Article pubs.acs.org/JPCA
Predicting Properties of Organic Optoelectronic Materials: Asymptotically Corrected Density Functional Study Archana Rajendran,† Takashi Tsuchiya,‡,⊥ So Hirata,§ and Tzvetelin D. Iordanov*,∥ †
Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611, United States Quantum Theory Project, Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States § Department of Chemistry, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States ∥ Department of Chemistry, Georgia Southwestern State University, Americus, Georgia 31709, United States ‡
ABSTRACT: A practical computational procedure has been proposed that provides key electronic parameters of a polymer (fundamental bandgap, ionization energy, electron affinity, and intrachain electron and hole mobilities) determining its suitability as a donor or acceptor in organic optoelectronic materials. Series of oligomer calculations at the Becke3−Lee− Yang−Parr level with and without a self-contained asymptotic correction using the 6-31G** basis set were performed. The bandgap, ionization energy, and electron affinities of a polymer are extrapolated from those of its oligomers obtained from the highest occupied and lowest unoccupied orbital energies in the Koopmans-like approximation. This scheme has been applied to conjugated polymers having the poly(p-phenylene), poly(thiophene), or poly(pyrrole) backbone as well as to PCBM. The observed values of the electronic parameters have been reproduced within less than 1 eV in most cases. With the predicted values of these parameters, estimates of the open-circuit voltage and drift potential have been made for 22 valid donor−acceptor combinations. Several potentially useful combinations have been identified including the poly(thiophene):PCBM. The electron and hole mobilities have been found to correlate more strongly with the conformation (planarity) than the bandgap, but otherwise do not differ significantly.
1. INTRODUCTION The recent advances in optoelectronic devices have been stimulated by the development of new semiconducting materials based on conjugated hydrocarbons. Applications include, but are not limited to, photovoltaic solar cells (PSC),1−3 light emitting diodes (LEDs),4,5 field effect transistors (FETs),6−8 sensing devices,9 batteries, and supercapacitors.10 The optoelectronic properties of these materials are determined by electronic parameters such as the fundamental bandgap (Eg), ionization energy (IP), electron affinity (EA), and charge mobility; they are key electronic parameters considered in the selection process of p-type electron-donor (D) and n-type electron-acceptor (A) compounds for optoelectronic applications. The importance of electronic parameters is easier to understand from the simplified energy band diagram of the organic solar cell heterojunction presented in Figure 1. Absorption of a photon by the absorber material(s) leads to promotion of an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). The electron− hole pair is generated, and the Coulomb attraction results in a formation of a bound excited state, exciton. Since the opencircuit voltage (Voc) of a solar cell is proportional to the LUMO2−HOMO1 difference, larger bandgaps are desirable. However, a greater short-circuit current (Isc) requires smaller excitation energies, ω1 or ω2; thus, smaller bandgaps are preferred. Since the maximum power (Pmax) attainable is © 2012 American Chemical Society
Figure 1. Energy band diagram of heterojunction. See text for the definitions of acronyms.
proportional to the product of open-circuit voltage and shortcircuit current (Voc, Isc), an efficient PSC must balance these two competing requirements. Received: August 24, 2012 Revised: November 14, 2012 Published: November 16, 2012 12153
dx.doi.org/10.1021/jp3084315 | J. Phys. Chem. A 2012, 116, 12153−12162
The Journal of Physical Chemistry A
Article
In organic photovoltaics, it is highly desirable for the exciton to dissociate into a free electron and a free hole at the D/A interface. The dissociation is facilitated by the energy difference of the donor and acceptor HOMO or that in LUMO (αh and αe in Figure 1), which serves as an electric driving force separating an electron and a hole and preventing undesirable geminate recombination. The greater the drift potentials (αh and αe), the higher the efficiency, but the large drift potentials have the inevitable side effect of compressing the LUMO2−HOMO1 gap and thus Voc. Furthermore, the intrachain and interchain mobility of the electrons and holes should be greater for higher efficiency. The intrachain hole and electron mobility correlates with the valence (W1) and conduction band-widths (W2), respectively. Another practical consideration is the air stability. The ionization energies of both donor and acceptor materials should be greater than 5.2 eV lest the device lifetime is shorter. Consequently, it is critical to know the electronic parameters of donor and acceptor materials accurately and match them across the interface to obtain optimally efficient devices. Additionally, the device efficiency can be improved by modifying the molecular structure of these materials so as to tune the energy levels.11 Computational methods that can determine these parameters with the accuracy of 0.1 eV are highly desirable because expensive, difficult, and sometimes dangerous synthetic work can be avoided for all but a few computationally selected candidates.12,13 Electronic structure methods that are routinely applicable to conjugated polymers are presently limited to the ones based on density functional theory (DFT).14,15 Approximations to exchange-correlation functionals, inevitable in DFT, tend to cause substantial errors in the very electronic parameters of our interest.16−20 For instance, the local density approximation (LDA) and generalized gradient-correction approximation (GGA) to exchange-correlation functionals severely underestimate IP (within the Koopmans-like treatment) and Eg. They also lack the ability to describe charge separation and transfer, the very physical process underlying all molecular electronics. It has also been reported21,22 that LDA and GGA predict erroneously (nearly) metallic ground state for the prototypical conjugated polymer, trans-polyacetylene, at 0 K in violation of Peierls’ theorem. The cause of these shortcomings is well established: the incomplete cancellation of electron self-interaction between the classical Coulomb term and approximate exchange functional. They can thus be alleviated by a hybrid exchange-correlation functional, such as B3LYP,23 which includes a partial (20% in B3LYP) admixture of Hartree−Fock (HF) exchange, which has no self-interaction problem. Furthermore, schemes16−18 have been invented to correct the nonphysical asymptotes in exchange-correlation potentials that are caused by the spurious self-interaction and are responsible for the underestimation of IP’s. Hirata et al. have proposed such a scheme under the acronym B3LYP(AC),24 where AC stands for the asymptotic correction. It has been demonstrated that the AC reduces the errors in IP’s of small molecules from as much as 4−6 eV in GGA predictions to
