Energetic Disorder in Higher Fullerene Adducts: A Quantum Chemical and Voltammetric Study

Predicting Energetic Disorder: A quantum chemical method is used to calculate the LUMO energies of all possible isomers of the bis and tris adducts of the fullerene, 6,6-phenyl-C61-butyric acid methyl ester (PCBM). The calculated energy level distributions agree well with the observed mean and spread of LUMO energies as determined using solution differential pulse voltammetry (DPV). We propose this method as a powerful tool for the design and functional optimisation of novel fullerenes, as well as other classes of pi-conjugated molecules with multiple isomers. The abundance of new pi-conjugated materials with electronic and structural properties that can be controlled, in principle, through chemical synthesis offers the potential to generate improved materials for a wide range of applications in organic optoelectronics. However, the lack of a thorough understanding of how chemical structure influences electronic properties still limits the design and selection of suitable materials. A case of particular recent interest is the use of multiple adducts of fullerene derivatives to boost the power conversion efficiency of polymer:fullerene blend organic solar cells.1-3 The addition of multiple side chains raises the energy of the lowest unoccupied molecular orbital (LUMO) of the acceptor, so raising the open-circuit voltage,4 but inhibits the close packing of the fullerenes. Moreover, the current synthetic routes invariably generate a mix of isomers which introduces disorder into both the molecular packing and the electronic energy levels, both of which could adversely affect electronic properties. Design of new materials thus requires a means of evaluating the positive effects of raised LUMO level in relation to the adverse effects, of increased energetic or structural disorder.5 However, no direct study of energetic disorder of higher adduct fullerenes has yet been reported, nor has any accurate computational method of predicting spread in LUMO energy levels been demonstrated. In this paper, we use a quantum chemical method that combines density functional theory (DFT) with time-dependent density functional theory (TDDFT) using a hybrid functional to calculate the LUMO energies of all possible isomers of the bis and tris adducts of the fullerene, 6,6-phenyl-C61-butyric acid methyl ester (PCBM). The calculated energy level distributions agree well with the observed mean and spread of LUMO energies as determined using solution differential pulse voltammetry (DPV). We propose this method as a powerful tool for the design and functional optimisation of novel fullerenes, as well as other classes of pi-conjugated molecules with multiple isomers. Computational Method: Different fullerene adducts were generated as SMILES6 strings, which uniquely define a molecular chemistry as a simple linear code. Smi23D7 was used to automatically generate coarse 3D nuclear coordinates from the SMILES strings. These nuclear coordinates were then used as the input to successive rounds of geometry optimisation with the empirical Universal Force Field (UFF), Semi-Empirical Austin Model 1 (AM1), and hybrid density functional theory (DFT) (using the Becke, three-parameter, Lee-Yang-Parr (B3LYP) hybrid functional and 6–31 g* split valence Pople basis set) using Gaussian 03. The HOMO level of the adduct was taken as the energy of the highest occupied Kohn-Sham orbital with tight convergence of the self consistent field at the DFT level of theory. The LUMO was derived by adding the HOMO energy to the energy of the first singlet excitation calculated using time-dependent density functional theory (TD-DFT). Prior work8 indicated that this method led to increased accuracy in the LUMO energy compared to direct estimation of the LUMO from the first virtual (unoccupied) Kohn-Sham orbital. We find that the disagreement between these two measures is particularly pronounced for fullerene based acceptors (the discrepancy is greater than 700 meV for all studied systems, and with poor correlation). This suggests that prior calculations of fullerene acceptor strength using semi-empirical structures and estimation of the LUMO from the first unoccupied Kohn-Sham orbital9 may be inaccurate. We follow the Fullerene carbon site numbering and isomerism nomenclature of Hirsch.10-12 We use the Hirsch numbering scheme and connectivity graph to directly generate a SMILES string Supplementary information. Addition of the adducts is achieved by explicit links to the sites identified by Hirsch for the various 6,6 attachment sites. For bisPCBM we investigate all eight unique isomers including the three cis isomers. In the case of trisPCBM we neglect cis additions in order to restrict the number of isomers studied to ten.12 We believe this to be representative of experimental samples of trisPCBM due to the steric hindrance of phenyl butyric acid methyl ester. This method allows for the automatic generation of various fullerene adducts by simple concatenation of the moieties and is well suited to theoretical combinatorial chemistry sifts through large numbers of potential new structures. The method can be extended to other fullerenes (such as C70 or C84) by the derivation of SMILES strings for the fullerene. Computational Results: By the method described above we calculate that monoPCBM has a HOMO of −5.634 eV and a LUMO of −3.749 eV. For bisPCBM we get a range of LUMO energies from −3.71 eV to −3.54 eV. For the tris adduct of PCBM (trisPCBM) we get a range of LUMO energies from −3.59 eV to −3.24 eV Table 1. As far as we are aware there have been no direct studies of the relative populations of bisPCBM isomers produced experimentally. However, the relative abundance of the ethyl-ester bis adduct C62(COOEt)4 have been studied with high performance liquid chromatography.11 The resulting distribution of isomers is likely to be relevant for bisPCBM because the symmetric ethyl ester moiety presents a similar bulkiness to PBM. The T1 isomer, where the adducts are on opposite sides of the fullerene cage, has a low yield due to the strained teardrop shape adopted by the fullerene cage after the first addition making reaction with the T1 site energetically unfavorable;10 the cis adducts, where both adducts are present on the same hemisphere of the fullerene cage, are low in yield due to steric hindrance. This results in the regio isomeric mix being heavily dominated by the E, T2, T3 and T4 isomers. The relative abundance wi of isomer i from Ref11 is listed in Table 1. We have also considered a uniform distribution of isomers. Here we assume the relative abundance of bisPCBM will follow approximately the same distribution as that of the ethyl-ester bis adduct and thus calculate the weighted mean and the weighted sample variance for the calculated LUMOs of bisPCBM. This yields a mean eV (135 meV above the monoPCBM LUMO of −3.749 eV) and standard deviation meV. The distribution of LUMOs along with their abundance and a normal distribution with the sample weighted mean and calculated sample variance are presented in Figure 1. The mean and variance resulting from a uniform distribution of isomers are also presented. These suggest that the effect of the distribution of isomers is relatively minor. a) Relative abundance (open circles) of bis adducts vs. calculated TD-DFT LUMO; superimposed Gaussian of weighted mean () and variance () from sampled values (full line); superimposed Gaussian of flat mean () and variance () from sampled values (dashed line). b) Calculated TD-DFT LUMO values (open circles) for the ten trisPCBM adducts studied; superimposed Gaussian of mean () and variance () from sampled values (full line); superimposed convolution of the ten LUMO energies with Gaussian of meV to simulated experimental broadening in voltammetry (dashed line). For the ten isomers of trisPCBM we have no estimate of the distribution of isomers produced. The mean LUMO is eV, with standard deviation meV. The distribution of LUMO energies show the presence of two high-LUMO outliers, if we prune these from our data set the mean LUMO becomes −3.495 eV (a shift of 50 meV) with a much reduced standard distribution of meV. These high-LUMO outliers, tris-E,E,E and tris-T3,T3,T3, are the only species with C3 and D3 symmetry respectively.12 For comparison with experiment we generate a distribution by convolving our calculated LUMO values with a Gaussian representative of experimental broadening in solution voltammetry (σ = 56 meV), which indicates that these outliers Figure 1 could be resolved as separate peaks. In order to investigate the effect of a polar solvent compared to vacuum calculations, a brief study was made using the polarizable continuum model (PCM)13 with the acetonitrile parameters present in Gaussian 03. For monoPCBM, this resulted in a small increase in the HOMO level of 50 meV, and essentially no variation in the HOMO-LUMO gap as calculated by TDDFT. This distribution in the LUMO energies of the mix of isomers should be present experimentally as an increase in the energetic range of LUMO measured. The calculated magnitude of is considerably larger than the thermal energy (where kB is Boltzmann’s constant and T is room temperature) and so should be accessible. Our calculated values for will be a lower limit for the increase in energetic disorder within films of the higher adducts compared to films of monoPCBM, since molecular packing will also be affected by increased morphological disorder and decreased crystallisation. Differential Pulse Voltammetry for monoPCBM (full line), bisPCBM (dashed line) and trisPCBM (dotted line). All solutions with Ferrocene internal standard (0.01 mM for trisPCBM, 0.1 mM for mono and bis PCBM). Data is plotted relative to the fitted peak of the ferrocene reduction. Background differential currents derived from the Gaussian fits were subtracted (monoPCBM, 119nA; bisPCBM, 38nA; trisPCBM, 85nA). By this method of deconvolution the implicit distribution of LUMO levels in bisPCBM is meV and in trisPCBM is meV. The quality of the Gaussian fit for trisPCBM is relatively poor. There is significant skew present in the first reduction and the differential current does not return to the background level between the first two reduction potentials. These effects could be due to a mix of discrete energy levels being present in the sample, indicating either impurities with a similar reduction potential or variation of the reduction potential between the isomers of trisPCBM. The calculated LUMO energies agree well with the estimated figures from Cyclic Voltammetry of − 3.75 eV for monoPCBM and − 3.65 eV for the blend of bisPCBM isomers.1 Factors expected to influence the comparison include inaccuracies fundamentally present in DFT; the fact that DFT calculations are gas phase; and the cyclic voltammetry being performed in a polar solvent. There is some evidence that DPV on trisPCBM indicates high-lying LUMO isomers (by the non-return to background current between the two reduction first reduction potentials) as suggested by calculation (tris-E,E,E and tris-T3,T3,T3 isomers). Some of the disagreement in mean LUMO energy and variance can be attributed to the lack of information about the relative yield of the higher adduct isomers, and our neglect of all cis-isomers of trisPCBM in the computational study. Energetic disorder in the acceptor component of a bulk heterojunction has a number of effects on device operation. Disorder will lead to a lower electron mobility,5 a variation in the yield for charge separation16 and a variation in the efficiency of charge injection and extraction.17 In an operating solar cell with higher PCBM adducts one would expect that as the electron quasi Fermi level increased above the LUMO of the lower lying isomers, fewer pathways would be available to inject into the electrode and the contribution to current would decrease, resulting in a device with higher Voc compared to the monoPCBM standard but with a lower fill factor. Lower fill factors are indeed observed in solar cells made with bis or tris adducts of PCBM.5 We demonstrate that hybrid density functional theory provides an accurate description of the HOMO energy in fullerene acceptors. Calculating the first singlet excitation energy by time-dependent density functional theory gives the electronic band gap. Combining these two methods gives a good estimate for the HOMO and LUMO levels of a candidate fullerene acceptor in a highly automated manner. Comparison to experimental values of the LUMO energy and its variance with cyclic voltammetry in solution is good, and offers a method to validate the HOMO and LUMO calculations after an initial small volume synthesis of a new acceptor has been carried out. Differential pulse voltammetry on the bis and tris PCBM confirms the presence of additional energetic disorder which we ascribe to the different energy levels of the various individual isomers present in each case. So far the separate isomers of bis and tris PCBM have not been isolated. The quantum chemical calculations presented here thus offer insight into the individual energy levels of these isomers, which are not experimentally accessible. The distribution of energy levels in bisPCBM is predicted to be larger by TD-DFT than is experimentally observed. A likely source of error is the assumption made about the relative abundance of the bisPCBM isomers. Calculations on bis and tris PCBM acceptors reveal a large variation in energy levels as a function of the specific isomer, which agrees quantitatively with the increased energetic disorder present in both cyclic voltammetry of the adducts and the current-voltage characteristics of actual solar cells.5 Energetic disorder decreases charge carrier mobility through trapping and directly hinders solar cell performance. Isolating individual isomers post-synthesis, developing synthetic routes which preference particular isomers and choosing adduct moieties which express little energetic disorder in isomerism are all methods by which open-circuit voltage could be enhanced without reducing fill-factor due to increased energetic disorder. Until now, optimisation of the fullerene acceptor design has been neglected when compared to the vast array of polymer donors, but recent developments18-20 indicate the possibility of optimising the power conversion efficiency of organic solar cells via changing the chemistry of the acceptor fullerene. We suggest that designing higher adduct fullerenes with shorter sidechains (to less disrupt packing), or the synthesis of hetero adducts with distinct roles for the sidegroups of increasing solubility (requiring a large side group) and manipulating energy levels (which can be done with an extremely compact sidegroup), will lead to fullerene acceptors with superior performance for particular functions without the need for expensive isolation of isomers. The methods presented here can be extended to a wide range of pi-conjugated materials, especially where alternative configurations are produced in synthesis, to evaluate the likely influence of isomerism on electronic energy levels and so guide the design and choice of new functional organic semiconductors. Jarvist Moore Frost gratefully acknowledges funding from EPSRC and BP Solar. Jenny Nelson acknowledges support of the Royal Society through a Royal Society Industrial Fellowship. All calculations were carried out at the Imperial College High Performance Computing facility.21