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

Jun 30, 2017 - School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgi...
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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

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

Letter

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.





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.



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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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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