Article pubs.acs.org/JPCC
Dependence of the Structure and Electronic Properties of D−A−D Based Molecules on the D/A Ratio and the Strength of the Acceptor Moiety Priya Johari* and Samarendra P. Singh Department of Physics, School of Natural Sciences, Shiv Nadar University, Greater Noida, Gautam Budhha Nagar, UP 201 314, India S Supporting Information *
ABSTRACT: A series of donor−acceptor−donor (D−A−D) scheme based organic molecules was studied to examine the dependence of molecular structure and electronic properties on the D/A ratio and the strength of the acceptor moiety, using first-principles density-functional-theory based calculations. Thiophenes were taken as the donor moiety and a series of benzo-X-diazoles and benzobis-X-diazoles (X = O, S, Se, and Te) were considered to account the strength of the acceptor moieties. The role of different exchange−correlation functionals was also investigated to search for the functional that best describes the properties of such D−A−D based molecules. Our systematic calculations reveal that both the D/A ratio and the strength of the acceptor moiety largely affect the energy gap between energies of the highest occupied molecular orbital (H) and the lowest unoccupied molecular orbital (L). In thiophene−benzo-X-diazole molecules, the H−L gap varies from 7% to 25%, whereas in thiophene−benzobis-Xdiazoles, it can be tuned from 40% to 80%, by changing the D/A ratio from 0.5 to 4.0. In the latter case, higher steric hindrance (>50°) between A−A units disrupts the conjugation length with the increase in acceptor units. This leads to a monotonic decrease of the H−L gap with the increase in the D/A ratio, and a larger variation as compared to the case for thiophene−benzo-X-diazoles. On accounting for the effect of strength of the acceptor moiety, we observed that the H−L gap of the bis molecule was roughly 1 eV smaller than its respective non-bis configuration. A decrease in the H−L gap was also found on moving from S to Se to Te. Quantitatively, the H−L gap of the investigated molecules was found within a wide range of 0.2−2.4 eV, which not only is smaller than the H−L gap of isolated thiophene or the benzo-(bis)X-diazole molecules but also lies in the desired range for the applications in optoelectronic devices, including solar cells. Thus, our study affirms that by choosing a suitable acceptor moiety and the D/A ratio, the structural and electronic properties of D−A−D based materials can be widely tuned. Through this work we emphasize the need to understand the tuning of molecular properties by examining the structure−property correlation, which is essential for rational design of high performing novel organic materials.
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INTRODUCTION
have the potential to realize molecular electronics as the future of next-generation optoelectronic devices.5 Electronic and structural properties of organic π-conjugated molecules play a crucial role in deciding the applications of these materials in electronic devices, and hence, the structure− property relationship needs to be understood thoroughly. Such an understanding will be useful to control the properties of organic materials relevant to device applications like the position of energy levels, band gap, conjugation length, light absorption and emission, charge carrier mobility, and other photophysical properties.6−11 This will eventually help to design molecular materials with specific desired properties. In particular, there is high demand to tune the band gap of organic materials as this is one of the major limiting factors of their use in optoelectronic devices. Scientists and engineers are coming up with several schemes to reduce or tailor the band gap of organic molecules. One of the most successful approaches is
Molecule-based-electronics has been a subject to explore for around 50 years, however, in the past few years, interest in this area has accelerated due to remarkable development in our understanding of molecular systems, and in experimental and fabrication techniques. Using advanced experimental techniques, many researchers have already demonstrated the use of molecules in several electronic devices such as light emitting diodes, thin-film transistors, solar cells, sensors, switches, etc.1−4 A molecule can also be seen as a zero-dimensional nanostructure because the size of any molecule lies typically between 1 and 100 nm in all three directions, thus providing them the advantages of small size, cost effectiveness, and low power dissipation, over conventional bulk semiconducting materials, generally used in optoelectronic devices. Moreover, the choice for synthetic tailorability by choosing various compositions allows us to tune the electronic, optical, and transport properties of many of these materials. Organic πconjugated molecules have specifically come up as promising materials that fulfill all the above-mentioned advantages and © XXXX American Chemical Society
Received: March 12, 2015 Revised: May 22, 2015
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units present in the molecule and the ratio between them and (ii) the strength of the donor or acceptor moieties that can be varied by considering different configuations of them. To exploit all these possibilities and to obtain a deep understanding of the dependence of structure and electronic properties on above-mentioned factors, we performed a systematic study in the framework of first-principles density-functional-theory (DFT) to study various D−A−D based molecules. We considered thiophene, which is a widely used electron-rich entity as a common donor unit, whereas various acceptor moieties (benzo-X-diazole and benzobis-X-diazole, where X stands for O, S, Se, and Te) are coupled in between thiophenes of different lengths to investigate the impact of strength of the acceptor moiety. Moreover, to complete the study, we used several semilocal and hybrid exchange−correlation (xc) functionals to calculate the optimized structures of the examined D−A−D molecules and their electronic properties, to find the best suitable xc functional for them. Our comprehensive calculations give an insight into the dependence of structure of the molecules and its electronic properties on the D/A ratio and the strength of the acceptor moiety and constitute a structure−property correlation. We found that the structure and the H−L gap are highly responsive to both the D/A ratio and the chemical strength of the acceptor moiety. Our study reveals that by choosing a suitable number of units and the type of acceptor moieties in the D−A−D based molecules, the electronic properties of these systems can be very well tuned, which can help in designing optoelectronic devices of wide interest and functionality. Furthermore, we present a model study for the D−A−D scheme by considering thiophene and benzo(bis-)chalcogen−diazoles as a prototype and provide a platform to rationally design and investigate potential materials. Such studies can beforehand help experimentalist to synthesize and characterize only materials of interest.
based on coupling of a donor moiety (D) possessing small ionization potential with an acceptor moiety (A) having large electron affinity, which can reduce the band gap with respect to the band gap of the individual molecular entity.12−20 In the past few years, several studies have been made to examine the D−A based small molecules and polymers by choosing various types of donor and acceptor moieties.15−21 These studies have successfully demonstrated the possibility to tune the properties of the molecular systems with the change in donor−acceptor moieties.16,19−21 However, a detailed understanding of structure−property correlation in D−A−D based molecules is still in its infancy. Experimentally, Sonar et al.12,13 and Polander et al.14 have studied such molecules, but their study was restricted to a small number of molecules. Sonar et al. performed the synthesis and characterization of solution processable D−A−D molecules with thiophene (1T) and benzothiadiazole (benzo-S-diazole) as the electron donor and acceptor moieties, respectively, and reported the electrochemical as well as the optical gap for few thiophene− benzothiadiazoles.12,13 Polander et al., on the contrary, have shown that by changing the chemical composition of the moieties and by arranging them in D−A−D or A−D−A configuration, a tuning of the energy gap (i.e., the difference between energy of highest occupied molecular orbital (H) and lowest unoccupied molecular orbital (L)) can be achieved.14 They synthesized and characterized benzothiadiazole−dithienopyrrole based molecules and compared the results with model compounds based on benzene−dithienopyrrole, to demonstrate their findings. The synthesis and characterization of such molecules is, however, an expensive process in terms of cost, as well as time. Thus, it restricts the investigation of wide range of molecules to develop a global model through understanding of structure− property correlation that can help in rational designing of the novel materials. Here, computational studies can help to predict useful information about the stable configurations and compositions of any molecule, and its respective properties, well in advance. Hence, using modeling and simulations, various molecules with specific properties can be designed and investigated in much less time than in the experiments. This also gives a freedom to synthesize and characterize only materials of importance, for the fabrication of devices with desired applications. With this approach, a few materials were designed and studied in the past.22,23 This approach on D−A− D based molecules will strengthen the understanding of structure−property correlation, which will give more insight into the design of new molecules. Most of the promises of these D−A−D based molecules have come up due to tunability of their H−L gap (difference between the highest occupied and lowest unoccupied energy levels) with the variation in chemical composition.12−14,17−19,22,24−26 The low band gap materials are of particular interest because of their potential applications in optoelectronic devices like organic light emitting diodes (OLEDs),27−29 organic thin-film transistors (OTFTs),30−33 and organic photovoltaic cells (OPVs).25,26,34−37 Besides that, D−A−D based molecules may also exhibit high charge carrier mobility as a consequence of strong intermolecular interaction between the oligomers that leads to highly ordered crystalline film.12−14,38 Although few D−A−D based molecules have been investigated, a detailed study is still needed to be done to understand these materials in depth. Furthermore, it is required to explore the dependence of the properties of these materials on various aspects such as (i) the number of donor or acceptor
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COMPUTATIONAL DETAILS In the present paper, we investigated a series of D−A−D based molecules (total 48 molecules) by sandwiching the acceptor moiety between two donor moieties in various combinations. These combinations were made, in particular, to study the impact of the number of donor and acceptor units in a molecule (D/A ratio) and the strength of acceptor moiety due to its chemical composition on the structural and electronic properties of D−A−D based molecules. The examined molecules are discussed below. Examined Molecules. Thiophene−benzo-X-diazole and thiophene−benzobis-X-diazole molecules, represented by general formula mT-n(NXN-B)-pT and mT-n(NXN-B-NXN)-pT, respectively, are considered for the current study. In the general formula, m and p denote the number of donor units, n signifies number of acceptor units present within the molecule, and X represents the chalcogenide atom present in the acceptor units. To study the effect of the D/A ratio on the structural and electronic properties, we considered molecules with varied numbers of donor and acceptor units. This is done by having molecules with 1−4 acceptor units (n = 1, 2, 3, 4) enclosed between 2 donor units (k = m + p = 2), giving a D/A ratio ⩽2, and molecules with total of 2−4 donor units (k = m + p = 2, 3, 4) and single acceptor unit (n = 1), giving a D/A ratio ⩾2. Thus, this variation gives us a series of six molecules (having a particular type of acceptor moiety) with a D/A ratio ∼0.5 (n = 4, m = 1, p = 1), 0.66 (n = 3, m = 1, p = 1), 1.0 (n = 2, m = 1, p B
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molecular systems.55−57 However, we believe that hybrid functionals that include a certain percentage of exact exchange will also give a closer approximation, especially the HSE06 xc functional, which is also shown to give good agreement with experiments, as well as the meta GGA-TPSS xc functional.57,58 All calculations are done with a plane wave cutoff of 400 eV and single k-point, i.e., the Γ-point. An energy convergence criteria of 10−4 eV is taken to ensure electronic relaxation, whereas atomic relaxation is performed until the interatomic forces are less than 0.01 eV/Å, which is found sufficient to obtain the relaxed geometry. To realize the molecule, by avoiding any interaction between the translational images, a vacuum region of around 12 Å is adopted along all three spatial directions. Thus, an orthorhombic unit cell is chosen with lattice vectors along the x-, y-, and z-directions equivalent to the approximate molecular length in the x-direction (including methyl group) + 12 Å, molecular length in the y-direction + 12 Å, and molecular depth in the z-direction + 12 Å, respectively. To decide the optimized value of the vacuum, calculations were performed with various vacuum sizes (∼8, 10, 12, 14, and 16 Å) and a convergence in the ground state energy with respect to these vacuum sizes was checked. We found 12 Å vacuum to be sufficient to model the isolated molecules considered in this work. The optimized ground state geometry of all molecules is obtained by relaxing the molecules without imposing any constraint on them. However, to be ensured about obtaining the geometry corresponding to the global minima and not the local minima, we manually considered various dihedral angles between all D−D, D−A, and A−A units and relaxed the molecule. In several cases, the energy difference between a relaxed molecule with different dihedral angles between the units is found to be 2), as the dihedral angle between D−D and D−A units is negligible compared to that of A−A units. Other than the D/A ratio, the
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ASSOCIATED CONTENT
S Supporting Information *
Table of the optimized molecular length “a” corresponding to the aromatic chain of all examined thiophene−benzo-X-diazoles and thiophene−benzobis-X-diazoles. Table of dihedral angles between the D−A (ϕ) and the A−A (θ) units for the investigated molecules. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b02404.
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AUTHOR INFORMATION
Corresponding Author
*P. Johari. E-mail:
[email protected], psony11@gmail. com. H
DOI: 10.1021/acs.jpcc.5b02404 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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(19) Bundgaard, E.; Krebs, F. C. Low-Band-Gap Conjugated Polymers Based on Thiophene, Benzothiadiazole, and Benzobis(thiadiazole). Macromolecules 2006, 39, 2823−2831. (20) Wykes, M.; Begona, M.-M.; Gierschner, J. Computational Engineering of Low Bandgap Copolymers. Frontiers in Chem.: Theor. Comput. Chem. 1993, 1, 35. (21) Gibson, G. L.; McCormick, T. M.; Seferos, S. S. Atomistic Band Gap Engineering in Donor-Acceptor Polymers. J. Am. Chem. Soc. 2012, 134, 539−547. (22) Sokolov, A. N.; et al. From Computational Discovery to Experimental Characterization of a High Hole Mobility Organic Crystal. Nat. Commun. 2011, 2, 437. (23) Sharma, V.; et al. Rational Design of All Organic Polymer Dielectrics. Nat. Commun. 2014, 5, 4845. (24) Huang, J.; Kertesz, M. Electronic Structures and Charge Transport Properties of the Organic Semiconductor Bis[1,2,5]thiadiazolo-p-quinobis(1,3-dithiole), BTQBT, and Its Derivatives. J. Phys. Chem. B 2005, 109, 12891−12898. (25) Bundgaard, E.; Krebs, F. C. Large-Area Photovoltaics Based on Low Band Gap Copolymers of Thiophene and Benzothiadiazole or Benzo-bis(thiadiazole). Sol. Energy Mater. Sol. Cells 2007, 11, 1019. (26) Bundgaard, E.; Krebs, F. C. A Comparison of the Photovoltaic Response of Head-to-head and Head-to-tail Coupled Poly(Benzo2,1,3-Thiadiazol-4,7-Diyl)-(Dihexyl[2,2′]Dithiophene-5,5′-Diyl). Polym. Bull. 2005, 3, 157−164. (27) Ritonga, M. T. S.; Sakurai, H.; Hirao, T. Synthesis and Characterization of p-Phenylenediamine Derivatives Bearing a Thiadiazole Unit. Tetrahedron Lett. 2002, 43, 9009. (28) Neto, B. A. D.; Lopes, A. S. A.; Ebeling, G.; Goncalves, R. S.; Costa, V. E. U.; Quina, F. H.; Dupont, J. Photophysical and Electrochemical Properties of π-Extended Molecular 2,1,3-Benzothiadiazoles. Tetrahedron 2005, 46, 10975−10982. (29) Yamashita, Y.; Suzuki, K.; Tomura, M. Novel Electron Acceptors Containing Thiadiazole and Thiophene Units. Synth. Met. 2003, 133, 341−343. (30) Akhtaruzzaman, M.; Kamata, N.; Nishida, J.; S, A.; Tada, H.; Tomura, M.; Yamashita, Y. Synthesis, Characterization and FET Properties of Novel Dithiazolylbenzothiadiazole Derivatives. Chem. Commun. 2005, 25, 3183−3185. (31) Kono, T.; Kumaki, D.; Nishida, J.; Sakanoue, T.; Motoyasu, K.; Tada, H.; Tokito, S.; Yamashita, Y. High-Performance and LightEmitting n-Type Organic Field-Effect Transistors Based on Dithienylbenzothiadiazole and Related Heterocycles. Chem. Mater. 2007, 6, 1218−1220. (32) Zhang, M.; Tsao, H. N.; Pisula, W.; Yang, C.; Mishra, A. K.; Muellen, K. Field-effect Transistors Based on a BenzothiadiazoleCyclopentadithiophene Copolymer. J. Am. Chem. Soc. 2007, 129, 3472−3473. (33) Zaumseil, J.; Donley, C. L.; Kim, J. S.; Friend, R. H.; Sirringhaus, H. Efficient Top-Gate, Ambipolar, Light-Emitting Field-Effect Transistors Based on a Green-Light-Emitting Polyfluorene. Adv. Mater. 2006, 20, 2708−2712. (34) Huang, J.; Xu, Y.; Hou, Q.; Yand, W.; Yuan, M.; Cao, Y. Novel Red Electroluminescent Polymers Derived from Carbazole and 3,6Bis(2-thienyl)-1,2,7-benzothiadiazole. Macromol. Rapid Commun. 2002, 23, 709−712. (35) Svensson, M.; Zhang, F.; Veenstra, S. C.; Verhees, W. J. H.; Hummelen, J. C.; Kroon, J. M.; Inganas, O.; Andersoon, M. R. HighPerformance Polymer Solar Cells of an Alternating Polyfluorene Copolymer and a Fullerene Derivative. Adv. Mater. 2003, 12, 988− 991. (36) Muhlbacher, D.; Scharber, M.; Morana, M.; Zhu, Z. G.; Waller, D.; Gaudiana, R.; Brabec, C. High Photovoltaic Performance of a LowBandgap Polymer. Adv. Mater. 2006, 18, 2884−2889. (37) Blouin, N.; Michaud, A.; Leclerc, M. A Low-Bandgap Poly(2,7Carbazole) Derivative for Use in High-Performance Solar Cells. Adv. Mater. 2007, 19, 2295−2300.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS P.J. acknowledges the support provided by Grant No. SR/FTP/ PS-052/2012 from Department of Science and Technology (DST), Government of India. We thank Dr. Santosh Kumar for critical reading of the manuscript. The high performance computating facility available at the School of Natural Sciences, Shiv Nadar University, was used to perform all calculations.
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REFERENCES
(1) Heath, J. R.; Ratner, M. A. Molecular Electronics. Phys. Today 2003, 56, 43−49. (2) Joachim, C.; Gimzewski, J. K.; Aviram, A. Electronics using Hybrid-Molecular and Mono-Molecular Devices. Nature 2000, 408, 541. (3) Mujica, V., Ratner, M. A. In Handbook of Nanoscience, Engineering, and Technology; Goddard, W. A., III, et al., Eds.; CRC Press: Boca Raton, FL, 2002. (4) Nitzan, A. Electron Transmission Through Molecules and Molecular Interfaces. Annu. Rev. Phys. Chem. 2001, 52, 681. (5) Cuevas, J. C.; Scheer, E. Molecular Electronics: An Introduction to Theory and Experiment; World Scientific: Singapore, 2010. (6) Dimitrakopoulos, C. D.; Malenfant, P. R. L. Organic Thin Film Transistors for Large Area Electronics. Adv. Mater. 2002, 14, 99−117. (7) Mushrush, M.; Facchetti, A.; Lefenfeld, M.; Katz, H. E.; Marks, T. J. Easily Processable Phenylene-Thiophene-based Organic Field-Effect Transistors and Solution-Fabricated Nonvolatile Transistor Memory Elements. J. Am. Chem. Soc. 2003, 125, 9414−9423. (8) Muellen, K., Wegner, G. Electronic Materials: The Material Approach; Wiley-VCH: Weinheim, 1998. (9) Nalwa, H. S. Handbook of Advanced Electronic and Photonics Materials and Devices; Academia: San Diego, 2000. (10) Roncali, J. Synthetic Principles for Bandgap Control in Linear πConjugated Systems. Chem. Rev. 1997, 97, 173−205. (11) Yassar, A.; Demanze, F.; Jaafari, A.; Elldrissi, M.; Coupry, C. yano-Substituted Oligothiophenes: A New Approach to n-Type Organic Semiconductors. Avd. Funct. Mater. 2002, 12, 699−708. (12) Sonar, P.; Singh, S. P.; Leclere, P.; Surin, M.; Lazzaroni, R.; Lin, T. T.; Dodabalapur, A.; Sellinger, A. Synthesis, Characterization, and Comparative Study of Thiophene-Benzothiadiazole based DonotAcceptor-Donor (D−A−D) Materials. J. Mater. Chem. 2009, 19, 3228−3237. (13) Sonar, P.; Singh, S. P.; Sudhakar, S.; Dodabalapur, A.; Sellinger, A. High-Mobility Organic Thin Film Transistors Based on Benzothiadiazole-Sandwiched Dihexyl Quaterthiophenes. Chem. Mater. 2008, 20, 3184−3190. (14) Polander, L.- E.; et al. Benzothiadiazole-Dithienopyrrole DonorAcceptor-Donor and Acceptor-Donor-Acceptor Triads: Synthesis and Optical, Electrochemical, And Charge-Transport Properties. J. Phys. Chem. C 2011, 115, 23149−23163. (15) Cheng, Y.-J.; Yang, S.-H.; Hsu, C.-S. Synthesis of Conjugated Polymers for Organic Solar Cell Applications. Chem. Rev. 2009, 109, 5868−5923. (16) Pandey, L.; Risko, C.; Norton, J. E.; Bredas, J.-L. DonorAcceptor Copolymers of Relevance for Organic Photovoltaics: A Theoretical Investigation of the Impact of Chemical Structure Modifications on the Electronic and Optical Properties. Macromolecules 2012, 45, 6405−6414. (17) Li, J.-C.; Kim, S.-J.; Lee, S.-H.; Lee, Y.-S.; Zong, K.; Yu, S.-C. Synthesis and Characterization of a Thiophene-Benzothiadiazole Copolymer. Macromol. Res. 2009, 17, 356−360. (18) Li, J.-C.; Meng, Q. B.; Kim, J.-S.; Lee, Y.-S. A Thiophene, Benzothiadiazole, and Carbazole-Based Copolymer: Synthesis and Characterization. Bull. Korean Chem. Soc. 2009, 30, 951−954. I
DOI: 10.1021/acs.jpcc.5b02404 J. Phys. Chem. C XXXX, XXX, XXX−XXX
Article
The Journal of Physical Chemistry C (38) Park, Y. S.; Kim, D.; Hoosung, L.; Moon, B. Donor-AcceptorDonor-Type Liquid Crystal with a Pyridazine Core. Org. Lett. 2006, 8, 4699−4702. (39) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (40) Kresse, G.; Furthmuller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (41) Kresse, G.; Joubert, D. From ultrasoft Pseudopotentials to the Projector Augmented-wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (42) Sony, P.; Shukla, A.; Ambrosch-Draxl, C. Energetics and Electronic Structure of Phenyl-Disubstituted Polyacetylene: A FirstPrinciples Study. Phys. Rev. B 2010, 82, 035213. (43) Johari, P.; Shenoy, V. B. Tuning the Electronic Properties of Semiconducting Transition Metal Dichalcogenides by Applying Mechanical Strains. ACS Nano 2012, 6, 5449−5456. (44) Ataca, C.; Ciraci, S. Functionalization of Single-Layer MoS2 Honeycomb Structures. J. Phys. Chem. C 2011, 115, 13303−13311. (45) Kuc, A.; Zibouche, N.; Heine, T. Influence of Quantum Confinement on the Electronic Structure of the Transition Metal Sulfide TS2. Phys. Rev. B 2011, 83, 245213. (46) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (47) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1998, 38, 3098−3100. (48) Lee, C.; Yang, W.; Parr, R. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (49) Becke, A. D. Density-Dunctional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1998, 98, 5648−5652. (50) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207. (51) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Erratum: “Hybrid Functionals based on a Screened Coulomb Potential”. J. Chem. Phys. 2006, 124, 219906. (52) Paier, J.; Marsman, M.; Hummer, K.; Kresse, I. C.; Gerber, G.; Angyan, J. G. Screened Hybrid Density Functionals Applied to Solids. J. Chem. Phys. 2006, 124, 154709. (53) Paier, J.; Marsman, M.; Hummer, K.; Kresse, I. C.; Gerber, G.; Angyan, J. G. Erratum: ”Screened Hybrid Density Functionals Applied to Solids. J. Chem. Phys. 2006, 124, 154709. (54) Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for Mixing Exact Exchange with Density Functional Approximations. J. Chem. Phys. 1996, 105, 9982. (55) Modrzejewski, M.; Chalasinski, G.; Szczesniak, M. M. RangeSeparated meta-GGA Functional Designed for Noncovalent Interactions. J. Chem. Theory Comput. 2014, 10, 4297−4306. (56) Koppen, J. V.; et al. Density Functional Theory Approach to Gold-ligand Interactions: Separating True Effects from Artifacts. J. Chem. Phys. 2014, 140, 244313. (57) Kuemmel, S.; Kronik, L. Orbital-Dependent Density Functionals: Theory and Applications. Rev. Mod. Phys. 2008, 80, 3−60. (58) Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseris, G. E. TPSS: Climbing the Density Functional Ladder: Nonempirical MetaGeneralized Gradient Approximation Designed for Molecules and Solids. Phys. Rev. Lett. 2003, 91, 146401. (59) Bredas, J.-L. Mind the Gap! Mater. Horiz. 2014, 1, 17−19. (60) Diaz, A.; Crowley, J.; Bargon, J.; Gardini, G. P.; Torrance, J. B. Electrooxidation of Aromatic Oligomers and Conducting Polymers. J. Electroanal. Chem. 1981, 121, 355−361. (61) Rittmeyer, S. P.; Groβ, A. Structural and Electronic Properties of Oligo- and Polythiophenes Modified by Substituents. Beilstein J. Nanotechnol. 2012, 3, 909−919. (62) Niskanen, M.; Hukka, T. I. Modeling of Photoactive Conjugated Donor-Acceptor Copolymers: The Effect of the Exact HF Exchange in
DFT Functionals on Geometries and Gap Energies of Oligomer and Periodic Models. Phys. Chem. Chem. Phys. 2014, 16, 13294−13305. (63) Giannozzi, P. e. a. QUANTUM ESPRESSO: A Modular and Open-Source Software Project for Quantum Simulations of Materials. J. Phys.: Condens. Matter 2009, 21, 395502. (64) Malcioglu, O. B.; Gebauer, R.; Rocca, D.; Baroni, S. turboTDDFT - A Code for the Simulation of Molecular Spectra using the Liouville-Lanczos Approach to Time-Dependent Density-Functional Perturbation Theory. Comput. Phys. Commun. 2011, 182, 1744−1754. (65) Rocca, D.; Saad, Y.; Gebauer, R.; Baroni, S. Turbo Charging Time-Dependent Density-Functional Theory with Lanczos Chains. J. Chem. Phys. 2008, 128, 154105. (66) Sony, P.; Shukla, A. Large-Scale Correlated Calculations of Linear Optical Absorption and Low-Lying Excited States of Polyacenes: Pariser-Parr-Pople Hamiltonian. Phys. Rev. B 2007, 75, 155208.
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