Efficient Computational Screening of Organic Polymer Photovoltaics

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Efficient Computational Screening of Organic Polymer Photovoltaics Ilana Y. Kanal,‡ Steven G. Owens,‡ Jonathon S. Bechtel, and Geoffrey R. Hutchison* Department of Chemistry, University of Pittsburgh, 219 Parkman Avenue, Pittsburgh, Pennsylvania 15260, United States S Supporting Information *

ABSTRACT: There has been increasing interest in rational, computationally driven design methods for materials, including organic photovoltaics (OPVs). Our approach focuses on a screening “pipeline”, using a genetic algorithm for first stage screening and multiple filtering stages for further refinement. An important step forward is to expand our diversity of candidate compounds, including both synthetic and property-based measures of diversity. For example, top monomer pairs from our screening are all donor−donor (D− D) combinations, in contrast with the typical donor−acceptor (D−A) motif used in organic photovoltaics. We also find a strong “sequence effect”, in which the average HOMO−LUMO gap of tetramers changes by ∼0.2 eV as a function of monomer sequence (e.g., ABBA versus BAAB); this has rarely been explored in conjugated polymers. Beyond such optoelectronic optimization, we discuss other properties needed for high-efficiency organic solar cells, and applications of screening methods to other areas, including nonfullerene n-type materials, tandem cells, and improving charge and exciton transport.

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s the global population increases and world economies develop, energy consumption is increasing at an alarming rate. Abundant energy from the sun shows considerable promise for solving the world’s energy issues. For example, in 2004, the National Renewable Energy Laboratory (NREL) calculated that to satisfy the United States’ demand for electricity with solar power, covering only 0.4% of U.S. land mass (10 million acres) with typical commercial solar panels would be needed.1 Yet in 2011, only 9% of U.S. energy consumption came from renewable sources, 2% of that solar.2 The economic challenge with existing photovoltaic devices is the high up-front cost and the several year lag for a return on investment.3 Organic photovoltaics (OPVs) offer the promise of reduced cost through roll-to-roll processing and the high tailorability of synthetic organic chemistry.4 The first OPV was reported in 1986 by Tang, and the first bulk heterojunction (BHJ) cell was reported in 1995 by Heeger (Figure 1a,b).5,6 Over the past few years, efficiencies of singlejunction and tandem devices have increased slowly, with recent reports in the 8−10% range.7,8 Multiple factors act as limits on OPV efficiency (Figure 1c).9 While efficiencies continue to increase, truly transformative improvements will likely require new strategies such as rational design of new materials.10 OPV devices typically comprise a p-type conjugated molecule or polymer and an n-type material, usually a substituted fullerene. In this work, we will refer to the p-type phase as a polymer because such devices are predominate, but p-type small molecules are also used. The p-type polymer is typically a copolymer designed by combining donor (easily oxidized) and acceptor (easily reduced) monomers, providing a narrow band gap and good energy level alignment with the n-type fullerene.11 The n-type fullerene is often phenyl-C61-butyric acid methyl ester (PC61BM) or phenyl-C71-butyric acid methyl ester (PC71BM). The p-type and n-type materials are then mixed into planar heterojunction or BHJ films (Figure 1a,b). © XXXX American Chemical Society

Because of the complicated interplay of multiple factors in device efficiency, computationally directed materials design can accelerate the search for more efficient p-type polymers and ntype materials. Initial OPVs were fabricated in the planar heterojunction architecture with discrete p- and n-type layers sandwiched between two electrodes. A BHJ cell replaces the separate p-type and n-type layers with a single, bicontinuous network of the polymer and fullerene with domain sizes similar to the polymer exciton diffusion length.6 By keeping the domains in the active layer of a BHJ around this size, an efficient pathway for charge transport and collection is formed, allowing for increased film thickness.12,13 For OPVs to generate current, the polymer (and sometimes the fullerene) absorbs photons, generating bound electron−hole pairs (excitons). The excitons diffuse toward the p−n junction where they separate into free charge carriers.14−17 Electrons are transferred from the polymer to the fullerene through a charge-transfer state. In some cases where the fullerene has a significant optical extinction coefficient, holes are transferred from the fullerene to the polymer.18 The BHJ architecture provides the necessary interpenetrating network of the p- and n-type materials for efficient charge separation (Figure S1, Supporting Information). Without appropriate domain sizes, Received: January 29, 2013 Accepted: April 25, 2013

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The Journal of Physical Chemistry Letters

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Figure 1. (a) Schematic of a simple planar heterojuction cell compared with a (b) conventional bulk heterojuction cell. Note that in reality, multiple mixed phases typically occur at the organic−organic interfaces. (c) Schematic of energy conversion, transport, and loss processes.

molecular structure is known, often “alchemical” methods allow efficient optimization of elemental composition,45−51 although these methods require a fixed scaffold. Throughout all of these efforts, a key (and often rarely discussed) issue is the reliable automation of computational resources and analysis across large materials libraries.52

it is possible for excitons to undergo emission or recombination before they are able to migrate to the interface where they can separate.19−22 There are also many other loss mechanisms that terminate the electron dissociation pathway (Figure 1c), including interaction with impurities, defects, and charge traps in the device.23−26 Because of this complicated interplay of multiple factors in device efficiency, computationally directed materials design can accelerate the search for more efficient ptype polymers and n-type materials. Computationally Driven Materials Design. Over the past few years, there has been increasing interest in computationally driven design of new materials, showcased by the Materials Genome Initiative. Announced in 2011, the initiative seeks to foster both scientific and technological advancements and decrease the time required for breakthrough materials to become commercially available.27 The use of computational screening methods allows “virtual synthesis” and exploration of properties prior to synthesis. Combinatorial materials science is thus a promising technique for quickly surveying a wide array of variables by creating libraries in silico, similar to strategies used in the pharmaceutical industry.28 For example, computational exploration of various conjugated acenes uncovered a new compound with extremely high hole mobility.29 Similar computational exploration has also uncovered other experimentally verified trends affecting charge mobility.30,31 Not surprisingly, because the realm of materials research is vast, many different approaches have appeared to efficiently tackle computationally driven materials design and the Materials Genome challenges. For example, computational screening approaches have recently been used to explore perovskite metal oxides32,33 and oxynitrides for water splitting photocatalysts,34 pseudocapacitive electrodes,35 refrigerant fluids,36 chromophores for dye-sensitized solar cells,37 and rational design of porous metal−organic frameworks.38−42 Inverse design strategies attempt to locate materials with certain reactivity or other properties by starting with ideal target values and using an algorithm that works backward to find new materials matching the target.43 Other groups have used machine learning to rapidly estimate properties that would otherwise require computationally intensive calculations.44 Finally, when an inorganic or

The use of computational screening methods allows “virtual synthesis” and exploration of properties prior to synthesis. Combinatorial materials science is thus a promising technique for quickly surveying a wide array of variables.

One of the most difficult problems in this context of finding ideal p- and n-type materials for OPVs is the size of “molecular space”, estimated to contain over ∼1060 molecules.53,54 A search for ideal molecular and polymeric materials is thus similar in spirit, if not application, to computationally driven drug design.55 Following the approach of generating a large in silico library for “shotgun” screening, the Harvard Clean Energy project began with a molecular library of 2.6 million conjugated molecules and corresponding density functional theory calculations, attempting to find materials with ideal optoelectronic properties.56 A related study used a set of 50 “training molecules” with known current− voltage device characteristics and a set of physicochemical “descriptors” to fit empirical models for current−voltage parameters, the fill factor, and the power conversion efficiency.57 There are limitations to this simple approach because the descriptors used may not accurately describe the underlying physics in solar cells, but nonetheless, this can be used as a guide for finding new OPV materials because the empirical descriptor models can quickly filter out poor targets before time-consuming quantum calculations or experiments are performed. 1614



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AM1,60 PM6,61 and ZINDO/S,62 we can quickly compute lowenergy conformers, optical absorption spectra, notably the lowest-energy optical excitation, and ground-state energy levels. Such methods, while not state-of-the-art, nevertheless compute optical excitation energies in conjugated polymers accurate to ±0.3 eV63 and ionization potentials to ±0.2 eV59 in a fraction of the time required for DFT and TD-DFT methods. The GA, in turn, spends several generations sampling lower-efficiency oligomers, followed by increased sampling of oligomers predicted to have near-optimal optoelectronic properties. On average, only 4% of the entire pool of oligomers is sampled by the GA, but ∼60−70% of all oligomers with near-optimal properties are sampled, a considerable acceleration over brute force approaches. As noted in our previous work,59 the GA functions by selecting oligomers (i.e., varying the molecular structure) to minimize the geometric distance to the optimal HOMO and excitation energies, based on the predicted efficiencies by Scharber et al.64 Other optimization targets can be used, as discussed below. Beyond these criteria, the optimization function rewarded oligomers with large computed oscillator strength for the lowest-energy singlet transition. In this way, the optimizing function sought oligomers with the desired optoelectronic properties as well as reasonable oscillator strength (and thus high extinction coefficients). An initial population of 64 oligomers was generated from random dimers among the library of 130 monomers. Crossover occurred by selecting two oligomers at random from the “fittest” set and swapping their component monomers. Children in subsequent generations were mutated by selecting randomly among the monomers most similar by electronic structure (i.e., HOMO and LUMO orbital energies). This similarity measure was introduced to significantly speed convergence of the GA. In all cases, we ran the GA through 100 generations, although typically 5−6 generations were sufficient to obtain convergence. Oligomers generated after convergence all came from a population with high oscillator strengths and predicted efficiencies (by the Scharber criteria) ∼8% ± 2%. We followed the initial GA screening with an exhaustive search of only the top 20−30 monomers (out of 132) to ensure complete sampling of top oligomer targets. Because many of these were sampled by the GA, this step only added ∼50% novel oligomers (i.e., only increasing sampling from ∼4 to ∼6% of all possible oligomers). The final pool of oligomers included hundreds of targets with predicted efficiencies of >8% and dozens with predicted efficiencies of >10%. A subsequent filtering step used full DFT geometry optimizations on the top 100 targets to improve predictions of optoelectronic properties, largely due to more accurate dihedral angles.65−67 As a proof-ofconcept of the multistep screening, the internal reorganization energies for hole transport were also computed, which removed several top candidates due to high activation barriers for charge mobility.59 This GA search is clearly more efficient than brute force because only a small fraction of all possible oligomers is selected for computational investigation. While alchemical DFT methods can efficiently vary chemical composition, they require a fixed scaffold and are thus inefficient at sampling multiple monomer compositions (or allowing, as we do, for global minimization of polymer conformation). The remaining strategies generally fall under branch-and-bound algorithms, which, like the GA, eliminate subsets of compounds from investigation, usually by a set of screening criteria. Indeed, our GA is intended as the first

Multistage Screening for OPVs. In our work, we take a slightly different approach. Because the optimization of device efficiency requires a complex interplay of multiple properties (i.e., optical absorption, energy level offsets, exciton dynamics, charge separation and recombination, and charge transport) and subtle changes in polymer structure can lead to huge variations in performance, we believe a multistep screening and refinement process is required.58 Importantly, to find optimal or nearly optimal targets for device applications, we seek to survey a large, diverse fraction of molecular space and eventually establish a set of ∼100−200 highly promising targets. We also hope that at each step of refinement, beyond simply locating promising targets, we will learn structure/function correlations and “design rules” that may have applications outside of solar electricity generation. To efficiently sample millions of molecules without generating the entire set of structures, the early steps in our pipeline must be as fast as possible. Indeed, approaches such as branch-and-bound and genetic algorithms (GAs) can eliminate unproductive categories or subpopulations of candidate structures entirely; the fastest possible computational method is doing nothing at all. Furthermore, as seen in Figure 2, we seek to tackle easier problems first, for example, the prediction of optoelectronic properties.59 Using fast semiempirical quantum methods, such as

Figure 2. Schematic of a multistage screening pipeline for OPVs. Note that faster, more reliable methods are performed earlier in the process (i.e., predicting the 3D geometry and conformation of a polymer), and subsequent steps involve more complicated, slower evaluations. 1615



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step of multistage screening, followed by further refinement (i.e., “bounding” or filtering). An important consideration is that such “screening” steps need not be perfect. Even if a given filtering procedure is inaccurate and is used only to remove the worst 10−20% of candidates, avoiding false negatives, then filtering for multiple properties (such as charge-transfer energetics, reorganization energy, synthetic feasibility, solubility, etc.) using such screens will rapidly narrow the population of targets. For example, while the first stage of GA screening is optimized for computational speed, it relies on computed excitation energies and HOMO and LUMO energies of isolated molecules in the gas phase. More accurate treatments consider redox potentials using the ΔSCF procedure, which computes oxidation or reduction potentials as the difference in total energy of the charged and uncharged species.68,69 More accurate estimates of the open-circuit potential of a photovoltaic device would also consider the molecular or interfacial geometry and compute the energetics of the relevant charge-transfer state between multiple oligomers or as the exciton separates.22,70−74 Such methods necessarily are more computationally intensive and should thus be performed on small subsets further down the pipeline. For example, using the GA as a first-stage filter, one might consider all compounds with predicted excitation energies within ±0.3 eV of the optimal target and all compounds with a computed LUMO energy within ±0.3 eV of the desired target, followed by further refinement of oxidation and reduction potentials via ΔSCF, followed by computed reorganization energies, and followed further by computing the energetics of the relevant interfacial charge-transfer complex with PCBM or other n-type materials. Importantly, regardless of the computational methods used, they should be carefully calibrated against available experimental data to minimize any systematic shifts and to estimate the magnitude of the remaining random errors. In addition to efficiently uncovering hundreds of top oligomers with optimal or near-optimal optoelectronic properties, our work uncovered two new design principles. Unlike the traditional alternating donor−acceptor (D−A) synthetic strategy to tailor the optical band gap, the top oligomers from the GA search all featured a donor−donor (D−D) monomer combination and relied on complex sequences of monomers, as discussed below. Expanding Diversity: Both Synthetic and Electronic. Our initial screening efforts suggested oligomers that frequently included two novel monomers, both of which are expected to be highly synthetically challenging. An important question, then, is whether a larger and more synthetically diverse pool of monomers would generate better targets (e.g., both near-optimal properties and synthetic accessibility). To address this question, we compiled a set of 670 monomer fragments, including those culled from the recent literature, as well as some generated algorithmically from simple atomic or functional group substitutions. Because many of these fragments could potentially polymerize through multiple sites, a pool of 1948 polymeric repeat units was generated (Figures 3 and S2, Supporting Information). To address the synthetic accessibility of polymerization sites, repeat units for a particular fragment were ranked based on the computed atomic spin density of the radical cation at each aromatic carbon as a measure of the feasibility to create a C−C coupling. Considering only two- component copolymers, this set of repeat units yields a search space of ∼1.9 million targets, and three components would generate >1 billion possible targets. By considering different sequences of monomers, as

Figure 3. Plot of computed PM6 HOMO and LUMO energies of 1948 homotetramers, reflecting the wide diversity of electronic structure properties, across typical donors (i.e., less negative HOMO level), acceptors (more negative LUMO level), and wide-gap species. Similar diversity was found for ZINDO-computed energies.

discussed below, one can expand the synthetic diversity by a factor of 16 with sequenced tetramers or 64× by using sequenced hexamers as the polymeric repeat unit. While this produces a synthetically diverse pool, it is also important that diversity of optoelectronic properties exists. For comparison, we computed the ground-state electronic structure of the homotetramers as a model of the electronic structure of each of these 1948 polymers, as discussed below.

On the basis of our previous work, the “sequence effect” offers a new dimension to tailor optoelectronic properties beyond creating novel monomers. In addition to the D−D motif, our previous work led us to speculate that by modifying the monomer sequence, changes will occur in the HOMO and LUMO energies, thus changing the band gap. One may consider this technique as altering the potential energy distribution in a biased particle-in-a-box model for conjugated polymers. This strategy may lead to efficient OPV materials synthesized from monomers with relatively simple structures. Many groups are currently investigating monomers with increasing synthetic sophistication, but this method could achieve efficient OPVs without complicated monomers. Recently, work was published suggesting that it is possible to change the band gap by substituting atoms in monomers for which properties are already known. Examples of this include substituting sulfur, selenium, and tellurium in the benzochalcogenodiazole unit with reported decreasing band gaps of 1.59, 1.46, and 1.06 eV, respectively, and a selenophene analogue of PCDBT (where selenium replaces sulfur in the PCDBT compound) decreasing the band gap from 1.85 to 1.70 eV.75 Generally, polymers are made by joining monomers in a random order (ABBABA), alternating order (ABABAB), or blocks (AAABBB). Little work has occurred on systematic investigation of sequenced oligomers in π-conjugated systems. On the basis of our previous work, the “sequence effect” offers a new dimension to tailor optoelectronic properties beyond creating novel monomers. In our computational investigations of sequenced tetramers, we were able to attain a >1 eV change in band gap 1616



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Figure 4. Computed PM6 HOMO−LUMO gaps, demonstrating the potential to significantly tune the band gap (>1 eV) by changing the monomer sequence. Dihedral angles are listed in Figure S5, Supporting Information.

simply by altering the order of the monomers, as shown in Figure 4. We have also recently demonstrated the sequence effect experimentally by synthesizing oligophenylene vinylenes with different sequences with collaborators.69 Using the sequence effect to tune the band gap of polymers for OPVs is an alternative to the standard methods such as modification of monomers.76 Obviously, large sequence effects can be found in specific cases (e.g., Figure 4), but we also wish to test the average sequence effect. Twelve monomers (Figure S3, Supporting Information) were chosen at random from the pool of 670 monomers in our larger study, three from each “quadrant” in Figure 3. This ensures that any trends emerging from the analysis will likely be general to all monomers and not specific to one combination of energy levels (such as low HOMO and high LUMO) or monomer pairing. From the 12 monomers, all 66 dimers were generated (Figure S4, Supporting Information), and all possible tetramer sequences (spanning both composition and monomer order) were enumerated, yielding 1056 possible tetramers. Orbital energies and lowest-energy optical excitations were computed as discussed below. By comparing the band gaps among all sequences between a particular monomer and various coupling agents, consistent trends were established regarding certain monomers’ tendencies to change their associated tetramer band gap. For example, regardless of its coupling agent, a monomer with a five fused aromatic ring structure, trithieno[3,4-b:2′,3′-f:3″,2″-h]quinoxaline (Scheme 1, left), consistently produced the lowest band gap across all sequence patterns, no matter with which monomer it was coupled. Contrarily, coupled 4,4′-difluoro-[1,1′bi(cyclopentane)]-1,1′,4,4′-tetraene (Scheme 1, right) tended to raise the band gap of its associated tetramer.

Beyond the effects of particular monomer constituents on their associated tetramer properties, pure sequence-dependent phenomena were also examined. To this end, calculated HOMO, LUMO, and band gap values for every tetramer were averaged across each monomer combination. For example, for the A−D combination in Figure 4, the average HOMO−LUMO gap is ∼1.9 eV. Particular sequences (e.g., DDDD) are then compared relative to this average value (i.e., +0.7 eV in Figure 4). Once this method was performed for all 66 combinations and all sequence permutations, several patterns emerged. First, for averaged LUMO and band gap energies, there exists a drastic jump between the ADDD and DAAA sequences. For HOMO energies, the opposite holds true, and a drastic decrease is observed between the ADDD and DAAA sequences. Moreover, for HOMO, LUMO, and band gap values, the DDDD sequence consistently lies far from the other sequence averages. These observations support the hypothesis that sequence order plays a significant role in the determination of HOMO, LUMO, and band gap energies. To confirm our hypothesis, an analysis of variance (ANOVA) was performed for the sequenced averaged band gap energies. There is a statistically significant difference in means among the 16 sequence permutations. Notably, when comparing the six sequenced tetramers with equal composition of A and D monomers (i.e., AADD, ADAD, ADDA, DAAD, DADA, and DDAA), we find an increase in HOMO energy of ∼0.2 eV going from ADDA to DAAD sequences and an associated decrease in LUMO and band gap energy of ∼0.2 eV going from ADDA to DAAD sequences (Figures 5 and S6−10, Supporting Information). Note that because not all of the monomers are symmetric, sequences such as AADD and DDAA are not necessarily geometrically equivalent. This general sequence effect suggests that in addition to tailoring the monomer structure, modulating the oligomeric sequence can lead to optimized optoelectronic properties for OPVs. These oligomeric repeats can be polymerized either as conjugated macromonomers or as conjugated segments surrounded by short nonconjugated linkers. For example, while ABBA and BAAB tetramers would generate the same repeat (AABBAABB) in a conjugated polymer, short nonconjugated sections (e.g., a −CH2− or −C2H4− spacer) would preserve the sequence. Longer sequenced oligomers, such as pentamers or hexamers, are likely to generate more complex sequences for distinct macromonomer polymerization. Tailoring sequence is

Scheme 1. (left) Trithieno[3,4-b:2′,3′-f:3″,2″-h]quinoxaline and (right) 4,4′-Difluoro-[1,1′-bi(cyclopentane)]-1,1′,4,4′tetraene

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Figure 5. (a) Schematic of all 16 possible sequenced tetramer combinations and line plots with standard error compared to monomer-averaged changes in energy for computed (b) HOMO, (c) LUMO, and (d) band gap as a function of sequence for the six sequences with equal “A” and “D” composition.

efficiency.78 The main difference between the D−A and D−D architectures is that the D−D combination yields a smaller band gap because of greater delocalization of electrons across the polymer backbone. The delocalization in a D−D motif, in turn, yields a large energetic “splitting” from the monomer orbitals. Because a high degree of delocalization may improve other properties of device performance (e.g., charge mobility, charge separation), we believe that this may be a new strategy toward designing improved p-type OPV materials. While defects, polymer twisting, and self-trapping 79 may decrease the delocalization of a D−D motif relative to an idealized “perfect” polymer, along-chain delocalization is still likely to be greater than that for corresponding D−A polymers. In the case of some high-performance, low-band-gap D−A copolymers, charge-transfer excitations have been found both between oligomers and across the heterojunction. Such effects are critical in decreasing the energetic offset across the heterojunction and boosting efficiency in these materials. Nevertheless, a highly delocalized hole in a D−D copolymer would be effectively farther from the heterojunction interface, minimizing electrostatic trapping. In short, while highly optimized D−A copolymers exist and charge-transfer excitations are an important effect in D−A materials, we believe that the D− D motif is promising. A key question in this new strategy is how to find monomer pairs that yield a high degree of delocalization and splitting. To this end, our screening efforts have found several combinations of known monomers that have not been previously paired and are predicted to have near-optimal optoelectronic properties,

also likely to affect crystal packing, molecular conformation, and other properties that alter the film morphology. By picking species with different sequences but similar optoelectronic properties, one could optimize multiple properties relevant for optimal OPV devices. Importantly, the use of computational screening methods is critical toward such efforts because the number of possible sequences increases exponentially with oligomer length. New Polymer Design Paradigms. As discussed above, in previous work,59 we found that the overwhelming majority of the most efficient oligomers were D−D combinations. This is contrary to the conventional D−A or push−pull design of conjugated polymers for OPVs (Scheme 2) to yield low band gaps. Such D− A strategies have been found to generally increase the opencircuit voltage (Voc) of BHJ cells77 and can produce very high Scheme 2. Comparison of (left) Conventional D−A and (right) D−D Synthetic Strategies to Tailor the HOMO− LUMO Gap

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only changing the p-type polymer material. While this model has helped to motivate improvements in OPV device efficiencies, as a simple two-factor model, it ignores many properties, such as the optical absorption coefficient and charge mobility.80 Incidentally, standard ZINDO/S or TD-DFT methods predict both the lowest-energy optical excitation energies and the oscillator strength, proportional to the extinction coefficient, and are easily used in our screening procedures. Many other models have been developed to predict the ultimate efficiency of OPV devices.81,82 A recent approach, proposed by Koster and Shaheen, suggests using a three-pronged effort to design OPV materials to be as efficient as inorganic photovoltaic cells.83 This would require controlling losses from the exciton charge-transfer state, minimizing the Marcus reorganization energy for charge transfer in both phases, and increasing the dielectric constant to decrease long-range electrostatic attraction between holes and electrons, leading to relaxation and recombination. From their work, they were able to conclude that by increasing the dielectric constant in organic semiconductors and optimizing other parameters, there could be an increase in efficiency of next-generation OPVs beyond 20% for many cases, near the thermodynamic efficiency limit.84 Given such parameters, a computational screening pipeline can find targets with optimized band gaps, followed by filtering for low reorganization energies and predicted dielectric constants. A second strategy has been to focus on improvements in the ntype “acceptor” phase. The vast majority of research in this field has used PC61BM and similar substituted fullerenes, which have clearly shown wide utility and excellent performance. One avenue includes speculation as to the underlying physical chemistry parameters that allow for excellent performance of fullerene-based OPVs.85 There have not been many reports, however, of efficient devices using other n-type phases, suggesting that this could be an area leading to many novel discoveries.86,87 Certainly, using n-type materials with greater optical absorption intensities than PC61BM will allow for harvesting of other parts of the solar spectrum beyond that of the p-type polymer phase. Such schemes would involve hole transfer from the n-type phase to the p-type polymer, in addition to electron transfer from the polymer to the n-type, and should generally boost photocurrent generation. Novel nonfullerene ntype materials should also be designed to minimize miscibility in the p-type polymer88 because recent evidence suggests that multiple mixed phases exist and likely decrease efficiencies.89 Screening strategies can be used to design novel n-type targets, including those with matched optoelectronic spectra, to maximize generated photocurrents.

including strong optical absorptions. We are currently synthesizing oligomers and polymers to test the strategy experimentally. A further aim of our screening efforts is also to determine which molecular properties or structural motifs (e.g., functional group pairs, orbital symmetries, etc.) yield the greatest D−D delocalization and can be used as design rules for further synthesis. “Hot Spot” and Data Mining/Clustering Techniques. The use of tailored sequences and D−D strategies offers the ability to tailor optoelectronic properties using existing monomers, rather than synthesizing increasingly complicated fused-ring systems. Our larger, diverse set of 1948 polymer repeat units enables us to sample a wide range of electronic and molecular structure motifs in search of optimal and near-optimal targets. Nevertheless, new monomer designs may still be needed for ideal OPV devices. Rather than generating larger screening sets, we have begun to explore statistical data mining analysis of our results. For example, Figure 6 shows a plot of the INDO-computed HOMO

Figure 6. INDO-computed HOMO and LUMO energies of the 36 monomers found most frequently in top oligomers from ref 59. Due to the difference in computational methods, the energy scale is different from that in Figure 3. Note that a cluster of similar orbital energies is found.

and LUMO energies of the 36 monomers most frequently found among the efficient targets in our previous work. While some particular monomers may be difficult to synthesize, a clear “cluster” of monomers appears with very similar electronic structure properties. Such analysis is critical because even a large set of monomers cannot include all possible analogues. Our screening methods now also include methods to generate diverse novel monomers by “mutation” substituting individual atoms (e.g., C → N, F → Cl, etc.), adding or removing functional groups, modifying ring systems, deleting atoms and bonds, and so forth, but these methods are limited compared to human creativity. Moving to High Eff iciencies: Community Needs. The discussion above centers mainly on tailoring optoelectronic properties of the p-type polymer in a single-junction OPV. Obviously, to improve power efficiencies, many other properties of the solar cell must be improved. In short, ideal energy level alignment and band gap are necessary but not sufficient for highly efficient devices. The core of much of the efficiency modeling of OPV systems relies on a MIM (metal−insulator−metal) model for BHJ cells as described by Scharber et al., where a simple relation between the HOMO energy level of a polymer and the Voc and optical band gaps are used to estimate the efficiency of BHJ solar cells.64 The model is optimized assuming PCBM as the n-type phase while

Our efforts in organic solar cells have focused on combining fast approximate semiempirical quantum chemical methods with a GA to quickly screen for nearoptimum optoelectronic properties. Many other strategies have been employed to boost OPV device efficiency, highlighting the complexity of the problem. For example, an “inverted” device design improves ohmic contact between layers,8 use of photonic crystals and optical modeling can boost optical collection, and novel approaches such as singlet 1619



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fission and harvesting of triplet excitons promise to push efficiencies beyond the Shockley−Queisser limit for single p−n junction devices.16 We believe that in all cases, such strategies may change the desired target materials, but the need for efficient computational screening will remain. Tandem Devices. While tandem (i.e., multijunction) devices should produce increased power efficiencies, the rational design of tandem cells clearly demands a computational approach. For example, if both p- and n-type phases are to be optimized for high optical absorption (as discussed above) across both layers in a tandem cell, the optimization procedure must find four perfectly matched materials with tuned optoelectronic properties, optical absorption coefficients, high charge mobilities, refractive indices, and so forth. While brute force screening methods that generate large libraries will likely include all possible targets for tandem cells, a more efficient strategy is to adapt a multiobjective GA. Simple modeling can suggest approximate multichromaphore band gaps, so that the GA would then select the best combination of four compounds with aligned energy levels, nearly optimal band gaps, and optical absorption coefficients. This work is underway. Morphology, Interfaces, Excitons, and Charge Transport. The vast majority of this discussion has omitted discussion of transport, either for excitons or for separated charge carriers. Obtaining optimum optoelectronic properties is necessary for highly efficient devices but not sufficient. A further challenge is to understand the role of exciton dynamics, charge separation and recombination, and subsequent transport of separated holes and electrons across interfaces and defects.14,90,91 Synthetically, methods used to enhance charge carrier mobilities include engineering of monomer side chains and modifying molecular structures toward reducing reorganization energies.92,93

would point toward design rules for materials design compatible with screening efforts. Future Outlook. As described above, computationally driven design of materials is an important strategy, not only to locate promising targets for synthesis and experimental investigation but also to uncover fundamental design rules and relationships in complex systems. Our efforts in organic solar cells have focused on combining fast approximate semiempirical quantum chemical methods with a GA to quickly screen for near-optimum optoelectronic properties. The GA method allows us to efficiently sample oligomer and polymer conformations and a wide range of monomer motifs, and more time-consuming screening procedures with DFT or other methods can be performed on smaller target subsets. We have recently worked to improve both synthetic and electronic diversity, through a larger pool of monomer units, sampling D−D coupling strategies, and tailoring monomer sequence. Each of these methods suggests new routes to efficient OPV materials. Finally, while many properties are required for efficient organic solar cells, computational screening strategies can be used to find novel targets for almost all properties under consideration. We believe that these methods are also broadly applicable outside of π-conjugated polymers to other materials design problems.

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COMPUTATIONAL METHODS For all calculations discussed in this work, the lowest-energy conformer was found using Open Babel98 and the MMFF94 force field,99−102 followed by geometry optimizations using PM661 and optoelectronic properties (including HOMO and LUMO energies) using both PM6 and ZINDO62 with Gaussian 09, revision A.02.61

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We have recently worked to improve both synthetic and electronic diversity, through a larger pool of monomer units, sampling D−D coupling strategies, and tailoring monomer sequence.

ASSOCIATED CONTENT

S Supporting Information *

Schematics of exciton and charge separation mechanisms, potential polymerization sites, pairs of monomers considered in the sequenced tetramers, and full statistical analysis is available at http://hutchison.chem.pitt.edu. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: geoff[email protected].

A critical question remains about the role of morphology in transport. Put simply, given a morphology and known materials properties, can one predict the expected current−voltage performance of the OPV device? This task is complicated by the variation in morphology with different processing conditions and the fact that experimental morphologies are seldom known to atomic accuracies given the buried interfaces and high level of disorder in OPV devices. Furthermore, computational prediction of solid-state crystal structures and packing is a challenging problem in its own right. Among others, our group has focused on developing accurate Monte Carlo simulations of charge transport in organic semiconductors with intentional defects, traps, and mixtures.94−97 Our results have highlighted the importance in treating electrostatic interactions, particularly between carriers and charged traps, and suggest that given an assumed nanomorphology, one can predict current−voltage curves and other device parameters. Given such tools, an important question is to predict a set of optimized morphologies even in the presence of diffuse interfaces and molecular-scale intermixing. Such results

Author Contributions ‡

I.Y.K. and S.G.O contributed equally.

Notes

The authors declare no competing financial interest. Biographies Ilana Y. Kanal received her B.S. in chemistry from the University of Pittsburgh. She is currently at the University of Pittsburgh in the Hutchison research group, performing automated electronic structure calculations and statistical data mining on polymer solar cell targets. Steven G. Owens received his B.S. in chemistry from the Pennsylvania State University in 2009, studying bioerodible polymers under Harry R. Allcock. He is currently at the University of Pittsburgh in the Hutchison research group, focusing on the screening and synthesis of novel organic polymers with tailored sequences. Jonathon S. Bechtel is an undergraduate chemistry/math dual major at the University of Pittsburgh. His research in the Hutchison group has focused on understanding the sequence effect in π-conjugated 1620



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oligomers, and he anticipates starting graduate school in materials science in Fall 2013. Geoffrey R. Hutchison received his B.A. in chemistry from Williams College, studying the synthesis and characterization of platinumcontaining liquid crystals. He received a Ph.D. in chemistry from Northwestern University in 2004 with a joint dissertation with Mark Ratner and Tobin Marks on the optical and charge-transport properties of π-conjugated polymers. After postdoctoral studies at Cornell University with Héctor Abruña on single-molecule wires, conjugated transition-metal oligomers, and conjugated polymers for energy storage, he began his independent research at the University of Pittsburgh in 2007. His group combines experimental and computational studies of molecular piezoelectrics, inverse design of organic materials, and charge transport in organic semiconductors and photovoltaics. http:// hutchison.chem.pitt.edu

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ACKNOWLEDGMENTS We thank the University of Pittsburgh, including the Center for Energy for support. G.R.H. thanks Dr. Noel O’Boyle and Prof. Tara Meyer for discussions.

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