Effect of Solid-State Polarization on Charge-Transfer Excitations and

Letter pubs.acs.org/JPCL

Effect of Solid-State Polarization on Charge-Transfer Excitations and Transport Levels at Organic Interfaces from a Screened RangeSeparated Hybrid Functional Zilong Zheng,† David A. Egger,‡ Jean-Luc Brédas,*,† Leeor Kronik,*,‡ and Veaceslav Coropceanu*,† †

School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States ‡ Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel S Supporting Information *

ABSTRACT: We develop a robust approach for the description of the energetics of chargetransfer (CT) excitations and transport levels at organic interfaces based on a screened range-separated hybrid (SRSH) functional. We find that SRSH functionals correctly capture the effect of solid-state electronic polarization on transport gap renormalization and on screening of the electrostatic electron−hole interaction. With respect to calculations based on nonscreened optimally tuned RSH (long-range corrected) functionals, the SRSH-based calculations can be performed for both isolated molecular complexes and systems embedded in a dielectric medium with the same range-separation parameter, which allows a clear physical interpretation of the results in terms of solid-state polarization without any perturbation of the molecular electronic structure. By considering weakly interacting donor/ acceptor complexes of pentacene with C60 and poly-3-hexylthiophene (P3HT) with PCBM, we show that this new approach provides CT-state energies that compare very well with experimental data.

I

as a long-range corrected functional), the Coulomb interaction is partitioned using the error function, in the form

n organic solar cells (OSCs), the charge-transfer (CT) electronic states that appear at the interface between the electron-donor (D) and electron-acceptor (A) components play a major role in both exciton-dissociation and chargerecombination processes,1−4 which explains why they are the focus of extensive experimental5−12 and theoretical studies.12−30 Organic materials used currently for photovoltaics applications are characterized by low dielectric constants (in the range of 3−5), which is believed to be a major factor limiting OSC efficiency.31−34 Low dielectric constants result, for example, in substantial hole−electron binding energies at D/ A interfaces and thus reduced dissociation rates of the CT states into free charge carriers. However, an in-depth understanding of how electronic processes in OSCs are impacted by the materials dielectric features is still lacking. Therefore, the development of computational approaches that can account for the effects stemming from both the chemical structures of the D and A materials and the electronic polarization (dielectric screening) is highly desirable. Here we focus on the role played by electronic polarization on the CT excitations and transport levels. Density functional theory (DFT) is currently the method of choice for the quantum-mechanical description of the interfacial CT states. Because standard semilocal and global hybrid exchange-correlation functionals do not provide the correct asymptotic, 1/r, dependence of the long-range potential of a gas-phase system,35−38 most recent DFT studies on CT states are based on range-separated hybrid (RSH) functionals.20,24−26,36,39 In a simple RSH functional (also referred to © 2017 American Chemical Society

erf(ωr ) 1 − erf(ωr ) 1 = + r r r

(1)

where the first and second terms on the right-hand side of the equation correspond to long-range and short-range repulsion, respectively, and ω is the range-separation (RS) parameter. Hartree−Fock (HF) exchange is employed to treat long-range exchange, whereas a local or semilocal DFT functional is used to treat short-range exchange. It has been shown that RSH functionals provide the best predictions for gas-phase chargetransfer excitations when the RS parameter is optimally tuned (OT), for a given system, using a physically motivated “tuning condition”,40,41 an issue elaborated further on below. Initial studies by Minami et al. and independently by some of the present authors on pentacene/C60 complexes24−26 used an OT-RSH approach with a tuning procedure based on results derived for an isolated system (in vacuum; referred to below as DFT/ωvac). While these calculations yielded a significantly lower CT energy than calculations based on the default ω values (by up to 1 eV), the CT energy was still too high with respect to experimental data obtained at the solid-state interface. Specifically, it was found to be higher than the lowest Received: May 22, 2017 Accepted: June 30, 2017 Published: June 30, 2017 3277

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The Journal of Physical Chemistry Letters local pentacene and C60 valence excitation energies,24 in contrast with experimental observations.9 Gas-phase CT energies of such D/A complexes are indeed expected to overestimate the solid-state experimental values because DFT calculations performed on isolated systems do not account for electronic polarization. The impact of the solidstate environment on the isolated complex can be mimicked by combining an OT-RSH functional based on eq 1 with the polarizable continuum model (PCM).42 Indeed, PCM-based total energy corrections of gas-phase OT-RSH calculations were found to be useful for estimating the fundamental gaps of organic solids.43 However, if the gas-phase optimal ω value is used, then the PCM treatment was found to have a minimal effect (typically 8. For εD values in the range of 3− 5 the values that are most relevant for organic semiconductors, the calculated Ee and Em el do not compare in the same consistent way as in the SRSH calculations. This means that while modifying the RS parameter in the unscreened RSH can mimic electrostatic screening, it does not do so in a complete way. It is also important to note that for εD > 3 the ECT derived by means of the unscreened OT-RSH calculations shows only a marginal dependence on the dielectric constant. For example, the change in ECT when εD increases from 3 to 8 is only 6 meV, in comparison with the 431 meV value obtained by means of screened RSH calculations. In conclusion, we have investigated the performance of SRSH functionals in describing the energetics of charge-transfer states in weakly interacting pentacene/C60 and P3HT/PCBM donor/acceptor complexes. We found that SRSH functionals are capable of correctly capturing the effect of solid-state electronic polarization on the gap renormalization and on the screening of the electrostatic electron−hole interaction, thereby providing CT energies that compare very well with experimental data. With respect to calculations based on nonscreened RSH (LRC) functionals, the calculations based on the SRSH functionals can be performed for both isolated molecules or molecular complexes and systems embedded in a dielectric medium with the same range-separated parameter. This makes the results of such calculations much more amenable to a clear physical interpretation in terms of solidstate polarization without perturbation of the molecular electronic structure. In particular, they allow a well-defined partitioning of the charge-transfer energy into contributions from the HOMOD − LUMOA (transport) gap and the electron−hole attraction. Finally, we stress that in designing organic materials with large dielectric constants, the ionization potential of the donor component and the electron affinity of the acceptor component must be carefully managed so that the benefit obtained from enhancing dielectric screening and charge separation does not come at the expense of lowering the open-circuit voltage.

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pentacene/C60 and P3HT/PCBM complexes as a function of 1/ε; dependence of the gap energy, CT state energy, and electrostatic energy computed from TDDFT and using the Mulliken charges of the pentacene/C60 complex as a function of the RS parameter; optimized ωvac and ωPCM values for the pentacene/C60 and P3HT/PCBM complexes. (PDF)

AUTHOR INFORMATION

Corresponding Authors

*J.-L.B.: E-mail: [email protected]. *L.K.: E-mail: [email protected]. *V.C.: E-mail: [email protected]. ORCID

Zilong Zheng: 0000-0003-4310-2755 Jean-Luc Brédas: 0000-0001-7278-4471 Veaceslav Coropceanu: 0000-0003-1693-2315 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.K. acknowledges support from the European Research Council and the historic generosity of the Perlman Family. D.A.E. was additionally supported by the Austrian Science Fund (FWF): J3608-N20. The work at the Georgia Institute of Technology was supported by the Department of the Navy, Office of Naval Research, under the MURI “Center for Advanced Organic Photovoltaics” (Awards Nos. N00014-14-10580 and N00014-16-1-2520) and by the Army Research Office (Award No. W911NF-13-1-0387).

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REFERENCES

(1) Brédas, J. L.; Norton, J. E.; Cornil, J.; Coropceanu, V. Molecular Understanding of Organic Solar Cells: The Challenges. Acc. Chem. Res. 2009, 42, 1691−1699. (2) Vandewal, K.; Albrecht, S.; Hoke, E. T.; Graham, K. R.; Widmer, J.; Douglas, J. D.; Schubert, M.; Mateker, W. R.; Bloking, J. T.; Burkhard, G. F.; Sellinger, A.; Frechet, J. M. J.; Amassian, A.; Riede, M. K.; McGehee, M. D.; Neher, D.; Salleo, A. Efficient Charge Generation by Relaxed Charge-Transfer States at Organic Interfaces. Nat. Mater. 2013, 13, 63−68. (3) Gelinas, S.; Rao, A.; Kumar, A.; Smith, S. L.; Chin, A. W.; Clark, J.; van der Poll, T. S.; Bazan, G. C.; Friend, R. H. Ultrafast Long-Range Charge Separation in Organic Semiconductor Photovoltaic Diodes. Science 2014, 343, 512−516. (4) Beljonne, D.; Cornil, J.; Muccioli, L.; Zannoni, C.; Brédas, J. L.; Castet, F. Electronic Processes at Organic-Organic Interfaces: Insight from Modeling and Implications for Opto-electronic Devices. Chem. Mater. 2011, 23, 591−609. (5) Deotare, P. B.; Chang, W.; Hontz, E.; Congreve, D. N.; Shi, L.; Reusswig, P. D.; Modtland, B.; Bahlke, M. E.; Lee, C. K.; Willard, A. P.; Bulovic, V.; Van Voorhis, T.; Baldo, M. A. Nanoscale Transport of Charge-Transfer States in Organic Donor-Acceptor Blends. Nat. Mater. 2015, 14, 1130−1134. (6) Devižis, A.; De Jonghe-Risse, J.; Hany, R.; Nüesch, F.; Jenatsch, S.; Gulbinas, V.; Moser, J.-E. Dissociation of Charge Transfer States and Carrier Separation in Bilayer Organic Solar Cells: A TimeResolved Electroabsorption Spectroscopy Study. J. Am. Chem. Soc. 2015, 137, 8192−8198. (7) Vandewal, K. Interfacial Charge Transfer States in Condensed Phase Systems. Annu. Rev. Phys. Chem. 2016, 67, 113−133. (8) Guan, Z.; Li, H. W.; Zhang, J.; Cheng, Y.; Yang, Q.; Lo, M. F.; Ng, T. W.; Tsang, S. W.; Lee, C. S. Evidence of Delocalization in

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01276. Dependence of the IP, EA, HOMO, and LUMO energies of the pentacene/C60 and P3HT/PCBM molecules and complexes as a function of 1/ε; dependence of the lowest charge-transfer state and lowest local excited state energies of pentacene/C60 and P3HT/PCBM complexes as a function of 1/ε; HOMO(D)−LUMO(A) gap energy and energy of the CT state obtained from TDDFT and an electrostatic model using Mulliken charges for 3281

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The Journal of Physical Chemistry Letters Charge-Transfer State Manifold for Donor:Acceptor Organic Photovoltaics. ACS Appl. Mater. Interfaces 2016, 8, 21798−21805. (9) Brigeman, A. N.; Fusella, M. A.; Yan, Y.; Purdum, G. E.; Loo, Y.L.; Rand, B. P.; Giebink, N. C. Revealing the Full Charge Transfer State Absorption Spectrum of Organic Solar Cells. Adv. Energy Mater. 2016, 6, 1601001. (10) Bakulin, A. A.; Rao, A.; Pavelyev, V. G.; van Loosdrecht, P. H. M.; Pshenichnikov, M. S.; Niedzialek, D.; Cornil, J.; Beljonne, D.; Friend, R. H. The Role of Driving Energy and Delocalized States for Charge Separation in Organic Semiconductors. Science 2012, 335, 1340−1344. (11) Jailaubekov, A. E.; Willard, A. P.; Tritsch, J. R.; Chan, W.-L.; Sai, N.; Gearba, R.; Kaake, L. G.; Williams, K. J.; Leung, K.; Rossky, P. J.; Zhu, X. Y. Hot Charge-Transfer Excitons Set the Time Limit for Charge Separation at Donor/Acceptor Interfaces in Organic Photovoltaics. Nat. Mater. 2012, 12, 66−73. (12) Scholz, R.; Luschtinetz, R.; Seifert, G.; Jägeler-Hoheisel, T.; Körner, C.; Leo, K.; Rapacioli, M. Quantifying Charge Transfer Energies at Donor−Acceptor Interfaces in Small-Molecule Solar Cells with Constrained DFTB and Spectroscopic Methods. J. Phys.: Condens. Matter 2013, 25, 473201. (13) Shen, X.; Han, G.; Yi, Y. The Nature of Excited States in Dipolar Donor/Fullerene Complexes for Organic Solar Cells: Evolution with the Donor Stack Size. Phys. Chem. Chem. Phys. 2016, 18, 15955− 15963. (14) Yi, Y. P.; Coropceanu, V.; Brédas, J. L. Exciton-Dissociation and Charge-Recombination Processes in Pentacene/C-60 Solar Cells: Theoretical Insight into the Impact of Interface Geometry. J. Am. Chem. Soc. 2009, 131, 15777−15783. (15) Chen, X.-K.; Ravva, M. K.; Li, H.; Ryno, S. M.; Brédas, J.-L. Effect of Molecular Packing and Charge Delocalization on the Nonradiative Recombination of Charge-Transfer States in Organic Solar Cells. Adv. Energy Mater. 2016, 6, 1601325. (16) Few, S.; Frost, J. M.; Nelson, J. Models of Charge Pair Generation in Organic Solar Cells. Phys. Chem. Chem. Phys. 2015, 17, 2311−2325. (17) Lee, M. H.; Dunietz, B. D.; Geva, E. Donor-to-Donor vs Donorto-Acceptor Interfacial Charge Transfer States in the PhthalocyanineFullerene Organic Photovoltaic System. J. Phys. Chem. Lett. 2014, 5, 3810−3816. (18) Lin, B.-C.; Koo, B. T.; Clancy, P.; Hsu, C.-P. Theoretical Investigation of Charge-Transfer Processes at Pentacene−C60Interface: The Importance of Triplet Charge Separation and Marcus Electron Transfer Theory. J. Phys. Chem. C 2014, 118, 23605−23613. (19) Ma, H.; Troisi, A. Direct Optical Generation of Long-Range Charge-Transfer States in Organic Photovoltaics. Adv. Mater. 2014, 26, 6163−6167. (20) Manna, A. K.; Balamurugan, D.; Cheung, M. S.; Dunietz, B. D. Unraveling the Mechanism of Photoinduced Charge Transfer in Carotenoid-Porphyrin-C60 Molecular Triad. J. Phys. Chem. Lett. 2015, 6, 1231−1237. (21) Tamura, H.; Burghardt, I. Ultrafast Charge Separation in Organic Photovoltaics Enhanced by Charge Delocalization and Vibronically Hot Exciton Dissociation. J. Am. Chem. Soc. 2013, 135, 16364−16367. (22) Zhao, Y.; Liang, W. Charge Transfer in Organic Molecules for Solar Cells: Theoretical Perspective. Chem. Soc. Rev. 2012, 41, 1075− 1087. (23) Zheng, Z.; Brédas, J. L.; Coropceanu, V. Description of the Charge Transfer States at the Pentacene/C60 Interface: Combining Range-Separated Hybrid Functionals with the Polarizable Continuum Model. J. Phys. Chem. Lett. 2016, 7, 2616−2621. (24) Zhang, C.-R.; Sears, J. S.; Yang, B.; Aziz, S. G.; Coropceanu, V.; Brédas, J.-L. Theoretical Study of the Local and Charge-Transfer Excitations in Model Complexes of Pentacene-C-60 Using Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2014, 10, 2379−2388. (25) Minami, T.; Ito, S.; Nakano, M. Functional Dependence of Excitation Energy for Pentacene/C60 Model Complex in the

Nonempirically Tuned Long-Range Corrected Density Functional Theory. Int. J. Quantum Chem. 2013, 113, 252−256. (26) Minami, T.; Nakano, M.; Castet, F. Nonempirically Tuned Long-Range Corrected Density Functional Theory Study on Local and Charge-Transfer Excitation Energies in a Pentacene/C-60 Model Complex. J. Phys. Chem. Lett. 2011, 2, 1725−1730. (27) Sampat, S.; Mohite, A. D.; Crone, B.; Tretiak, S.; Malko, A. V.; Taylor, A. J.; Yarotski, D. A. Tunable Charge Transfer Dynamics at Tetracene/LiF/C60 Interfaces. J. Phys. Chem. C 2015, 119, 1286− 1290. (28) Niedzialek, D.; Duchemin, I.; de Queiroz, T. B.; Osella, S.; Rao, A.; Friend, R.; Blase, X.; Kümmel, S.; Beljonne, D. First Principles Calculations of Charge Transfer Excitations in Polymer−Fullerene Complexes: Influence of Excess Energy. Adv. Funct. Mater. 2015, 25, 1972−1984. (29) D’Avino, G.; Muccioli, L.; Olivier, Y.; Beljonne, D. Charge Separation and Recombination at Polymer−Fullerene Heterojunctions: Delocalization and Hybridization Effects. J. Phys. Chem. Lett. 2016, 7, 536−540. (30) Akimov, A. V.; Prezhdo, O. V. Nonadiabatic Dynamics of Charge Transfer and Singlet Fission at the Pentacene/C-60 Interface. J. Am. Chem. Soc. 2014, 136, 1599−1608. (31) Koster, L. J. A.; Shaheen, S. E.; Hummelen, J. C. Pathways to a New Efficiency Regime for Organic Solar Cells. Adv. Energy Mater. 2012, 2, 1246−1253. (32) Leblebici, S.; Lee, J.; Weber-Bargioni, A.; Ma, B. W. Dielectric Screening To Reduce Charge Transfer State Binding Energy in Organic Bulk Heterojunction Photovoltaics. J. Phys. Chem. C 2017, 121, 3279−3285. (33) Zhang, G. R.; Clarke, T. M.; Mozer, A. J. Bimolecular Recombination in a Low Bandgap Polymer:PCBM Blend Solar Cell with a High Dielectric Constant. J. Phys. Chem. C 2016, 120, 7033− 7043. (34) Armin, A.; Stoltzfus, D. M.; Donaghey, J. E.; Clulow, A. J.; Nagiri, R. C. R.; Burn, P. L.; Gentle, I. R.; Meredith, P. Engineering Dielectric Constants in Organic Semiconductors. J. Mater. Chem. C 2017, 5, 3736−3747. (35) Cohen, A. J.; Mori-Sánchez, P.; Yang, W. Challenges for Density Functional Theory. Chem. Rev. 2012, 112, 289−320. (36) Kümmel, S.; Kronik, L. Orbital-Dependent Density Functionals: Theory and Applications. Rev. Mod. Phys. 2008, 80, 3−60. (37) Dreuw, A.; Head-Gordon, M. Failure of Tme-Dependent Density Functional Theory for Long-Range Charge-Transfer Excited States: The Zincbacteriochlorin-Bacterlochlorin and Bacteriochlorophyll-Spheroidene Complexes. J. Am. Chem. Soc. 2004, 126, 4007− 4016. (38) Tozer, D. J. Relationship Between Long-Range Charge-Transfer Excitation Energy Error and Integer Discontinuity in Kohn−Sham Theory. J. Chem. Phys. 2003, 119, 12697−12699. (39) Manna, A. K.; Lee, M. H.; McMahon, K. L.; Dunietz, B. D. Calculating High Energy Charge Transfer States Using Optimally Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2015, 11, 1110−1117. (40) Stein, T.; Kronik, L.; Baer, R. Reliable Prediction of Charge Transfer Excitations in Molecular Complexes Using Time-Dependent Density Functional Theory. J. Am. Chem. Soc. 2009, 131, 2818−2820. (41) Stein, T.; Kronik, L.; Baer, R. Prediction of Charge-Transfer Excitations in Coumarin-Based Dyes Using a Range-Separated Functional Tuned From First Principles. J. Chem. Phys. 2009, 131, 244119. (42) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3093. (43) Phillips, H.; Zheng, Z. L.; Geva, E.; Dunietz, B. D. Orbital Gap Predictions For Rational Design of Organic Photovoltaic Materials. Org. Electron. 2014, 15, 1509−1520. (44) de Queiroz, T. B.; Kümmel, S. Charge-Transfer Excitations in Low-Gap Systems Under the Influence of Solvation and Conformational Disorder: Exploring Range-Separation Tuning. J. Chem. Phys. 2014, 141, 084303. 3282

DOI: 10.1021/acs.jpclett.7b01276 J. Phys. Chem. Lett. 2017, 8, 3277−3283

Letter

The Journal of Physical Chemistry Letters (45) Sun, H. T.; Ryno, S.; Zhong, C.; Ravva, M. K.; Sun, Z. R.; Korzdorfer, T.; Brédas, J. L. Ionization Energies, Electron Affinities, and Polarization Energies of Organic Molecular Crystals: Quantitative Estimations from a Polarizable Continuum Model (PCM)-Tuned Range-Separated Density Functional Approach. J. Chem. Theory Comput. 2016, 12, 2906−2916. (46) de Queiroz, T. B.; Kümmel, S. Tuned Range Separated Hybrid Functionals for Solvated Low Bandgap Oligomers. J. Chem. Phys. 2015, 143, 034101. (47) Bokareva, O. S.; Grell, G.; Bokarev, S. I.; Kuhn, O. Tuning Range-Separated Density Functional Theory for Photocatalytic Water Splitting Systems. J. Chem. Theory Comput. 2015, 11, 1700−1709. (48) Baer, R.; Neuhauser, D. Density Functional Theory with Correct Long-Range Asymptotic Behavior. Phys. Rev. Lett. 2005, 94, 043002. (49) Refaely-Abramson, S.; Sharifzadeh, S.; Jain, M.; Baer, R.; Neaton, J. B.; Kronik, L. Gap Renormalization of Molecular Crystals from Density-Functional Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 88, 081204. (50) Yanai, T.; Tew, D. P.; Handy, N. C. A New Hybrid ExchangeCorrelation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (51) Lüftner, D.; Refaely-Abramson, S.; Pachler, M.; Resel, R.; Ramsey, M. G.; Kronik, L.; Puschnig, P. Experimental and Theoretical Electronic Structure of Quinacridone. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 075204. (52) Refaely-Abramson, S.; Jain, M.; Sharifzadeh, S.; Neaton, J. B.; Kronik, L. Solid-State Optical Absorption from Optimally Tuned Time-Dependent Range-Separated Hybrid Density Functional Theory. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 081204. (53) Liu, Z.-F.; Egger, D. A.; Refaely-Abramson, S.; Kronik, L.; Neaton, J. B. Energy Level Alignment at Molecule-Metal Interfaces from an Optimally Tuned Range-Separated Hybrid Functional. J. Chem. Phys. 2017, 146, 092326. (54) Shao, Y.; Molnar, L. F.; Jung, Y.; Kussmann, J.; Ochsenfeld, C.; Brown, S. T.; Gilbert, A. T. B.; Slipchenko, L. V.; Levchenko, S. V.; O’Neill, D. P.; DiStasio, R. A., Jr.; Lochan, R. C.; Wang, T.; Beran, G. J. O.; Besley, N. A.; Herbert, J. M.; Yeh Lin, C.; Van Voorhis, T.; Hung Chien, S.; Sodt, A.; Steele, R. P.; Rassolov, V. A.; Maslen, P. E.; Korambath, P. P.; Adamson, R. D.; Austin, B.; Baker, J.; Byrd, E. F. C.; Dachsel, H.; Doerksen, R. J.; Dreuw, A.; Dunietz, B. D.; Dutoi, A. D.; Furlani, T. R.; Gwaltney, S. R.; Heyden, A.; Hirata, S.; Hsu, C.-P.; Kedziora, G.; Khalliulin, R. Z.; Klunzinger, P.; Lee, A. M.; Lee, M. S.; Liang, W.; Lotan, I.; Nair, N.; Peters, B.; Proynov, E. I.; Pieniazek, P. A.; Min Rhee, Y.; Ritchie, J.; Rosta, E.; David Sherrill, C.; Simmonett, A. C.; Subotnik, J. E.; Lee Woodcock Iii, H.; Zhang, W.; Bell, A. T.; Chakraborty, A. K.; Chipman, D. M.; Keil, F. J.; Warshel, A.; Hehre, W. J.; Schaefer Iii, H. F.; Kong, J.; Krylov, A. I.; Gill, P. M. W.; HeadGordon, M. Advances in Methods and Algorithms in a Modern Quantum Chemistry Program Package. Phys. Chem. Chem. Phys. 2006, 8, 3172−3191. (55) Hirata, S.; Head-Gordon, M. Time-Dependent Density Functional Theory for Radicals - An Improved Description of Excited States with Substantial Double Excitation Character. Chem. Phys. Lett. 1999, 302, 375−382. (56) Srebro, M.; Autschbach, J. Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient. J. Phys. Chem. Lett. 2012, 3, 576− 581. (57) Rohrdanz, M. A.; Martins, K. M.; Herbert, J. M. A Long-RangeCorrected Density Functional that Performs Well for Both GroundState Properties and Time-Dependent Density Functional Theory Excitation Energies, Including Charge-Transfer Excited States. J. Chem. Phys. 2009, 130, 054112. (58) Refaely-Abramson, S.; Sharifzadeh, S.; Govind, N.; Autschbach, J.; Neaton, J. B.; Baer, R.; Kronik, L. Quasiparticle Spectra from a Nonempirical Optimally Tuned Range-Separated Hybrid Density Functional. Phys. Rev. Lett. 2012, 109, 226405.

(59) Kronik, L.; Stein, T.; Refaely-Abramson, S.; Baer, R. Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2012, 8, 1515−1531. (60) Vandewal, K.; Tvingstedt, K.; Gadisa, A.; Inganas, O.; Manca, J. V. Relating the Open-Circuit Voltage to Interface Molecular Properties of Donor:Acceptor Bulk Heterojunction Solar Cells. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 125204. (61) Veldman, D.; Ipek, O.; Meskers, S. C. J.; Sweelssen, J.; Koetse, M. M.; Veenstra, S. C.; Kroon, J. M.; van Bavel, S. S.; Loos, J.; Janssen, R. A. J. Compositional and Electric Field Dependence of the Dissociation of Charge Transfer Excitons in Alternating Polyfluorene Copolymer/Fullerene Blends. J. Am. Chem. Soc. 2008, 130, 7721− 7735. (62) Bernardo, B.; Cheyns, D.; Verreet, B.; Schaller, R. D.; Rand, B. P.; Giebink, N. C. Delocalization and Dielectric Screening of Charge Transfer States in Organic Photovoltaic Cells. Nat. Commun. 2014, 5, 3245. (63) Loi, M. A.; Toffanin, S.; Muccini, M.; Forster, M.; Scherf, U.; Scharber, M. Charge Transfer Excitons in Bulk Heterojunctions of a Polyfluorene Copolymer and a Fullerene Derivative. Adv. Funct. Mater. 2007, 17, 2111−2116. (64) Chen, S.; Tsang, S. W.; Lai, T. H.; Reynolds, J. R.; So, F. Dielectric Effect on the Photovoltage Loss in Organic Photovoltaic Cells. Adv. Mater. 2014, 26, 6125−6131. (65) Hwang, J.; Wan, A.; Kahn, A. Energetics of Metal-Organic Interfaces: New Experiments and Assessment of the Field. Mater. Sci. Eng., R 2009, 64, 1−31. (66) Schwedhelm, R.; Kipp, L.; Dallmeyer, A.; Skibowski, M. Experimental Band Gap and Core-Hole Electron Interaction in Epitaxial C-60 Films. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 58, 13176−13180.

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DOI: 10.1021/acs.jpclett.7b01276 J. Phys. Chem. Lett. 2017, 8, 3277−3283