Energy Alignment of Frontier Orbitals and Suppression of Charge

Nov 6, 2015 - Blends of poly(3-hexylthiophene) (P3HT) and single-walled carbon nanotubes (SWNTs) have been studied as promising materials for organic ...
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Energy Alignment of Frontier Orbitals and Suppression of Charge Recombinations in P3HT/SWNT Katsuhiko Nishimra,†,‡ Mikiya Fujii,†,‡ Ryota Jono,†,‡ and Koichi Yamashita*,†,‡ †

Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan CREST-JST, Tokyo 113-8656, Japan

‡

S Supporting Information *

ABSTRACT: Blends of poly(3-hexylthiophene) (P3HT) and single-walled carbon nanotubes (SWNTs) have been studied as promising materials for organic photovoltaic devices because of the excellent electronic properties of SWNT and a broad interfacial area guaranteed by the helical structure of P3HT at the interface. However, the P3HT/SWNT blends show a low energy conversion efficiency, and thus, a deeper understanding of the charge separation process in the P3HT/ SWNT blends is required to achieve improved efficiency. In this paper, the electronic structures of P3HT at the interface and in the bulk phase were studied to elucidate the charge separation process in the P3HT/SWNT blends. We show the existence and origin of the difference between the HOMO levels at the interface and those in the bulk phase. This explains observations in a previous experiment where long-lived charge carriers were only observed in blends containing excess P3HT. In the course of the investigation on the electronic structures, the role of the side chains on the polythiophene (PT) that form the helical structure at the interface was also investigated.

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INTRODUCTION

In addition to the morphological properties, a remaining issue is finding promising pairs of donor and acceptor molecules with suitable electronic structures for OPV devices. Numerous organic molecules have been studied as candidate materials for the active layers ever since the first BHJ cell was reported in 1995.5 Semiconducting π-conjugate polymers and fullerene derivatives have been extensively studied as electron donor and acceptor molecules, respectively.5−7 Among fullerene derivatives, phenyl-C61-butyric acid methyl ester (PCBM) has been widely studied as an electron acceptor material because it is soluble to common organic solvents8 and its electronic structure is suitable for forming so-called type II heterojunctions with various donor molecules.9 In particular, the pair of regioregular poly(3-hexylthiophene) (P3HT) and PCBM is known as one of the most studied donor/acceptor pairs since 2002 when the first report of the working photovoltaic device using this pair.10,11 However, there has been no progress in power conversion efficiency (PCE) of P3HT/PCBM OPVs since 2009 when it marked 6.5%.11,12 Through trying numerous novel donor/acceptor pairs, the leading OPVs nowadays have achieved PCE of ca. 10%.13−15 While there have been plenty of novel donor materials including polymers and small molecules,15,16 PCBM or PC71BM is used as an acceptor material in most of applications

Organic photovoltaic (OPV) cells are being eagerly researched and developed. In particular, bulk heterojunction (BHJ) photovoltaic cells have many attractive properties, such as a high mass productivity and a lower energy requirement for production. Energy payback time (EPBT) is a very important factor in life cycle assessment of photovoltaic devices, which is defined as EPBT = [production energy requirement]/[(power rating) × (isolation)].1 Low production energy requirement for BHJ cells leads to as short an EPBT as a few months2,3 currently. It is expected to be as short as a few weeks4 in the future. Besides, the plastic materials make the devices flexible and lightweight.3 These features are very useful to spread solar energy harvesting devices ubiquitously around our living space, such as on walls of houses as well as roofs or even on our clothing. The mass productivity and the lower energy requirement originate in the fabrication processes of BHJ cells. Providing that a donor and an acceptor are chosen properly, the active layer of a BHJ cell can be fabricated by simply casting a solution of a blend of the donor and the acceptor molecules onto a substrate. After casting, the blend separates into the donor phase and the acceptor phase during the solvent drying process, and a BHJ forms spontaneously. These fabrication processes do not require high vacuum and high temperature techniques, both of which are disadvantageous for mass production and lower energy consumption. © 2015 American Chemical Society

Received: July 16, 2015 Revised: October 23, 2015 Published: November 6, 2015 26258

DOI: 10.1021/acs.jpcc.5b06876 J. Phys. Chem. C 2015, 119, 26258−26265

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The Journal of Physical Chemistry C even in recent days.15,16 Toward the development of the innovative acceptor material, it is reasonable to begin with replacing PCBM in the well-studied P3HT/PCBM system with another material and comparing various characteristics with each other. Single-walled carbon nanotubes (SWNTs) are well-known for their excellent electronic properties, such as their even higher electron mobility (ca. 104−105 cm2 V−1 s−1)17,18 than that of PCBM (ca. 10−3 cm2 V−1 s−1).19,20 This high mobility is desirable for a material of OPV because higher mobility leads to shorter time-of-flight before the charge carriers are collected by the electrodes, which suppresses charge recombinations. Moreover, carbon nanotube morphology, with its large aspect ratio, can lead to the nanotubes being well percolated with BHJs having a large interfacial area. Recent experimental techniques have enabled us to purify specific semiconducting SWNTs (sc-SWNTs) selectively, without any metallic SWNTs21,22 which acts as a recombination center and deteriorates the device performance significantly.21,23,24 Furthermore, it has been reported that regioregular poly(3alkylthiophene)s (P3ATs), including P3HT, can disperse scSWNTs selectively and in a nonaggregated form.25 Thus, blends of P3ATs and sc-SWNTs can be expected to be very advantageous candidates for BHJ active layer materials. However, many experimental studies on BHJ cells using pairs of polymers such as P3ATs and SWNT have shown only very low energy conversion efficiencies.26−31 To enlighten the charge separation process at the P3HT/ SWNT heterojunction, Stranks et al. measured the timeresolved pump−probe photoluminescence from blends of P3HT and highly purified sc-SWNT with small diameter whose chirality index is (6, 5). They showed that the low efficiency of a blend of 50 wt % SWNT and 50 wt % P3HT was not from the absence of charge separation, but because of very fast charge recombinations.32 Furthermore, Stranks et al. also observed long-lived charge carriers in a 1 wt % SWNT blend with excess P3HT. They attributed the significant ratio dependence of the charge carrier lifetimes to a lowering of the HOMO level of the P3HT at the interface compared with the HOMO in the bulk phase. This lowering was assumed to arise from the interaction with the SWNT at the interface, where P3HT coils helically around the SWNT,33 and was regarded as the driving force for the escape of holes away from the interface. This driving force was considered as the physical origin of the long-lived charge carriers. The goals of this work were to clarify the mechanism where P3HT coils helically around SWNT at the interface and to verify the proposal presented by Stranks et al. To this end, we investigated stable structures at the interface of P3HT and SWNT and estimated differences between the HOMO level at the interface and that in the bulk phase. Thereafter, we will present a (de)stabilization mechanism that is different from the proposal presented by Stranks et al.

Besides, monolayers of P3HT formed at the P3HT/SWNT interface exhibit a different periodic structure, which is in the form of a helical structure around the SWNT. Therefore, if an atomistic model is constructed under a given periodic boundary condition, then the three periodic structures would be constrained artificially, and thus, the pristine relaxed structure will not be obtained. With this in mind, we prepared isolated bimolecular models that consisted of P3HT and SWNT to investigate the interfacial structure of P3HT/SWNT blends. Hydrogen atoms terminated the edges of the models. Then, apart from this interfacial structure, the bulk phase of P3HT was modeled under the periodic boundary conditions in all three directions. Next, the diameter of SWNT needs to be appropriately chosen because the electronic structure of sc-SWNT strongly depends on the diameter. Furthermore, it is also known that P3HT/SWNT blends can only form type II heterojunctions when sc-SWNT with a small diameter is used.41,42 Hence, we set the chiral index of the model SWNT molecule to be (6, 5), which has the same chirality as the model SWNT molecule used by Stranks et al. in their photoluminescence experiments.32 We prepared three atomistic models to investigate the mechanism of helix formation and the electronic properties at the SWNT/P3HT interface. The first model consisted of a SWNT molecule and a polythiophene (PT) molecule, which was regarded as a P3AT molecule without side chains. Both the second and third models consisted of a SWNT molecule and a P3HT molecule, where different types of regioregular P3HT were adopted, respectively. That is, P3HT molecules in the second and third models consisted of 100% “head-to-tail−headto-tail” (HT−HT)43 and 100% “head-to-head−tail-to-tail” (HH−TT)43 coupled triads, respectively (see Figure 1 for the

Figure 1. (a) “HT−HT” and (b) “HH−TT” coupled triads of P3AT, where “R” denotes an arbitrary side-chain group, such as a hexyl or dodecyl group.

configurations of the P3AT “HT−HT” and “HH−TT” coupled triads). The first model was introduced to investigate whether helix formation required the existence of side chains. The other two models were introduced to investigate how regioregularities influenced the interfacial morphology and electronic structure. In addition to the atomistic models for the interface, we also prepared an atomistic and periodic model of molecules in the bulk phase to compare the electronic structures of P3HT at the interface and in the bulk phase. In this crystalline P3HT model, the regioregularity was chosen as 100% “HT−HT” couplings because some studies have been done on crystalline P3AT with the “HT−HT” regioregularity.44,45 An initial structure used to estimate the periodic stable structure was obtained from an earlier electron diffraction analysis,45 with a slight modification to avoid structural conflicts between the side chains; i.e., the unit cell size was increased by 0.1 nm. In the optimization routine, we used a supercell that contained two columns of

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COMPUTATIONAL CONDITIONS Atomistic Models of the P3HT/SWNT Interface. Various studies have revealed that atomistic configuration and molecular packing affect the charge transfer and separation processes via electronic structures.34−40 With the spirit of the analysis of electronic structures, we construct atomistic models for the P3HT/SWNT interface. To do so, we first need to consider the periodicity of the atomistic models. The lengths of the periodic units of P3HT and SWNT differ from each other. 26259

DOI: 10.1021/acs.jpcc.5b06876 J. Phys. Chem. C 2015, 119, 26258−26265

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tetramers stacked in four layers (Ncolumns = 2, Nrings = 4, Nlayers = 4), as shown in Figure 2.

Article

RESULTS

Stable Morphologies. P3HT Monolayers Coiled around SWNT. First, we obtained the stable structure of an isolated and hydrogen-terminated (6, 5)-SWNT molecule using the PM3 method and the ORCA software package, where the initial structure for the geometry optimization was prepared by rolling up a hydrogen-terminated rectangle of a graphene sheet. The axial edge of the rectangle was chosen as the shortest nontrivial integral vector orthogonal to the chiral vector (−16, 17). Similarly, stable structures of planar P3HT and PT that were initially constrained under Cs symmetry were also obtained. Next, we prepared initial structures of the interfacial structures by projecting the planar P3HT or PT structures obliquely to virtual cylindrical surfaces around the SWNT, where the initial pitches of the helical P3HT molecules were selected to avoid structural conflicts between the side chains. Then, geometry optimizations were carried out on the supermolecules consisting of SWNT and helical P3HT or PT. The initial and stable structures of an interface consisting of PT and SWNT are shown in Figures 3a and 3b, respectively. As can be seen in those figures, the PT/SWNT interface is not stable in a helical structure; i.e., the stable structure consists of a straight PT molecule adhered to a SWNT by dispersion forces. The instability of the helical structure was revealed to arise from the rigidity of the PT molecule. The difference between the total energy before and after optimization (|ΔEtot| = 1.4 eV) mostly comes from the coiling energy of the PT molecule (|ΔEcoiling| = 1.2 eV). These results indicate that the alignment between the PT and the SWNT is not significant in the formation mechanism of the interface configuration. The initial and stable structures of the “HH−TT” P3HT/ SWNT and the “HH−TT” P3HT/SWNT surfaces are shown in Figure 4. In contrast to PT/SWNT, the helical configuration of P3HT/SWNT was found to be stable. This result indicates that the side chains of the polymer play an important role in the formation mechanism of a sheathlike morphology. Comparing the stable structures of the “HH−TT” P3HT/SWNT and the “HT−HT” P3HT/SWNT interfaces, the stable pitches of the helical P3HT molecules were virtually the same, regardless of any difference in the regioregularities. In addition, we confirmed that differences in the pitch in the initial structures do not have an effect on the stable structure. Besides, the calculated pitch of 1.5 nm is very close to the experimentally observed pitch of 1.66 nm,33 although the calculated diameter of 1.5 nm is significantly different from the experimentally observed diameter of 2.1−2.5 nm. The difference in the diameter of helical P3HT is from the different diameters of SWNT, which were 0.77 nm and ca. 1.4 nm in our calculations and in experiments, respectively. There are two models that can be used to describe how polymers adhere to SWNT surfaces. One model, proposed by Lei et al.,64 regards the alignment of the polymer strands with hexagonal graphene lattices as being the determining factor of

Figure 2. Supercell used in the optimization of the crystalline configuration.

Calculation Methods. Semiempirical molecular orbital methods were adopted to obtain stable structures for the atomistic models we introduced in the previous subsection because these atomistic models contain a sufficiently large number of atoms (e.g., 840 atoms for the interfacial model with side chains), and it is difficult to carry out geometry optimization for these structures using ab initio methods, even with modern computational resources. Among the available semiempirical methods,46−48 the PM3 method49 is known to produce relatively better optimized structures and is widely utilized. In addition, London dispersion forces need to be taken into account to evaluate correctly the stability of a given supermolecular system that consists of multiple conjugated molecules. Thus, we used a modified version of the PM3 developed by McNamara et al., denoted as PM3-D.50 This method takes London dispersion forces into account as the Grimme’s empirical dispersion correction.51,52 All geometrical optimizations using the PM3-D method were performed employing the molecular dynamics simulation based on the semiempirical quantum chemistry (MolDS) software package.53 The structural optimization of the periodic model of crystalline P3HT was carried out using the PM6D354,55 method in MOPAC 2012 code.56,57 To qualitatively verify the assumptions related to the HOMO levels of P3HT at the interface and in the bulk phase by Stranks et al., we tested three electronic structure methods: density functional theory (DFT) with the B3LYP functional,58,59 PM3 method, and the Hartree−Fock (HF) method.60 We adopt the 6-31G* basis set61,62 for DFT and HF. As shown in the Supporting Information, electronic structures estimated using the PM3 or HF with the 6-31G* basis sets are inconsistent with a previous study that observed a type II heterojunction between P3HT and small diameter SWNT.41 Thus, we adopted the DFT/B3LYP/6-31G* methodology in our qualitative electronic structure analysis. The electronic structure calculations using the DFT and HF methods were performed using the ORCA software package63 version 2.9.1.

Figure 3. (a) Initial and (b) stable structures of the atomistic interface between PT and SWNT. Key: gray = carbon atoms in SWNT, red = carbon atoms in thiophene rings, yellow = sulfur atoms, and white = hydrogen atoms. 26260

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The Journal of Physical Chemistry C

Figure 4. Initial and stable structures of the atomistic interfaces of P3HT and SWNT. Initial structures of (a) “HT−HT” P3HT/SWNT and (b) “HH−TT” P3HT and stable structures of (c) “HH−TT” P3HT/SWNT and (d) “HH−TT” P3HT/SWNT. Key: red = carbon atoms in the main chains of P3HT, green = carbon atoms in the side chains of P3HT, gray = carbon atoms in SWNT, and yellow = sulfur atoms.

the angle for polymer monolayers to coil around SWNT. The other model, proposed by Coleman and Ferreira,65 focuses on the maximum coverage rather than the alignment. Our results, shown in Figures 3 and 4, imply that the alignment-dependent potential is small compared with the rigidity of the P3AT and that the model by Coleman and Ferreira is more appropriate for predicting the morphology of P3HT/SWNT interfaces. These results do not contradict previous studies on poly(phenylenevinylene) (PPV)/SWNT and polyacetylene (PA)/ SWNT systems employing force field simulations.66,67 Though our results give no information about solvent drying processes where the structures are formed from solution, a previous work incorporating MD simulation with classical force field68 exhibits rapid (ca. 500 ps) adsorption of P3HT onto SWNT and formation of helices. Considering the stability of the stable structure, we obtain it is reasonable to conclude that the stable structure are formed on large part of the interface after the drying process. Crystalline P3HT. The stable structure of periodic crystalline P3HT was determined using the PM6-D3 method, as shown in Figure 5. The obtained structure had a monoclinic lattice with a

Figure 6. Frontier orbitals of the interfacial “HT−HT” P3HT/SWNT supermolecule: (a) HOMO and (b) LUMO of the supermolecule.

structures of isolated molecules extracted from the interfacial supermolecules separately and compared them with those of the supermolecules. The MO levels of the supermolecules were found to be nearly identical when compared with the isolated P3HT molecules, as shown in Figure 7. These results suggest that neither orbital mixing nor electrostatic interactions between the P3HT and SWNT affect the HOMO level of the P3HT molecules at the interface. Therefore, in the

Figure 5. Stable configuration of crystalline P3HT: a = 3.49 nm, b = 1.60 nm, c = 1.58 nm, α = 86.6°, β = γ = 90.0°. The interplanar distance between two polythiophene rings was in the range of 0.28− 0.34 nm.

= 3.49 nm, b = 1.60 nm, c = 1.58 nm, α = 86.6°, and β = γ = 90.0°. Although the interplanar distance between two neighboring PT main chains was in the range of 0.28−0.34 nm, the electronic structures shown afterward do not seem to be affected by this variation. Orbital Energy Analysis. Molecular Orbitals at the Interfaces. We calculated the electronic structures of P3HT/ SWNT supermolecules at their interfaces using the DFT/ B3LYP/6-31G* method, and Figure 6 confirms that the HOMO and LUMO orbitals were localized on the P3HT and the SWNT, respectively. We also calculated the electronic

Figure 7. Comparison of the MO levels of isolated molecules and a supermolecule at the interface. Left = isolated “HT−HT” P3HT, middle = “HT−HT” P3HT/SWNT supermolecule, and right = isolated SWNT. All the results were obtained with structures taken from the stable structure of “HT−HT” P3HT/SWNT (Figure 4d). 26261

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The Journal of Physical Chemistry C following analysis of the frontier orbitals of P3HT at the interface, we omit the SWNT and only deal with the P3HT molecules that were coiled like a sheath. In contrast, in the next subsection, we show that the HOMO level of crystalline P3HT increases as more layers of crystalline P3HT are stacked. Before proceeding on to our analysis of crystalline P3HT, an extrapolation technique was introduced to investigate the frontier orbitals of P3HT with an infinite length. This technique is based on a rule of conjugated polymers that states that band gaps and the energy levels of frontier orbitals depend linearly on the reciprocal of the chain length.69,70 To minimize the influence of the terminations at the edge of the model molecules, various sheathlike oligomers were reconstructed from the P3HT at the interface and analyzed. Namely, the 18mers of P3HT in the stable configuration of the interface (Figures 4c,d) were decomposed into 18 3-hexylthiophene units, and then the pieces were rejoined to constitute the various oligomers. The edges of the reconstructed oligomers were hydrogen-terminated with the same bond lengths, bond angles, and dihedral angles as the hydrogen atoms at the edges of the original 18-mers. As a result, the HOMO and LUMO levels of the reconstructed P3HT molecules exhibited a linear dependence on the reciprocal of the chain lengths, Nrings−1, as shown in Figure 8. This crystalline electronic structure perhaps

Figure 9. HOMO−LUMO levels of crystalline P3HT and their dependence on chain length.

the HOMO level of double-layered crystalline P3HT with infinite chain length (ca. −4.0 eV). In addition to the dependence on the chain length, we estimated the dependence on Nlayers, where the chain lengths were fixed to Nrings = 4 and observed that the HOMO levels were linearly dependent on

Figure 10. HOMO levels changing along the number of stacking layers for Nrings = 4. Figure 8. HOMO−LUMO levels of P3HT at the interfaces and their dependence on the chain length. Error bars display maximum and minimum values for a given chain length.

Nlayers−2/3, as shown in Figure 10. These two dependences can be summarized into one equation as E HOMO = aNrings−1 + bNlayers−2/3 + c

came from the smoothness of SWNT walls on which P3HT molecules adhere. In addition, the interlocking morphology of the side chains also might have contributed to this quasicrystallinity. Our calculation did not include any effects of thermal disturbance, but the work by McMahon et al.71 suggests that thermal effects are insignificant on HOMO− LUMO levels. From the extrapolation of the result displayed in Figure 8, the HOMO−LUMO levels of a sheathlike P3HT with an infinite chain length were estimated to be ca. −4.0 and −2.2 eV, respectively. Molecular Orbitals in the Crystalline Phases. We also estimated the energy levels of the frontier orbitals of crystalline P3HT and their dependence on the chain length in the same manner as discussed in the previous subsection. As shown in Figure 9, the HOMO levels of crystalline P3HT depended linearly on Nrings−1 for all numbers of stacking layers (Nlayers). It was also observed that the coefficient of Nrings−1 was independent of Nlayers. On comparing the HOMO levels in Figures 8 and 9, we can assert that the HOMO level of the sheathlike P3HT is destabilized compared with the HOMO level of single-layered crystalline P3HT and corresponds with

(1)

where a = −1.9 eV, b = −0.8 eV, and c = −3.5 eV. The second term bNlayers−2/3 suggests the existence of a band structure with relatively weak coupling along the stacks of P3HT layers as well as along the conjugated chains.72,73 Note that no interchain interactions were observed in the direction of the side chains (Ncolumns). From eq 1, we estimated the HOMO level of P3HT with an infinite chain length (Nrings → ∞) and infinite layers stacked (Nlayers → ∞) to be c = −3.5 eV.

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CONCLUDING REMARKS In this paper, we investigated two matters related to exciton dissociation at the P3HT/SWNT interface. First, the formation of helical morphology structures at the interface was investigated using semiempirical molecular orbital methods. As a result, the importance of the side chains of PT derivatives was revealed. While the alignment between the PT main chains of P3AT and graphene lattices of SWNT had little effect on the interface structures, the length of the side chains of P3AT was a crucial factor in the formation of the unique structures at P3AT/SWNT interfaces. In other words, the interfacial 26262

DOI: 10.1021/acs.jpcc.5b06876 J. Phys. Chem. C 2015, 119, 26258−26265

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The Journal of Physical Chemistry C structures of P3AT/SWNT blends can be explained well by the simple model proposed by Coleman and Ferreira65 and not by the model of Lei et al.64 This knowledge should help us when fabricating OPV devices using P3AT/SWNT blends. Second, DFT calculations on the interface structures revealed the mechanism of the suppression of charge recombination from the presence of excess P3HT, which was reported experimentally by Stranks et al.32 Although the HOMO levels of P3HT at the interface were revealed to increase in comparison with straight P3HT by the helical deformation of the main chain of PT, the flexibility of the main chains keeps the HOMO levels of sheathlike P3AT relatively low. On the other hand, the HOMO level of multilayered crystalline P3AT is more destabilized because of interchain interactions compared with crystalline P3AT; i.e., the HOMO of the crystalline P3AT main chains forms a weak band structure along the stacking direction, which stabilizes the holes in the crystalline phase rather than at the interface. As a result, the HOMO level of crystalline P3HT in the bulk phase was estimated to be approximately 0.5 eV higher than the HOMO level of sheathlike P3HT at the interface. This difference in energy is the driving force that makes holes escape from the interface to the bulk phase. From the above, we have shown the mechanism that prolongs the lifetime of photogenerated charge carriers in P3HT/SWNT blends with excess P3HT. Moreover, it is also suggested that the electronic structure of the interfacial P3HT monolayers is rather similar to crystalline one because the HOMO level is linearly dependent on the reciprocal of the main-chain length. This feature probably arises from rigidity of P3HT monolayers due to the strong interactions between P3HT and smooth SWNT walls and interlocking side chains. It is known that configurations of P3HT molecules are disordered at rough P3HT/PCBM interface and that there are region with wider gap where holes are less stable than in the bulk P3HT phase due to the configurational disorder.71,74 Although there is a wide-gap region also at the P3HT/SWNT interface, our results suggest that the widening is smaller than at the P3HT/PCBM interface due to the rigidity of sheathlike P3HT. Smaller widening of the gap means the lower barrier for charge transfer of the carriers at the interface. This mechanism can account for the ultrafast charge separation in the P3HT/SWNT blend observed by Stranks et al. The present study has provided an insight into the dynamics of how holes escape from the interface of P3AT/SWNT using the modeling theories for the electronic ground states. In particular, knowledge about the mechanism under prolonged lifetimes of photogenerated charge carriers will contribute to the future development of novel light-harvesting devices utilizing SWNT and other materials with one-dimensional morphologies. Nevertheless, exciton dissociation and charge recombination are dynamical processes in electronic excited states after photoillumination. Therefore, additional research focusing on the electronic excited states and their dynamics75,76 including nonadiabatic effects77,78 is required to elucidate the details of charge separation and recombination processes at macromolecular interfaces.

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Comparison of the molecular levels calculated by HF/631G, PM3, and DFT/B3LYP/6-31G* (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Fax +81 3 3818 5012 (K.Y.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We appreciates valuable discussions with Assis. Prof. Dr. Y. Ohnishi concerning the reciprocals of chain length. This work was supported by JST, CREST, and JSPS KAKENHI Grant No. 24750012. The Computations were performed using Research Center for Computational Science, Okazaki, Japan, and the facilities of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b06876. 26263

DOI: 10.1021/acs.jpcc.5b06876 J. Phys. Chem. C 2015, 119, 26258−26265

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