ARTICLE pubs.acs.org/JPCC
From Molecules to Materials: Molecular and Crystal Engineering Design of Organic Optoelectronic Functional Materials for High Carrier Mobility Ying-fei Chang,†,§ Zhong-yuan Lu,*,‡ Li-jia An,*,† and Jing-ping Zhang§ †
State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China ‡ State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, China § Faculty of Chemistry, Northeast Normal University, Changchun 130024, China
bS Supporting Information ABSTRACT: The reorganization energy and the charge transfer integral between the initial and final states are two key parameters of charge transport. In this study, we find that the internal reorganization energies of molecules can be reduced effectively by cyanation on the tetracene molecule, which is helpful to improve the carrier mobilities of investigated molecules. On the basis of the polymorph predictor, the appreciated crystal structures of 5-cyanotetracene (1CT), 5,11-dicyanotetracene (2CT), and 5,6,11,12-tetracyanotetracene (4CT) with ππ stacking favorable to enhance the charge transfer integral were obtained. Benefiting from a low internal reorganization energy and dense packing structure, high hole motilities (6.0 and 6.2 cm2 V1 s1 for 1CT-9 and 4CT-2, respectively) were achieved. Both 1CT-9 and 4CT-2 are promising candidates for high carrier mobility organic optoelectronic functional materials. The process that constructs crystal structures from single molecules provides a rational way for the search of high-performance organic photovoltaic materials.
’ INTRODUCTION Due to advantages such as low cost, versatility of chemical synthesis, ease of processing, and flexibility, organic semiconductors have been very important materials in the development of new generations of organic-based devices for many years.13 They possess great potential in the application of light-emitting diodes,4,5 field-effect transistors,6,7 and solar cells.8,9 Carrier mobility is one of the most important factors for evaluating the performance of organic semiconductor devices; thus, enhancing the carrier mobility is the main target for designing and developing new microelectronic devices. At room temperature, one may use the thermally activated hopping model to describe the mechanism of charge transport in which the charge carriers are localized on a single molecule and have the possibility of jumping from one molecule to the adjacent molecules.1012 Within the hopping description, Marcus theory was employed to estimate the charge transfer rate, which depends on two microscopic parameters: i.e., the charge transfer integral V and the reorganization energy λ (see eq 1).13 Therefore, to retrieve high carrier mobility, we need to enhance the charge transfer integral and/or reduce the reorganization energy. The reorganization energy can be partitioned into two parts, i.e., the internal reorganization energy, which is induced by the relaxation in molecular geometry, and the external reorganization energy, which is caused by the surrounding media in bulk materials. A change in substituent is a common method to adjust r 2011 American Chemical Society
the internal molecular reorganization energy. Some functional groups (for example, F, OR, CF 3 , and NH 2 ) tend to enhance the reorganization energy, but the cyano group (CN) contributes oppositely,14 since the nonbinding interaction of cyano groups can enhance the delocalization of electrons and then result in a smaller reorganization energy. For example, the hole and electron reorganization energies are 75 and 87 meV for cyanated pentacene derivatives, respectively, which are smaller than those of pentacene (94 and 133 meV, respectively).15 The charge transfer integral (also called the electronic coupling term or hopping matrix element), which measures the interaction between the two charge-localized states, is another key factor influencing the charge transfer rate. The results of Bredas et al. indicated that the charge transfer integrals are sensitive to the changes of the relative orientations of the molecules.16 This provides a good opportunity for molecular design since either functionalizing the molecular structure or changing the environmental condition may modify the intermolecular positions in a manner that increases the charge transfer integral. In this respect, polyacenes (such as tetracene and pentacene)1720 are extensively studied systems. For example, in spite of the reorganization energy of rubrene (which is the Received: August 22, 2011 Revised: October 24, 2011 Published: December 01, 2011 1195
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four-phenyl derivative of tetracene) being larger than that of tetracene due to the presence of bulky side groups, the carrier mobility of rubrene is still higher than that of tetracene, benefiting from a favorable intermolecular displacement.21 In this context, the goal of this work is to predict the high hole mobility crystal structures with nothing more than the molecular geometry as the starting point. The influence of mono-, di-, and tetracyano substitutions on the reorganization energy of tetracene has been studied systematically. According to the calculation results, the molecules with lower reorganization energies than the parent tetracene molecule are selected as initial structures for the crystal structure prediction by the polymorph predictor in Cerius2,22,23 and the carrier mobilities of the optimum crystal structures have been calculated. The results show that cyanated tetracene derivatives are promising candidates for high hole mobility organic optoelectronic functional materials, with the highest carrier mobility being 6.2 cm2 V1 s1.
’ THEORETICAL AND COMPUTATIONAL METHODS A detailed description of the computational methods for the design of organic materials with high charge mobility was reviewed in ref 24. Here we only make a brief introduction of the methods. Marcus Charge Transfer Theory. A widely used method to estimate the charge transfer rate is Marcus theory: V 2 π 1=2 λ exp k¼ ð1Þ 4kB T p λkB T Here, kB is the Boltzmann constant, T is the temperature, V is the charge transfer integral between the initial and final states, and λ is the reorganization energy. For the reorganization energy, since the external reorganization energy is quite complicated to evaluate at this stage, we will focus on the internal reorganization energy exclusively. The internal reorganization energy can be calculated directly from the adiabatic potential energy surfaces (see the Supporting Information, Figure S1).16,25 By definition λ ¼ λ1 þ λ2 ¼ ðE EÞ þ ðEþ Eþ Þ
ð2Þ
Here, λ1 is due to the geometric relaxation energy of one molecule from the neutral state to the charged state and λ2 is due to the geometric relaxation energy from the charged state to the neutral state.26,27 For each molecule, the geometry is optimized for both neutral and charged states by using the Gaussian 03 package with the B3LYP/6-311G(d,p) method.28 We then calculate four energies, in which E and E+ are the ground-state energies of the neutral and charged states, respectively, E* is the energy of the neutral molecule at the optimized charged geometry, and E+* is the energy of the charged state energy at the geometry of the optimized neutral molecule. The charge transfer integral for hole transfer can be obtained through a direct approach,29,30 which can be written as site1 ^ 0, site2 V ¼ Æϕ0,HOMO jF jϕHOMO æ
ð3Þ
0,site2 where ϕ0,site1 HOMO and ϕHOMO represent the highest occupied molecular orbitals (HOMOs) of isolated molecules 1 and 2, respectively. F^ is the Fock operator for the dimer with a density matrix from the noninteracting dimer of F^ = SCεC1, where S is the intermolecular overlap matrix and C and ε are the molecular orbital coefficients and energies from one-step diagonalization
without iteration, respectively. The calculations are carried out via density functional theory (DFT) using PW91 exchange and PW91 correlation functionals with the 6-31G* basis set. It was shown that this choice can give the best description of the charge transfer integral at the DFT level.31 This direct method is very simple in the calculations, and the equivalence of its result and that of other methods such as the site-energy correction method and minimal energy splitting method have been proved by Shuai and co-workers.3234 Transport Properties. Within the thermally activated hopping model, the diffusion coefficient can be evaluated from35 D¼
1 2n
∑i di 2 ki Pi
ð4Þ
where d is the intermolecular center-to-center distance, n is the spatial dimension, ki is the charge transfer rate due to charge transfer to the ith neighbor, and Pi is the relative probability for charge transfer to a particular ith neighbor, i.e. Pi ¼
ki ki
ð5Þ
∑i
Summing over all possible hops leads to the diffusion coefficient in eq 4. The drift mobility of hopping, μ, is then evaluated from the Einstein relation36 e D ð6Þ μ¼ kB T where e is the electron charge. Crystal Structure Prediction. Crystal structure prediction has been performed by using the polymorph predictor (PP) module in Cerius2. According to the results of reorganization energy calculations, three molecules, i.e., cyanotetracene, dicyanotetracene, and tetracyanotetracene, with low reorganization energies are selected as initial structures for the crystal structure prediction. In the first step, a quantum chemical optimization for the molecules was performed with the 6-31G** basis set, and Gaussian electrostatic potential (ESP) charges that are more representative of all atoms are obtained. Then the Dreiding force field,37 which is one of the most appropriate force fields for molecular crystal prediction with ESP charges generated by quantum mechanical calculations, is employed in the PP runs. van der Waals and Coulomb interactions are calculated by using the Ewald summation method with a cutoff of 6 Å, and the Ewald accuracy tolerance is set to 0.0001 kcal 3 mol1. For all molecules, the PP calculations are restricted to the six most popular space groups, P21/c, P1, P212121, P21, C2c, and P1, since many organic structures are found in these space groups according to the statistics of the Cambridge Structural Database.
’ RESULTS AND DISCUSSION Internal Reorganization Energy. The molecular structures of isomers for cyanotetracene (3 isomers), dicyanotetracene (21 isomers), and tetracyanotetracene (5 isomers) are optimized in both neutral and charged states via DFT using the hybrid B3LYP functional with the 6-311G(d,p) basis set. Then the internal reorganization energies of these molecules are obtained via eq 2. According to the calculated results (see the Supporting Information, Figure S2 and Table S1), three molecules, 5-cyanotetracene (1CT), 5,11-dicyanotetracene (2CT), and 5,6,11,12-tetracyanotetracene (4CT), which possess the lowest reorganization 1196
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Figure 1. Chemical structures (top) and side views (bottom) of (a) 1CT, (b) 2CT, and (c) 4CT.
Table 1. Relaxation Energies λ1 and λ2 and Internal Hole Reorganization Energies λ for Tetracene, 1CT, 2CT, and 4CT (meV) molecule
λ1
λ2
λ
tetracene
57.5
57.5
115
1CT
51.0
51.6
102.6
Δλa 0 12.4
2CT
44.3
44.9
89.2
25.8
4CT
38.5
39.5
78.0
37.0
Δλ refers to the difference in reorganization energy between tetracene and its derivatives.
a
energies, are selected as the initial structures for the crystal structure prediction. On the basis of frequency calculations, all three structures are confirmed as the minima on the potential energy surface, and their chemical structures are shown in Figure 1. We find that the planar conformation of tetracene is retained in 1CT and 2CT, but distorted by about 10.2 due to the steric hindrance of four cyano groups, as shown Figure 1. The calculated results for the relaxation energies λ1 and λ2 together with the internal reorganization energies for the three molecules are listed in Table 1. For comparison, the internal reorganization energy of tetracene is also given. In contrast to halogen,15,38 cyanated tetracene derivatives exhibit a lower internal reorganization energy than their parent molecule. As shown in Table 1, for each molecule, λ1 and λ2 are found to be nearly equal. The internal hole reorganization energy can be decreased significantly (almost 10 meV) when one cyano group is introduced onto tetracene. For understanding the trends of internal reorganization energies, we check the Mulliken-type atomic charge population analyses of tetracene and 4CT, as shown in Figure 2. It is shown that the populations on both the tip and the bridging C atoms of 4CT are smaller than those of tetracene and result in the reduction of the bonding and antibonding interactions, as discussed in ref 15. More intriguingly, electron delocalization on the cyano groups has a strong nonbonding character. Due to the strong nonbonding character of the cyano group and the effect of the reduced bonding/antibonding of the core structure, incorporating a cyano group in tetracene may not contribute significantly to the geometric distortion of the tetracene framework, but may greatly enhance the electron delocalization. Thus, cyanation is an efficient way of reducing the reorganization energy. From the perspective of the reorganization energy, these compounds are more conductive to hole transport than tetracene. Crystal Structure and Transport Properties. The crystal structure predictions of 1CT, 2CT, and 4CT are based on the polymorph predictor module in the Cerius2 package. We sort the obtained crystal structures by their energies, and then the 10 crystal structures with the lowest total energies are selected as the
Figure 2. Mulliken-type atomic charge population analyses of (a) tetracene and (b) 4CT.
crystal structure candidates for further DFT calculations in evaluating their hole mobilities. On the basis of Marcus theory, the charge transfer integral should be calculated to obtain the charge transfer rate. The transmission paths are selected according to the optimized crystal structures. First, we choose a molecule in the crystal as the carrier donor and take all its neighboring molecules as paired elements. Each pair is defined as a transmission path. Then the charge transfer integral can be calculated according to the transmission path, and the mobility can be estimated from the Einstein relation. For 1CT, the crystal cell parameters and the estimated hole mobilities for the 10 crystal structures with the lowest total energies are shown in the Supporting Information, Table S2. According to the calculated results, 1CT-1, 1CT-3, and 1CT-9 possess high hole mobilities at 300 K; their crystal structures are shown in the Supporting Information, Figure S3. Although these three compounds form herringbone packing structures like tetracene, the calculated hole mobilities (2.72 cm2 V1 s1 for 1CT-1, 3.12 cm2 V1 s1 for 1CT-3, and 6.0 cm2 V1 s1 for 1CT-9) are higher than that for tetracene (1.63 cm2 V1 s1) and that obtained by the experimental structure (2.38 cm2 V1 s1).39 This can be attributed to the packing modes with not only faceto-edge dimers, but also face-to-face dimers (ππ stacking) in the crystal structures for these three 1CT derivatives. Both molecular modeling and experimental evidence suggest that a high mobility is expected for an organic semiconductor with a dense packing structure. For 1CT-1, the ππ plane distance for the ππ stacking dimer is 3.404 Å, and the calculated charge transfer integral of the dimer is 0.0951 eV. The ππ plane distance for 1CT-3 is 3.379 Å, corresponding to the high charge transfer integral (0.1350 eV). For 1CT-9, the highest charge transfer integral is 0.1629 eV for the ππ stacking dimer with a distance of 3.521 Å. For 2CT, the crystal cell parameters and the estimated hole mobilities for the 10 crystal structures with the lowest total energies are given in the Supporting Information, Table S3. According to the calculated results, only two structures (2CT-3 and 2CT-10) with higher hole mobilities at 300 K are obtained; their crystal structures are shown in the Supporting Information, Figure S4. In contrast to 1CT derivatives, these two compounds form face-to-face slipped stacking. Although their hole mobilities are lower than those of three 1CT derivatives, they are still higher than that of tetracene. For 4CT, the crystal cell parameters and the estimated hole mobilities for the 10 crystal structures with the lowest total energies are listed in the Supporting Information, Table S4. According to the calculated results, five crystal structures (4CT-2, 4CT-4, 4CT-5, 4CT-7, and 4CT-8) with higher calculated hole mobilities (more than 2.5 cm2 V1 s1) at 300 K are obtained. These five compounds show face-to-face slipped stacking (4CT-2, 4CT-7, and 4CT-8) similar to that of 2CT derivatives and two 1197
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Figure 4. Theoretical estimation of the hole mobility as a function of the external reorganization energy for 1CT-9 and 4CT-2 at 300 K.
Figure 3. HOMO and most efficient charge transfer packing for (a) 1CT-9, (b) 2CT-10, and (c) 4CT-2.
face-to-face packing modes (4CT-4 and 4CT-5) with an edge edge stacking framework. The distorted planar conformation of tetracene due to the steric hindrance of four cyano groups can be seen in the Supporting Information, Figure S5. To understand the charge transport behavior of the compounds with high mobility, the frontier orbitals and the most efficient charge transfer packing modes are compared in Figure 3. As shown in Figure.3, all the HOMO distributions of the three compounds show a bonding interaction. For the most efficient charge transfer route, the overall overlap is enhanced by the inphase bonding of one molecule on top of the bonding of the other molecule. Thus, from the intermolecular interaction point of view, the charge transfer integral can be enhanced due to the existence of cyano groups. It is intriguing to understand why 2CT behaves differently from 1CT and 4CT. From the packing modes of the most efficient charge transfer route for 1CT-9 and 2CT-10, one can see (from Figure 3) that although both of them are characterized by the slipping face-to-face dimers, their slip directions are totally different. In 1CT-9, two molecules slip in the direction parallel to the tetracene skeleton, but in 2CT-10, the slip direction is perpendicular to the tetracene skeleton. The packing mode of 1CT-9 will retain most of the molecular overlap; thus, it is more conducive to charge transfer. Also, as a consequence, the reorganization energy of 2CT is lower, and it possesses a lower mobility. So far, the external reorganization energy λext, which is caused by polarization of the surrounding medium in the bulk materials, is completely neglected. Recently, the external reorganization energy of polyacene had been computed using a polarizable force field.40 According to the computations, the calculated external reorganization energy is very small as compared to the internal reorganization energy, ca. 3 meV for tetracene. However, this evaluation only considered the contribution of the surrounding molecules to the external reorganization energy, and the influence of impurities had not been taken into account. As the external reorganization energy is bound to affect the absolute value of the mobility, we simply calculate the hole mobilities for
two crystal structures (1CT-9 and 4CT-2) by considering the external reorganization energy from 0 to 200 meV to estimate the effect of the polarization of the surrounding medium. The theoretical estimation of the mobilities of these two structures as a function of λext is shown Figure 4. It clearly reveals that the mobility decreases about 1 order of magnitude when λext goes from 0 to 200 meV. It should be noted that such an evaluation is quite simple since the charge transfer integral should also be changed by the polarization effect of the surrounding molecules, but this analysis shows the apparent influence of the external reorganization energy on the charge mobility, which should be taken into account carefully in further studies.
’ CONCLUSION In summary, a new way to search for a high carrier mobility organic semiconductor with nothing more than the molecular geometry as the starting point is proposed. By introducing cyano groups into the tetracene framework, the internal hole reorganization energy can be reduced effectively, and favorable molecular packing between neighboring molecules such as ππ overlap in crystals can be formed. Benefiting from these good characteristics, high hole transfer material can be achieved. In our study, two cyanated tetracene derivatives (1CT-9 and 4CT-2) with high hole mobilities (6.0, and 6.2 cm2 V1 s1, respectively) are identified. The results show that cyanated tetracene derivatives are promising candidates for high carrier mobility organic optoelectronic functional materials. This suggests that, if the two compounds can be synthesized and their packing modes are controlled, high hole mobility material can be achieved. This process, constructed from single molecules to crystal materials, provides a new strategy for the design of high-performance organic photovoltaic materials. ’ ASSOCIATED CONTENT
bS
Supporting Information. Evaluation of the internal reorganization energies and predicted crystal cell parameters, corresponding hole mobilities, and stacking modes for 1CT, 2CT, and 4CT. This material is available free of charge via the Internet at http://pubs.acs.org.
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’ AUTHOR INFORMATION Corresponding Author
*Phone: +86 431 88498017 (Z.-y.L.); +86 431 85262138 (L.-j.A.). Fax: +86 431 88498026 (Z.-y.L.); +86 431 85262969 (L.-j.A.). E-mail:
[email protected] (Z.-y.L.);
[email protected] (L.-j.A.).
’ ACKNOWLEDGMENT We are indebted to Professor Zhigang Shuai for valuable discussions. This work is supported by a China Postdoctoral Science Foundation funded project (20080431046), the National Science Foundation of China (Grant 21025416), and the Open Research Fund of the State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences. ’ REFERENCES (1) Pope, M.; Swenberg, C. E. Electronic Processes in Organic Crystals and Polymers, 2nd ed.; Oxford University Press: New York, 1999; pp 337340. (2) Dimitrakopoulos, C. D.; Malenfant, P. R. L. Adv. Mater. 2002, 14, 99–117. (3) Ebata, H.; Izawa, T.; Miyazaki, E.; Takimiya, K.; Ikeda, M.; Kuwabara, H.; Yui, T. J. Am. Chem. Soc. 2007, 129, 15732–15733. (4) Chen, A. C. A.; Culligan, S. W.; Geng, Y.; Chen, S. H.; Klubek, K. P.; Vaeth, K. M.; Tang, C. W. Adv. Mater. 2004, 16, 783–788. (5) Zojer, E.; Pogantsch, A.; Hennebicq, E.; Beljonne, D.; Bredas, J. L.; de Freitas, P. S.; Scherf, U.; List, E. J. W. J. Chem. Phys. 2002, 117, 6794–6802. (6) Horowitz, G.; Hajlaoui, M. E. Adv. Mater. 2000, 12, 1046–1050. (7) Nagamatsu, S.; Kaneto, K.; Azumi, R.; Matsumoto, M.; Yoshida, Y.; Yase, K. J. Phys. Chem. B 2005, 109, 9374–9378. (8) Padinger, F.; Rittberger, R. S.; Sariciftci, N. S. Adv. Funct. Mater. 2003, 13, 85–88. (9) Smith, A. P.; Smith, R. R.; Taylor, B. E.; Durstock, M. F. Chem. Mater. 2004, 16, 4687–4692. (10) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 2005, 127, 16866–16881. (11) Coropceanu, V.; Cornil, J.; da Silva Filho, D. A.; Olivier, Y.; Silbey, R.; Bredas, J. L. Chem. Rev. 2007, 107, 926–952. (12) Bredas, J. L.; Calbert, J. P.; da Silva Filho, D. A.; Cornil, J. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 5804–5809. (13) Marcus, R. A. Rev. Mod. Phys. 1993, 65, 599–610. (14) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. J. Am. Chem. Soc. 2005, 127, 2339–2350. (15) Kuo, M. Y.; Chen, H. Y.; Chao, I. Chem.—Eur. J. 2007, 13, 4750–4758. (16) Bredas, J. L.; Beljonne, D.; Coropceanu, V.; Cornil, J. Chem. Rev. 2004, 104, 4971–5003. (17) Anthony, J. E. Chem. Rev. 2006, 106, 5028–5048. (18) Anthony, J. E. Angew. Chem., Int. Ed. 2008, 47, 452–483. (19) Wen, S. H.; Li, A.; Song, J. L.; Deng, W. Q.; Han, K. L.; Goddard, W. A., III. J. Phys. Chem. B 2009, 113, 8813–8819. (20) Sancho-García, J. C.; Perez-Jimenez, A. J. Chem. Phys. Lett. 2010, 499, 146–151. (21) da Silva Filho, D. A.; Kim, E. G.; Bredas, J. L. Adv. Mater. 2005, 17, 1072–1076. (22) Baur, W. H.; Kassner, D. Acta Crystallogr., Sect. B 1992, 48, 356–369. (23) Belsky, V. K.; Zorkii, P. M. Acta Crystallogr., Sect. A 1977, 33, 1004–1006. (24) Wang, L. J.; Nan, G. J.; Yang, X. D.; Peng, Q.; Li, Q. K.; Shuai, Z. G. Chem. Soc. Rev. 2010, 39, 423–434. (25) Coropceanu, V.; Nakano, T.; Gruhn, N. E.; Kwon, O.; Yade, T.; Katsukawa, K.; Bredas, J. L. J. Phys. Chem. B 2006, 110, 9482–9487.
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