Importance of Side-Chains on Molecular Characteristics of Interacting

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Article Cite This: ACS Omega 2019, 4, 10396−10404

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Importance of Side-Chains on Molecular Characteristics of Interacting Organic Molecules Kenji Mishima*,† and Koichi Yamashita Department of Chemical System Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan

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S Supporting Information *

ABSTRACT: In this work, we have calculated several physical quantities related to two interacting semiconductor organic molecules to reveal the significance and the role of the sidechains. The molecular systems of our target are the geometryoptimized dimer systems: that consisting of two [6,6]-phenyl-C61butyric acid methyl ester molecules and that consisting of two peryline diimide-related molecules. The physical quantities shown in the present work are their relative molecular geometries, optimized energies, barycentric distances, angles between the two molecular planes, dipole moments, and electronic couplings. We have found that these physical quantities show quite different tendencies among the systems, which results from the absence/ presence of the side-chains in these molecular species. It is emphasized that the presence of side-chains brings about the diversity of molecular characteristics in interacting molecules. This may point out the importance of side-chains in the various organic materials in general.

1. INTRODUCTION Recently, organic solar cells have been attracting much attention in the effort to achieve efficient and low-cost renewable energy supply. The prototypical organic solar cells consist of two semiconductor organic molecules: electrondonating (donor) and electron-accepting (acceptor) molecules. In the past few decades, almost all of the researches have focused on the donor molecule consisting of a p-typeconjugated polymer and the acceptor molecules consisting of an n-type fullerene derivative. However, quite recently, nonfullerene acceptors have emerged as a promising alternative to fullerene-based acceptor molecules.1 This is due to the diversity, easy functionalization, low fabrication cost of the formers. Recently, the solar cell efficiency greater than 13% has been achieved using nonfullerene acceptors,2,3 which exceeds that of fullerene-based solar cells. In particular, peryline diimide (PDI) has long been investigated in detail since before the advent of organic solar cells. PDI has several prominent features, which fullerene derivatives are devoid of. The most striking characteristic of PDIs is that there is a strong intermolecular π−π stacking interaction between their rigid aromatic cores so that they tend to self-assemble into various ordered forms.4−14 Other important merits are their low cost, high absorption coefficient, good photochemical stability, high electron mobility, high electron affinity, and chemical versatility.15 These advantageous features make a series of PDI molecules useful for several materials design. As far as the organic solar cells nowadays are concerned, to improve the solar cell performance of nonfullerene-based © 2019 American Chemical Society

architectures, much endeavor has been paid to making the best of the above-mentioned advantages as well as to functionalizing16−20 and to twisting the aromatic core plane of PDI molecules.21,22 In fact, we have witnessed the increase of the solar cell performance utilizing these procedures.21,22 However, quite recently, the importance of side-chains has gradually been recognized, and several works on the subject have been published.23−27 In ref 26, it was found that three perylene diimide−spirobifuluorene derivatives with different kinds of alkyl side-groups showed identical highest occupied molecular orbital (HOMO)/lowest unoccupied molecular orbital (LUMO) energy levels and very similar optical properties but different photovoltaic responses. Using the benefit of the effect of side-chain, side-chain engineering has also been proposed.28 In spite of the seemingly important role of side-chains, the quantum chemical calculations related to organic solar cells have so far neglected them in most of the cases, taking into account only the molecular central core. Much emphasis has been put on the comparison and improvement of core units of the molecules. For example, Yi et al. studied the donor− acceptor complexes in α-sexithienyl/C60 and α-sexithienyl/PDI model systems, in which each molecule is fixed at 3.5 Å apart neglecting the side-chains.29 Nevertheless, the arbitrariness of the values of the intermolecular distance and orientation and the absence of side-chains might invoke various artificial errors Received: January 2, 2019 Accepted: May 31, 2019 Published: June 17, 2019 10396

DOI: 10.1021/acsomega.9b00012 ACS Omega 2019, 4, 10396−10404

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in the calculations. Note that not only the intermolecular distance but also the intermolecular orientation are very important for estimating the photoinduced charge-transfer kinetics of donor−acceptor arrays.30 Instead, in this work, we have performed the full geometry optimization (including side-chains) from a variety of initial guess intermolecular configurations as a first step using the quantum chemical approach. Then, we have classified globally and locally stable bimolecular states. Finally, we have calculated important physical quantities such as barycentric distances, angles between the molecular planes, dipole moments, and electronic couplings of two interacting molecules have been evaluated.

configurations of two molecules by the relative angles (the Euler angles) with regard to the line between the barycenters of two molecules

2. THEORETICAL DETAILS To obtain the optimized molecular geometries and to evaluate barycentric distances, angles between the molecular planes, dipole moments, and electronic couplings of two interacting molecules, the Gaussian16 suite of programs31 was used to carry out all of the quantum chemistry calculations shown below. The semiempirical methods are extremely useful for medium to large molecules at the sacrifice of the accuracy that is fairly comparable to any other quantum chemistry methods. It was shown that PM632 predicts gas-phase heats of formation fairly accurately.33 In connection with the computational elucidation and numerical design of organic materials, the adequacy of semiempirical methods was investigated.34 In another report, the performance of semiempirical and density functional methods (B3LYP, PM6, and PM7) was compared for reproducing solar cell efficiencies such as open circuit voltages (Voc) of C60 fullerene derivatives, e.g., [6,6]-phenyl-C61-butyric acid methyl ester (PCBM).35 In the report, it was shown that although B3LYP showed the best performance in the principal component analysis (PCA), PM6 and PM7 were satisfactory in PCA. In particular, although PM6 is not recommended due to the overestimation of Voc, PM7 is suitable for preliminary estimations of Voc and electron binding energies of fullerene derivatives. Therefore, we adopt the PM7-D method to approximately evaluate all of the physical quantities related to two interacting semiconductor molecules in this work as well. The scheme of our optimization procedure is demonstrated in Figure 1. Our calculations start from only one initial arbitrary given relative configurations of two molecules. Various initial guess internal positions of the atoms in each molecule are calculated from the initial arbitrary given relative

where (x,y,z) is the initial Cartesian coordinate of the atom calculated from the preliminary optimization of one molecule by PM7-D, (x0,y0,z0) is the initial coordinate of the barycenter of the molecule, (xint,yint,zint) is the internal guess internal coordinate of the atom, and (ϕ,ψ,θ) is the Euler angle. In other words, various initial guess positions of the atoms are calculated by the seven parameters: the barycenter distance between the two molecules, r, and the two sets of Euler angles for each molecule, (ϕ1,ψ1,θ1), (ϕ2,ψ2,θ2) once the initial arbitrary given relative configurations of two molecules is chosen. In our present calculations, the parameters lie in the following regions

jij xint zyz jj y zz jj int zz = jj zz jj zz k z int { ij cos ψ cos ϕ cos ψ sin ϕ sin ψ sin θ yzzz jj zz jj zzi x − x0 y jj − sin ψ cos θ sin ϕ + sin cos cos ψ θ ϕ zzjj jj zzjj y − y zzzz jj zzjj jj z 0z zzjj jj − sin ψ cos ϕ sin sin cos sin − ψ ϕ ψ θ zz zzjj jj zz z jj − cos ψ cos θ sin ϕ z z − zzk + cos ψ cos θ cos ϕ 0{ jj zz jj zzz jj sin θ sin ϕ cos θ − sin θ cos ϕ { k

(1)

r = 3.0−16.5 Å, ϕ1 = 0.0−360.0°, ψ1 = 0.0−360.0°, θ1 = 0.0−180.0°, ϕ2 = 0.0−360.0°, ψ2 = 0.0−360.0°, θ2 = 0.0−180.0°

(2)

In eq 2, r, is evenly divided into three segments and the remaining angular parameters into five segments, the geometry optimizations amounting up to 3 × 53 × 53 = 46 875 for one bimolecular system.

3. RESULTS AND DISCUSSION In this study, we are interested in the bimolecular systems of PCBM, PDI, EP-PTC investigated in ref 36 and perylene3,4,9,10-tetracarboxylic acid diimide (hereafter, called PDI 1 as in ref 21). The reason why we have chosen these systems will become evident from the calculations shown below. In Figure 2, the optimized molecular structures of PCBM, PDI, EP-PTC, and PDI 1 are demonstrated. As is well known, PCBM contains the sphere composed of C60 as a core and an alkyl and a phenyl side-chains. Panel (a) actually shows that this is the case. On the other hand, panels (b)−(d) show that PDI-related molecules have a planar aromatic core in common. From the completely different forms of the core of PCBM- and PDI-related molecules, one can imagine that these two types of molecules will behave quite differently. Therefore, comparing the results of (a) and those of (b)−(d), the difference between the fullerene and nonfullerene will become clear. On the other hand, panels (b)−(d) differ only in terms of the side-chains. PDI (panel (b)) is devoid of alkyl chains, whereas PDI 1 (panel (d)) has a side-chain longer than EPPTC (panel (c)) does. Therefore, comparing panels PDI, EPPTC, and PDI 1, one can concentrate on the investigation of the effect of the side-chains. From Figure 2, another striking feature worthy of detailed investigation in our molecular systems is that the side-chains of

Figure 1. Geometry optimization of two nonfullerene acceptor molecules using the initial guesses of the barycentric distance, three relative angles for each molecule, and molecular structure of each molecule. 10397


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Figure 2. Geometry-optimized structures of (a) PCBM, (b) PDI, (c) EP-PTC, and (d) PDI 1.

Figure 3. Dependence of energy on the rotational angle of a side-chain for (a) EP-PTC and (b) PDI 1. The insets show the directional arrows of the rotations of the side-chains.

Figure 4. Dependence of (a) barycentric distance, (b) angle between the two molecular planes, (c) dipole moment, and (d) electronic coupling on the stabilization energy of the bimolecular PCBM system. In addition, representative bimolecular geometries at the corresponding energies are shown by numbers (i)−(v).

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configurations shown in (i)−(v), one can see that as the stabilization energy increases, the two molecules approach each other gradually and they begin to interact with each other via the van der Waals interactions through the side-chains. The strong intermolecular interaction via the side-chains is seen for the geometries, (i)−(iii). For the geometries (iv) and (v), there may be intermolecular interactions but through seemingly week long-range van der Waals interactions via the side-chain of one PCBM and C60 of the other PCBM, which leads to a slight stabilization energy, as shown in panels (a)− (d). On the other hand, from panel (b), in the strong stabilization energy region (−1.2 to −1.0 eV), there is a slight correlation between the angle between the two molecular planes and the stabilization energy (correlation function ∼ −0.304), but in the weak stabilization energy region (−1.0−0 eV), almost no correlation (correlation function ∼ −0.00226). This is because the side-chains interact with each other strongly in the strong stabilization energy region, which leads to restricted relative molecular configurations with restricted relative orientation. On the other hand, in the weak stabilization energy region, the intermolecular interaction is so weak that the molecules orient themselves rather freely. Therefore, there are a variety of relative intermolecular orientations in the weak stabilization energy region. From panels (c) and (d), we can see that the correlations smaller than those shown in panels (a) and (b) in Figure 4 exist between the dipole moment and the stabilization energy and between the electronic coupling and the stabilization energy (see Table 1). The dipole moment is a vectorial physical quantity so that the complicated pattern exhibited in panel (c) reflects the free orientational dependence of the relative position exhibited in panel (b). Note that not only the barycentric distance but also the relative orientation play a pivotal role in determining the electronic coupling, because the overlap of wavefunctions of the two molecule is important in determining the strength of the electronic coupling.39 Therefore, a variety of relative orientations shown in panel (b) leads to various strengths of electronic couplings shown in panel (d). One of the interesting features peculiar to bimolecular PCBM system is that there is hardly bimolecular combinations between the stabilization energies of −0.4 and −0.3 eV. Referring to the molecular configurations of (iii) and (iv), this restriction seems to stem from the structural hindrance caused by the presence of the side-chain of one PCBM sandwiched between the two C60 spheres. Next, in Figure 5, we show the dependence of (a) barycentric distance, (b) angle between the two molecular planes, (c) dipole moment, and (d) electronic coupling on stabilization of bimolecular PDI system. One of the striking features of this system is that there are much less bimolecular configurations compared with bimolecular PCBM system shown in Figure 4. This is due to the well-known fact that there is a very strong intermolecular π−π stacking interaction between their rigid aromatic cores.4−14 This can also be seen from the relative molecular configurations (i) and (ii) in Figure 5. In particular, the molecular configuration (i) corresponds to the most stable configuration, which is reflected in the two neatly matched parallel molecular planes. The molecular configuration (ii) has a little bit unmatched staggered molecular planes so that it has a slightly smaller stabilization energy.

the PDI-related molecules are directed almost perpendicular to the plane of the stable aromatic core (panels (c) and (d)). This is a commonly observed feature in an electron-rich core with perpendicular side-chains.37 Although this feature has not been investigated in detail so far, it will be important to get insight on how this phenomenon takes place. Figure 3 shows the dependence of energy on the rotational angle of a side-chain. One can see that in both panels (a) and (b), as the angle increases up to around 100 or 120°, the energy increases. As the angle further increases up to 180°, the energy instead decreases, and the energy returns to the original stable value at the angle 180°. In fact, this clearly shows that the configurations with the side-chains perpendicular to the molecular plane are the most stable in both EP-PTC and PDI 1. This provides one of the examples showing that it is energetically important at which angle the side-chain is attached to the main part of the molecule. Another important characteristic to note is that the rotational energy barrier is higher in the case of the bulkier alkyl chain (panel (b)) than in the case of the less bulky sidechain (panel (a)). Because the differences of the energy barriers in panels (a) and (b) (around 1 eV) are comparable to the stabilization energies in the bimolecular systems shown below (up around 1−2 eV), the difference of rotational energy barriers in panels (a) and (b) caused by the different kinds of side-chains cannot be neglected. In particular, Figure 3 shows that bulky side-chains may influence the whole molecular characteristics to a large extent. This provides one of the examples showing the importance of the difference of the sidechain in a single molecular system although the side-chain is often overlooked in numerical calculations.29 In general, rotational barriers are originated from either steric repulsion or hyperconjugation.38 Because there is apparently no steric bulkiness between two alkyl groups in EP-PTC and PDI 1, the rotational barriers in Figure 3 seem to stem from the hyperconjugation. For the subsequent calculations of physical quantities of our interest, 4688, 35, and 1537 converged geometries for PCBM, PDI, and PDI 1 are chosen from the geometry optimizations mentioned at the end of Section 2. These values already indicate that PDI may contain a small number of bimolecular configurations, whereas PCBM and PDI 1, a lot of configurations, as shown in detail below. In Figure 4, we show the dependence of (a) barycentric distance, (b) angle between the two molecular planes, (c) dipole moment, and (d) electronic coupling on the stabilization energy of bimolecular PCBM system. From panel (a), it is seen that as the stabilization energy (hereafter, note that the stabilization energy is meant to the absolute value of the energy value on the abscissa) increases, the barycentric distance decreases, which shows a large value of the correlation function (0.788; see Table 1). Referring to the molecular Table 1. Correlation Functions for Figures 4−6a panel

(a)

(b)

(c)

(d)

Figure 4 Figure 5 Figure 6

0.788 0.537 0.821

−0.0508 0.440 0.551

0.146 0.000396 0.363

−0.300 0.133 −0.613

If the value of the correlation function approaches either −1 or 1, there is a strong correlation between the two variables. On the other hand, if it approaches 0, there is no correlation. a

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Figure 5. Dependence of (a) barycentric distance, (b) angle between the two molecular planes, (c) dipole moment, and (d) electronic coupling on the stabilization energy of the bimolecular PDI system. In addition, representative bimolecular geometries at the corresponding energies are shown by numbers (i)−(v).

Figure 6. Dependence of (a) barycentric distance, (b) angle between the two molecular planes, (c) dipole moment, and (d) electronic coupling on the stabilization energy of the bimolecular PDI 1 system. In addition, representative bimolecular geometries at the corresponding energies are shown by numbers (i)−(v).

molecules to be almost parallel (angle ∼ 0°) until the intermolecular interaction can be negligible (until stabilization energy ∼0.5 eV). As the stabilization energy decreases, the intermolecular π−π stacking interaction becomes weaker so that the two molecules can take on a variety of relative orientations at around the stabilization energy ∼−0.4 eV. From panels (c) and (d), similar to panels (c) and (d) of Figure 4, we can see that the correlations much smaller than those shown in panels (a) and (b) in Figure 5 exist between the dipole moment and the stabilization energy and between the electronic coupling and the stabilization energy (see Table 1). As mentioned before, the dipole moment is a vectorial physical quantity. In addition, as exemplified by the molecular configuration (ii), which has unmatched staggered molecular planes, there may be a slight change of the direction and/or the

Panel (a) shows that as the stabilization energy increases, the barycentric distance tends to decrease. Unlike the case seen in panel (a) of Figure 4, instead of the influence of the side-chain (in PDI, there is no side-chain), this is because the strong intermolecular π−π stacking interaction between their rigid aromatic cores becomes weaker as the barycentric distance grows. On the other hand, from panel (b), unlike the panel (b) of Figure 4, there is a correlation between the angle between the two molecular planes and the stabilization energy over a wide range of stabilization energy (compare the value of the correlation function of −0.508 for panel (b) of Figure 4 and that of 0.440 for panel (b) of Figure 5, as shown in Table 1). This is because the very strong intermolecular π−π stacking interaction between their rigid aromatic cores restricts the two 10400


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of Figure 6 and that of −0.616 of panel (d) of Figure 6 as shown in Table 1). As mentioned before, the dipole moment and the electronic coupling are affected not only by the intermolecular distance but also by the intermolecular orientation. The bulky side-chains in Figure 6 are large and influential enough to cause a variety of bimolecular distances and orientations to take place. But in some cases, some geometrical hindrance, e.g., the absence of bimolecular PCBM configurations between the stabilization energies of −0.4 to −0.3 eV, as mentioned before, may also occur for PDI 1. For example, this seems to be reflected in the absence of the geometries corresponding to the dipole moment of 0.0−1.0 Debye in the stabilization energy interval of −1.5 to −0.5 eV in the panel (c) of Figure 6. All in all, each panel of Figure 6 is an extension of the counterpart of Figure 5. This points out that the molecular characteristics of the core play an important role in determining multimolecular behaviors. However, the prominent feature that cannot be ignored as much as this is that the presence of the side-chain brings about the diversity of the multimolecular characteristics that are absent in the absence of the side-chains. This is reflected in the much more dots present in Figure 6 than those in Figure 5. As a final remark, some more general conclusions from the comparison of Figures 4−6 will be given:

strength of dipole moments among the various bimolecular configurations. On the other hand, as remarked in connection with panel (4) of Figure 4, the overlap of wavefunctions of two molecules is determined by relative orientations of the wavefunctions of molecules. Therefore, a slightly staggered configuration leads to an electronic coupling quite different from that of the neatly matched parallel bimolecular systems. From the above reasons, we can hardly see correlations between the dipole moment and the electronic coupling and the stabilization energy. Finally, in Figure 6, we show the dependence of (a) barycentric distance, (b) angle between the two molecular planes, (c) dipole moment, and (d) electronic coupling on the stabilization energy of bimolecular PDI 1 system. From panel (a), it is clearly seen that as the stabilization energy increases, the barycentric distance decreases over a wide stabilization energy range of −2.2 to −0.5 eV, which shows a large value of the correlation function (0.821; see Table 1). This is also due to the well-known strong intermolecular π−π stacking interaction between the rigid aromatic cores of PDI derivatives. This can also be seen from the relative molecular configurations (i) and (ii) in Figure 6. In particular, the molecular configuration (i) corresponds to the most stable configuration, which is reflected in the two neatly matched parallel molecular planes. The molecular configuration (ii) has a little bit unmatched staggered molecular planes so that it has a slightly smaller stabilization energy. These tendencies certainly resemble those of panel (a) of Figure 5. But it should be noticed that even if the side-chains of PDI 1 seem to be very bulky as pointed out in the panel (b) of Figure 3, the bulkiness is not so large as to distort the most stable bimolecular geometry of (i) in Figure 6 far from that of Figure 5. In fact, in most of the cases, the bimolecular geometries in the stabilization energy interval of ∼2.3 to −1.3 eV in panel (a) of Figure 6 and those in the interval of −1.0 to −0.75 eV in panel (a) of Figure 5 are similar. But the bimolecular geometries in the stabilization energy interval of −1.3 to 0.0 eV in panel (a) of Figure 6 are very peculiar to PDI 1. As can be seen from the bimolecular geometries, (iii)−(v), these arise from the intermolecular interactions between the molecular core of one molecule and the side-chain of the other molecule and from those between the side-chains of each molecule. In fact, these cannot arise for PDI, which involves no side-chains. On the other hand, from panel (b), there seems to be a correlation between the angle between the two molecular planes and the stabilization energy over a wide range of stabilization energy (correlation function ∼ 0.551 from Table 1). This is also because of the very strong intermolecular π−π stacking interaction between their rigid aromatic cores over the large stabilization energy region. However, there are much more bimolecular geometries, i.e., dots in the figures, which have no counterpart in the panel (b) of Figure 5. This is due to the fact that the presence of side-chains makes various patterns of intermolecular interactions to occur, in particular, interactions involving weak van der Waals interactions via side-chains. From panels (c) and (d), unlike panels (c) and (d) of Figure 5, there seem to be a correlation between the dipole moment and the stabilization energy and that between the electronic coupling and the stabilization energy (compare the value of the correlation function of 0.000396 for panel (c) and that of 0.113 for panel (d) of Figure 5 and that of 0.363 for panel (c)

(1) All of the panels (a) show the tendency similar to that of the panel (b) of Figure S5 of ref 40. This is quite a reasonable result. In other words, if the barycentric distance increases, the intermolecular stabilizing interaction decreases so that the stabilization energy decreases. (2) From the comparison of electronic couplings shown in panel (d), the electronic couplings of a series of PDI molecules (0.0−0.1 eV) are much larger than those of PCBM molecules (0.0−0.007 eV). This is indicative of the fact that the formers have much larger electron mobilities than the latter. (3) As far as the organic solar cells concerned, increased complexity of the distribution of the data corresponds to the increasing number of the amorphous structures with the increasing complexity of the side-chain in disordered films.41,42 Therefore, it may be no wonder that the introduction of linear alkyl chains brings about a drastic change in polymer orientation, leading to the alteration of the charge transport in solar cells.43 In addition, it is clear that the side-chains serve to avoid the aggregation and crystallization of PDIs at the interface, which will lead to a better device performance. (4) As mentioned in Introduction, in ref 26, it was found that three perylene diimide−spirobifuluorene derivatives with different kinds of alkyl side-groups showed identical HOMO/LUMO energy levels and very similar optical properties but different photovoltaic responses. This may be due to the fact that the intermolecular side-chain interactions bring about a variety of intermolecular configurations as shown in our calculations and, therefore, the molecular systems in ref 26 have taken full advantage of the merits both of the fullerene derivatives and of PDI mentioned in this work. 10401


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4. CONCLUSIONS The main purpose of the present work was to point out the effect of side-chains in the various organic materials in general. To show that by quantum chemistry method, we calculated several physical quantities related to two interacting organic semiconductor molecules to reveal the significance and the role of the side-chains. The molecular systems of our target were the geometry-optimized dimer systems: that consisting of two PCBM molecules and that consisting of two PDI-related molecules. The physical quantities shown in the present work are their relative molecular geometries, optimized energies, barycentric distances, angles between the two molecular planes, dipole moments, and electronic couplings. The emphasis was put on the important influence of the molecular core and the side-chains on the molecular characteristics of the multimolecular system. In particular, from our calculations, it turned out that the presence of the side-chain brings about the diversity of the multimolecular characteristics that are absent in the absence of the side-chains. This was due to the intermolecular van der Waals interactions between the sidechains, which yield various patterns of intermolecular configurations. This implies the importance of side-chains in the organic materials in general. For example, as far as organic solar cells are concerned, a variety of the nonfullerene bimolecular configurations shown in Figure 6 will contribute a lot in disordered films in organic solar cells. In fact, it was pointed out that the molecular orientation is very important for ultrafast energy transfer at organic semiconductor interfaces.44 Our study showed that one of the reasons for the determination of relative molecular orientation is how the side-chains of one molecule interact with those of the other molecule. This has a great impact not only on the single molecular structure but also on the molecular packing and the charge transport properties. This also indicates the importance of the side-chain affecting the solar cell characteristics. Finally, as pointed out by Pollino et al.,45 after the traditional covalent-based synthetic strategies become mature, the “noncovalent”-based strategies using the side-chain interactions will turn out to be an alternative route in the materials engineering including the organic solar cells discussed in the present work.

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correlations between two of the stabilization energy, the barycentric distance, the angle between the two molecular planes, the dipole moment, and the electronic coupling for PDI 1 bimolecular system (Figure S5); correlations among three of the stabilization energy, the barycentric distance, the angle between the two molecular planes, the dipole moment, and the electronic coupling for PDI 1 bimolecular system (Figure S6) (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Kenji Mishima: 0000-0001-5079-373X Koichi Yamashita: 0000-0002-6226-3194 Present Address †

Center for Computational Sciences, University of Tsukuba, Tennodai 1-1- 1, Tsukuba, Ibaraki, 305-8577, Japan (K.M.). Author Contributions

The manuscript was written through contributions of all authors. K.M. performed the quantum chemistry calculations. Funding

This research was supported by MEXT as "Priority Issue on Post-K computer” (Development of new fundamental technologies for high-efficiency energy creation, conversion/ storage and use) and by JSPS KAKENHI in Scientific Research on Innovative Areas "Innovations for Light-Energy Conversion (I4LEC)". Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Computations were performed using Research Center for Computational Science, Okazaki, Japan.

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REFERENCES

(1) Zhang, G.; Zhao, J.; Chow, P. C. Y.; Jiang, K.; Zhang, J.; Zhu, Z.; Zhang, J.; Huang, F.; Yan, H. Nonfullerene acceptor molecules for bulk heterojunction organic solar cells. Chem. Rev. 2018, 118, 3447− 3507. (2) Zhao, W.; Li, S.; Yao, H.; Zhang, S.; Zhang, Y.; Yang, B.; Hou, J. Molecular optimization enables over 13% efficiency in organic solar cells. J. Am. Chem. Soc. 2017, 139, 7148−7151. (3) Zhang, J.; Tan, H. S.; Guo, X.; Facchetti, A.; Yan, H. Material insights and challenges for non-fullerene organic solar cells based on small molecular acceptors. Nat. Energy 2018, 3, 720−731. (4) Idé, J.; Méreau, R.; Ducasse, L.; Castet, F.; et al. Supramolecular organization and charge transport properties of self-assembled π-π stacks of polylene diimide dyes. J. Phys. Chem. B 2011, 115, 5593− 5603. (5) Delgado, M. C. R.; Kim, E.-G.; da Silva Filho, D. A.; Brédas, J.-L. Tuning the charge-transport parameters of perylene diimide single crystals via end and/or core functionalization: a density functional theory investigation. J. Am. Chem. Soc. 2010, 132, 3375−3387. (6) Zhao, H.-M.; Pfister, J.; Settels, V.; Renz, M.; Kaupp, M.; Dhem, V. C.; Würthner, F.; Fink, R. F.; Engels, B. Understanding groundand excited-state properties of perylene tetracarboxylic acid bisimide crystals by means of quantum chemical computations. J. Am. Chem. Soc. 2009, 131, 15660−15668. (7) Mirjani, F.; Renaud, N.; Gorszak, J.; Grozema, F. C. Theoretical investigation of singlet fission in molecular dimers: the role of charge

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.9b00012. Correlations between two of the barycentric distances, the angle between the two molecular planes, the dipole moment, and the electronic coupling for PCBM bimolecular system (Figure S1); correlations among three of the stabilization energy, the barycentric distance, the angle between the two molecular planes, the dipole moment, and the electronic coupling for PCBM bimolecular system (Figure S2); correlations between two of the barycentric distance, the angle between the two molecular planes, the dipole moment, and the electronic coupling for PDI bimolecular system (Figure S3); correlations among three of the stabilization energy, the barycentric distance, the angle between the two molecular planes, the dipole moment, and the electronic coupling for PDI bimolecular system (Figure S4); 10402


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