- Email: [email protected]
Organic Photovoltaics
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17
Organic Photovoltaics Carlos Amador-Bedolla , Roberto Olivares-Amaya†, Johannes Hachmann‡ and Alán Aspuru-Guzik‡
Facultad de Quı´mica, Universidad Nacional Auto´noma de Me´xico, Mexico Department of Chemistry, Princeton University, NJ, USA Department of Chemistry and Chemical Biology, Harvard University, MA, USA
†
‡
1. CHEMICAL SPACE, ENERGY SOURCES, AND THE CLEAN ENERGY PROJECT Chemical space, the collection of all different molecules that can exist, is extremely vast, and a credible estimation of its size has not even been attempted. However, some subgroups of this space, with particular characteristics, have been estimated (Reymond et al., 2012): The number of drug-like molecules most organic molecules of perceived relevance in all kinds of applications were estimated at around 1060 (Bohacek et al., 1996) and, more recently, the organic chemistry space accessible by current synthetic methods in between 1020 and 1024 molecules (Ertl, 2003). Within this vast space theoretical and experimental scientists are looking for particular compounds that have the best possible properties for use in selected applications. Automated high-throughput methods have allowed experimentalists to start charting these territories, both for synthesis and screening of large numbers of compounds. Pharma and biotech companies have led this effort during the past 20 years. High-throughput screening (HTS), allowing the number of compounds tested to be in the range of 10,000100,000 per day, has recently been followed by ultra-high throughput, which can screen compounds in numbers above 100,000 per day (Mayr and Bojanic, 2009). More recently, similar efforts have been developed for HTS of functional materials in combinatorial materials science (Potyrailo et al., 2011; Xiang, 2004). These methods are actively used in the exploration of superconductor (Xiang et al., 1995), ferroelectric (Chang et al., 1998), magnetoresistive (Bricen˜o et al., 1995) and luminescent materials (Danielson et al., 1998), materials for hydrogen storage (Olk, 2005), organic light emission (Zou et al., 2001), solar cells (Ha¨nsel et al., 2002), and catalysts (Hagemeyer et al., 2001), to name a
Informatics for Materials Science and Engineering DOI: http://dx.doi.org/10.1016/B978-0-12-394399-6.00017-5
© 2013 Elsevier Inc. All rights reserved.
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few. On the other hand, the extremely fast growth of computational capabilities during the past 40 years (no other technology merit figure has advanced six orders of magnitude ever, not even considering that for digital computation this happened in only 40 years) and the advances in semi-empirical and ab initio techniques are allowing computational HTS to search for optimal materials for particular applications, again both for synthesis (Dias, 2010; Wilmer et al., 2012a) (including crystal structure prediction; Hautier et al., 2012) and screening of compounds and materials for energy applications in hydrogen storage (Hummelshøj et al., 2009), lithium-ion batteries (Mueller et al., 2011), thermoelectrics (Wang et al., 2011), organic photovoltaics (Olivares-Amaya et al., 2011), catalysis (Greeley et al., 2006) and photocatalysis (Castelli et al., 2012), and carbon capture (Wilmer et al., 2012b). For all that, it has been considered that these modern capabilities experimental and theoretical HTS as all the capabilities that define our civilization are only possible because of our availability of huge amounts of inexpensive energy. Current human consumption amounts to some 260 million barrels of oil equivalent (MBOE) per day, and current mainstream expectations of economical growth predict an increase of almost 40% in the next 20 years (Conti et al., 2010). This huge increase in available energy will be difficult to satisfy, as maintaining present supply of energy 88% of which is currently provided by combustion of fossil fuels is already questionable for at least two reasons: first, energy return on investments is decreasing and, second, the continued use of fossil fuels will increase the impact of global climate change. All renewable energy sources are to be considered in order to satisfy present and future society energy needs. Solar-cell production of electricity is a prominent source of renewable energy, helping attend both problems with our current sources of energy due to its extremely high potential for generating energy and its greenhouse gas generation independence. Solar cells consist of thin layers of photovoltaic materials that can absorb sunlight and convert it into electricity. The equilibrium between production cost and conversion efficiency has favored the commercial dominance of crystalline silicon solar cells over more efficient but also much costlier GaAsbased devices but at around 25% efficiency and still high production costs, its use has had no impact on the dominance of fossil fuels. With only 25 years since its discovery, organic photovoltaic (OPV) cells are particularly promising due to the abundance of their constituent elements and base materials, their low cost, and relative ease of chemical synthesis.
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Figure 17.1 (A) Device architecture of a bulk heterojunction solar cell. Light is incident upon the glass substrate. (B) Bulk heterojunction photophysics: (1) A photon excites an electron to form an exciton, which migrates to the donor/acceptor interface; (2) a difference between the LUMO levels of the donor and acceptor (typically of the order of 30 meV or greater) causes the exciton to dissociate; (3) electrons and holes are transported towards the cathode and anode respectively; (4) charge is collected at the electrodes, thus transforming light into current. (Reproduced from Olivares-Amaya et al., 2011.)
Additionally, organic chemistry knowledge increases the potential of rational design to improve their performance by charting ample regions of chemical space. This versatility has allowed efficiency of OPVs to be improved considerably in the past 10 years, from 4% in 2002 to 10% by 2012. If power efficiencies closer to 15% in combination with a lifetime of more than 10 years can be achieved, OPVs could become a commercially viable alternative for producing electricity from sunlight in multiple applications and may even have the potential to help both satisfaction of present and future demand of energy and decrement of greenhouse gas emissions. State-of-the-art OPVs are based on a bulk heterojunction (BHJ) architecture of two semiconductor compounds, one acting as an electron donor (typically a polymer, or a small molecule) and the other acting as an electron acceptor (a high electron affinity molecule; Yu et al., 1995). Figure 17.1 shows a schematic illustration of a BHJ solar cell. The photovoltaic process begins with light absorption and ends with charge transport to the electrodes. It occurs through the following steps: (i) optical absorption and exciton formation; (ii) exciton migration; (iii) exciton dissociation at the donoracceptor interface; (iv) charge carrier migration to the electrodes; and (v) charge collection at the electrodes. These five steps are summarized in Figure 17.1B. The Harvard Clean Energy Project (CEP; Hachmann et al., 2011) is a high-throughput in silico screening and design effort to develop novel high-performance materials
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for OPVs. CEP features an automated, high-throughput infrastructure for the systematic screening of millions of OPV candidates at different levels of theoretical chemistry approaches reaching first-principles electronic structure calculations. These calculations provide some of the main parameters relevant for the photovoltaic process that can be explored by use of cheminformatics-type techniques to screen for the most promising candidates for increasing efficiency of OPV solar cells. CEP has started by investigating the molecular motifs which, used as monomers, constitute the donor structure of OPVs solar cells. We note that efficiency of OPVs is determined ultimately by many subtle details that are not necessarily included in approximated theoretical chemistry calculations; however, a suitable motif is a necessary condition for successful OPV development. Proposal of these motifs for synthesis and experimental realization of the associated OPVs is the main objective of CEP.
2. THE MOLECULAR LIBRARY In order to search for donor molecules that have the best combination of electronic properties, we built a molecular library of approximately 2.6 million conjugated molecules. The molecular library employed is built via a combinatorial molecule generation scheme starting from the set of 30 basic heterocyclic units (building blocks) shown in Figure 17.2. These units include the most prevalent molecular motifs used in the experimental design of OPVs to date. We note that R groups play an important role in OPV materials but for the present work we have chosen to focus only on the molecular backbone. We populate the library using a virtual reaction-based approach that either links or fuses the fragments together, as shown in Figure 17.3. We also extend the size of the co-monomers by properly adding molecular handles, so they can be further linked or fused. The building blocks are written in the SMILES (Simplified Molecular Input LinE System; Weininger et al., 1989) format so it can be manipulated via SMARTS (Smiles ARbitrary Target Specification; Daylight Theory Manual, 2008) atom mapping. We generated all possible products allowed by this reaction scheme using the 30 blocks shown above (plus their corresponding chemical handles). All building blocks were allowed to link, fuse or combine fusion and linkage up to tetramers. This scheme is represented in Figure 17.4 and the number of molecules created for each combination is quoted in Table 17.1 for a grand total of 2,671,405 molecules.
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Figure 17.2 The 30 building blocks used for generating the CEP molecular library.
3. MERIT FIGURES FOR ORGANIC PHOTOVOLTAICS The parameters that determine the overall efficiency in energy conversion for a solar cell are defined in terms of its currentvoltage characteristics. The power conversion efficiency (PCE) is defined as the percentage of the ratio of power output (Pout) to power input (Pin). Pout is the maximum (m) obtainable electric power, the product of current Jm and voltage
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Figure 17.3 A reaction-based approach for enumerating a molecular library. (A) Linking reaction: Benzene molecule with Mg chemical handles in the para position reacts with pyrrole with Mg chemical handles at the 2,5-position. One set of Mg (green) reacts to form a linked co-monomer of these moieties. (B) Fusion reaction: Benzene molecule with Mg chemical handles in the para position reacts with pyrrole with Mg chemical handles at the 2,5-position to form benzopyrrole. In both cases, a second set of Mg handles (red) is present so that this product can be used as a reagent and enable the generation of co-monomers of greater size.
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Figure 17.4 Depiction of the reactions that we simulate to build the molecular library. BB indicates the building blocks; F is a fragment. When multiple fragments are linked, they are hyphenated (e.g. F-F); fused molecules are shown without a hyphen (e.g. FF). Boxes in dark green indicate products that are added to the library, while those in orange show the building blocks added to generate the products.
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Table 17.1 Molecular Library Generated Using the Reaction Scheme Products Molecules
FF FFF FFFF Total fused F-F F-F-F F-F-F-F Total linked F-FF FF-FF F-FFF F-F-FF Total hybrid Total
230 3903 64,525 68,658 861 33,989 1,345,620 1,380,470 15,889 59,682 267,447 879,259 1,222,277 2,671,405
The linked reaction scheme results in a larger number of molecules generated. F represents a fragment. When multiple fragments are linked, they are hyphenated (e.g. F-F); fused molecules are shown without a hyphen (e.g. FF).
Vm. It is also possible to define Pout as depending on the product of the short-circuit current density (Jsc), the open circuit voltage (Voc), and the fill factor (FF). The fill factor is the ratio of the maximum power, JmVm to the product JscVoc. The product JmVm represents the potential power available under the ideal conditions imposed by JscVoc. The FF then becomes a parameter that measures the capacity of the device to obtain the most power available. Losses depend on the parasitic resistance of the device and other inefficiencies, which are related to the cell morphology. Thus, the formula to compute power conversion efficiency can be written as %PCE 5
FFUJsc UVoc 3 100: Pin
ð17:1Þ
Jsc and Voc are quantities that can easily be determined under device illumination and largely depend on the molecular properties of the donor and acceptor moieties. As detailed by Brabec et al. (2008), Voc is related to exciton dissociation, which leads to the charge separation process (step iii above). Voc scales linearly with respect to the energy difference between the highest occupied molecular orbital (HOMO) of the donor and the lowest unoccupied molecular orbital (LUMO) of the acceptor (Brabec et al., 2001).
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Jsc, in turn, largely depends on the charge mobility and the bandgap of the donor, which determines the spectral overlap: the smaller the bandgap, the higher the spectral overlap. The theoretical understanding of the important parameters for high photovoltaic efficiency has led to models that predict the efficiency of a donor material with respect to a given acceptor, commonly PCBM (1-(3-methoxycarbonyl)propyl-1-phenyl[6,6]C61), as a function of their energy levels (Koster et al., 2006; Scharber et al., 2006). Theoretical methods applied to materials discovery of bulk heterojunction solar cells face the additional challenge that their ultimate efficiency also depends on annealing conditions and co-solvents, also known as additives. The general complexity and multiscale nature of the device morphology is very hard to model with electronic structure theory. Therefore, we expect to find better correlations between descriptors derived from electronic structure-related calculations and organic photovoltaics merit parameters Jsc and Voc than with merit parameters FF and, because of its relation with the latter, PCE.
4. DESCRIPTORS FOR ORGANIC PHOTOVOLTAICS We use previously introduced descriptors for an initial characterization of our molecular library. We employ the Marvin code by ChemAxon (2011). ChemAxon provides a set of over 200 descriptors that are relevant for drug design applications, but they nonetheless proved useful in the application for OPV donor materials. We selected descriptors corresponding to elemental analysis, charge, geometry, and electronic states based on Hu¨ckel theory for the study of monomers for use as donors in OPVs. For atomic-based properties, which result in one parameter for each atom in the molecule, we assessed the maximum, minimum, and average values. There are a total of 33 descriptors in our model; their classes are listed in Table 17.2. Other than more precise properties from quantum mechanical calculations, these can be easily computed for the whole library within a few days on a single workstation. A specific example of a descriptor that displayed statistically significant correlation is the electrophilic localization energy, L(1), which is an atom-centered property based on the Hu¨ckel method: the simplest semiempirical approach for obtaining quantum-mechanical properties of conjugated molecules (Isaacs, 1996). L(1) is the energy related to removing an atom from conjugation, effectively donating two π-electrons to the
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Table 17.2 Classes of Physicochemical and Topological Descriptors Employed in the Presented Models Descriptor Description
Molecular mass Log P
Ring count Hydrogen bond acceptor count Hydrogen bond donor count Rotatable bond count Molecular polarizability
Refractivity
van der Waals surface area van der Waals volume Water accessible area Electronic localization energy Partial charge Electron density Steric hindrance σ orbital electronegativity π orbital electronegativity
Molecular mass Octanolwater partition coefficient, a measure of hydrophobicity based on group contributions from a set of basic fragments fitted to experimental values (Klopman et al., 1994) Number of rings in the molecule Number of hydrogen bond acceptor atoms Number of hydrogen bond donor atoms Excludes bonds connecting hydrogens and terminal atoms Empirical calculation based on a dipole interaction model from atomic polarizabilities, experimental and ab initio values (Miller and Savchik, 1979; van Duijnen and Swart, 1998) Empirical calculation of atomic refractivity; related to London dispersion forces (Viswanadhan et al., 1989) Molecular surface area as defined by van der Waals radii Molecular surface as defined by van der Waals radii Water accessible surface area based on atomic properties Energy related to removing an atom from conjugation (Isaacs, 1996; Ramsey, 1965) Partial atomic charges for π systems and electronegativity-based calculation for the σ network (Dixon and Jurs, 1992) Based on occupancy of atomic-centered orbitals (Isaacs, 1996; Ramsey, 1965) Steric hindrance of an atom calculated from the covalent radii values Mulliken atomic orbital electronegativity from σ orbitals (Dixon and Jurs, 1992) Mulliken atomic orbital electronegativity from π orbitals (Dixon and Jurs, 1992)
Note that these 17 descriptor classes amount to 33 individual descriptors. An asterisk denotes that the descriptor is based on semi-empirical Hu¨ckel model calculations.
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electrophile. The lower the value of L(1), the more reactive the compound. Therefore, a small value of electrophilic localization energy means that the atom contributes little to the overall conjugation of the molecule. We consider a simple linear regression model for correlating properties and descriptors in this initial investigation. The descriptors chosen above are assembled accordingly and the resulting model is parameterized using a training set of organic monomers with experimentally known currentvoltage characteristics. We selected a set of 50 training molecules compiled from the literature (Ando et al., 2005a, b; Blouin et al., 2008; Chen and Cao, 2009; Ebata et al., 2007; Mamada et al., 2008; Meng et al., 2005; Mondal et al., 2009; Mu¨hlbacher et al., 2006; Okamoto and Bao, 2007; Reyes-Reyes et al., 2005; Slooff et al., 2007; Tian et al., 2005; Wang et al., 2008). These molecules include aliphatic side chains used to control packing structures that we have stripped off as they do not influence the electronic properties we are considering. It has to be noted, though, that these side chains may have an effect on the fill factor parameter. The current work is concerned with donor materials of BHJ design, but this method can naturally be applied to other device architectures and materials given the appropriate training set. As mentioned above, we focus on the four most relevant parameters for the performance characteristics of a solar cell. These are PCE, and its components as expressed in Equation (17.1): FF, Voc, and Jsc. Note that Voc and Jsc largely depend on properties intrinsic to the donor and acceptor. FF broadly depends on the morphology and the specific device architectures. We therefore expect that the molecular descriptors used and the experimental values will show a better correlation for the first two than for the latter. The expression to determine PCE includes all three parameters and its correlation should thus fit in between the others. The multiple linear regression for the descriptor models with respect to these four parameters was performed using the R code (R Development Core Team, 2008). The correlation, as obtained by the use of the 33 descriptors, varied from very good (RV2 oc 5 0:95, RJ2sc 5 0:92) 2 2 or good (RPCE 5 0:89) to poor (RFF 5 0:66). We performed a significance test on the descriptors and eliminated the least significant ones, which only slightly reduced the precision of the fit (as an example, results for Voc are shown in Table 17.3). The significance of the descriptors was obtained from a two-sided t-statistics test. The p-value for each descriptor ranged from 1023 to 1021.
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Table 17.3 Results for the Fitting of Voc to 20 Statistically Significant Descriptors Estimate Std. error t value Pr( . 9t9)
(Intercept) Log P RingCount AcceptorCount RotBondCount Refractivity VdWArea VdWVolume ASA ASAH ElecLocEn(lo) PartialCh(lo) PartialCh(hi) PartialCh(avg) ElecDen(lo) ElecDen( avg) StericHind(hi) σ ElecNeg(lo) σ ElecNeg(hi) σ ElecNeg(avg) π ElecNeg(hi)
17.0788482 2 0.1328980 0.2204759 2 0.0996894 0.2374734 2 0.0075611 0.0063744 2 0.0083368 2 0.0037351 0.0024702 0.0371339 2 1.6637886 2 3.3145356 50.3586495 2 0.8402735 2 2.3826616 2 0.8950969 0.1993522 0.0448449 2 1.4447603 0.2316545
1.9956354 0.0155249 0.0279730 0.0139580 0.0240348 0.0017250 0.0009059 0.0013763 0.0010949 0.0010328 0.0157293 0.4416521 0.5805118 6.6593831 0.2704179 0.2394278 0.1545381 0.0588838 0.0190354 0.2073776 0.0345617
8.558 2 8.560 7.882 2 7.142 9.880 2 4.383 7.036 2 6.057 2 3.411 2.392 2.361 2 3.767 2 5.710 7.562 2 3.107 2 9.951 2 5.792 3.386 2.356 2 6.967 6.703
1. 99e-09 1.98e-09 1.08e-08 7.35e-08 8.67e-11 0.00014 9.72e-08 1.36e-06 0.00192 0.02347 0.02517 0.00075 3.54e-06 2.46e-08 0.00420 7.37e-11 2.82e-06 0.00206 0.02545 1.17e-07 2.36e-07
Signif. codes: 0 , 0.001 , 0.01 , 0.05, 0.1, 1. Residual standard error: 0.04702 on 29 degrees of freedom (eight observations deleted due to absence). Multiple R2: 0.9455; adjusted R2: 0.9079. F-statistic: 25.15 on 20 and 29 DF; p-value: 4.09e-13.
To evaluate the relevance of these predictions we also built a model for the use of descriptors to describe the product VocJsc, which is proportional to PCE but only contains parameters well represented in our cheminformatics approach. We summarize the results related to the coefficients of determination (R2) of the fitting in Table 17.4. The particular relevance of the fitting is present in the comparison of the predicted properties against the measured ones in Figure 17.5. As stressed above, it is not unexpected that the parameters that depend on the material properties, Voc and Jsc, result in a much better fit than the FF, and that the difficulty of this fitting is carried over into the PCE fitting. The fit resulted in sets of significant descriptors that were different for each of the experimental parameters. The best description included 20 descriptors for Voc and Voc Jsc, 18 for Jsc and 15 for PCE. Four descriptors are present in the models of each four
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Table 17.4 Summary of Linear Fitting Results for each of the Properties Studied Property R2(all desc.) Descriptors R2
Voc Jsc %PCE FF VocJsc
0.9580 0.9202 0.8937 0.6567 0.9025
20 18 15 20 20
0.9455 0.8989 0.8409 0.6170 0.8809
Jsc (from descriptors)
Voc (from descriptors)
We compare the coefficients of determination (R2) using all 33 descriptors (all desc.) and the statistically significant ones. The number of significant descriptors ranges from 15 to 20, but the R2 is not largely affected in all cases.
1 0.8 0.6 0.4 0.6
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Figure 17.5 Results for the multiple linear regression of the four models and the values of the training set. The predicted value from fitted descriptors is compared to the experimental value originally used for fitting. Units are mA/cm2 for Jsc and V for Voc.
parameters: rotatable bond count, electron density (lowest), orbital electronegativity (σ; average) and orbital electronegativity (π; highest). We notice that each descriptor in this subset has either a positive or a negative correlation for all four values. The separation between estimates is never larger than two orders of magnitude. Therefore, these descriptors form a tight set of estimates that affect each of the parameters in a similar fashion.
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Figure 17.6 Results of the “leave 1/3 out” correlation test for Voc.
A common test of the calibration of the training set to the descriptors is the “leave 1/3 out” technique. The whole set of calibration molecules is randomly divided into three subsets: A (17 molecules in this case), B (17 molecules), and C (16 molecules). For Voc, the set of 20 descriptors previously selected is used to fit separately to the subsets AB (34 molecules), AC (33 molecules), and BC (33 molecules). The coefficients thus obtained are used to predict Jsc for the set not used in the fitting (C for AB, for instance). Results are shown in Figure 17.6. As can be seen, the prediction of excluded molecules is consistent.
5. PREDICTIONS FROM CHEMINFORMATICS We now apply the models created in the previous section to the 2.6 million molecules of the candidate library and summarize our findings. The histograms of the obtained results are shown in Figure 17.7. In the cases of Voc and Jsc (and therefore in Voc Jsc) there are a considerable number of molecules with predicted values well above the largest observed to date. These molecules constitute the most promising candidates for BHJ donor OPV materials within the presented cheminformatics approach. Some
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Figure 17.7 Histograms of the predicted currentvoltage parameters (open circuit voltage (Voc), short-circuit current density (Jsc), and the product VocJsc) for the screening of 2.6 million molecules. Units are mA/cm2 for Jsc and V for Voc. The vertical lines correspond to the experimental values of the molecules in the training set (i.e. independent of the y-axis value). Note that some predicted values are larger than the best experimental ones.
molecules are predicted to have an unrealistic negative value. The fraction of molecules in this situation is small for all parameters except for the FF, which can easily be explained by its relatively poor model. Noting the limitations of the extrapolation, we find that for Voc nearly half of the molecules are predicted to have a value higher than the best of the experimental molecules (1.04 V), and only 0.8% have a negative value; for Jsc, 41.5% of the molecules have a value higher than the best experimental, and 8.3% have a negative value; only 1.5% of the molecules have a predicted value of PCE higher than the highest experimental, and the highest value is 10.4%, but there are 43.4% of molecules with a value of the product VocJsc higher than the highest experimental; these molecules, combined with an appropriate value of the FF (which is not predicted well by these descriptors and was not related to the molecules in this calculation) could have values of PCE above current records. We further investigate how the highest rated molecules in each of the three currentvoltage parameters considered (Voc, Jsc, VocJsc) score with respect to the additional parameters. This is, we test if a promising
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Figure 17.8 Top 10% molecules with highest predicted values of Voc (green), Jsc (blue), and VocJsc (red). The intensity of the point corresponding to a given molecule is coded according to the value of the product VocJsc. The best molecules, according to the present study, are located in the upper left region of the figure. Units are mA/cm2 for Jsc and V for Voc.
molecule for Voc is also a good candidate for Jsc and VocJsc. We selected the top 10% from each group and compared them. We find that molecules predicted to have a high value of Voc only rarely also have a high value of Jsc, and vice versa. Figure 17.8 shows the position in the predicted Voc vs. Jsc space of the top 10% of molecules from each group: Voc, Jsc, and VocJsc. We observe that molecules predicted to have the highest values of the product VocJsc have mostly a high value of Jsc and an average value of Voc, i.e. they have a higher overlap with the top values of Jsc. This suggests that the search for high-efficiency monomers is particularly promising with molecules based on motifs present in both the Jsc and VocJsc optimization. For a more detailed analysis of the results we focus on the top 1000 molecules (all the following quantities are taken with respect to the top 1000) with the best currentvoltage characteristics. For Voc, we notice that these have at least one silicon atom and are built mostly by both linking and fusing the 30 basic fragments. A typical molecule from this set is shown in Figure 17.9A. For Jsc, silicon atoms are not as common (161 molecules have at least one) but instead selenium-containing heteroatoms are more frequent (313 molecules have at least one) and the thienopyrrole motif is present in 822 molecules. The molecules of this set have a
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Figure 17.9 Typical molecules from the set of cheminformatics predictions for the highest: (A) Voc (note the mixed linked and fused heterocyclic units with silicon); (B) Jsc (note the linked backbone, the selenium atoms, and the thienopyrrole motif); (C) VocJsc (note the mixed linked and fused structure and the benzothiadiazole and thienopyrrole motifs).
predominantly linked rather than fused backbone. Figure 17.9B shows a typical molecule from this set. Again, the best expected co-monomers for application in heterojunction OPVs correspond, according to this QSPR analysis, to the ones with the highest value of VocJsc, for which the set of the best 1000 have molecules with silicon atoms (375), selenium atoms (131), silicon and selenium atoms (53), and come mostly from linking the basic units (890). The benzothiadiazole or pyridinethiadiazole motifs are prevalent in this set of candidates (see Figure 17.10), present in 463 molecules. Similarly, units that can potentially have quinoid stabilization are prominent in this set.
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Figure 17.10 Ubiquitous motifs present in many of the most promising molecules according to the predicted VocJsc parameter: (A) benzothiadiazole or pyridinethiadiazole motif; (B) thienopyrrole motif.
Specifically, 117 present the thienothiophene moiety. This suggests that the search for monomers with high efficiency as OPVs should start with molecules based on the motifs presented in Figure 17.10.
6. CONCLUSIONS We have carried out the construction of a large library of organic molecules to be evaluated as donors for bulk heterojunction organic photovoltaics. Our ultimate goal is the analysis of their possibilities by means of high-level ab initio quantum chemistry calculations. The large computing resources that CEP demands is largely provided by the World Community Grid (WCG), a distributed volunteer computing platform organized by IBM (http://www.worldcommunitygrid.org). Additionally, the library of organic molecules can be analyzed by less computationally intensive techniques like the QSPR-based approach that has been described in this work. We are currently working on a cross-validation of the present predictions with the ones from the quantum chemical studies within the Clean Energy Project. As an example of the capabilities of quantum chemistry calculations in correlating with experimental measurements we compare a Scharber plot of some of the molecules from the training set with the results from calculations (BP86 density functional, SVP basis set) adjusted by a constant shift (Figure 17.11). Predictions based on semi-empirical descriptors and quantum chemistry calculations are not expected to be precise, but will no doubt help charting the territories of the vast chemical space. This situation is analogous to the situation in the pharmaceutical industry, where informatics methods aid in the ranking of potential candidates. Success stories involve the close collaboration between theory and experiment to hone in the right candidate materials.
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Scharber plot
LUMO level (eV)
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Band Gap (eV)
Figure 17.11 Scharber plot for 14 molecules form the training set used in this study. Experimental results are compared to results from DFT calculations (BP86/SVP) adjusted by a constant shift. Good candidates for OPVs are reproduced.
ACKNOWLEDGMENTS We are grateful for support from Stanfords Global Climate Energy Project and the Department of Energy’s Program of Theory and Computation. A.A.-G. also acknowledges generous support from the Corning Foundation.
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Organic Photovoltaics Carlos Amador-Bedolla , Roberto Olivares-Amaya†, Johannes Hachmann‡ and Alán Aspuru-Guzik‡
Facultad de Quı´mica, Universidad Nacional Auto´noma de Me´xico, Mexico Department of Chemistry, Princeton University, NJ, USA Department of Chemistry and Chemical Biology, Harvard University, MA, USA
†
‡
1. CHEMICAL SPACE, ENERGY SOURCES, AND THE CLEAN ENERGY PROJECT Chemical space, the collection of all different molecules that can exist, is extremely vast, and a credible estimation of its size has not even been attempted. However, some subgroups of this space, with particular characteristics, have been estimated (Reymond et al., 2012): The number of drug-like molecules most organic molecules of perceived relevance in all kinds of applications were estimated at around 1060 (Bohacek et al., 1996) and, more recently, the organic chemistry space accessible by current synthetic methods in between 1020 and 1024 molecules (Ertl, 2003). Within this vast space theoretical and experimental scientists are looking for particular compounds that have the best possible properties for use in selected applications. Automated high-throughput methods have allowed experimentalists to start charting these territories, both for synthesis and screening of large numbers of compounds. Pharma and biotech companies have led this effort during the past 20 years. High-throughput screening (HTS), allowing the number of compounds tested to be in the range of 10,000100,000 per day, has recently been followed by ultra-high throughput, which can screen compounds in numbers above 100,000 per day (Mayr and Bojanic, 2009). More recently, similar efforts have been developed for HTS of functional materials in combinatorial materials science (Potyrailo et al., 2011; Xiang, 2004). These methods are actively used in the exploration of superconductor (Xiang et al., 1995), ferroelectric (Chang et al., 1998), magnetoresistive (Bricen˜o et al., 1995) and luminescent materials (Danielson et al., 1998), materials for hydrogen storage (Olk, 2005), organic light emission (Zou et al., 2001), solar cells (Ha¨nsel et al., 2002), and catalysts (Hagemeyer et al., 2001), to name a
Informatics for Materials Science and Engineering DOI: http://dx.doi.org/10.1016/B978-0-12-394399-6.00017-5
© 2013 Elsevier Inc. All rights reserved.
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few. On the other hand, the extremely fast growth of computational capabilities during the past 40 years (no other technology merit figure has advanced six orders of magnitude ever, not even considering that for digital computation this happened in only 40 years) and the advances in semi-empirical and ab initio techniques are allowing computational HTS to search for optimal materials for particular applications, again both for synthesis (Dias, 2010; Wilmer et al., 2012a) (including crystal structure prediction; Hautier et al., 2012) and screening of compounds and materials for energy applications in hydrogen storage (Hummelshøj et al., 2009), lithium-ion batteries (Mueller et al., 2011), thermoelectrics (Wang et al., 2011), organic photovoltaics (Olivares-Amaya et al., 2011), catalysis (Greeley et al., 2006) and photocatalysis (Castelli et al., 2012), and carbon capture (Wilmer et al., 2012b). For all that, it has been considered that these modern capabilities experimental and theoretical HTS as all the capabilities that define our civilization are only possible because of our availability of huge amounts of inexpensive energy. Current human consumption amounts to some 260 million barrels of oil equivalent (MBOE) per day, and current mainstream expectations of economical growth predict an increase of almost 40% in the next 20 years (Conti et al., 2010). This huge increase in available energy will be difficult to satisfy, as maintaining present supply of energy 88% of which is currently provided by combustion of fossil fuels is already questionable for at least two reasons: first, energy return on investments is decreasing and, second, the continued use of fossil fuels will increase the impact of global climate change. All renewable energy sources are to be considered in order to satisfy present and future society energy needs. Solar-cell production of electricity is a prominent source of renewable energy, helping attend both problems with our current sources of energy due to its extremely high potential for generating energy and its greenhouse gas generation independence. Solar cells consist of thin layers of photovoltaic materials that can absorb sunlight and convert it into electricity. The equilibrium between production cost and conversion efficiency has favored the commercial dominance of crystalline silicon solar cells over more efficient but also much costlier GaAsbased devices but at around 25% efficiency and still high production costs, its use has had no impact on the dominance of fossil fuels. With only 25 years since its discovery, organic photovoltaic (OPV) cells are particularly promising due to the abundance of their constituent elements and base materials, their low cost, and relative ease of chemical synthesis.
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Figure 17.1 (A) Device architecture of a bulk heterojunction solar cell. Light is incident upon the glass substrate. (B) Bulk heterojunction photophysics: (1) A photon excites an electron to form an exciton, which migrates to the donor/acceptor interface; (2) a difference between the LUMO levels of the donor and acceptor (typically of the order of 30 meV or greater) causes the exciton to dissociate; (3) electrons and holes are transported towards the cathode and anode respectively; (4) charge is collected at the electrodes, thus transforming light into current. (Reproduced from Olivares-Amaya et al., 2011.)
Additionally, organic chemistry knowledge increases the potential of rational design to improve their performance by charting ample regions of chemical space. This versatility has allowed efficiency of OPVs to be improved considerably in the past 10 years, from 4% in 2002 to 10% by 2012. If power efficiencies closer to 15% in combination with a lifetime of more than 10 years can be achieved, OPVs could become a commercially viable alternative for producing electricity from sunlight in multiple applications and may even have the potential to help both satisfaction of present and future demand of energy and decrement of greenhouse gas emissions. State-of-the-art OPVs are based on a bulk heterojunction (BHJ) architecture of two semiconductor compounds, one acting as an electron donor (typically a polymer, or a small molecule) and the other acting as an electron acceptor (a high electron affinity molecule; Yu et al., 1995). Figure 17.1 shows a schematic illustration of a BHJ solar cell. The photovoltaic process begins with light absorption and ends with charge transport to the electrodes. It occurs through the following steps: (i) optical absorption and exciton formation; (ii) exciton migration; (iii) exciton dissociation at the donoracceptor interface; (iv) charge carrier migration to the electrodes; and (v) charge collection at the electrodes. These five steps are summarized in Figure 17.1B. The Harvard Clean Energy Project (CEP; Hachmann et al., 2011) is a high-throughput in silico screening and design effort to develop novel high-performance materials
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for OPVs. CEP features an automated, high-throughput infrastructure for the systematic screening of millions of OPV candidates at different levels of theoretical chemistry approaches reaching first-principles electronic structure calculations. These calculations provide some of the main parameters relevant for the photovoltaic process that can be explored by use of cheminformatics-type techniques to screen for the most promising candidates for increasing efficiency of OPV solar cells. CEP has started by investigating the molecular motifs which, used as monomers, constitute the donor structure of OPVs solar cells. We note that efficiency of OPVs is determined ultimately by many subtle details that are not necessarily included in approximated theoretical chemistry calculations; however, a suitable motif is a necessary condition for successful OPV development. Proposal of these motifs for synthesis and experimental realization of the associated OPVs is the main objective of CEP.
2. THE MOLECULAR LIBRARY In order to search for donor molecules that have the best combination of electronic properties, we built a molecular library of approximately 2.6 million conjugated molecules. The molecular library employed is built via a combinatorial molecule generation scheme starting from the set of 30 basic heterocyclic units (building blocks) shown in Figure 17.2. These units include the most prevalent molecular motifs used in the experimental design of OPVs to date. We note that R groups play an important role in OPV materials but for the present work we have chosen to focus only on the molecular backbone. We populate the library using a virtual reaction-based approach that either links or fuses the fragments together, as shown in Figure 17.3. We also extend the size of the co-monomers by properly adding molecular handles, so they can be further linked or fused. The building blocks are written in the SMILES (Simplified Molecular Input LinE System; Weininger et al., 1989) format so it can be manipulated via SMARTS (Smiles ARbitrary Target Specification; Daylight Theory Manual, 2008) atom mapping. We generated all possible products allowed by this reaction scheme using the 30 blocks shown above (plus their corresponding chemical handles). All building blocks were allowed to link, fuse or combine fusion and linkage up to tetramers. This scheme is represented in Figure 17.4 and the number of molecules created for each combination is quoted in Table 17.1 for a grand total of 2,671,405 molecules.
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Figure 17.2 The 30 building blocks used for generating the CEP molecular library.
3. MERIT FIGURES FOR ORGANIC PHOTOVOLTAICS The parameters that determine the overall efficiency in energy conversion for a solar cell are defined in terms of its currentvoltage characteristics. The power conversion efficiency (PCE) is defined as the percentage of the ratio of power output (Pout) to power input (Pin). Pout is the maximum (m) obtainable electric power, the product of current Jm and voltage
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Figure 17.3 A reaction-based approach for enumerating a molecular library. (A) Linking reaction: Benzene molecule with Mg chemical handles in the para position reacts with pyrrole with Mg chemical handles at the 2,5-position. One set of Mg (green) reacts to form a linked co-monomer of these moieties. (B) Fusion reaction: Benzene molecule with Mg chemical handles in the para position reacts with pyrrole with Mg chemical handles at the 2,5-position to form benzopyrrole. In both cases, a second set of Mg handles (red) is present so that this product can be used as a reagent and enable the generation of co-monomers of greater size.
BB
FF
BB
FF-FF
BB
BB
FFFF
FFF
FFF-F
BB
FF
F-F
FF-F
BB
FF-F-F
BB
F-F-F
BB
F-F-F-F
FFFF-F
Figure 17.4 Depiction of the reactions that we simulate to build the molecular library. BB indicates the building blocks; F is a fragment. When multiple fragments are linked, they are hyphenated (e.g. F-F); fused molecules are shown without a hyphen (e.g. FF). Boxes in dark green indicate products that are added to the library, while those in orange show the building blocks added to generate the products.
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Table 17.1 Molecular Library Generated Using the Reaction Scheme Products Molecules
FF FFF FFFF Total fused F-F F-F-F F-F-F-F Total linked F-FF FF-FF F-FFF F-F-FF Total hybrid Total
230 3903 64,525 68,658 861 33,989 1,345,620 1,380,470 15,889 59,682 267,447 879,259 1,222,277 2,671,405
The linked reaction scheme results in a larger number of molecules generated. F represents a fragment. When multiple fragments are linked, they are hyphenated (e.g. F-F); fused molecules are shown without a hyphen (e.g. FF).
Vm. It is also possible to define Pout as depending on the product of the short-circuit current density (Jsc), the open circuit voltage (Voc), and the fill factor (FF). The fill factor is the ratio of the maximum power, JmVm to the product JscVoc. The product JmVm represents the potential power available under the ideal conditions imposed by JscVoc. The FF then becomes a parameter that measures the capacity of the device to obtain the most power available. Losses depend on the parasitic resistance of the device and other inefficiencies, which are related to the cell morphology. Thus, the formula to compute power conversion efficiency can be written as %PCE 5
FFUJsc UVoc 3 100: Pin
ð17:1Þ
Jsc and Voc are quantities that can easily be determined under device illumination and largely depend on the molecular properties of the donor and acceptor moieties. As detailed by Brabec et al. (2008), Voc is related to exciton dissociation, which leads to the charge separation process (step iii above). Voc scales linearly with respect to the energy difference between the highest occupied molecular orbital (HOMO) of the donor and the lowest unoccupied molecular orbital (LUMO) of the acceptor (Brabec et al., 2001).
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Jsc, in turn, largely depends on the charge mobility and the bandgap of the donor, which determines the spectral overlap: the smaller the bandgap, the higher the spectral overlap. The theoretical understanding of the important parameters for high photovoltaic efficiency has led to models that predict the efficiency of a donor material with respect to a given acceptor, commonly PCBM (1-(3-methoxycarbonyl)propyl-1-phenyl[6,6]C61), as a function of their energy levels (Koster et al., 2006; Scharber et al., 2006). Theoretical methods applied to materials discovery of bulk heterojunction solar cells face the additional challenge that their ultimate efficiency also depends on annealing conditions and co-solvents, also known as additives. The general complexity and multiscale nature of the device morphology is very hard to model with electronic structure theory. Therefore, we expect to find better correlations between descriptors derived from electronic structure-related calculations and organic photovoltaics merit parameters Jsc and Voc than with merit parameters FF and, because of its relation with the latter, PCE.
4. DESCRIPTORS FOR ORGANIC PHOTOVOLTAICS We use previously introduced descriptors for an initial characterization of our molecular library. We employ the Marvin code by ChemAxon (2011). ChemAxon provides a set of over 200 descriptors that are relevant for drug design applications, but they nonetheless proved useful in the application for OPV donor materials. We selected descriptors corresponding to elemental analysis, charge, geometry, and electronic states based on Hu¨ckel theory for the study of monomers for use as donors in OPVs. For atomic-based properties, which result in one parameter for each atom in the molecule, we assessed the maximum, minimum, and average values. There are a total of 33 descriptors in our model; their classes are listed in Table 17.2. Other than more precise properties from quantum mechanical calculations, these can be easily computed for the whole library within a few days on a single workstation. A specific example of a descriptor that displayed statistically significant correlation is the electrophilic localization energy, L(1), which is an atom-centered property based on the Hu¨ckel method: the simplest semiempirical approach for obtaining quantum-mechanical properties of conjugated molecules (Isaacs, 1996). L(1) is the energy related to removing an atom from conjugation, effectively donating two π-electrons to the
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Table 17.2 Classes of Physicochemical and Topological Descriptors Employed in the Presented Models Descriptor Description
Molecular mass Log P
Ring count Hydrogen bond acceptor count Hydrogen bond donor count Rotatable bond count Molecular polarizability
Refractivity
van der Waals surface area van der Waals volume Water accessible area Electronic localization energy Partial charge Electron density Steric hindrance σ orbital electronegativity π orbital electronegativity
Molecular mass Octanolwater partition coefficient, a measure of hydrophobicity based on group contributions from a set of basic fragments fitted to experimental values (Klopman et al., 1994) Number of rings in the molecule Number of hydrogen bond acceptor atoms Number of hydrogen bond donor atoms Excludes bonds connecting hydrogens and terminal atoms Empirical calculation based on a dipole interaction model from atomic polarizabilities, experimental and ab initio values (Miller and Savchik, 1979; van Duijnen and Swart, 1998) Empirical calculation of atomic refractivity; related to London dispersion forces (Viswanadhan et al., 1989) Molecular surface area as defined by van der Waals radii Molecular surface as defined by van der Waals radii Water accessible surface area based on atomic properties Energy related to removing an atom from conjugation (Isaacs, 1996; Ramsey, 1965) Partial atomic charges for π systems and electronegativity-based calculation for the σ network (Dixon and Jurs, 1992) Based on occupancy of atomic-centered orbitals (Isaacs, 1996; Ramsey, 1965) Steric hindrance of an atom calculated from the covalent radii values Mulliken atomic orbital electronegativity from σ orbitals (Dixon and Jurs, 1992) Mulliken atomic orbital electronegativity from π orbitals (Dixon and Jurs, 1992)
Note that these 17 descriptor classes amount to 33 individual descriptors. An asterisk denotes that the descriptor is based on semi-empirical Hu¨ckel model calculations.
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electrophile. The lower the value of L(1), the more reactive the compound. Therefore, a small value of electrophilic localization energy means that the atom contributes little to the overall conjugation of the molecule. We consider a simple linear regression model for correlating properties and descriptors in this initial investigation. The descriptors chosen above are assembled accordingly and the resulting model is parameterized using a training set of organic monomers with experimentally known currentvoltage characteristics. We selected a set of 50 training molecules compiled from the literature (Ando et al., 2005a, b; Blouin et al., 2008; Chen and Cao, 2009; Ebata et al., 2007; Mamada et al., 2008; Meng et al., 2005; Mondal et al., 2009; Mu¨hlbacher et al., 2006; Okamoto and Bao, 2007; Reyes-Reyes et al., 2005; Slooff et al., 2007; Tian et al., 2005; Wang et al., 2008). These molecules include aliphatic side chains used to control packing structures that we have stripped off as they do not influence the electronic properties we are considering. It has to be noted, though, that these side chains may have an effect on the fill factor parameter. The current work is concerned with donor materials of BHJ design, but this method can naturally be applied to other device architectures and materials given the appropriate training set. As mentioned above, we focus on the four most relevant parameters for the performance characteristics of a solar cell. These are PCE, and its components as expressed in Equation (17.1): FF, Voc, and Jsc. Note that Voc and Jsc largely depend on properties intrinsic to the donor and acceptor. FF broadly depends on the morphology and the specific device architectures. We therefore expect that the molecular descriptors used and the experimental values will show a better correlation for the first two than for the latter. The expression to determine PCE includes all three parameters and its correlation should thus fit in between the others. The multiple linear regression for the descriptor models with respect to these four parameters was performed using the R code (R Development Core Team, 2008). The correlation, as obtained by the use of the 33 descriptors, varied from very good (RV2 oc 5 0:95, RJ2sc 5 0:92) 2 2 or good (RPCE 5 0:89) to poor (RFF 5 0:66). We performed a significance test on the descriptors and eliminated the least significant ones, which only slightly reduced the precision of the fit (as an example, results for Voc are shown in Table 17.3). The significance of the descriptors was obtained from a two-sided t-statistics test. The p-value for each descriptor ranged from 1023 to 1021.
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Table 17.3 Results for the Fitting of Voc to 20 Statistically Significant Descriptors Estimate Std. error t value Pr( . 9t9)
(Intercept) Log P RingCount AcceptorCount RotBondCount Refractivity VdWArea VdWVolume ASA ASAH ElecLocEn(lo) PartialCh(lo) PartialCh(hi) PartialCh(avg) ElecDen(lo) ElecDen( avg) StericHind(hi) σ ElecNeg(lo) σ ElecNeg(hi) σ ElecNeg(avg) π ElecNeg(hi)
17.0788482 2 0.1328980 0.2204759 2 0.0996894 0.2374734 2 0.0075611 0.0063744 2 0.0083368 2 0.0037351 0.0024702 0.0371339 2 1.6637886 2 3.3145356 50.3586495 2 0.8402735 2 2.3826616 2 0.8950969 0.1993522 0.0448449 2 1.4447603 0.2316545
1.9956354 0.0155249 0.0279730 0.0139580 0.0240348 0.0017250 0.0009059 0.0013763 0.0010949 0.0010328 0.0157293 0.4416521 0.5805118 6.6593831 0.2704179 0.2394278 0.1545381 0.0588838 0.0190354 0.2073776 0.0345617
8.558 2 8.560 7.882 2 7.142 9.880 2 4.383 7.036 2 6.057 2 3.411 2.392 2.361 2 3.767 2 5.710 7.562 2 3.107 2 9.951 2 5.792 3.386 2.356 2 6.967 6.703
1. 99e-09 1.98e-09 1.08e-08 7.35e-08 8.67e-11 0.00014 9.72e-08 1.36e-06 0.00192 0.02347 0.02517 0.00075 3.54e-06 2.46e-08 0.00420 7.37e-11 2.82e-06 0.00206 0.02545 1.17e-07 2.36e-07
Signif. codes: 0 , 0.001 , 0.01 , 0.05, 0.1, 1. Residual standard error: 0.04702 on 29 degrees of freedom (eight observations deleted due to absence). Multiple R2: 0.9455; adjusted R2: 0.9079. F-statistic: 25.15 on 20 and 29 DF; p-value: 4.09e-13.
To evaluate the relevance of these predictions we also built a model for the use of descriptors to describe the product VocJsc, which is proportional to PCE but only contains parameters well represented in our cheminformatics approach. We summarize the results related to the coefficients of determination (R2) of the fitting in Table 17.4. The particular relevance of the fitting is present in the comparison of the predicted properties against the measured ones in Figure 17.5. As stressed above, it is not unexpected that the parameters that depend on the material properties, Voc and Jsc, result in a much better fit than the FF, and that the difficulty of this fitting is carried over into the PCE fitting. The fit resulted in sets of significant descriptors that were different for each of the experimental parameters. The best description included 20 descriptors for Voc and Voc Jsc, 18 for Jsc and 15 for PCE. Four descriptors are present in the models of each four
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Table 17.4 Summary of Linear Fitting Results for each of the Properties Studied Property R2(all desc.) Descriptors R2
Voc Jsc %PCE FF VocJsc
0.9580 0.9202 0.8937 0.6567 0.9025
20 18 15 20 20
0.9455 0.8989 0.8409 0.6170 0.8809
Jsc (from descriptors)
Voc (from descriptors)
We compare the coefficients of determination (R2) using all 33 descriptors (all desc.) and the statistically significant ones. The number of significant descriptors ranges from 15 to 20, but the R2 is not largely affected in all cases.
1 0.8 0.6 0.4 0.6
0.4
0.8
12 10 8 6 4 2 0 0
1
2
4
0.7 0.6 0.5 0.4 0.3 0.3
0.4
0.5 FF
6
8
10
12
4
5
6
Jsc %PCE (from descriptors)
FF (from descriptors)
Voc
0.6
0.7
6 5 4 3 2 1 0 0
1
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parameters: rotatable bond count, electron density (lowest), orbital electronegativity (σ; average) and orbital electronegativity (π; highest). We notice that each descriptor in this subset has either a positive or a negative correlation for all four values. The separation between estimates is never larger than two orders of magnitude. Therefore, these descriptors form a tight set of estimates that affect each of the parameters in a similar fashion.
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A common test of the calibration of the training set to the descriptors is the “leave 1/3 out” technique. The whole set of calibration molecules is randomly divided into three subsets: A (17 molecules in this case), B (17 molecules), and C (16 molecules). For Voc, the set of 20 descriptors previously selected is used to fit separately to the subsets AB (34 molecules), AC (33 molecules), and BC (33 molecules). The coefficients thus obtained are used to predict Jsc for the set not used in the fitting (C for AB, for instance). Results are shown in Figure 17.6. As can be seen, the prediction of excluded molecules is consistent.
5. PREDICTIONS FROM CHEMINFORMATICS We now apply the models created in the previous section to the 2.6 million molecules of the candidate library and summarize our findings. The histograms of the obtained results are shown in Figure 17.7. In the cases of Voc and Jsc (and therefore in Voc Jsc) there are a considerable number of molecules with predicted values well above the largest observed to date. These molecules constitute the most promising candidates for BHJ donor OPV materials within the presented cheminformatics approach. Some
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molecules are predicted to have an unrealistic negative value. The fraction of molecules in this situation is small for all parameters except for the FF, which can easily be explained by its relatively poor model. Noting the limitations of the extrapolation, we find that for Voc nearly half of the molecules are predicted to have a value higher than the best of the experimental molecules (1.04 V), and only 0.8% have a negative value; for Jsc, 41.5% of the molecules have a value higher than the best experimental, and 8.3% have a negative value; only 1.5% of the molecules have a predicted value of PCE higher than the highest experimental, and the highest value is 10.4%, but there are 43.4% of molecules with a value of the product VocJsc higher than the highest experimental; these molecules, combined with an appropriate value of the FF (which is not predicted well by these descriptors and was not related to the molecules in this calculation) could have values of PCE above current records. We further investigate how the highest rated molecules in each of the three currentvoltage parameters considered (Voc, Jsc, VocJsc) score with respect to the additional parameters. This is, we test if a promising
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Figure 17.8 Top 10% molecules with highest predicted values of Voc (green), Jsc (blue), and VocJsc (red). The intensity of the point corresponding to a given molecule is coded according to the value of the product VocJsc. The best molecules, according to the present study, are located in the upper left region of the figure. Units are mA/cm2 for Jsc and V for Voc.
molecule for Voc is also a good candidate for Jsc and VocJsc. We selected the top 10% from each group and compared them. We find that molecules predicted to have a high value of Voc only rarely also have a high value of Jsc, and vice versa. Figure 17.8 shows the position in the predicted Voc vs. Jsc space of the top 10% of molecules from each group: Voc, Jsc, and VocJsc. We observe that molecules predicted to have the highest values of the product VocJsc have mostly a high value of Jsc and an average value of Voc, i.e. they have a higher overlap with the top values of Jsc. This suggests that the search for high-efficiency monomers is particularly promising with molecules based on motifs present in both the Jsc and VocJsc optimization. For a more detailed analysis of the results we focus on the top 1000 molecules (all the following quantities are taken with respect to the top 1000) with the best currentvoltage characteristics. For Voc, we notice that these have at least one silicon atom and are built mostly by both linking and fusing the 30 basic fragments. A typical molecule from this set is shown in Figure 17.9A. For Jsc, silicon atoms are not as common (161 molecules have at least one) but instead selenium-containing heteroatoms are more frequent (313 molecules have at least one) and the thienopyrrole motif is present in 822 molecules. The molecules of this set have a
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Figure 17.9 Typical molecules from the set of cheminformatics predictions for the highest: (A) Voc (note the mixed linked and fused heterocyclic units with silicon); (B) Jsc (note the linked backbone, the selenium atoms, and the thienopyrrole motif); (C) VocJsc (note the mixed linked and fused structure and the benzothiadiazole and thienopyrrole motifs).
predominantly linked rather than fused backbone. Figure 17.9B shows a typical molecule from this set. Again, the best expected co-monomers for application in heterojunction OPVs correspond, according to this QSPR analysis, to the ones with the highest value of VocJsc, for which the set of the best 1000 have molecules with silicon atoms (375), selenium atoms (131), silicon and selenium atoms (53), and come mostly from linking the basic units (890). The benzothiadiazole or pyridinethiadiazole motifs are prevalent in this set of candidates (see Figure 17.10), present in 463 molecules. Similarly, units that can potentially have quinoid stabilization are prominent in this set.
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Figure 17.10 Ubiquitous motifs present in many of the most promising molecules according to the predicted VocJsc parameter: (A) benzothiadiazole or pyridinethiadiazole motif; (B) thienopyrrole motif.
Specifically, 117 present the thienothiophene moiety. This suggests that the search for monomers with high efficiency as OPVs should start with molecules based on the motifs presented in Figure 17.10.
6. CONCLUSIONS We have carried out the construction of a large library of organic molecules to be evaluated as donors for bulk heterojunction organic photovoltaics. Our ultimate goal is the analysis of their possibilities by means of high-level ab initio quantum chemistry calculations. The large computing resources that CEP demands is largely provided by the World Community Grid (WCG), a distributed volunteer computing platform organized by IBM (http://www.worldcommunitygrid.org). Additionally, the library of organic molecules can be analyzed by less computationally intensive techniques like the QSPR-based approach that has been described in this work. We are currently working on a cross-validation of the present predictions with the ones from the quantum chemical studies within the Clean Energy Project. As an example of the capabilities of quantum chemistry calculations in correlating with experimental measurements we compare a Scharber plot of some of the molecules from the training set with the results from calculations (BP86 density functional, SVP basis set) adjusted by a constant shift (Figure 17.11). Predictions based on semi-empirical descriptors and quantum chemistry calculations are not expected to be precise, but will no doubt help charting the territories of the vast chemical space. This situation is analogous to the situation in the pharmaceutical industry, where informatics methods aid in the ranking of potential candidates. Success stories involve the close collaboration between theory and experiment to hone in the right candidate materials.
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Figure 17.11 Scharber plot for 14 molecules form the training set used in this study. Experimental results are compared to results from DFT calculations (BP86/SVP) adjusted by a constant shift. Good candidates for OPVs are reproduced.
ACKNOWLEDGMENTS We are grateful for support from Stanfords Global Climate Energy Project and the Department of Energy’s Program of Theory and Computation. A.A.-G. also acknowledges generous support from the Corning Foundation.
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