Computational evolution of high-performing unfused non-fullerene acceptors for organic solar cells

Organic solar cells (OSCs) offer the vast tailorability of organic molecular, oligomer, and polymer motifs to convert light into electrons. To improve the performance of OSCs, there has been much research focusing on the optimization of p-type donor materials, with conjugated organic polymers being the most popular.^1–4 However, for a p-type donor material to perform well, it needs to be paired with a complementary n-type acceptor, frequently small molecules. Multiple properties can determine whether the materials are a good match, such as strong absorption of different wavelengths, energy level alignment for efficient exciton splitting and low energy loss, and optimal solubility to form suitable domains within the active layer.

Up until recently, fullerenes were the most frequently used acceptor due to their excellent electron transport and good energy alignment with commonly used donors.⁵ However, they have drawbacks when acting as acceptors, including weak light absorption, complex synthesis, limited tunability, and poor photostability.^6,7 As an alternative, non-fullerene small molecules emerged, showing highly tunable optical and electronic properties, strong absorption of visible and near-infrared (NIR) light, and low production cost.^6–8 The most common design for non-fullerene acceptors (NFAs) is joining electron-withdrawing units and electron-donating units, due to their “push–pull” effect and enhanced intramolecular charge transfer (ICT). This effect has been shown to improve the power conversion efficiency (PCE) by broadening the absorption spectrum and improving the charge mobility.^9,10

Huge strides have been made in the last two years due to the emergence of the Y-series acceptors,^11,12 with the PCE surpassing 18%,^13,14 much higher than the highest PCE of 11.7% for fullerene binary devices.^15,16 Due to their extended conjugation, they have narrower optical bandgaps, allowing for the absorption of visible to NIR light.¹⁷ The general configuration is A-DA′D-A, with the fused backbone allowing for planarity that increases the crystallinity and π orbital stacking within the device.¹⁸ While fused NFAs have shown great promise, they have some drawbacks that limit their commercial potential. Forming the fused backbone structure requires complex synthesis, often with 5–15 steps.^19,20 This difficult synthesis process increases the cost and results in low yield. Recent studies also show poor stability of fused ring NFA devices, due to their tendency to undergo photo-oxidation when exposed to light and air.^21–25 A recent strategy to mitigate some of these issues is to use unfused analogs of these acceptors. Unfused NFAs are similarly designed with electron-withdrawing (acceptor) and electron-donating (donor) organic conjugated units, but they are separated by single bonds instead of fused rings. This allows a much simpler synthesis (around 2–4 steps), higher yield, and generally better photostability.^22,26,27

It has been previously shown that the arrangement of acceptor and donor units in conjugated polymers affects their optoelectronic properties.^28–30 While A-DA′D-A is the most common sequence, attributed to the high success of this sequence in Y-series NFAs, other sequences are emerging as strong contenders, with asymmetry showing much promise.¹⁹ Asymmetric NFAs may have larger dipole moments, broader absorption, higher electron mobility, and lower crystallinity than their symmetric counterparts.^31–35 

The current highest PCE for organic solar cells is 19%.³⁶ However, there is no clear maximum PCE for OSCs with two absorbers. Shockley and Quisser predict the theoretical limit for single-absorber inorganic devices to be 33%.³⁷ However, this was based on inorganic semiconductor cells and does not take into account the unique loss mechanisms of OSCs.³⁸ Multiple efforts have modeled optimum efficiencies for fullerene OSCs, including the popular Scharber model.³⁹ Research by Koster et al.⁴⁰ used multiple pathways to predict that the theoretical limit for fullerene OSCs could exceed 20%; however, this is still based on one absorbing material. In NFA OSCs with the perfect combination of two absorber materials, we should be able to exceed 20%. However, finding these materials is similar to finding two needles in different haystacks. Not only do we need optimal acceptor and donor materials, but they need to be perfectly complementary for energy level alignment and light absorption to minimize energy losses. To discover new materials, the use of computational screening methods has emerged as a promising alternative to experimental screening.^41–53 The molecular chemical space for organic molecules is estimated to be 10¹⁸–10²⁰⁰ compounds,^54,55 which is impossible to evaluate experimentally. Computational screening allows for “virtual synthesis,” a quick and relatively cheap method to explore promising materials and create in silico molecular libraries.^44,48 One type of computational screening is high-throughput virtual screening (HTVS), where every candidate in a library is screened.^41,43,56 The largest HTVS for organic photovoltaics (OPVs) is the Harvard Clean Energy Project, which used electronic structure calculations to evaluate the PCE for 2.6 × 10⁶ conjugated donor molecules and 51 000 NFAs by using the Scharber model.^50,52 However, HTVS and other brute-force searches are inefficient and screen a massive number of molecules unlikely to be high-performing candidates.

An alternative technique is the use of inverse design strategies, which set an ideal target value of a property as a starting point and use algorithms to design new materials that optimize that property. One such technique is a genetic algorithm (GA), a type of evolutionary algorithm based on natural selection in which the fittest candidates pass to the next generation. In a GA designed for materials discovery, a population of potential molecules is generated that optimize a given property and their suitability is evaluated with a “fitness function.” Considering that many fitness functions require quantum chemical calculations, low cost semi-empirical methods should be used for fast and efficient chemical searches. Since the goal of this work is to evaluate potential NFAs, the Organic Photovoltaic Efficiency Predictor using the simplified time-dependent density functional theory (OPEP/sTD-DFT) model proposed in our earlier work⁵⁷ is used as the fitness function to quickly evaluate the PCE of NFAs. Although this model does not include descriptors related to film morphology or crystal packing, it can predict PCE better than commonly used methods, such as the Scharber model, with an R² of 0.55. This model requires the difference in energy between the HOMO and HOMO-1 and the sum of the oscillator strengths of the acceptor, obtained through sTD-DFT calculations. The other descriptors are of the donor, with no terms relating the donor and acceptors; thus, the donor can be optimized independently of the acceptor. A total of 22 donor polymers commonly used in OSCs were screened during the GA with each acceptor, with Poly[(2,6-(4,8-bis(5-(2-ethylhexylthio)-4-fluorothiophen-2-yl)-benzo[1,2-b:4,5-b′]dithiophene))-alt-(5,5-(1′,3′-di-2-thienyl-5′,7′-bis(2-ethylhexyl)benzo[1′,2′-c:4′,5′-c′]dithiophene-4,8-dione)] (PBDB-T-SF) optimizing these terms the best and yielding the highest PCEs. This donor has strong absorption in the UV and high-energy visible regions (Fig. S1), most likely attributing to its good performance. Since the goal of the GA is to find high-performing NFAs, PBDB-T-SF is selected as the donor material to pair with new NFAs in the GA. Elitism is used to pass the top 50% of candidates to the next generation to ensure high-performers in each population. These candidates are randomly selected to undergo crossover and mutation operations to ensure the exploration of nearby chemical space, producing children for the next generation. This cycle of parent selection, crossover, mutation, and evaluation of fitness continues until the target property has been satisfied, or after a certain number of generations, as seen in Fig. 1. The main advantage of using a GA is to learn from each successive generation to design even better candidates. Our group previously used a GA to efficiently screen donor polymers for fullerene-based OPVs, producing hundreds of promising targets and discovering design principles related to the sequence of the monomers.³⁰ 

In this work, we report new design principles for NFAs discovered by screening thousands of molecules with a genetic algorithm. The types of building blocks, sequence, and symmetry are analyzed, and new NFAs are proposed that can reach PCEs over 22%.

For version 1, a dataset of 192 organic conjugated electron-withdrawing/accepting units with three fused rings or less was constructed by examining high-performing NFAs reported in the literature. Versions 2 and 3 used the dataset from version 1 with the addition of 1221 units from a previous GA project in our group.^58,59 Structures were generated for each unit with any side chains truncated with ethyl groups, since these groups should only affect the solubilization and crystallinity with no impact on the optical and electronic properties. The lowest energy conformer is generated by using Open Babel⁶⁰ with MMFF94⁶¹ or UFF⁶² force fields before additional optimization with GFN2-xTB.^63–65 Further geometry optimization was performed with Orca 4.2.0⁶⁶ by using B3LYP-D3BJ/def2-SVP.^67–70 While multiple conformers likely contribute to the properties in real devices, properly sampling all low-energy conformers is currently a computationally intensive process. For oligomers of the size considered here, this would likely defeat the purpose of rapid screening.

To classify the units as electron acceptors or donors, their HOMO values were compared to thiophene’s HOMO. If the unit’s HOMO is lower than thiophene’s, it is considered an acceptor; if the HOMO is higher, it is a donor. Thiophene was chosen as an arbitrary midpoint since it is a common organic semiconductor unit and is commonly found as π-bridges in OPV materials, with no strong electron-withdrawing/donating effect. The dataset was grouped into four categories—acceptor terminal, acceptor core, donor terminal, and donor core, where the terminal refers to one point of attachment, so it must be an end unit, and the core refers to two points of attachment and can be used as either a terminal unit or a central unit.

The OPEP/sTD-DFT PCE⁵⁷ model was selected as the fitness function due to the high accuracy and low computational cost of the sTD-DFT method. This model has six terms, four of which are from the donor and two from the acceptor. For evaluation of fitness, 22 donors were analyzed with sTD-DFT to optimize the donor term, resulting in PBDB-T-SF being selected as the best performer. The two terms for the acceptor are the sum of the oscillator strengths and the difference in energy between the HOMO and HOMO-1 eigenvalues. To evaluate these properties for each candidate acceptor, force field and GFN2-xTB geometry optimization were performed, and the electronic and optical properties are calculated with sTD-DFT^71–73 by using CAM-B3LYP with def2-SVP⁶⁹ basis set in Orca 4.2.0. The maximum energy threshold is set to 5.0 eV, since the majority of the solar spectrum we are interested in for solar cell applications is below this energy.

The GA is constructed to design high-performing unfused NFAs with an A-D-A′-D-A sequence, meaning the central A′ is a different unit than the terminal A units and results in a symmetrical structure. In this GA, 32 NFAs are chosen as the initial population, with each NFA constructed from random A and D units. In each generation, the PCE of each candidate is evaluated and the population is ranked from the highest to the lowest PCE with the top 50% selected as parents for the next generation. Each successive generation contains 32 NFAs, 16 are the parents from the previous generation and 16 are newly formed NFAs created by using crossover and mutation operators on the parents. These children are constructed through a crossover operation that randomly chooses two units to keep from one random parent and one to keep from another. The crossover operation is repeated until 16 new children are constructed and added to the generation. The mutation rate is set to 40%, and if selected, the mutation operator will replace one of the three types of units with a new building block, chosen at random. Termination occurs when the top performer remains constant for 30 generations or until 100 generations have occurred, whichever is later.

To further expand the search space, the sequence restriction of A-D-A′-D-A was lifted. Version 2 allowed for symmetrical sequences, while version 3 allowed any sequence. Both versions used the expanded dataset. To initialize the first generation, sequences and units were chosen randomly. For version 3, sequences are first randomly selected to be symmetric or asymmetric, as required due to a large number of possible asymmetric sequences, and then a random sequence is selected from within the given symmetry subgroup. During the crossover operation, the units and sequences of two parents are crossed; however, if there are not enough of the required unit types for that sequence, then the units are reused. For the mutation operator, either the sequence or unit type is altered. If the sequence is chosen, the units are rearranged to fit the sequence; however, if there are not enough units to satisfy the sequence, random units are pulled from the initial dataset. If swapping a unit is chosen, a randomly chosen unit is replaced with a random unit from the initial dataset, ensuring the unit is of the same type as the one it is replacing so that the sequence does not change.

The dataset of units was created by selecting units from versions 1 and 2 that were used in an NFA more than five times. The sequence was unrestricted and the GA operations were the same as version 3. Unfortunately, an error occurred during this version due to a mismatch in labeling between the units and their corresponding designation of acceptor or donor. This resulted in the GA occasionally selecting a different sequence than intended and it being mislabeled. For example, during the crossover step, the sequence A-D-A′-D-A was selected to pass to the next generation. However, the unit it selected as D may have been mislabeled and is actually an acceptor. Therefore, while the GA was not perfect, the results still indicate that high-performing NFAs were discovered, and all figures shown have the true sequence.

Four versions of the genetic algorithm were implemented to understand the structure–property relationships and provide design rules for optimized NFAs. In all four versions, an initial population of 32 NFAs was randomly selected. The PCE of each was evaluated with the OPEP/sTD-DFT model and the top 50% of performers were passed down as parents for the next generation. In version 1, the GA searched for high-performing NFAs with an A-D-A′-D-A structure. This is a commonly used sequence, especially it being the unfused analog of the high-performing y-series acceptors. The acceptor and donor units comprising these NFAs were chosen from a library of units found in high-performing NFAs. This library was compiled by examining hundreds of NFAs previously published in the literature. Within this library, the units were classified as either terminal or core units, where terminal refers to end-capping units and the core can be anywhere in NFA. The library for version 1 contains 104 acceptor units and 88 donor units (Fig. 2). In the GA, the crossover step swaps units between two parents, while the mutation operator replaces either an acceptor or donor unit with a new one from the library, all while maintaining the A-D-A′-D-A arrangement.

To expand the search space, the library was extended to small conjugated organic molecules not frequently employed in NFAs. Previous work in our group utilized a GA to search for donor materials for OSCs,³⁰ which uses units similarly found in NFAs. In versions 2 and 3, the unit library was expanded to 949 donor units and 295 acceptor units (Fig. 2). In addition to expanding the search space, the arrangements of the units are analyzed. In version 2, the sequence was restricted to symmetrical arrangements, and in version 3, any sequence was permitted. Version 2 had the same crossover and mutation steps as version 1. Since the sequence can vary in version 3, the crossover operator swapped the sequence of one parent and the units of the other. The mutation operation had an equal chance of selecting a new sequence or replacement of a unit from the library while maintaining the current sequence. To ensure that most of the top candidates were found, a fourth version was performed whose dataset comprised the units frequently selected in versions 1 and 2, and allowed any sequence of these units, following the GA scheme of version 3.

The GA was allowed to run for 100 generations, or until the best PCE remained steady for ∼30 generations, whichever occurred later. Figure 3 shows the best PCE among 32 NFAs from each generation. As expected, the PCE increases as the generations evolve, confirming that the GA works and is efficiently exploring the chemical space. Version 1, with the dataset containing units already used in NFAs and restricted to the sequence A-D-A′-D-A, found the best performing NFA with a PCE of 20.9% after 26 generations. Version 2, containing the expanded dataset and restricted to symmetrical sequences, found the top performing NFA with a PCE of 22.9% after 39 generations. Once the sequence was unrestricted in versions 3 and 4, the best PCE took longer to stabilize, mainly due to the increase in the magnitude of the size of the search space. Version 3 found the best NFA after 84 generations with a PCE of 20.2%, while version 4 found the best NFA after 70 generations of 22.3%. As the search space increases, the GA requires more generations to efficiently search for top candidates. With the current record PCE of 15.2% for unfused NFAs,⁷⁴ these results show tremendous potential. Utilization of a GA instead of a brute-force approach shows a massive speedup, up to a magnitude of 10¹², as seen in Table I. While the search space for each version is massive, on the order of 10⁵, 10⁷, 10¹⁵, and 10¹¹, for versions 1–4, respectively, tiny percentages of these areas had to be traversed to find high-performing NFAs.

Examination of the sequences selected in versions 2–4 shows a preference for donor cores and acceptor end groups. Over 80% of the NFAs in version 2 had either the A-D-D′-D-A or A–A′-D-A′-A sequence (Fig. S2). Version 3 shows over 80% of the NFAs have one central donor unit flanked by two acceptor units, while version 4 shows over 60% of the NFAs discovered have three donor core units and acceptor terminal units (Figs. S3a and S4a). Similar results within all three versions suggest that a donor core and acceptor end groups are essential for improving the PCE. The symmetry of the arrangement of A and D units was also examined. The symmetry is of the sequence only, not if the monomer itself is symmetrical. Around 70% of the sequences in version 3 were asymmetric, while around 70% of sequences in version 4 were symmetric (Figs. S3b and S4b), suggesting that there is no clear correlation between the symmetry of the sequence and PCE. This could be due to the stochastic nature of a GA, resulting in convergence to different results for various runs.

The types of units frequently selected were explored to examine if current experimental NFAs efficiently select promising building-blocks. Figure 4 demonstrates that there are multiple units that appeared in hundreds or even thousands of NFAs throughout the GA. The top ten units most commonly selected as terminal groups all originated from the initial dataset used in version 1. This indicates that experimental NFAs currently employ the top high-performing end groups. However, out of the top ten core units, eight of them are from the expanded dataset of units. A common motif found in seven out of eight of these new units is a vinylene bridge. A recent paper by Hai et al.¹⁸ shows adding vinylene bridges into Y6 can significantly redshift the absorption edge, yielding ultra-narrow bandgap materials. This extra conjugation also leads to a broader absorption range and higher HOMO energy levels compared to Y6. These differences can lead to enhanced performance, which is why the GA may have selected them. In addition, many of these units have nonintuitive polymerization sites. We suggest that these new types of units and polymerization sites be incorporated into future NFAs and explored further.

To understand the impact of the electron-withdrawing/ donating strength of the building units on the PCE, the HOMO energy of each unit is examined. In Fig. 5, the HOMO energy levels of the top five candidates from each version are examined. Since there is no universal standard for the classification of electron acceptors and donors, thiophene was selected as a reference to compare electron-withdrawing/donating strength to. A thiophene monomer is commonly labeled as a π-bridge,^75–81 with the general acceptance that it is neither an acceptor nor a donor. Using it as a middle-ground with a monomer HOMO of −6.55 eV, units with a HOMO lower than this are considered acceptors, while a HOMO greater than this are considered donors. The deeper the color, the stronger the electron-withdrawing/donating strength.

When the sequence was not restricted (versions 2–4), the top performing NFAs all contained similar electronic sequences. The results suggest that having NFAs with acceptor end groups and donor cores can result in better performing NFAs. To further verify this, 50 high-performing NFAs from version 1 with the A-D-A′-D-A sequence were compared to their A-D-D-D-A analogs (Fig. S5). If there were multiple NFAs from version 1 that would result in the same A-D-D-D-A sequence (same terminal acceptor and donor core), then the NFA with the highest PCE was selected for comparison, since this is the theoretical highest PCE analyzed for that sequence. When comparing the PCE, 57.1% of the NFAs showed better performance with the A-D-D-D-A sequence. This is an encouraging result, since it negates the need to limit NFAs to the alternating A-D sequence and instead attach three donor units together as a synthetic alternative. In addition, the overall top performers from version 2 all have a strong donating core, suggesting charge transfer to the end units. This agrees with our understanding of the current design rules of π–π stacking with the end units.⁸² The results from versions 3 and 4 support this as well and show that it is not necessary to have strongly withdrawing/donating units to obtain a high PCE.

Throughout all four versions, 5426 unique NFAs were analyzed. Of these, 1087 have a PCE above 18% and of those, 159 have a PCE above 20%. Figure 6(a) is a histogram of all NFAs discovered, showing the average PCE of 15.8%. This distribution can be split up into each version’s contributions, as seen in the kernel density estimate plot in Fig. 6(b). Version 3 had the widest range of PCEs, which was anticipated due to having the largest chemical search space. Version 1 had the most narrow distribution, as expected due to the smallest search space and less drastic modifications in the GA. Version 4 discovered the largest percentage of the NFAs above 18%, validating the purpose of this version to find the top candidates by using the top performing units from previous versions.

The optical and electronic properties of all NFAs discovered were analyzed. Figure S6 shows the optical bandgap and its predicted oscillator strength of every NFA examined, with NFAs with a PCE above 20% colored. There is a wide range of bandgaps with varying oscillator strengths, indicating that there is no optimal bandgap for high performance. The fundamental bandgap of all NFAs was analyzed in Fig. S7. All high-performing NFAs have a fundamental bandgap between 2 and 3.5 eV. This small bandgap range is consistent with the idea of small bandgap NFAs absorbing in lower energy regions and complementary to a donor’s absorption, thus increasing the PCE. Although this range is still relatively large, it indicates that there is leeway in the ideal fundamental bandgap range for the design of new NFAs. There are clearly multiple strategies to yield efficient NFAs in the literature. Ultimately, the bandgap is only one of the multiple important properties for efficient devices. For example, a compound could have an “ideal” bandgap, yet low oscillator strength, for excitations at that energy.

The top six performing NFAs were examined in Fig. 7. The NFAs displayed in Figs. 7(a), 7(b), 7(d), and 7(e) were discovered in version 2, while the NFAs in Figs. 7(c) and 7(f) were discovered in version 4. The OPEP fitness function scored these NFA candidates highly on two properties: the sum of the oscillator strengths and the difference in the energy between the HOMO and HOMO-1. Examination of the absorption spectra shows strong absorption in the UV and high-energy visible regions for all top NFAs, with NFAs c and f showing broad absorption across the visible and near-IR region, a highly desired property in photovoltaics. The difference in energy between HOMO and HOMO-1 is conceptually connected to the density of states and delocalization of holes, and is maximized in each of these NFAs as well. Finally, we note that the central core unit seen in Figs. 7(a), 7(b), 7(d), and 7(e) breaks the aromaticity with an sp³-hybridized carbon and a non-conjugated side-chain. At first, we believed the monomer was incorrectly specified to the GA, but we note that several other top candidates exhibit broken aromaticity or conjugation. These motifs may modulate the electronic structure, and the side chain appears to serve as a conformational lock on the neighboring monomers. Analogs of these NFAs that kept the conjugation intact were examined (Fig. S8), and the predicted PCEs were ∼5%–6% lower than the GA predicted top NFAs. While the sum of the oscillator strengths is slightly higher for the discontinuously conjugated molecules, the energy gap between the HOMO and HOMO-1 drastically changed. The broken aromaticity molecules have a HOMO-HOMO-1 gap between 0.6 and 1.2 eV larger than their conjugated counterparts, giving it its superior performance. Further inspection of these NFAs showed the conjugated analogs have deeper HOMO levels, with differences ranging from 0.6 to 1.1 eV. When pairing the NFAs with the selected donor PBDB-T-SF, the broken aromaticity NFAs have a very small energy difference between their HOMO and the donor’s HOMO, potentially allowing for highly efficient hole transfer from the NFA to the p-type donor.

In this work, the chemical design rules for high-performing NFAs were established. Through the utilization of a genetic algorithm, 5426 NFAs were discovered, of which 1087 are predicted to have a PCE above 18% and 159 above 20%. The results indicate that the best sequence for high-PCE is A-D-D-D-A or A-A-D-A-A, with a donor core and acceptor end groups. There is no significant difference in the performance if the sequence is symmetric or asymmetric. When selecting individual building blocks, current terminal acceptor units employed in common NFAs are found to be top performers in the GA candidates. However, for core units, further exploration is needed, with strategies such as extending conjugation with vinylene bridges and nonintuitive polymerization sites providing some interesting starting points. The acceptor terminal groups can be weakly electron-withdrawing, and the donor core performs well when it is strongly electron-donating. Overall, this work suggests that new design rules for unfused NFA materials can yield further improvements in the power conversion efficiency.

See the supplementary material for analysis of sequences in versions 2–4, symmetry of sequences for versions 3 and 4, comparison of the A-D-A′-D-A sequence to A-D-D-D-A, and optical and fundamental bandgaps of every NFA discovered.

We acknowledge the support from the Department of Energy-Basic Energy Sciences Computational and Theoretical Chemistry (Award No. DE-SC0019335) and the University of Pittsburgh Center for Research Computing through the computational resources provided.

The authors have no conflicts to disclose.

The genetic algorithms and the data that support the findings of this study are openly available at https://github.com/hutchisonlab/GA_unfused_NFAs.