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Copolymers with similar comonomers: tuning frontier orbital energies for application in organic solar cells.

INTRODUCTION

Today, there is a wide spectrum of important applications for organic conducting polymers (OCPs) in organic electronics [1-5]. Therefore, a control mechanism for the energies of the highest occupied and lowest unoccupied molecular orbitals ([E.sub.HOMO] and [E.sub.LUMO]). the bandgap [E.sub.LUMO]-[E.sub.HOMO] ([DELTA][E.sub.HL]) and optical properties is desirable in order to optimize the various types of devices [6, 7]. These properties are crucial to the development of the promising technology of organic solar cells (OSC) [8, 9].

Currently, the scientific community has focused on two different ways of improving the efficiency of solar cells by controlling the electronic properties of OCPs [8-10]. The first adopted strategy has been to adjust the frontier electronic energy levels of the donor material to the levels of a given acceptor material. Normally, this is achieved through the design of OCPs with a lower [E.sub.HOMO] in order to increase the open-circuit voltage in the device ([V.sub.OC]) [8-13]. The use of chemical substitutions is an effective way of implementing this change in the energies of the frontier orbitals, but with no major changes in the bandgap, as recently shown for poly(3-hexylthiophene) (P3HT) derivatives [14, 15]. The second strategy is based on the design of new OCPs with a low bandgap in order to collect more photons of the solar spectrum and to increase the electric current in the device [8-10, 16, 17]. The donor-acceptor (DA) concept, which is the most frequently employed approach, is the synthesis of copolymers in which there is a mix of electron donor monomers with others that are electron acceptors [7, 10]. Usually, the monomers have a very different structure and the resulting OCPs demonstrate a lower bandgap, but also a significant worsening in the other properties [18] as a decrease in the open-circuit voltage and the enhancement of exciton binding energy [8, 9, 18]. However, predicting the new values of the energies of the frontier orbitals is not possible with these two approaches. It is also not possible to predict the new energies of the frontier orbitals of the derivative compounds for chemical substitutions, although it is possible to observe trends. Using the DA copolymers approach, it is only known that EHomois above the highest and [E.sub.LUMO] is almost the same the lowest respective energies of the homopolymers [19].

After our recent work with P3HT derivatives, in which we investigated the properties of homopolymers obtained from chemical substitutions, we began to investigate the properties of copolymers comprising the monomers of those homopolymers. The result was a copolymer with very similar comonomers. The only difference was the substituent at position 4 of the thiophenic ring. It is already known that the proportion and form of distribution of the comonomers influences the electronic properties [20-22]. After a considerable number of studies, we observed that it is possible to predict the values of [E.sub.HOMO] and [E.sub.LUMO] through a simple linear relationship once the values for the energies for the homopolymers are known.

Moreover, the recent experimental work by Yang et al. [23], which describes the synthesis and characterization of copolymers based on P3HT and poly (3-hexyloxythiophene) (P3HOT) monomer units, indicates that this ability to make a prediction is not restricted to copolymers derived from the same base polymer, and can be extended to at least copolymers that have similar comonomers. The copolymers obtained by Yang et al. have varying proportions of each comonomer. We noticed from the results reported in this work (in the same way in which it was observed in our studies on copolymers derived from comonomers of P3HT derivatives) that the electronic properties of the obtained copolymers apparently correlate with the amount of each type of comonomer. For example, the more P3HT monomers the copolymer presents, the closer its electronic properties are to those of P3HT.

The common finding to our study and to that by Yang et al. is that the [E.sub.HOMO] and [E.sub.LUMO] energies of the resulting copolymers always fall within the range defined by the respective levels of the parent compounds. This is different to the effect that is typically observed, suggesting that copolymers based on similar comonomers behave differently.

We report on a methodology according to which the electronic properties of copolymers with similar comonomers can be predicted. Once the energies of the frontier molecular orbitals of two types of homopolymers with a similar structural basis (in our case, polythiophene derivatives) are known, we show that it is possible to anticipate the values of the same energy levels of the copolymer with any number of each comonomer. Although this method does not provide materials with smaller bandgaps than those of the homopolymers, electronic levels adjustments can be performed more accurately, which is important when optimizing the performance of the organic solar cells.

MATERIALS AND METHODS

It is interesting to choose two homopolymers with similar monomeric units and with reasonably different energies with respect to the frontier electronic levels. In this way, one of the homopolymers provides the electron donor comonomers and the other the electron acceptor comonomers.

We chose to study copolymers built from P3HT and P3HOT homopolymers, similar to the study by Yang et al. [23]. To enhance the number of cases to test, we employed the homopolymers proposed and studied by us previously [14, 15]. These are derivatives of P3HT, with the following chemical substitutions for the hydrogen atom at position 4 of its monomeric units: hidroxyl (P3HT-OH), cyano (P3HT-CN), fluorine (P3HT-F) and trifluoromethyl (P3HT-[CF.sub.3]). We present the studied systems in Fig. 1.

Regarding the monomeric unit proportions of the homopolymer in the copolymer, we decided to study three different proportions, and to build copolymers in a periodic way (Fig. 2). So, assuming that there are two homopolymers, A and B, we built copolymers with the following proportions: 75% A + 25% B (3:1), 50% A + 50% B (1:1) and 25% A + 75% B (1:3).

We adopted the oligomers approach to calculate the properties of the homopolymers and copolymers [24-26]. We built oligomers of the homopolymers ranging from 2 to 10 monomeric units. We employed oligomers ranging from 1 to 5 monomeric units for the copolymers, as the monomeric unit can contain up to four comonomers. We decided to use an optimized geometric structure in vacuo via the semi-empirical method Parametric Method 6 (PM6) [27], with the MOPAC20/2 package [28], and to obtain the electronic structure data from Density Functional Theory (DFT) calculations [29]. Such an approach has been applied with satisfactory results in conjugated polymer studies [14, 15, 26, 30, 31]. This methodology makes our study possible as exclusive use of ab initio methods would have result in a high computational cost because of the size of the systems and the number of conformers analyzed.

Today, there are numerous available functionals and the use of a long-range corrected (LC) exchange and correlation functional would be advised for obtaining the electronic structure of the systems present in our article, since it could better describe the interactions between the alkyl side chains and the n electron system in the main chain [32, 33]. To evaluate the influence of these interactions on the energy of the frontier electronic levels, and consequently the need for the use of a LC functional, we should know what is the intensity of the distortions imposed on the main chain by the alkyl side chains in the solid state. This is important since it is known that the energies of the frontier electronic levels are determined by the conformation of the main chain and dependent on the degree of planarity.

We find in the literature that is quite possible that interactions between the side chains should not cause large variations from the planar configuration in the solid state. For polymeric thin films of polythiophenes and derivatives (including P3HT, without adopting simplifications to the ramifications) there are studies in the literature on the molecular dynamics and ab initio theory levels suggesting that polymeric structures close to planar configurations are the most likely to occur [15, 24, 34-40]. Apparently, in the solid state the side chains are responsible only for the accommodation of the chains, through interdigitation [36, 38, 40]. Furthermore, in copolymers the planarization trend is increased by the intramolecular charge exchange effect between donor and acceptor moieties [19, 41]. Studies which we have made comparing theoretical results and optical data specifically for P3HT in the solid state indicate that the conjugation length is similar to a planar chain, although the chains are not completely planar [30]. Calculations employing periodic boundary conditions shows that (i) polythiophene and derivatives with alkyl side chains tend to be planar and inter-rings dihedral angles up to 36[degrees] in the solid state are plausible and (ii) dihedral angles up to 16[degrees] do not significantly alter the energy of the frontier electronic levels when compared to the fully planar systems [42]. Our other work for P3HT and derivatives [15] also supports the idea of adopting planar chains to calculate the energies of the frontier electronic levels; we built a "sandwich" with three parallel polymer chains, all with initially coplanar conformation and approximately 4 [Angstrom] from each other, as observed for P3HT in the solid state [40, 43, 44]. All geometrical parameters of the middle chain were optimized, while for the external chains we only allowed optimization of alkyl side chains, keeping the main chain restricted to the plane. In this way, we performed the geometry optimizations for the "sandwich" of P3HT and several derivatives and found that the planes of the thiophene rings rotate up to 14[degrees] out of the initial common plane. Thus, these results lead us to believe that the most probable configuration for the studied systems in solid state is close to the planar one.

As for the influence of a LC functional on the energies of the frontier orbital energies, McCormick et al. [45] carried out a study with a group of 22 polymers and copolymers in order to determine which functional, B3LYP [46-48] or CAM-B3LYP [49], would give the best results in comparison with experimental data. Note that the CAM-B3LYP is the functional most frequently employed among those that incorporate long-range interactions [33, 35, 45, 50, 51]. It was concluded that B3LYP predicts better the energies of the frontier electronic levels. Similarly, Wikes et al. [35] examined the performance of some functionals in predicting optical properties of conducting polymers; the authors demonstrated that the functionals with LC have shown to be system dependent, with good predictions for some cases but large deviations for others. Previously, without including functionals with LC, Yang, Olishevski, and Kertesz [31] studied the predictability of electronic properties of planar conjugated polymers employing Hartree-Fock (ab initio and semiempirical) and DFT methods. According to the authors, the electronic structure data calculated by B3LYP showed the best results compared with experimental data. Thus, the use of a LC functional, which could represent more adequately the influence of alkyl side chains seems to be not essential.

This set of results lead us to adopt planar configurations for all systems studied and B3LYP as the correlation and exchange functional. We also adopted a fully planar configuration for P3F10T as theoretical and experimental studies indicate that this conformation is the most stable [23, 52]. The hexyl side chains were replaced with the methyl group for all structures, an approach that has been shown to be feasible as the electronic and optical properties basically remain unchanged [44, 45, 53-56]. The DFT calculations were carried out with the basis set functions 6-31G(1d) [57] and GAUSSIAN09 program [58].

Besides analyzing the data from the electronic structure of the oligomers, we also evaluated the optical properties, by calculating the vertical transition energy from the ground state to the first dipole-allowed excited state ([E.sub.vert]). The [E.sub.vert] was calculated by using the time-dependent DFT [59] with the same functional, basis set and software described previously. We carried out the calculation for 10 transitions (roots) for each oligomer, considering only transitions between the singlet states.

As we had adopted the oligomer approach, the electronic and optical properties of the polymers were estimated through an extrapolation method from the results obtained for the oligomers [60]. There are reports of several methods of extrapolation of the electronic properties of organic polymers in the literature. The fit proposed by W. Kuhn is one of the most popular and well accepted [34, 35, 60]. However, according to Gierschner et al. [34], the Kuhn fit can present some deficiencies in substituted polymers. Therefore, the authors proposed the insertion of an exponential term in the original Kuhn fit so that it could provides a better adjustment and satisfactory results. As the studied structures have side chains, we employed the modified Kuhn fit (Eq. 1) for all electronic and optical properties extrapolations. In Eq. 1, E represents the energy of the orbital (or optical transition), N the number of double bonds of the shortest path in the main chain, and the other constants are adjustable parameters.

E(N) = [E.sub.0] [square root of (1 - Acos ([pi]/N + 1))) - [Be.sup.-CN] (1)

RESULTS AND DISCUSSION

Copolymers Based on P3HT and Its Derivatives

Table 1 indicates the [E.sub.HOMO], [E.sub.LUMO], [DELTA][E.sub.HL], and [E.sub.vert] values obtained for P3HT and its derivatives employed for studying similar comonomer copolymers. As we can see, there are homopolymers with reasonably different values for [E.sub.HOMO] and [E.sub.LUMO], which is important in order to have well defined donor and acceptor moieties to build the copolymers. Among P3HT and its derivatives, we know the experimental electronic structure data for P3HT ([E.sub.HOMO] = -4.76 eV, [E.sub.LUMO] =-2.46 eV, [DELTA][E.sub.Hl] = 2.34 eV and [E.sub.vert] = 1.95 eV [61]) and P3HT-CN ([E.sub.HOMO] = -6.1 eV and [E.sub.LUMO] = -3.6 eV [41]); comparing with our theoretical results, we found the following deviations for P3HT: 5%, 15%, -4%, and -8% for [E.sub.HOMO], [E.sub.LUMO], [DELTA] [E.sub.HL], and [E.sub.vert], respectively, and about 8% for [E.sub.HOMO] and [E.sub.LUMO] of P3HT-CN. It is known from the literature that modeling studies on polymers which employ the DFT method with B3LYP functional showed the best results. Using this methodology, the values for [E.sub.HOMO], [DELTA][E.sub.HL], and [E.sub.vert] usually have deviations of approximately 10%, when compared to the experimental ones [31, 45]. However, deviations up to 1 eV have been observed for [E.sub.LUMO] [45]. Therefore, the deviations found for P3HT are in agreement with those estimated for the tools of calculations adopted in this work.

The values for [E.sub.HOMO] and [E.sub.LUMO] present total variations of 2.0 and 1.5 eV while [DELTA][E.sub.HL] and [E.sub.vert] have much smaller variations, of 0.6 and 0.4 eV. Except for the P3HT-OH case, the values for [DELTA][E.sub.HL] and [E.sub.vert] can be considered practically constant, whereas variations for [E.sub.HOMO] and [E.sub.LUMO] still remain at a high level around 1.2 eV.

Based on the results of Table 1, to have well defined donor and acceptor comonomers, we chose to study copolymers based on the combinations P3HT-OH plus P3HT-CN, P3HT-F plus P3HT-CN, P3HT-[CF.sub.3] plus P3HT-CN, and P3HT plus P3HTCN. The P3HT-CN monomer is always the acceptor in the copolymers as its [E.sub.HOMO] and [E.sub.LUMO] are the lowest of all the studied homopolymers, which provides a more noticeable result. Figure 3 shows the studied copolymers, as well as the nomenclature used to identify each one.

The results obtained for [E.sub.HOMO] and [E.sub.LUMO] of copolymers are shown in Fig. 4. It can be seen that these values, which always fall between the respective values of the the employed homopolymers, follow a linear relationship with respect to the proportions of comonomers present in the chain.

Figure 4 suggests that the values for [E.sub.HOMO] and [E.sub.LUMO] of copolymers can be obtained by a linear interpolation:

[E.sup.Copolymer.sub.HOMO(LUMO)] = x.[E.sup.HomopolymerA.sub.HOMO(LUMO)] + (1-x).[E.sup.HomopolymerB.sub.HOMO(LUMO)] (2)

in which x varies from 0 to 1 and is the fraction of the monomers of homopolymer A present in the copolymer. Such behavior, as discussed before, does not occur in conventional DA copolymers.

The same effect has already been reported in the literature, however in studies of bandgap energies and optical properties of copolymers of similar comonomers [22, 62, 63]. As currently adjusting frontier electronic orbital energies is vitally important to improve organic solar cell properties, and not only the value of bandgap, it is very interesting to note that these energies can also be predicted by a simple linear relationship. According to the previous works [22, 62, 63], the expected linear behavior is also observed for [DELTA][E.sub.HL] and [E.sub.vert] for the copolymers studied in this work, as can be observed in Fig. 5.

It is apparent from Figs. 4 and 5 that it is possible to have a significant variation of the energies of frontier electronic states, even in cases where the variation of the bandgap is negligible.

Another important difference compared to conventional DA copolymers is the value for ELumo> which generally is almost the same of the acceptor homopolymer employed to build the copolymer [19]. This occurs due to the LUMO orbital localization around acceptors comonomers in the copolymer, whereas the HOMO orbital remains extended throughout the whole chain [19, 35, 63]. As for the copolymers of similar comonomers studied in this work, both HOMO and LUMO orbitals are delocalized (see Fig. S1 of Supporting Information).

The frontier orbitals delocalization observed for the copolymers studied here can be understood by analyzing the interactions between orbitals of the monomers of each copolymer. According to works of Hung et al. [63-65], if the frontier orbitals energies of the homopolymer's monomers employed to build copolymer's monomers are >1 eV, a weak interaction between the orbitals will occur, which causes the localization of molecular orbitals; otherwise, the orbital will be delocalized along the whole copolymer chain. This is the case for the monomers derived from P3HT, for which these differences are <1 eV (see Fig. S2 of Supporting Information).

The linear behavior predicted by Eq. 2 ceases to exist if the aromaticity of similar comonomers have distinct character in the homopolymers ground state. Karsten et al. [66] studied copolymers of thiophene derivatives, employing comonomers with aromatic and quinoid character. The authors found that the frontier orbitals of the copolymers were delocalized throughout the copolymer chain, but the bond length alternation (BLA) behaves differently compared to that of the homopolymers, which causes a nonlinear relationship between the optical properties of the copolymers in relation to the constituents proportion. None of the cases studied by us in this work presents quinoidal character in the ground state; the BLA of the copolymer were similar to those of homopolymers, without abrupt changes between the comonomers and intermediate values to the parent homopolymers (see Fig. S3 of Supporting Information).

This set of results confirms that this approach allows for modification of the values of EHOMO and ELUMO in a planned way. This is very useful when optimizing the donor polymer for use in solar cells with a particular type of acceptor. For example, according to studies by Zhou et al. [10, 18], an ideal donor polymer for a heterojunction in relation to phenyl-C61-butyric acid methyl ester (PCBM), should have an [E.sub.HOMO] of around -5.4 eV and an [E.sub.LUMO] of ~ -3.9 eV ([DELTA][E.sub.HL] of 1.5 eV). This would ensure a reasonable Voc, as well as permitting a good dissociation and difficult recombination of excitons. Within our copolymers, we noted that COP4, COP7, COP8, and COP10 presented [E.sub.HOMO] values very similar to what would constitute the ideal for a combination with PCBM. These same copolymers are those for which the [E.sub.LUMO] is closer to the ideal in combination with PCBM, but with less satisfactory results than [E.sub.HOMO]. In principle, this kind of copolymer facilitates a better fit with PCBM as other properties effectively depend upon experimental conditions [67-71].

Copolymers Based on P3HT and P3HOT

In this section, our theoretical results and those experimentally obtained by Yang et al. [23] for copolymers based on P3HT and P3HOT are analyzed. We built copolymers with the P3HT and P3HOT homopolymers, that are shown in Fig. 6 together with the adopted nomenclature. Table 2 shows the theoretical results for P3HT and P3HOT, as well as those obtained for the copolymers.

As we can see, the deviations vary from -0.1 to 4.5%, demonstrating good agreement between the obtained and predicted values that were calculated using Eq. 2. Following the same trend observed for copolymers of P3HT and its derivatives, the obtained values for [E.sub.HOMO], [E.sub.LUMO], [DELTA][E.sub.HL], and [E.sub.vert] that were obtained for the P3HT and P3HOT copolymers were always intermediate to those of the parent homopolymers. P3HT and P3HOT homopolymers do not have quinoidal character on ground state and the frontier molecular orbitals of its copolymers are delocalized throughout the main chain (see Fig. S4 of Supporting Information).

The experimental data published for P3HT, P3HOT and the three copolymers in the study by Yang et al. [23] are reproduced in Table 3. The copolymers have 70, 50, and 30% of the 3-hexylthiophene comonomers (3HT). We present the prediction of the experimental values for [E.sub.HOMO], [E.sub.LUMO], and [E.sub.vert] according to Eq. 2. The predicted values can be compared to the experimental ones. The observed percentage deviation is also shown.

It can be noted in Table 3 that the differences between the predicted and the measured values were small. We observed from both the theoretical and experimental point of view that the prediction rule for the energies of the frontier electronic levels of copolymers with similar comonomers (Eq. 2) has been shown to be valid.

It should be taken into account that the copolymers studied by Yang et al. [23] were synthesized randomly. In our work, we studied copolymers that were built in an ordered way. So, we did some calculations comparing the COP 15 dodecamer (an ordered copolymer) with a set of 10 copolymers with the same composition, but with the comonomers arranged in a random order. When comparing the results of these copolymers, we realized that its individual electronic properties were slightly different, but when we compared the average results obtained for this set of 10 random copolymers with those attained for the COP 15 ordered dodecamer, we noted that these values were approximately equal.

CONCLUSIONS

This article presents a way of predicting the values of the energies of the frontier electronic levels of organic conducting copolymers, provided that they are built from similar comonomers. We studied a group of 15 copolymers with similar comonomers, based on six homopolymers of thiophene derivatives: P3HT, P3HOT, P3HT-OH, P3HT-CN, P3HT-F, and [P3HT-CF.sub.3]. It is verified that the frontier orbital energies of these copolymers can be predicted based on the same energies of the homopolymers and the proportion of each comonomer intended to be used, as expressed by Eq. 2.

Both our theoretical results and the available experimental data in the literature confirmed the validity of the proposed rule, since the predicted and obtained or observed values were in excellent agreement.

In our opinion, this is an important tool when designing new donor organic conducting polymers for active layers of solar cells as it opens up the possibility to plan the electronic levels, once the acceptor material has been chosen, even if a lowering of the bandgap is not achieved or wanted.

It is worth mentioning that our study was based on polymers of thiophene derivatives only. We believe that the rule remains valid for other types of conjugated organic polymers since the same results hold for our preliminary calculations for poly(p-phenylene vinylene) derivatives.

ACKNOWLEDGMENT

The authors thank Dr. Johannes Gierschner (IMDEA Nanoscience, Madrid) for important suggestions.

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Eliezer Fernando Oliveira, (1) Francisco Carlos Lavarda (1, 2)

(1) UNESP--Univ Estadual Paulista, POSMAT-Programa De Pds-Graduaqao Em Ciencia E Tecnologia De Materials, Bauru, SP 17033-360, Brazil

(2) Departamento de Fisica, Faculdade de Ciencias, UNESP-Univ Estadual Paulista, Bauru, SP 17033-360, Brazil

Correspondence to: F.C. Lavarda; e-mail: lavarda@fc.unesp.br Contract grant sponsor: Brazilian Agency FAPESP; contract grant numbers: proc. 2012/21983-0, 2014/20410-1; contract grant sponsor: Center for Scientific Computing (NCC/GridUNESP) of the Sao Paulo State University (UNESP).

Additional Supporting Information may be found in the online version of this article.

DOI 10.1002/pen.24275

TABLE 1. Extrapolated electronic properties of the homopolymers of
P3HT and its derivatives.

Polymer             [E.sub.HOMO] (eV)      [E.sub.LUMO] (eV)

P3HT                      -4.446                -2.109
P3HT-CN                   -5.592                -3.316
P3HT-OH                   -3.604                -1.802
P3HT-F                    -4.546                -2.283
P3HT-C[F.sub.3]           -5.213                -2.924

Polymer           [DELTA][E.sub.HL] (eV)   [E.sub.vert] (eV)

P3HT                      2.235                  1.878
P3HT-CN                   2.191                  1.812
P3HT-OH                   1.594                  1.475
P3HT-F                    2.156                  1.846
P3HT-C[F.sub.3]           2.201                  1.870

TABLE 2. Theoretical results obtained for the P3HT and P3HOT
homopolyniers and its copolymers.

Polymer     [E.sub.HOMO] (eV)      [E.sub.LUMO] (eV)

P3HT              -4.445                -2.109
P3HOT             -4.011                -2.156
COP 13        Pred.: -4.337          Pred.: -2.121
               Obt.: -4.324          Obt.: -2.193
               % dif.: -0.2           % dif.: 3.4
COP 14        Pred.: -4.228          Pred.: -2.133
               Obt.: -4.286          Obt.: -2.132
               % dif.: 1.4           % dif.: -0.02
COP 15        Pred.: -4.119          Pred.: -2.144
               Obt.: -4.098          Obt.: -2.228
                o. 1 o L/i            % dif.: 3.9

Polymer   [DELTA][E.sub.HL] (eV)   [E.sub.vert] (eV)

P3HT              2.235                  1.878
P3HOT             1.717                  1.505
COP 13         Pred.: 2.106          Pred.: 1.785
               Obt.: 2.112            Obt.: 1.796
               % dif.: 0.3            % dif.: 0.6
COP 14         Pred.: 1.976          Pred.: 1.692
               Obt.: 2.064            Obt.: 1.755
               % dif.: 4.5            % dif.: 3.8
COP 15         Pred.: 1.847          Pred.: 1.598
               Obt.: 1.833            Obt.: 1.622
               % dif.: -0.7           % dif.: 1.5

Pred.: Predicted values; Obt.: Obtained values; % dif.: percentage
difference between the predicted and the obtained values.

TABLE 3. Experimental results for the P3HT and P3HOT homopolymers
and its derived copolymers (Ref. 23).

Polymer                                       [E.sub.HOMO] (eV)

P3HT                                                -5.27
P3HOT                                               -4.56
[(3HT (a)).sub.70%] + [(3HOT (b)).sub.30%]      Pred.: -5.06
                                                 Obt: -5.08
                                                 % dif.: 0.4
[(3HT).sub.50%] + [(3HOT).sub.50%]              Pred.: -4.92
                                                 Obt.: -4.82
                                                % dif.: -2.1
[(3HT).sub.30%] + [(3HOT).sub.70%]              Pred.: -4.77
                                                 Obt.: -4.56
                                                % dif.: -4.4

Polymer                                       [E.sub.LUMO] (eV)

P3HT                                                -3.33
P3HOT                                               -2.98
[(3HT (a)).sub.70%] + [(3HOT (b)).sub.30%]      Pred.: -3.23
                                                 Obt.: -3.28
                                                 % dif.: 1.5
[(3HT).sub.50%] + [(3HOT).sub.50%]              Pred.: -3.15
                                                 Obt.: -3.12
                                                % dif.: -0.9
[(3HT).sub.30%] + [(3HOT).sub.70%]              Pred.: -3.09
                                                 Obt.: -3.09
                                                 % dif.: 0.0

Polymer                                       [E.sub.vert] (eV)

P3HT                                                1.94
P3HOT                                               1.58
[(3HT (a)).sub.70%] + [(3HOT (b)).sub.30%]       Pred.: 1.83
                                                 Obt.: 1.80
                                                % dif.: -1.6
[(3HT).sub.50%] + [(3HOT).sub.50%]               Pred.: 1.76
                                                 Obt.: 1.70
                                                % dif.: -3.4
[(3HT).sub.30%] + [(3HOT).sub.70%]               Pred.: 1.69
                                                 Obt.: 1.62
                                                % dif.: -4.1

Pred.: Predicted values by Eq. 2; Obt.: Obtained values; % dif.:
percentage difference between the predicted and the obtained values.
(a) 3HT: 3-hexylthiophene monomer; (b) 3HOT: 3-hexyloxythiophene
monomer.
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Date:Apr 1, 2016
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