.; Wudl, F. J. Org. Chem. 1995, 60, 532. (7) Hino, T.; Ogawa, Y.; Kuramoto, N. Carbon 2006, 44, 880. (8) Kooistra, F. B.; Knol, J.; Kastenberg, F.; Popescu, L. M.; Verhees, W. J. H.; Kroon, J. M.; Hummelen, J. C. Org. Lett. 2007, 9, 551. (9) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (10) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R. et al. Gaussian, Inc.: Pittsburgh PA, 2003. (11) Anderson, H. L.; Boudon, C.; Diederich, F.; Gisselbrecht, J. P.; Gross, M.; Seiler, P. Angew. Chem., Int. Ed. Engl. 1994, 33, 1628. (12) Osterodt, J.; Nieger, M; Vo¨gtle, F. J. J. Chem. Soc., Chem. Commun. 1994, 1607. (13) Timmerman, P.; Anderson, H. L.; Faust, R.; Nierengarten, J. F.; Habicher, T.; Seiler, P.; et al. Tetrahedron 1996, 52, 4925–47. (14) Paolucci, F.; Marcaccio, M.; Roffia, S.; Orlandi, G.; Zerbetto, F.; Prato, M.; Maggini, M.; Scorrano, G. J. Am. Chem. Soc. 1995, 117, 6572. (15) Janssen, R. A. J.; Hummelen, J. C.; Wudl, F. J. Am. Chem. Soc. 1995, 117, 544. (16) Eiermann, M.; Wudl, F.; Prato, M.; Maggini, M. J. Am. Chem. Soc. 1994, 116, 8364.
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