Modulating the Electronic Properties of Multimeric Thiophene

Article pubs.acs.org/JPCC

Modulating the Electronic Properties of Multimeric Thiophene Oligomers by Utilizing Carbon Nanotube Confinement Takashi Yumura* and Hiroki Yamashita Department of Chemistry and Materials Technology, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto, 606-8585, Japan S Supporting Information *

ABSTRACT: We investigated the arrangement of methylterminated terthiophenes inside a nanotube by using density functional theory (DFT) including dispersion corrections. After DFT calculations were conducted, a variety of arrangements of the inner terthiophene chains was found, depending on host-tube diameters and the number of chains. Because of the various inner thiophene arrangements, the terthiophene chains interact differently. The interactions in a smaller nanotube are stronger than those within a larger nanotube, indicating the importance of nanotube confinements to the interchain couplings. The interchain interactions split the orbitals of the multimeric terthiophene chains, which are built from single-chain frontier orbitals, broadening their energy levels. Therefore, nanotube confinements are key factors in determining the energy levels of the frontier orbitals of contained multimeric terthiophenes. As a result, their electronic transitions are affected by the encapsulation in a restricted nanotube space. According to time-dependent DFT calculations, a specific electronic transition occurs from a HOMO-built orbital to a LUMO-built orbital. The broadening of the orbital energies by the aggregation of terthiophene chains in a nanotube leads to a widened range of excitation energies (Ex) in their electronic transitions relative to the single-chain. With respect to the strongest transition of multimeric terthiophenes, the excitation energy is enhanced by confinement to a nanotube. The Ex enhancement within a smaller nanotube is more significant than that within a larger nanotube because of the stronger interchain interactions in a smaller nanotube. Therefore, it is proposed from the DFT calculations that nanotube confinements can modulate electronic and absorption properties of multimeric terthiophene chains by changing the interchain interactions.

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INTRODUCTION Organic molecules inside the nanometer-sized inner volume of carbon nanotubes1,2 exhibit unusual characters because host− guest interactions can influence their electronic properties.3 Accordingly, unusual chemistry is expected inside nanotubes. Until now, various organic molecules with rigid or flexible frameworks have been reported to be encapsulated inside nanotubes.4−14 When flexible π conjugate molecules (e.g., polyene,5,6 β-carotene,8 and thiophene oligomers9−12) are on the inside of nanotubes, the encapsulation can induce structural distortion of the guests. The characteristics derived from their π conjugation, such as optical and electronic properties,15−21 are perturbed by host−guest interactions. Many researchers have become interested in carbon nanotubes because they have the potential to become “nano-vessels” that can confine flexible molecules and change the original properties through interactions. For example, the encapsulation of thiophene oligomers in nanotubes is of great interest because the hybrid materials are optically active in the visible region. Previously, their properties were investigated by using aberration-corrected high-resolution transmission electron microscopy, Raman spectroscopy, and optical spectroscopy.9−12 References 9 and 10 reported that sexithiophene oligomers inside nanotubes with a diameter of 1.2 nm exhibit visible photoluminescence with quantum yields © 2014 American Chemical Society

up to 30%. In the high-energy region, their photoluminescence properties are different from those of the same oligomers in solution. According to ref 10, the differences come from interactions of the molecules with the nanotube walls or between neighboring molecules. Despite the excellent experimental work in this research field, computational approaches, especially density functional theory (DFT) calculations, are indispensable for obtaining atomistic information of π-conjugated molecules inside nanotubes.22−28 In the relevant studies,9,10,23,27 DFT functionals with and without dispersion corrections were used to evaluate the interactions between the inner thiophene oligomers and the nanotubes. Our previous study27 found that a single thiophene oligomer prefers to be located near the inner wall of a nanotube, shown in Figure S1 of Supporting Information. The orientational preference comes from attractive CH−π and π−π interactions between the guest and the nanotube host. The attractive host−guest interactions have the power to enhance the planarity of the inner thiophene oligomers.27 Although our understanding of the interactions between one thiophene oligomer and a nanotube has increased, the arrangement of thiophene multimers inside nanotubes has Received: July 3, 2013 Published: February 20, 2014 5510

dx.doi.org/10.1021/jp5006555 | J. Phys. Chem. C 2014, 118, 5510−5522

The Journal of Physical Chemistry C

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Figure 1. Schematic view of the encapsulation of methyl-terminated terthiophenes in a (10,10) or (8,8) nanotube. The diameters of the (10,10) and (8,8) tubes are 13.7 and 10.9 Å, respectively.

To select basis sets suitable for large-scale calculations of n × 3T@(m,m), we considered four types of combination of basis sets to investigate the frontier orbitals of a single terthiophene encapsulated in the (10,10) tube, as shown in Figure S2 of Supporting Information. Then we focused on orbitals built from the highest occupied molecular orbital (HOMO) or lowest unoccupied molecular orbital (LUMO) of single terthiophene surrounded by the tube, as well as on the HOMO−LUMO gap. According to the comparative analysis, the HOMO- and LUMO-built orbitals obtained by using the 631++G** basis set for terthiophene and 128 neighboring tubeatoms and the 6-31G** basis set for the others (BS1) can be reproduced by the calculations with the 6-31++G** basis set for terthiophene and the 6-31G** basis set for the tube (BS2). In addition, similar HOMO−LUMO gaps were obtained in the BS1 and BS2 calculations. Because of limited computational resources, we used the 6-31++G** basis set45−47 for the thiophene oligomers and the 6-31G** basis set45,46 for the finite-length tube models. Accordingly, the optimization of the nanotubes containing some terthiophenes involved up to 7080 contracted basis functions. When electronic properties of n × 3T@(m,m) optimized from B97D calculations, especially their frontier orbitals, are discussed, one should be careful. This is because B97D functional, a GGA-based functional, tends to underestimate the HOMO−LUMO gaps of thiophene oligomers, as shown in Figure S3 of Supporting Information. Figure S3 shows that the HOMO−LUMO gap decreases with increasing l and converges to a specific value at l = 15. The B97D-computed gaps converged at approximately 1.1 eV, which is smaller than the experimental value. On the other hand, B3LYP calculations yield the converged gap of approximately 2.2 eV, which is consistent with the experimental value (2.1 eV)48 and extended Hückel value (2.0 eV).49 Underestimating the HOMO−LUMO gaps in the B97D calculations is inevitable because the functional does not include exact exchange terms.50 Considering the advantages and disadvantages of the B97D and B3LYP functionals, we chose the following procedures to investigate the geometric and electronic properties of thiophene oligomers inside nanotubes. First, we optimized n × 3T@(m,m) structures by using the B97D functional. Then we used the B3LYP functional to perform single-point calculations of the B97D optimized n × 3T@(m,m) structures with the aim of obtaining the energy levels of orbitals and orbital distributions, especially orbitals derived from the multimeric terthiophenes within the nanotubes.51

not been thoroughly explored. In contrast to a single thiophene oligomer inside a tube, not only host−guest interactions but also guest−guest interactions are key factors in determining the inner multimer arrangements. Therefore, nanotube confinement has an impact on the balance between the host−guest and guest−guest interactions. In general, the arrangement of multimeric thiophene oligomers plays an essential role in their electronic and optical properties because the intermolecular interactions have a direct impact on the energy levels of their frontier orbitals. Therefore, it is important to elucidate the arrangements of thiophene multimers inside a nanotube as well as the role of nanotube confinement in perturbing the electronic properties. To answer these questions, we performed DFT calculations including dispersion corrections.

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METHOD OF CALCULATION By using DFT calculations implemented in Gaussian 09 code,29 we would like to obtain geometrical information on nanotubes containing oligomers with three thiophene rings (terthiophene, abbreviated 3T) (Figure 1). We constructed the nanotube models by using armchair (8,8) and (10,10) nanotubes terminated with H atoms (C304H32 and C380H40, 22.1 Å length). These nanotube clusters are large enough to accurately model the electronic properties of the corresponding infinitely long nanotubes.30−36 As in ref 11, the terminal carbon atoms in terthiophene are bound with methyl groups rather than H atoms. The notation of n × 3T@(m, m) will be used throughout this study as an abbreviation for an armchair (m, m) nanotube containing n terthiophenes. To describe the weak host−guest interactions, such as the π−π interactions and van der Waals interactions, we employed the B97D functional37,38 instead of the popular function, B3LYP functional, that is not good at describing weak interactions.39−43 In the B97D functional, an empirical atom−atom dispersion potential is added to the GGA B97D functional. Reference 44 indicates that the B97D method performs very well for the potential energy surface of dimers governed by van der Waals forces (e.g., benzene dimers) because the B97D results agree within a few tenths of 1 kcal/ mol with those in couple cluster with perturbative triple excitations (CCSD(T)) calculations. Although the CCSD(T) method is accurate for the evaluation of van der Waals interactions, such calculations are time-consuming. Thus, our choice of B97D functional is a compromise to study properties of n × 3T@(m,m) whose structures are ruled by weak van der Waals forces because it provides a relatively accurate description of van der Waals interactions and at the same time reduces computational cost. 5511



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Figure 2. B97D-optimized structures for terthiophenes encapsulated in a nanotube, abbreviated by n × 3T@(m,m). Here, n ranges from 2 to 4, and m is 8 or 10. Relatively short carbon contacts between adjacent terthiophenes in n × 3T@(m,m) are shown in angstroms. EBE values are also displayed.

Chart 1

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RESULTS AND DISCUSSION Optimized Geometries for Terthiophene inside Carbon Nanotubes. In a previous study,27 we found that a single terthiophene is located near the inner wall of the (8,8) and (10,10) tubes (Figure S1 of Supporting Information). The stabilization energies in the 1 × 3T@(10,10) and 1 × 3T@(8,8) structures were −48.5 and −57.8 kcal/mol, respectively. As shown in Figure S1 of Supporting Information, 1 × 3T@(10,10) and 1 × 3T@(8,8) have large spaces available for the accommodation of additional oligomers. Following the previous study, we investigate how some terthiophenes are arranged inside an armchair nanotube ((8,8) or (10,10) tube) using B97D calculations. Here, we focus on n × 3T@(m,m) structures where inner terthiophenes interact through π−π interactions. The π−π multimers in Figure S5 of Supporting Information require a relatively large space, however the space surrounded by the tube wall is restricted. Accordingly, the number of arrangements of a multimer inside a tube is limited. Considering these situations, we constructed initial geometries of n × 3T@(m,m). Detailed procedures to construct the initial geometries are given in Supporting Information (Section S5). After optimization of initial n × 3T@(m,m) geometries, we obtained their local minima in Figure 2. As shown in Figure 2, there is a variety of arrangements of multimeric terthiophenes inside a nanotube, depending on the diameter of the nanotube

host and the number of chains. In all of the arrangements, the inner terthiophenes prefer to be located near the wall of the nanotubes. The thiophene arrangements within a nanotube in Figure 2 are quite different from herringbone structures (Chart 1a), which are usually obtained experimentally.52−69 According to the B97D calculations, the (10,10) nanotube can accommodate up to four terthiophenes, as shown in Figure 2. Because inner space of the (10,10) tube is large enough to accommodate two (three) terthiophenes, there are two isoenergetic optimized structures of 2 × 3T@(10,10) (3 × 3T@(10,10)). Their two optimized structures, which are labeled (I) and (II) in Figure 2, can be distinguished by how the inner terthiophenes are arranged. In contrast, we obtained only one local minimum in the 4 × 3T@(10,10) structure because the inner space is too small to accommodate four terthiophenes with various arrangements. In 4 × 3T@(10,10), 3 × 3T@(10,10) (I), and 2 × 3T@(10,10) (II) structures of Figure 2, adjacent terthiophenes are perpendicular. The arrangements are reminiscent of T-arrangement in benzene dimers (Chart 1c). In contrast to the T arrangement (Chart 1c and Figure 3T-I), one inner terthiophene shifts along a shortaxis, as shown in Figures 2 and 3T-III. In the shifted perpendicular arrangements, the shortest carbon contacts between the adjacent terthiophenes range from 3.06 to 3.34 Å. 5512



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Figure 3. Relative orientations of terthiophene dimers generated from the original (C) cofacial and (T) T-type motifs (Chart 1). In each motif, two types of relative orientation were considered. One type of orientation is created from an original arrangement (I) by shifting one terthiophene (red) along the long axis (longitudinal shift (II)), and the other type is created by shifting along the short axis (lateral shift (III)). The longitudinal and lateral displacements, given by y and x, respectively, can be viewed by using the top-views of each dimer motif (bottom panels). Interchain spacing (zis) is defined by the separation between the two green positions, which are the midpoints of the carbon atoms adjacent to the sulfur atom in the middle five-membered ring in the original arrangement.

Table 1. Energetics in B97D-Optimized n×3T@(m,m) Structuresa in Which Some Methyl-Terminated Terthiophenes Are on the Inside of the (m,m) Tube 1 2 3 1 2 2 3 3 4

× × × × × × × × ×

structure labels

Ebindb

Einteractc

3T@(8,8) 3T@(8,8) 3T@(8,8) 3T@(10,10) 3T@(10,10) 3T@(10,10) 3T@(10,10) 3T@(10,10) 3T@(10,10)

−57.8 −125.1 −36.1 −48.5 −101.5 −102.5 −156.3 −156.7 −191.2

− −9.6 137.2 − −4.5 −5.5 −10.7 −11.1 2.8

(I)d (II)d (I)d (II)d

arranged cofacially as shown in Chart 1b and Figure 3C. The cofacial arrangement is sometimes observed in the crystal structures of the thiophene oligomers substituted by bulky groups as well as that of oligomers containing both electronrich and electron-deficient aryl rings.70−72 Although strong interchain interactions operate in the crystal structures,70−72 two terthiophene chains within the (10,10) tube do not interact with each other because of excessively long carbon contacts. Similarly, an unusual arrangement was found in the 3 × 3T@(10,10) (II): a triangular arrangement constructed from three terthiophene whose shortest carbon contact is 4.03 Å. In contrast to the n × 3T@(10,10) structures, up to three terthiophenes can be contained in the smaller (8,8) tube. Because of limitation of inner space to accommodate a π−π dimer or trimer, we obtained only one optimized n × 3T@(8,8) structure. As shown in Figure 2, a triangular arrangement was found in the 3 × 3T@(8,8) structure and a cofacial arrangement was found in the 2 × 3T@(8,8) structure. Although these arrangements are similar to those inside the (10,10) tube, separations between terthiophenes inside the (8,8) tube are smaller than those inside the (10,10) tube. Actually, smaller interchain spacings were confirmed from the shortest carbon contacts between adjacent terthiophenes (3.31 Å for the inner dimer and 2.67 Å for the inner trimer). Note

a Optimized n × 3T@(m, m) structures can be observed in Figure S3 of Supporting Information and Figure 2. bEbind (in kilocalories per mole): Etotal(n × 3T@(m,m)) − Etotal((m,m)) − n × Etotal(3T). cEinteract (in kilocalories per mole): Ebind(n × 3T@(m,m) − n × Ebind(1 × 3T@(m,m)). dLabels (I) and (II) in 2 × 3T@(10, 10) and 3 × 3T@(10, 10) can be seen in Figure 2.

The other 2 × 3T@(10,10) and 3 × 3T@(10,10) structures have different arrangements. In the 2 × 3T@(10,10) (I) structure, two terthiophenes are opposed diametrically and are 5513



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Figure 4. Schematic view of the evolution of orbitals of multimeric terthiophene chains built from the single-chain HOMO or LUMO. Orbital amplitudes of the HOMO and LUMO of a single terthiophene chain are also given.

terthiophenes in the (10,10) ((8,8)) tube is energetically preferable. In the encapsulation in the (10,10) tube, the absolute Ebind values increase with an increase in the number of contained terthiophenes. In contrast, the stabilization in the 3 × 3T@(8,8) is less significant than in the 2 × 3T@(8,8). To further increase our understanding of the energetics of the n × 3T@(m,m), we estimated the interaction energies (Einteract) using the following equation: E interact = E bind(n × 3T@(m , m)) − n × E bind(1 × 3T@(m , m))

Interaction energies were initially introduced by Kertesz and Yumura to evaluate how the first covalent addition stabilizes the second covalent addition at a certain site.74 In this study, we applied eq 2 to the n × 3T@(m,m) structures where the guests interact with the tube host in a noncovalent manner. Roughly speaking, the Einteract values in the noncovalent systems indicate interchain interactions between terthiophene chains. Positive and negative Einteract values indicate repulsive and attractive interchain interactions, respectively. As shown in Table 1, the absolute Einteract values for the encapsulation in the (8,8) tube are significantly larger than for those for the (10,10) tube. The results indicate that strong (weak) interchain interactions operate between terthiophenes within the (8,8) ((10,10)) tube. Different signs of Einteract values are observed in the n × 3T@(m,m): positive values in 3 × 3T@(8,8) and 4 × 3T@(10,10) and negative values in the other structures. The positive Einteract values indicate that the inner terthiophenes interact repulsively in the 3 × 3T@(8,8) and 4 × 3T@(10,10) structures. The repulsive interactions are understandable because some carbon atoms on the chain are too close to those on neighboring chains;75 thus, the tightly packed terthiophenes repel each other, according to Figures S6 and S7 of Supporting Information. However, the repulsive interactions are counteracted by the attractive host−guest interactions, which stabilize the 3 × 3T@(8,8) and 4 × 3T@(10,10) structures. In the other n × 3T@(m,m) structures with negative Einteract values, the inner space can contain a certain number of terthiophenes without repulsively interacting with each other. The negative Einteract values range from −11.1 to −4.5 kcal/mol. Judging from the Einteract values, substantial attractive interchain interactions operate between the terthiophenes in the 2 × 3T@(8,8) structure. The (8,8) tube can separate two terthiophenes by 3.31 Å at minimum and make them interact effectively. However, terthiophenes within the (10,10) tube

Figure 5. Changes in the energy levels of the frontier orbitals of dimeric terthiophenes, which are built from monomer HOMO or LUMO, as a function of interchain spacing (zis). Here, (C) cofacial and (T) T-type motifs are considered in elucidating the arrangement of the two terthiophenes (Figure 3-I). Their orbital energies were obtained from B3LYP-single point calculations of the dimers constructed by two B97D-optimized terthiophenes.

that the cofacial dimer has one thiophene oligomer shifting by 1.68 Å along the long axis with respect to the other (Figure 3CII). To examine the energetics of optimized n × 3T@(m,m) structures, we estimated their binding energies (Ebind(n × 3T@(m,m))) as follows (shown in Table 1): E bind(n × 3T@(m , m)) = Etotal(n × 3T@(m , m)) − Etotal((m , m)) − n × Etotal(3T)

(2)

(1)

Here, Etotal(n × 3T@(m,m)) is the total energy of n × 3T@(m,m), Etotal((m,m)) the energy of the (m,m) tube, and Etotal(3T) the energy of a single terthiophene (3T). Basis set superposition errors (BSSEs)73 were corrected in estimating the Ebind values in the B97D calculations. Table 1 shows negative Etotal values in all optimized n × 3T@(m,m) geometries considered. Negative Ebind values in the n × 3T@(m,m) suggest that encapsulation of up to four (three) 5514



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Figure 6. Roles of the relative orientations of (1) longitudinally and (2) laterally shifted terthiophene dimers in the energy levels of orbitals built from the monomer HOMO or LUMO. Here, (C) cofacial and (T) T-type motifs are considered in elucidating the arrangement of the two terthiophenes. Their orbital energies were obtained from B3LYP single-point calculations of the dimers constructed by two B97D-optimized terthiophenes. The energy levels are displayed as a function of the longitudinal or lateral shift of one terthiophene from its original position. The longitudinal and lateral directions correspond to the y and x directions, respectively (Figure 3). During the longitudinal and lateral shifts, the interchain spacings (zis) are fixed to 3.6 and 5.4 Å, respectively.

weakly interact. The relatively weaker interactions are due to the perpendicular arrangement of adjacent terthiophenes, which will be discussed below. Role of Interchain Interactions in the Frontier Orbitals of Multimeric Terthiophenes. Because of the variety of terthiophene arrangements in n × 3T@(m,m), the inner chains interact differently. When n terthiophene chains are aggregated to interact with each other, their HOMOs (LUMOs) split into n energy levels, as shown in Figure 4. The splitting of HOMO (LUMO)-built orbitals is determined by the interchain interactions.76−81 To evaluate the relationship between the interchain interactions and the splitting width, we considered dimeric terthiophenes arranged in the cofacial and T motifs (Figure 3-I) and then changed their interchain spacings (zis).82 Figure 5 displays the energy levels of the frontier orbitals of the terthiophene dimers as a function of the interchain spacing in each motif. We see from Figure 5 that the energy difference between HOMO and HOMO−1 enhances with a decrease in the zis values, independent of the two motifs. Similar behaviors can be observed in the gap between LUMO and LUMO+1. Additionally, the relative orientations of the terthiophene dimers are important in determining the frontier orbital splitting, according to refs 76−81. To check whether this importance could be found in our case, we considered two

types of relative orientations in each motif of the terthiophene dimers (Figure 3-II or 3-III). One type of orientation was created from the original cofacial or T arrangement by shifting one terthiophene along the long-axis (longitudinal shift, Figure 3-II). The other type had one terthiophene shifting along the short-axis (lateral shift, Figure 3-III). The longitudinal and lateral displacements from the original cofacial (T) arrangement are given by y(C) (y(T)) and x(C) (x(T)), respectively (Figure 3). During the shifts in the dimers, we fixed the interchain spacing (zis) at a specific value. To determine the optimal interchain spacing (zis) in the shifted dimers, we plotted the total energy of the dimers as a function of zis and y in Figure S6 of Supporting Information and a function of zis and x in Figure S7 of Supporting Information. Figures S6 and S7 show that the optimal zis value in the shifted cofacial dimers is approximately 3.6 Å83 and that in the shifted T dimers is approximately 5.4 Å.84 The optimal longitudinally and laterally shifted cofacial dimers have interchain interactions of −9.9 and −9.6 kcal/mol, respectively.83 A similar degree of interchain interactions are found in the shifted T-type dimers (−7.1 and −7.5 kcal/mol for the longitudinal- and lateral-shifted dimers, respectively).84 The values are significantly smaller than the host−guest interaction values. 5515



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Table 2. Excitation Energies (Ex) and Oscillator Strength ( f) of the Electronic Transitions of the Single Terthiophene Taken from the B97D-Optimized 1 × 3T@(m,m), Obtained from TD-DFT B3LYP Calculations (m,m)a

Exb

fc

electronic transitiond

(8,8) (10,10)

2.96 (418.6) 2.97 (418.0)

0.86 0.88

72 → 73 (0.71) 72 → 73 (0.71)

a

(m,m): Nanotube chirality. bEx: Excitation energy is given in electronvolts and the value in parentheses is in nanometers. cf: Oscillator strength. dElectronic transition: Assignment of electronic transition from an occupied orbital to an unoccupied orbital. Labels of the frontier orbitals: HOMO, 72; LUMO, 73. Values in parentheses indicate a CI coefficient in a certain excited configuration, obtained from the TD-DFT calculations.

decrease in an oscillatory manner (Figure 6C-1), which comes from the reduction of orbital overlaps between the terthiophenes during the shift. The periodicity of the oscillatory change in the HOMO splitting is different from that in the LUMO splitting, which is consistent with previous studies.76−81 The different periodicity reflects the nodal properties of the HOMO and LUMO of the monomer. A detailed discussion on the importance of nodal properties in changing the HOMO or LUMO splittings can be seen in Figure S8 of Supporting Information. During the lateral shift, oscillatory changes in the LUMO splitting are also observed (Figure 6C-2). In contrast, the HOMO splitting decreases with the lateral shift. In the T arrangement, π orbitals on the upper terthiophene are perpendicular to those on the lower terthiophene. Compared to the cofacial arrangement cases, featureless changes in the splittings are found during the longitudinal or lateral shift from the original T arrangement. The HOMO and LUMO splittings remain almost unchanged during the longitudinal shift (Figure 6T-1). The results indicate that the interchain interactions do not change with the shift. The insensitivity is understandable because the degree of orthogonal orbital overlap does not change with the longitudinal shift. When one terthiophene shifts along the short axis, the splitting widths decrease by reducing the orbital overlaps (Figure 6T-2). In fact, the HOMO and LUMO splittings are almost 0 eV at x(T) = 4.5 Å.

Figure 7. (a) Splittings of the orbitals of the multimeric terthiophenes surrounded by a nanotube (n × 3T@(m,m)) displayed as a function of n. Their orbital energies were obtained from B3LYP single-point calculations of B97D-optimized n × 3T@(m,m) structures. The HOMO splittings in n × 3T@(8,8) and n × 3T@(10,10) are given by red and black circles, respectively. The LUMO splittings in n × 3T@(8,8) and n × 3T@(10,10) are given by green and blue squares, respectively. Dotted lines are guides for the eye. (b) Frontier orbital splittings of multimeric terthiophenes taken from optimized n × 3T@(m,m) structures displayed as a function of n.

Using the optimal interchain spacings (zis), we investigated how the frontier orbital energies change upon the longitudinal or lateral shifting of one terthiophene from the original arrangement in Figure 6. In the original cofacial arrangement (y(C) = 0 Å), a frontier π orbital on the upper terthiophene interacts with a π orbital on the lower terthiophene in σfashion. As a result, substantial HOMO and LUMO splittings of 0.59 and 0.69 eV, respectively, were found. Upon longitudinally shifting, the HOMO and LUMO splittings

Figure 8. Electronic transitions of multimeric terthiophenes taken from the B97D-optimized n × 3T@(m,m) structures, obtained from TD-DFT B3LYP calculations. Here, we focus on their electronic transitions with oscillator strength f larger than 0.01. Calculated excitation energies Ex (in electonvolts) in the electronic transitions are displayed as a function of the number of terthiophenes (n) taken from the (a) n × 3T@(8,8) and (b) n × 3T@(10,10) structures. The excitation energy in the strongest transition of a contained multimeric terthiophene (that is, the electronic transition with maximum f value) is circled in red. 5516



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Table 3. Excitation Energies (Ex) and Oscillator Strengths (f) of the Electronic Transitions of Dimeric Terthiophenes Taken from the B97D-Optimized 2 × 3T@(m,m), Obtained from the TD-DFT B3LYP Calculations (m,m)a (8,8) (10,10)e (10,10)f

Exb 2.51 3.20 3.01 2.71 2.72 3.07

(494.3) (387.2) (411.3) (457.9) (455.2) (403.4)

fc 0.214 1.238 1.621 0.079 0.068 1.431

electronic transitiond 143 143 143 143 143 143

→ → → → → →

146(−0.23), 144 → 145(0.67) 146(0.66), 144 → 145(0.24) 145(−0.38), 143 → 146 (−0.31), 144 → 145(−0.27), 144 → 146 (0.43) 145(0.34), 143 → 146(0.21), 144 → 145(0.54), 144 → 146 (0.21) 145(0.57), 143 → 146(−0.23), 144 → 145(−0.31), 144 → 146 (0.14) 146(0.62), 144 → 145(−0.31), 144 → 146 (0.10)

a

(m,m): Nanotube chirality. bEx: Excitation energy is given in electronvolts and the value in parentheses is in nanometers. cf: Oscillator strength. Electronic transition: Assignment of electronic transition from an occupied orbital to an unoccupied orbital. Labels of frontier orbitals: HOMO−1, 143; HOMO, 144; LUMO, 145; LUMO+1, 146. Values in parentheses indicate a CI coefficient in a certain excited configuration, obtained from TDDFT calculations. e2 × 3T@(10,10): In the structure, the two terthiophenes are diametrically opposed. The structure corresponds to the 2 × 3T@(10,10) structure (I) in Figure 2. f2 × 3T@(10,10): In the structure, the two terthiophenes are perpendicular. The structure corresponds to the 2 × 3T@(10,10) structure (II) in Figure 2. d

Interchain Interactions in Multimeric Terthiophenes inside Nanotubes. Considering the importance of the thiophene arrangements to the interchain interactions, we studied the splittings of the frontier orbitals of multimeric terthiophenes surrounded by a nanotube (n × 3T@(m,m)). Figure 7 displays the HOMO and LUMO splittings of multimeric terthiophenes in the n × 3T@(m,m) structures as a function of n, which are given by circles and squares, respectively. Detailed information on the features of the orbitals derived from the inner terthiophenes in n × 3T@(m,m) is given in Figures S9 and S10 of Supporting Information. From Figure 7a, we found that the frontier orbital splittings of the inner terthiophenes are sensitive to the diameter of the host tube. Within the (10,10) nanotube, the splitting gradually enhances with an increase in the number of terthiophenes (n) (Figure 7a). The changes in the splittings basically follow the schematic view of Figure 4, which shows that the splitting widths increase with an increase of n. In multimeric terthiophenes surrounded by the (8,8) tube (n × 3T@(8,8)), more significant frontier orbital splittings are found. The significant splittings are indicative of interchain interactions between the terthiophenes within the (8,8) tube that are stronger than those within the (10,10) tube. These results are in line with the trends expected from the Einteract values (see Table 1). The different splitting widths between the (8,8) and (10,10) cases, accompanied by the different interchain interactions, are due to the arrangement of the inner terthiophenes. Because of the restriction of the inner space of the (8,8) tube, the inner terthiophenes are located close together to strongly interact with each other. In contrast, the (10,10) tube has a relatively large space that allows some terthiophenes to be arranged near the inner wall by maximizing the attractive host−guest interactions. The thiophene arrangements within the (10,10) tube are not suitable for effective interchain interactions because a terthiophene is not located above neighboring terthiophenes, as shown in Figures 2 and 6T-2. Here, we discuss the roles of the nanotube surroundings in perturbing the HOMO or LUMO splittings of multimeric terthiophenes. For this purpose, we obtained frontier orbital splittings of multimeric terthiophenes taken from the n × 3T@(m,m) structures in Figure 7b. A comparison between panels a and b of Figure 7 tells us that the orbital splittings of multimeric terthiophenes surrounded by a nanotube are slightly deviated from those without nanotube surroundings. The results indicate that frontier orbital splittings of multimeric

terthiophenes surrounded by a nanotube are slightly modulated by orbital interactions between the host and guests. In particular, the host−guest interactions have the power to change the LUMO splitting of 3 × 3T@(8,8) and 4 × 3T@(10,10) because tightly packed terthiophenes are close to the tube wall. However, the deviations in the LUMO splitting by the orbital interactions are less than 0.18 eV. Accordingly, the DFT calculations show that the tube host serves as a template for arranging the multimeric terthiophenes in a restricted space through long-range CH−π and π−π interactions. In other words, nanotube confinement determines the arrangement of the multimeric terthiophenes within a nanotube. On the basis of the thiophene arrangements within the nanotubes, orbitals built from single-chain frontier orbitals split because of substantial interchain interactions. The strength of the interchain interactions is strongly dependent on the terthiophene arrangements within a nanotube. Therefore, one can modulate the frontier orbital splittings of the inner multimeric terthiophenes by utilizing nanotube confinement. Electronic Transitions of Multimeric Terthiophenes Taken from n × 3T@(m,m). Finally, we looked at the electronic transitions of multimeric terthiophenes in the B97D optimized n × 3T@(m,m) structures by performing timedependent (TD) DFT B3LYP calculations. Previously, we found that the orbital interactions between a tube and a multimeric terthiophene slightly perturb the frontier orbital splittings. To have a baseline knowledge of electronic transitions derived from multimeric terthiophenes contained in a nanotube (n × 3T@(m,m) structure), we evaluated those of multimeric terthiophenes taken from n × 3T@(m,m) structures. We focused on electronic transitions with oscillatory strength f values greater than 0.01. The calculated excitation energies Ex are displayed in Figure 8 as a function of the number of terthiophenes. Detailed information on the electronic transitions (assignment of a certain transition, as well as its Ex and f values) is tabulated in Tables 2−5. According to the TD-DFT calculations, an electronic transition of a single terthiophene taken from 1 × 3T@(m,m) occurs from the HOMO to the LUMO independent of m. The HOMO → LUMO transition, whose excitation energy Ex is 2.96 eV, has a significant oscillatory strength (f = 0.88). When terthiophene chains are aggregated, as in Figure 2, an electron is excited from an orbital built from single-chain HOMOs to an orbital built from single-chain LUMOs. By the interchain interactions in multimeric terthiophenes, the energy levels of the HOMO- and LUMO-built orbitals broaden, 5517


0.099 0.076 0.021 0.069 1.348 0.149 0.021 0.056 0.026 0.026 0.057 1.941 0.026 0.042 2.087

fc 216 214 214 214 213 212 214 214 214 215 214 214 214 214 214

→ → → → → → → → → → → → → → →

217(0.67), 216 → 218(−0.13) 218(−0.14), 216 → 217(0.11), 216 → 218(0.66) 217(0.61), 215 → 218(−0.30), 215 → 219(−0.12), 216 → 218(0.10) 218(−0.13), 214 → 219(0.67) 217(−0.18), 214 → 217(0.13), 214 → 218(−0.40), 214 → 219(−0.17), 215 → 219(0.44), 216 → 217(−0.13) 217(0.24), 213 → 217(0.61), 214 → 218(−0.11), 215 → 219(0.14) 217(0.15), 215 → 217(−0.27), 216 → 217(0.62) 217(0.16), 215 → 217(0.61), 215 → 218(−0.10), 215 → 219(−0.13), 216 → 217(0.20), 216 → 219(0.13) 217(0.65), 214 → 219(−0.10), 216 → 217(−0.18) 218(0.62), 215 → 219(−0.17), 216 → 219(0.24) 218(0.57), 214 → 219(0.26), 215 → 219(0.10), 216 → 218(−0.24), 216 → 219(0.17) 218(−0.20), 214 → 219(−0.46), 215 → 217(−0.16), 215 → 218(−0.24), 215 → 219(−0.20), 216 → 217(−0.19), 216 → 218(0.12), 216 → 219(0.24) 217(0.50), 215 → 217(−0.38), 215 → 219(0.10), 216 → 217(0.19), 216 → 219(0.15) 217(0.46), 214 → 218(−0.19), 215 → 217(0.42), 216 → 217(−0.22) 218(0.45), 215 → 217(0.24), 215 → 219(0.26), 216 → 217(−0.14), 216 → 219(0.38)

electronic transitiond

a (m,m): Nanotube chirality. bEx: Excitation energy is given in electronvolts and the value in parentheses is in nanometers. cf: Oscillator strength dElectronic transition: Assignment of the electronic transition from an occupied orbital to an unoccupied orbital. Labels of the frontier orbitals: HOMO−2, 214; HOMO−1, 215; HOMO, 216; LUMO, 217; LUMO+1, 218; LUMO+2, 219. Values in parentheses indicate a CI coefficient in a certain excited configuration, obtained from TD-DFT calculations. e3 × 3T@(10,10): In the structure, the three terthiophenes are perpendicular. The structure corresponds to 3 × 3T@(10,10) (I) in Figure 2. f3 × 3T@(10,10): In the structure, the three terthiophenes take a triangular arrangement. The structure corresponds to 3 × 3T@(10,10) (II) in Figure 2.

(10,10)f

(10,10)e

(520.7) (461.3) (448.5) (372.9) (369.7) (365.5) (470.1) (462.2) (460.3) (433.6) (427.2) (393.0) (460.0) (459.2) (398.2)

(8,8)

2.38 2.68 2.76 3.32 3.35 3.39 2.64 2.68 2.69 2.86 2.90 3.15 2.69 2.70 3.11

Exb

(m,m)a

Table 4. Excitation Energies (Ex) and Oscillator Strengths ( f) of the Electronic Transitions of the Trimeric Terthiophenes Taken from the B97D-Optimized 3 × 3T@(m,m), Obtained from TD-DFT B3LYP Calculations

The Journal of Physical Chemistry C Article

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compared to the single-chain case. Because of the broadening of the energy levels, electronic transitions with higher and lower excitation energies occur in contained multimeric terthiophenes. As expected, we found from Figure 8 that the range of calculated Ex values widens by the aggregation of terthiophene chains within a nanotube, compared with the single-chain case. In the dimer (trimer) taken from the n × 3T@(8,8) structures, the calculated Ex values range from 2.50 (2.38) to 3.20 (3.39) eV in Figure 8a. Similar widening can be observed in the Ex values of the multimeric terthiophenes taken from the n × 3T@(10,10) structures (Figure 8b). The Ex ranges in the (10,10) tube are less significant than those in the (8,8) case because interchain interactions in the n × 3T@(10,10) are weaker than those in the n × 3T@(8,8) cases (Figure 7). We now turn to electronic transitions with the maximum f value (the strongest transition), whose Ex values are circled in red in Figure 8. With respect to the strongest absorption, the excitation energy enhances with an increase in the number of contained terthiophenes. For example, the excitation energy was calculated to be 3.35 eV in the trimeric terthiophene taken from the 3 × 3T@(8,8) case, which was larger than the monomer case (2.96 eV). The increment of the Ex value is significant relative to the 3 × 3T@(10,10) case (0.19 eV). The difference is understandable because interchain interactions between terthiophenes within a smaller (8,8) tube are stronger than those within the (10,10) tube. Thus, DFT calculations found that encapsulation of multimeric terthiophenes in a nanotube influences their electronic transitions by modulating the interchain interactions.

a (m,m): Nanotube chirality. bEx: Excitation energy is given in electronvolts and the value in parentheses is in nanometers. cf: Oscillator strength. dElectronic transition: Assignment of the electronic transition from an occupied orbital to an unoccupied orbital. Labels of the frontier orbitals: HOMO−3, 285; HOMO−2, 286; HOMO−1, 287; HOMO, 288; LUMO, 289; LUMO+1, 290; LUMO+2, 291; LUMO+3, 292. Values in parentheses indicate a CI coefficient in a certain excited configuration, obtained from the TD-DFT calculations.

292(0.11), 287 → 289(−0.12), 288 → 289(0.66) 289(0.68), 288 → 289(0.11) 290(0.39), 285 → 292(−0.12), 286 → 291(−0.32), 287 → 290(0.29), 287 → 292(−0.31), 288 → 291(0.13) 290(0.16), 285 → 291(0.63), 286 → 292(0.13), 288 → 290(0.16) 290(0.48), 285 → 291(−0.19), 285 → 292(0.11), 286 → 291(0.18), 287 → 290(−0.10), 287 → 292(0.35), 288 → 291(0.14) 290(−0.10), 285 → 292(−0.35), 286 → 291(−0.26), 286 → 292(0.12), 287 → 290(0.21), 287 → 292(0.46) 292(0.56), 286 → 291(−0.24), 287 → 290(0.22), 287 → 292(0.14), 288 → 289(−0.17) (473.2) (470.4) (417.4) (412.8) (412.1) (406.2) (376.9) 2.62 2.64 2.97 3.00 3.00 3.05 3.29 (10,10)

0.123 0.011 0.071 0.011 0.067 0.193 2.015

285 287 285 285 285 285 285

→ → → → → → →

electronic transitiond fc Exb (m,m)a

Table 5. Excitation Energies (Ex) and Oscillator Strengths ( f) of the Electronic Transitions of Tetrameric Terthiophenes Taken from B97D-Optimized 4 × 3T@(m,m), Obtained from the TD-DFT B3LYP Calculations


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CONCLUSIONS From density functional theory (DFT) calculations including dispersion corrections (B97D functional), we found a variety of arrangements of methyl-terminated terthiophenes (3T) within an armchair (m,m) carbon nanotube, abbreviated by n × 3T@(m,m). The arrangements of the inner multimeric terthiophene chains depend on the nanotube diameter and the number of chains (n). A key factor in determining how terthiophenes are arranged within a nanotube is the long-range attractive forces derived from CH−π and π−π interactions between the guests and host. Because of the attractive longrange interactions, the inner terthiophenes tend to sit near the wall of the nanotubes. Because of the various arrangements in n × 3T@(m,m), the inner terthiophene chains interact differently. The interchain interactions in n × 3T@(m,m) split orbitals of multimeric terthiophenes, which are constructed from single-chain frontier orbitals (HOMO or LUMO), to broaden their energy levels. Through the interchain interactions, the frontier orbital splittings are influenced by the encapsulation in a nanotube. The multimeric terthiophenes within smaller tubes have frontier orbital splittings that are more significant than the larger tube cases. Accordingly, nanotube confinements have a strong impact on determining the energy levels of the frontier orbitals derived from the inner multimeric terthiophenes. Because of the importance of the confinement effects to the orbital energies, the electronic transitions of multimeric terthiophenes are also perturbed by encapsulation in a nanotube. On the basis of time-dependent (TD)-DFT B3LYP calculations of multimeric terthiophenes taken from B97D-optimized n × 3T@(m,m) structures, a specific electronic transition occurs from HOMO-built orbitals to LUMO-built orbitals. Because of the broadening of their 5519



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(5) Nishide, D.; Dohi, H.; Wakabayashi, T.; Nishibori, E.; Aoyagi, S.; Ishida, M.; Kikuchi, S.; Kitaura, R.; Sugai, T.; Sakata, M.; Shinohara, H. Single-Wall Carbon Nanotubes Encaging Linear Chain C10H2 Polyyne Molecules Inside. Chem. Phys. Lett. 2006, 428, 356−360. (6) Nishide, D.; Wakabayashi, T.; Sugai, T.; Kitaura, R.; Kataura, H.; Achiba, Y.; Shinohara, H. Raman Spectroscopy of Size-Selected Linear Polyyne Molecules C2nH2 (n = 4−6) Encapsulated in Single-Wall Carbon Nanotubes. J. Phys. Chem. C 2007, 111, 5178−5183. (7) Fujita, Y.; Bandow, S.; Iijima, S. Formation of Small-diameter Carbon Nanotubes from PTCDA Arranged Inside the Single-Wall Carbon Nanotubes. Chem. Phys. Lett. 2005, 413, 410−414. (8) Yanagi, Y.; Miyata, Y.; Kataura, H. Highly Stabilized β-Carotene in Carbon Nanotubes. Adv. Mater. 2006, 18, 437−441. (9) Loi, M. A.; Gao, J.; Cordella, F.; Blondeau, P.; Menna, E.; Bártová, B.; Hébert, C.; Lazar, S.; Botton, G. A.; Milko, M.; AmbroschDraxl, C. Encapsulation of Conjugated Oligomers in Single-Walled Carbon Nanotubes: Towards Nanohybrids for Photonic Devices. Adv. Mater. 2010, 22, 1635−1639. (10) Gao, J.; Blondeau, P.; Salice, P.; Menna, E.; Bártová, B.; Hébert, C.; Leschner, J.; Kaiser, U.; Milko, M.; Ambrosch-Draxl, C.; Loi, M. A. Electronic Interactions between “Pea” and “Pod”: The Case of Oligothiophenes Encapsulated in Carbon Nanotubes. Small 2011, 7, 1807−1815. (11) Alvarez, L.; Almadori, Y.; Arenal, R.; Babaa, R.; Michel, T.; Le Parc, R.; Bantignies, J.-L.; Jousselme, B.; Palacin, S.; Hermet, P.; Sauvajol, J.-L. Charge Transfer Evidence between Carbon Nanotubes and Encapsulated Conjugated Oligomers. J. Phys. Chem. C 2011, 115, 11898−11905. (12) Kalbác,̌ M.; Kavan, L.; Gorantla, S.; Gemming, T.; Dunsch, L. Sexithiophene Encapsulated in a Single-Walled Carbon Nanotube: An In Situ Raman Spectroelectrochemical Study of a Peapod Structure. Chem.Eur. J. 2010, 16, 11753−11759. (13) Li, L.-J.; Khlobystov, A. N.; Wiltshire, J. G.; Briggs, G. A. D.; Nicholas, R. J. Diameter-selective Encapsulation of Metallocenes in Single-Walled Carbon Nanotubes. Nat. Mater. 2005, 4, 481−485. (14) Cambré, S.; Wenseleers, W.; Goovaerts, E. Charge Transfer Evidence between Carbon Nanotubes and Encapsulated Conjugated Oligomers. J. Phys. Chem. C 2009, 113, 13505−13514. (15) Brédas, J. L.; Street, G. B. Polarons, Bipolarons, and Solitons in Conducting Polymers. Acc. Chem. Res. 1985, 18, 309−315. (16) Swager, T. M. The Molecular Wire Approach to Sensory Signal Amplification. Acc. Chem. Res. 1998, 31, 201−207. (17) McQuade, D. T.; Pullen, A. E.; Swager, T. M. Conjugated Polymer-Based Chemical Sensors. Chem. Rev. 2000, 100, 2537−2574. (18) Kertesz, M.; Choi, C. H.; Yang, S. Conjugated Polymers and Aromaticity. Chem. Rev. 2005, 105, 3448−3481. (19) Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. v. R. Nucleus-Independent Chemical Shifts (NICS) as an Aromaticity Criterion. Chem. Rev. 2005, 105, 3842−3888. (20) Murphy, A. R.; Frechet, J. M. J. Organic Semiconducting Oligomers for Use in Thin Film Transistors. Chem. Rev. 2007, 107, 1066−1096. (21) Wang, C.; Dong, H.; Hu, W.; Liu, Y.; Zhu, D. Semiconducting π-Conjugated Systems in Field-Effect Transistors: A Material Odyssey of Organic Electronics. Chem. Rev. 2012, 112, 2208−2267. (22) McIntosh, G. C.; Tománek, D.; Park, Y. W. Energetics and Electronic Structure of a Polyacetylene Chain Contained in a Carbon Nanotube. Phys. Rev. B 2003, 67 (125419), 1−5. (23) Orellana, W.; Vásquez, S. O. Endohedral Terthiophene in Zigzag Carbon Nanotubes: Density Functional Calculations. Phys. Rev. B 2006, 74 (125419), 1−5. (24) Horn, P.; Kertesz, M. Conformational Preferences of βCarotene in the Confined Spaces inside Carbon Nanotubes. J. Phys. Chem. C 2010, 114, 12139−12144. (25) Milko, M.; Ambrosch-Draxl, C. Energetics and Structure of Organic Molecules Embedded in Single-Wall Carbon Nanotubes from First Principles: The Example of Benzene. Phys. Rev. B 2011, 84 (085437), 1−7.

frontier orbital energies by the aggregation of terthiophenes within a nanotube, the terthiophene-chain aggregates have a widened range of excitation energies Ex compared to the singlechain case. With respect to the strongest transition of multimeric terthiophenes, the Ex value was substantially enhanced by confinement in a nanotube. The Ex enhancement of multimeric terthiophenes within a smaller nanotube is more significant than within a larger nanotube. Because the nanotube confinements determine the arrangement of the inner multimeric terthiophene chains, concomitantly with their interchain interactions, one can utilize a restricted nanotube space to modulate the electronic and absorption properties of multimeric terthiophenes.

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ASSOCIATED CONTENT

S Supporting Information *

Optimized geometries for 1 × 3T@(8,8) and 1 × 3T@(10,10) (section S1); basis-set dependence of orbital features built from single terthiophene surrounded by the (10,10) nanotube (section S2); the HOMO−LUMO gaps of thiophene oligomers with different chain lengths (section S3); the reliability of B3LYP single-point calculations of the B97D optimized sexithiophene in terms of evaluating the HOMO−LUMO gap (section S4); arrangements of π−π multimers being restricted by inner space of a tube (section S5); roles of the relative orientation of terthiophene dimers in the cofacial motif in its energetics and optimal interchain separation (section S6); roles of the relative orientation of terthiophene dimers in the T motif in its energetics and optimal interchain separation (section S7); Walsh diagram of longitudinally shifted terthiophene dimers (section S8); Features of the orbitals of multimeric terthiophenes surrounded by the (8,8) tube (n × 3T@(8,8)) (section S9); features of the orbitals of multimeric terthiophenes surrounded by the (10,10) tube (n × 3T@(10,10)) (section S10); full citation for ref 29 (section S11). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The project was partially supported by a Grant-in-Aid for Young Scientists (B) from the Japan Society for the Promotion of Science (JSPS) (T.Y. at the Kyoto Institute of Technology, 22710088) and a Grant-in-Aid for Scientific Research (C) from JSPS (T.Y. at the Kyoto Institute of Technology, 23560934).

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REFERENCES

(1) Iijima, S. Helical Microtubules of Graphitic Carbon. Nature 1991, 354, 56−58. (2) Iijima, S.; Ichihashi, T. Single-shell Carbon Nanotubes of 1-nm Diameter. Nature 1993, 363, 603−605. (3) Khobystov, A. N.; Britz, D. A.; Briggs, G. A. D. Molecules in Carbon Nanotubes. Acc. Chem. Res. 2005, 38, 901−909. (4) Takenobu, T.; Takano, T.; Shiraishi, M.; Murakami, Y.; Ata, M.; Kataura, H.; Achiba, Y.; Iwasa, Y. Stable and Controlled Amphoteric Doping by Encapsulation of Organic Molecules Inside Carbon Nanotubes. Nat. Mater. 2003, 2, 683−688. 5520



Article

(26) Kuwahara, R.; Kudo, Y.; Morisato, T.; Ohno, K. Encapsulation of Carbon Chain Molecules in Single-Walled Carbon Nanotubes. J. Phys. Chem. A 2011, 115, 5147−5156. (27) Yamashita, H.; Yumura, T. The Role of Weak Bonding in Determining the Structure of Thiophene Oligomers inside Carbon Nanotubes. J. Phys. Chem. C 2012, 116, 9681−9690. (28) García, G.; Ciofini, I.; Fernández-Gómez, M.; Adamo, C. Confinement Effects on UV−Visible Absorption Spectra: β-Carotene Inside Carbon Nanotube as a Test Case. J. Phys. Chem. Lett. 2013, 4, 1239−1243. (29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al. Gaussian 09, Gaussian, Inc.: Wallingford, CT, 2009. (30) Yumura, T.; Hirahara, K.; Bandow, S.; Yoshizawa, K.; Iijima, S. A Theoretical Study on the Geometrical Features of Finite-length Carbon Nanotubes Capped with Fullerene Hemisphere. Chem. Phys. Lett. 2004, 386, 38−43. (31) Yumura, T.; Bandow, S.; Yoshizawa, K.; Iijima, S. The Role of Fullerene Hemispheres in Determining Structural Features of FiniteLength Carbon Nanotubes. J. Phys. Chem. B 2004, 108, 11426−11434. (32) Yumura, T.; Nozaki, D.; Bandow, S.; Yoshizawa, K.; Iijima, S. End-Cap Effects on Vibrational Structures of Finite-length Carbon Nanotubes. J. Am. Chem. Soc. 2005, 127, 11769−11776. (33) Yumura, T.; Kertesz, M.; Iijima, S. Local Modifications of Single-Wall Carbon Nanotubes Induced by Bond Formation with Encapsulated Fullerenes. J. Phys. Chem. B 2007, 111, 1099−1109. (34) Yumura, T.; Kertesz, M.; Iijima, S. Confinement Effects on Sitepreferences for Cycloadditions into Carbon Nanotubes. Chem. Phys. Lett. 2007, 444, 155−160. (35) Yumura, T.; Kertesz, M. Roles of Conformational Restrictions of a Bismalonate in the Interactions with a Carbon Nanotube. J. Phys. Chem. C 2009, 113, 14184−14194. (36) Yumura, T. Chemically Reactive Species Remain Alive inside Carbon Nanotubes: A Density Functional Theory Study. Phys. Chem. Chem. Phys. 2011, 13, 337−346. (37) Grimme, S. Semiempirical GGA-type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (38) Grimme, S. Semiempirical Hybrid Density Functional with Perturbative Second-Order Correlation. J. Chem. Phys. 2006, 124 (034108), 1−16. (39) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic Behavior. Phys. Rev. A 1988, 38, 3098−3100. (40) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (41) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623−11627. (42) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (43) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin-Density Calculations: A Critical Analysis. Can. J. Phys. 1980, 58, 1200−1211. (44) Vázquez-Mayagoitia, A.; David Sherril, C.; Aprá, E.; Sumpter, B. G. An Assessment of Density Functional Methods for Potential Energy Curves of Nonbonded Interactions: The XYG3 and B97-D Approximations. J. Chem. Theory Comput. 2010, 6, 727−734. (45) Hehre, W. J.; Ditchfield, R.; Pople, J. A. Self-consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. J. Chem. Phys. 1972, 56, 2257−2261. (46) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Selfconsistent Molecular Orbital Methods. XX. A Basis Set for Correlated Wave Functions. J. Chem. Phys. 1980, 72, 650−654.

(47) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. Efficient diffuse function-augmented basis sets for anion calculations. III. The 3-21+G basis set for first-row elements, Li−F. J. Comput. Chem. 1983, 4, 294−301. (48) Chung, T. C.; Kaufman, J. H.; Heeger, A. J.; Wuld, F. Charge Storage in Doped Poly(thiophene): Optical and Electrochemical Studies. Phys. Rev. B 1984, 30, 702−710. (49) Tachibana, M.; Tanaka, S.; Yamashita, Y.; Yoshizawa, K. Small Band-Gap Polymers Involving Tricyclic Nonclassical Thiophene as a Building Block. J. Phys. Chem. B 2002, 106, 3549−3556. (50) Yang, S.; Olishevski, P.; Kertesz, M. Bandgap Calculations for Conjugated Polymers. Synth. Met. 2004, 141, 171−177. (51) To check the reliability of B3LYP single-point calculations of a B97D optimized terthiophene-oligomer in terms of evaluating the HOMO−LUMO gap, let us discuss here sexithiophene. B3LYP singlepoint calculations of the B97D-optimized sexithiophene yielded the HOMO−LUMO gap of 2.45 eV. The value is 0.08 eV smaller than the B3LYP gap (2.53 eV). The error comes from slightly different degree of bond length alternations of oligomers, as shown in Figure S4 of Supporting Information. However, the error is not significant; thus, we adopt this procedure to discuss orbital energies of terthiophene multimers surrounded by a nanotube. (52) Barbarella, G.; Zambianchi, M.; Bongini, A.; Antolini, L. Crystal Structure of 4,4′,3″,4‴-Tetramethyl 2,2′:5′,2″:5″,2‴-Tetrathiophene: A Comparison with the Conformation in Solution. Adv. Mater. 1992, 4, 282−285. (53) Garnier, F.; Yassar, A.; Hajlaoui, R.; Horowitz, G.; Deloffre, F.; Servet, B.; Ries, S.; Alnot, R. Molecular Engineering of Organic Semiconductors: Design of Self-Assembly Properties in Conjugated Thiophene Oligomers. J. Am. Chem. Soc. 1993, 115, 8716−8721. (54) Horowitz, G.; Bachet, B.; Yassar, A.; Lang, P.; Demanze, F.; Fave, J.-L.; Garnier, F. Growth and Characterization of Sexithiophene Single Crystals. Chem. Mater. 1995, 7, 1337−1341. (55) Fichou, D.; Bachet, B.; Demanze, F.; Billy, I.; Horowitz, G.; Garnier, F. Growth and Structural Characterization of the Quasi−2D Single Crystal of α-Octithiophene. Adv. Mater. 1996, 8, 500−504. (56) Siegrist, T.; Kloc, C.; Laudise, R. A.; Katz, H. E.; Haddon, R. C. Crystal Growth, Structure, and Electronic Band Structure of α-4T Polymorphs. Adv. Mater. 1998, 10, 379−382. (57) Barbarella, G.; Zambianchi, M.; Antolini, L.; Ostoja, P.; Maccangani, P.; Bongini, A.; Marseglia, E. A.; Tedesco, E.; Gigli, G.; Cingolani, R. Solid-State Conformation, Molecular Packing, and Electrical and Optical Properties of Processable β-Methylated Sexithiophenes. J. Am. Chem. Soc. 1999, 121, 8920−8926. (58) Katz, H. E.; Bao, Z. The Physical Chemistry of Organic FieldEffect Transistors. J. Phys. Chem. B 2000, 104, 671−678. (59) Hong, X. M.; Tyson, J. C.; Collard, D. M. Controlling the Macromolecular Architecture of Poly(3-alkylthiophene)s by Alternating Alkyl and Fluoroalkyl Substituents. Macromolecules 2000, 33, 3502−3504. (60) Pappenfus, T. M.; Chesterfield, R. J.; Frisbie, C. D.; Mann, K. R.; Casado, J.; Raff, J. D.; Miller, L. L. A π-Stacking TerthiopheneBased Quinodimethane Is an n-Channel Conductor in a Thin Film Transistor. J. Am. Chem. Soc. 2002, 124, 4184−4185. (61) Pappenfus, T. M.; Raff, J. D.; Hukkanen, E. J.; Burney, J. R.; Casado, J.; Drew, S. W.; Miller, L. L.; Mann, K. R. Dinitro and Quinodimethane Derivatives of Terthiophene That Can Be Both Oxidized and Reduced. Crystal Structures, Spectra, and a Method for Analyzing Quinoid Contributions to Structure. J. Org. Chem. 2002, 67, 6015−6024. (62) Melucci, M.; Gazzano, M.; Barbarella, G.; Cavallini, M.; Biscarini, F.; Maccagnani, P.; Ostoja, P. Multiscale Self-Organization of the Organic Semiconductor α-Quinquethiophene. J. Am. Chem. Soc. 2003, 125, 10266−10274. (63) Facchetti, A.; Mushrush, M.; Katz, H. E.; Marks, T. J. n-Type Building Blocks for Organic Electronics: A Homologous Family of Fluorocarbon-Substituted Thiophene Oligomers with High Carrier Mobility. Adv. Mater. 2003, 15, 33−38. 5521



Article

(64) Facchetti, A.; Yoon, M.-H.; Stern, C. L.; Hutchison, G. R.; Ratnerm, M. A.; Marks, T. J. Building Blocks for N-Type Molecular and Polymeric Electronics. Perfluoroalkyl- versus Alkyl-Functionalized Oligothiophenes (nTs; n = 2−6). Systematic Synthesis, Spectroscopy, Electrochemistry, and Solid-State Organization. J. Am. Chem. Soc. 2004, 126, 13480−13501. (65) Kiriy, N.; Bocharova, V.; Kiriy, A.; Stamm, M.; Krebs, F. C.; Adler, H.-J. Designing Thiophene-Based Azomethine Oligomers with Tailored Properties: Self-assembly and Charge Carrier Mobility. Chem. Mater. 2004, 16, 4765−4771. (66) Kiriy, N.; Kiriy, A.; Bocharova, V.; Stamm, M.; Richter, S.; Plötner, M.; Fischer, W.-J.; Krebs, F. C.; Senkovska, I.; Adler, H.-J. Conformation, Molecular Packing, and Field Effect Mobility of Regioregular β,β′-Dihexylsexithiophene. Chem. Mater. 2004, 16, 4757−4764. (67) Hotta, S.; Goto, M.; Azumi, R.; Inoue, M.; Ichikawa, M.; Taniguchi, Y. Crystal Structures of Thiophene/Phenylene CoOligomers with Different Molecular Shapes. Chem. Mater. 2004, 16, 237−241. (68) Letizia, J. A.; Facchetti, A.; Stern, C. L.; Ratner, M. A.; Marks, T. J. High Electron Mobility in Solution-Cast and Vapor-Deposited Phenacyl−Quaterthiophene-Based Field-Effect Transistors: Toward N-Type Polythiophenes. J. Am. Chem. Soc. 2005, 127, 13476−13477. (69) Chisaka, J.; Lu, M.; Nagamatsu, S.; Chikamatsu, M.; Yoshida, Y.; Goto, M.; Azumi, R.; Yamashita, M.; Yase, K. Structure and Electrical Properties of Unsubstituted Oligothiophenes End-Capped at the βPosition. Chem. Mater. 2007, 19, 2694−2701. (70) Anthony, J. E.; Brooks, J. S.; Eaton, D. L.; Parkin, S. R. Functionalized Pentacene: Improved Electronic Properties from Control of Solid-State Order. J. Am. Chem. Soc. 2001, 123, 9482−9483. (71) Ando, S.; Murakami, R.; Nishida, J.; Tada, H.; Inoue, Y.; Tokito, S.; Yamashita, Y. n-Type Organic Field-Effect Transistors with Very High Electron Mobility Based on Thiazole Oligomers with Trifluoromethylphenyl Groups. J. Am. Chem. Soc. 2005, 127, 14996−14997. (72) Yoon, M.-H.; Facchetti, A.; Stern, C. E.; Marks, T. J. Fluorocarbon-Modified Organic Semiconductors: Molecular Architecture, Electronic, and Crystal Structure Tuning of Arene- versus Fluoroarene-Thiophene Oligomer Thin-Film Properties. J. Am. Chem. Soc. 2006, 128, 5792−5801. (73) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553−566. (74) Yumura, T.; Kertesz, M. Cooperative Behaviors in Carbene Additions through Local Modifications of Nanotube Surfaces. Chem. Mater. 2007, 19, 1028−1034. (75) The shortest carbon contact is 2.67 Å for the 3 × 3T@(8,8) structure and 3.06 Å for the 4 × 3T@(10,10) structure. See Figure 2. (76) Cornil, J.; Belionne, D.; Calbret, J.-P.; Brédas, J. L. Interchain Interactions in Organic π-Conjugated Materials: Impact on Electronic Structure, Optical Response, and Charge Transport. Adv. Mater. 2001, 13, 1053−1067. (77) Brédas, J. L.; Calbert, J. P.; da Silva Filho, D. A.; Cornil, J. A. Organic Semiconductors: A Theoretical Characterization of the Basic Parameters Governing Charge Transport. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 5804−5809. (78) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. Hopping Transport in Conductive Heterocyclic Oligomers: Reorganization Energies and Substituent Effects. J. Am. Chem. Soc. 2005, 127, 2339− 2350. (79) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. Intermolecular Charge Transfer between Heterocyclic Oligomers. Effects of Heteroatom and Molecular Packing on Hopping Transport in Organic Semiconductors. J. Am. Chem. Soc. 2005, 127, 16866−16881. (80) Hutchison, G. R.; Ratner, M. A.; Marks, T. J. Electronic Structure and Band Gaps in Cationic Heterocyclic Oligomers. Multidimensional Analysis of the Interplay of Heteroatoms, Substituents, Molecular Length, and Charge on Redox and Transparency Characteristics. J. Phys. Chem. B 2005, 109, 3126−3138.

(81) Koh, S. E.; Risko, C.; da Silva Filho, D. A.; Kwon, O.; Facchetti, A.; Brédas, J. L.; Marks, T. J.; Ratner, M. A. Modeling Electron and Hole Transport in Fluoroarene-Oligothiopene Semiconductors: Investigation of Geometric and Electronic Structure Properties. Adv. Funct. Mater. 2008, 18, 332−340. (82) To construct the motifs, we optimized a single terthiophene, and then the two optimized terthiophenes were arranged as in Figure 3I. When the interchain spacings (zis) in the terthiophene dimers were changed, each terthiophene structure was fixed to its optimized geometry. The definition of the interchain spacing can be observed in Figure 3. (83) The optimal longitudinally shifted terthiophene dimer in the cofacial motif has y(C) = 1.5 Å, and the laterally shifted dimer has x(C) = 1.5 Å. A detailed discussion can be seen in Figure S6 of Supporting Information. (84) The optimal longitudinally shifted terthiophene dimer in the T motif has y(T) = 0.0 Å, and the laterally shifted dimer has x(T) = 1.5 Å. A detailed discussion can be seen in Figure S7 of Supporting Information.

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Modulating the Electronic Properties of Multimeric Thiophene

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