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Letter

Effect of Solid-State Polarization on Charge-Transfer Excitations and Transport Levels at Organic Interfaces from a Screened Range-Separated Hybrid Functional Zilong Zheng, David A. Egger, Jean-Luc Bredas, Leeor Kronik, and Veaceslav Coropceanu J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b01276 • Publication Date (Web): 30 Jun 2017 Downloaded from http://pubs.acs.org on July 2, 2017

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The Journal of Physical Chemistry Letters

Effect of Solid-State Polarization on Charge-Transfer Excitations and Transport Levels at Organic Interfaces from a Screened Range-Separated Hybrid Functional

Zilong Zheng,1 David A. Egger2, Jean-Luc Brédas,1* Leeor Kronik,2* and Veaceslav Coropceanu1*

1

School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 2 Department of Materials and Interfaces, Weizmann Institute of Science, Rehovoth 76100, Israel *Emails: [email protected]; [email protected]; [email protected]

Abstract In this work, we develop a robust approach for the description of the energetics of charge-transfer (CT) excitations and transport levels at organic interfaces, based on a 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 1

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non-screened optimally tuned RSH (long-range corrected) functionals, the SRSH-based calculations can be performed for both isolated molecular complexes and systems embedded 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 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.

Table of Contents (TOC) Graphic

Pentacene/C60 (Donor) 4

Energy/eV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(Acceptor)

OT-SRSH

OT-RSH/PCM

∆E=EL(A)-EH(D)

3

ECT 2 1 0

∆E-ECT

|ECoulomb|

0.4 0.8

0.4 0.8 1/ε

1/ε

2


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In 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 charge-recombination 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. Since standard semi-local 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 CT states are based on range-separated hybrid (RSH) functionals.20, 24-26, 36, 39 In a simple

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functional (also referred to as a long-range corrected functional), the Coulomb interaction is partitioned using the error function, in the form:

1 erf (ωr ) 1 − erf (ωr ) = + , 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 semi-local DFT functional is used to treat short-range exchange. It has been shown that RSH functionals provide the best predictions for gas-phase charge-transfer excitations when the range-separation (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 local pentacene and C60 valence excitation energies,24 in contrast to experimental observations.9 Gas-phase CT energies of such D/A complexes are indeed expected to overestimate the solid-state experimental values since DFT calculations performed on isolated systems do not account for electronic polarization. The impact of the solid-state environment on the isolated complex can be mimicked by combining an OT-RSH functional based on Eq. (1) with the 4


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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, the PCM treatment was found to have a minimal effect (typically 3 the ECT derived by means of the unscreened OT-RSH calculations show 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 to the 431 meV value obtained by means of screened RSH calculations.

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Figure 4. Dependence of the gap energy (Egap), CT energy (ECT), and electrostatic energy (Eel=ECT-Egap), computed using DFT and TDDFT at the SRSH-PBEh/6-31G(d, p) level with ω=ωvac, as well as electrostatic energy (

) computed from Mulliken charges using

ε=1/(α+β) as the dielectric constant, for (a) the pentacene/C60 complex and (b) the P3HT/PCBM complex, as a function of 1/ε .

In conclusion, we have investigated the performance of screened range-separated hybrid (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 capturing correctly 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 non-screened RSH (LRC) functionals, the calculations based on the 17



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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 solid-state 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.

Ackowledgments: 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. N00014-14-1-0580 and N00014-16-1-2520) and by the Army Research Office (Award No. W911NF-13-1-0387).

Supporting Information Available: 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 18


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Mulliken charges for 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.

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