Local Modifications of Single-Wall Carbon Nanotubes Induced by

Insertion of C50 into single-walled carbon nanotubes: Selectivity in interwall spacing and C50 isomers. Zhen Zhou , Jijun Zhao , Paul von Ragué Schle...
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J. Phys. Chem. B 2007, 111, 1099-1109

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Local Modifications of Single-Wall Carbon Nanotubes Induced by Bond Formation with Encapsulated Fullerenes Takashi Yumura,*,†,‡ Miklos Kertesz,*,† and Sumio Iijima‡ Department of Chemistry, Georgetown UniVersity, 37th and O Streets, NW, Washington, DC 20057, and Department of Materials Science and Engineering, Meijo UniVersity, Tenpaku-ku, Nagoya 468-8502, Japan ReceiVed: October 3, 2006; In Final Form: NoVember 14, 2006

Defected fullerenes in nanopeapods form bonds with the encapsulating single-walled carbon nanotubes when irradiated by an electron beam leading to changes in the guest (fullerene) and the host (nanotube). Intrinsic reaction coordinate (IRC) analysis based on B3LYP hybrid density functional theory shows that a C1-C59 defect with a single protruding C atom is initially formed from the C60(Ih) cage. The high activation energy for this step (8.37 eV (193.0 kcal/mol)), being assumed to be accessible during irradiation, is lower than that of the Stone-Wales rearrangement on the sp2 network. The binding of the defected fullerene to the nanotube is preferential, orthogonal bonds relative to the tube axis being slightly preferred. Because of the covalent bonds formed between the guest and host, the carbon network on the nanotube is locally perturbed in the vicinity of the binding site. As a result of the new bonds, bisnorcaradiene-like as well as quinonoid-like patterns appear near the binding site. These results are interpreted using orbital interaction and Clar diagram arguments. The changes in the bonding pattern on the nanotube should be significant in further functionalization of carbon nanotubes.

Introduction Single-wall carbon nanotubes (SWNTs) are graphitic cylinders with diameters on the nanometer scale.1,2 Because of their high aspect ratio, the cylinder can be viewed as a quasi-onedimensional system.3 Their restricted inner spaces can be utilized as “nanocontainers” for aligning molecules in one dimension, enabling novel chemistry. For example, various fullerenes including C60 can be encapsulated within SWNTs.4,5 In these guest-host materials called nanopeapods, the inner guest molecules are affected by the SWNT containers.6 However, the couplings between a SWNT and C60 molecules are too weak to change significantly the properties of a SWNT and encapsulated molecules, because their separations are close to the van der Waals distance of 3.35 Å. Recent high-resolution transmission electron microscopy (HRTEM) observations of nanopeapods with inner fullerenes or metallofullerenes molecules7,8 suggested that electron-beam irradiation9 of nanpeapods led to the formation of a vacancytype defect in the fullerene cages, making the fullerenes into highly reactive defected fullerenes.7 According to the recent TEM observations7,8 a coordinatively unsaturated carbon atom was proposed to be generated during the defect formation of the fullerene cages inside a SWNT.7,8 These behaviors were also investigated by density functional theory (DFT) calculations.8,10 Moreover ref 7 suggested that the unsaturated C atom was trapped at an interstitial site between the cages and the SWNT. The trapping of unsaturated carbon atoms on the inner SWNT surface in a restricted environment offers opportunities for novel chemistry, because direct couplings between the SWNT and defected fullerenes can significantly modify the properties of both the guest and the SWNT host. * To whom correspondence should be addressed. E-mail: yumura@ ccmfs.meijo-u.ac.jp (T.Y.); [email protected] (M.K.). † Georgetown University. ‡ Meijo University.

The modifications of SWNT surfaces are quite important in terms of functionalizations of SWNTs, because seamless surfaces are difficult to functionalize.11 If SWNT structures are modified substantially, adsorbates can bind preferentially in a perturbed region to form specific addition patterns. Thus, nanopeapods should be prominent candidates for constructing perturbed SWNTs from the inside out. To make some realistic progress in this direction, it is essential to investigate how defected inner fullerenes perturb SWNTs. However, the specifics of the bond formation between a SWNT and a defected fullerene remained unexplored up to now. To elucidate how the SWNT structure is modified by interactions between the encapsulated defected fullerene and the SWNT, we discuss by means of density functional theory (DFT) calculations how a defected fullerene (C60) with a C1-C59 topology as a guest interacts with the (10,10) SWNT host, which is the smallest diameter SWNT that can encapsulate this fullerene. There are two issues in this study: One is the reaction mechanism for the conversion of the C60 cage into the C1-C59 defected fullerene. Next, we consider the interactions between the defected C1-C59 and the inner surface of the (10,10) SWNT and how the nanotube is changing as a consequence of the bond formation between the guest and host. Method of Calculation We carried out quantum chemical calculations on the basis of one of the most successful hybrid Hartree-Fock/density functional theory methods using the Gaussian 03 program package.12 The B3LYP method13,14 consists of the Slater exchange, the Hartree-Fock exchange, the exchange functional of Becke,13a the correlation functional of Lee, Yang, and Parr (LYP),14 and the correlation functional of Vosko, Wilk, and Nusair (VWN).15 According to previous papers,16-23 B3LYP calculations can yield reliable insights into the properties of carbon compounds and nanocarbon materials. In this paper, we

10.1021/jp066508r CCC: $37.00 © 2007 American Chemical Society Published on Web 01/12/2007

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Figure 1. Five representative defected C60 cages: Optimized geometries of the local minima of Stone-Wales type, C1-C59 defects, and C2-C58 defects (B3LYP/6-31G*). The main structural difference between the C60(Ih) cage and Stone-Wales type comes from the orientation of the blue C2 unit. During the formations of the C1-C59 and C2-C58 defects, the green C atom protrudes from the cage and then the two purple atoms bind together, resulting in the formation of the red five- or four-membered rings.

will discuss two issues: One is the reaction mechanism for the conversion of the C60 cage into the defected C60 cage with the topology of C1-C59. The other is the bond formations of C1C59 to the inside wall of a (10,10) nanotube. We used the 6-31G* basis set25,26 to obtain local minima and saddle points on potential energy surfaces in search of reaction pathways of the defect formation of the C60 cage. In the analysis of the interactions between the defected C60 cage and a nanotube, we adopt the finite-length nanotube C420H40 as a model of the (10, 10) armchair nanotube. In the model, C atoms at the ends are terminated by H atoms to saturate dangling bonds. A main difference in electronic properties between the finite- and infinite-length nanotubes comes from quantum size effects in the finite-length nanotubes.16b In finite-length nanotubes, the number of states allowed by the quantization increases, as its tube length increases. To the best of our knowledge, the tube length in this finite-length (10,10) nanotubes is larger than any other similar nanotube models using full DFT calculations in the literature.18-24 Since computational resources are limited, we optimized geometries of the defected C60 cage inside the (10,10) nanotube at the B3LYP/3-21G level of theory (4400 contracted basis functions).27 After the B3LYP/3-21G optimizations, we calculated the single-point energy for each optimized geometry using the 6-31G* basis set with the total of 7280 contracted basis functions. Information of optimized geometries can be found in the Supporting Information.

Results and Discussion Defected C60 Structures. Before discussing the defected C60 cage encapsulated inside a single-walled carbon nanotube, we focus on the properties of defected C60 cages. There are many possible topologies of defected C60 molecules as reported previously.23,28-32 Figure 1 shows five representative structures of defected C60 cages: one Stone-Wales-type (SW-type) defect with two adjacent pentagons pairs, two structures with a C1C59 topology, and the other two structures with a C2-C58 topology. The SW-type defect with nearly C2V symmetry is 1.68 eV (38.7 kcal/mol) above the C60(Ih) cage at the B3LYP/6-31G* level of theory, and the C1-C59 and C2-C58 structures are even higher by ∼7.0 eV (∼161.4 kcal/mol) or more. The energy difference between the C60(C2V) and C60(Ih) cages that we obtained is essentially the same as obtained from DFT calculations within the local density approximations by Murry et al.,28 Yi et al.,30 and Heggie et al.31 and within the hybrid DFT method by Bettinger et al.,23 ranging from 1.47 to 1.68 eV (from 33.9 to 38.7 kcal/mol). A slightly larger value of 2.1 eV (48.4 kcal/ mol) was obtained from AM1 calculations by Osawa et al.32 As shown in Figure 1, the SW-type defect, whose structure violates the isolated pentagon rule (IPR), has only threecoordinated C atoms, whereas the C1-C59 structures have one singly coordinated C atom and the C2-C58 structures have two two coordinated C atoms. With respect to the C1-C59 structures, we obtained two optimized structrues; one has a newly formed five-membered ring due to the C atom displacement from its

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J. Phys. Chem. B, Vol. 111, No. 5, 2007 1101 TABLE 1: Energetics of Reaction Intermediates during the Formation of the C60 Defect with Topology of C1-C59(A) Relative to the C60(Ih) Cagea type

B3LYP/ 3-21G

B3LYP/6-31G*// B3LYP/3-21G

B3LYP/ 6-31G*

transition state (TS) C1-C59(A)

8.45 (194.9) 7.16 (165.2)

8.40 (193.7) 7.02 (161.9)

8.37 (193.0) 7.05 (162.6)

a Relative energies in eV, values in kcal/mol are also given in parentheses.

Figure 2. Reaction mechanism for the C1-C59 (A) defect formation (B3LYP/6-31G*). Bond lengths (Å) in the optimized geometries in the singlet spin state are given. During the process where the green C1 atom protrudes from the cage, the purple C2 and C3 atoms bind together, resulting in the formation of the red five-membered ring.

original position (A), and the other has a newly formed fourmembered ring (B). From the viewpoint of energetics, the C1C59 (A) structure with the five-membered ring is 0.17 eV (3.9 kcal/mol) lower than that with the four-membered ring (C1C59 (B)). Because of a migration of the protruding C atom, the C1-C59 structures can convert to the corresponding C2-C58 structures, forming a local defect structure that is similar to a defect in C82.8 Since the singly coordinated protruding C atom in a C1-C59 structure becomes part of a six- or seven-membered ring in both of the C2-C58 structures, the C1-C59 structures should exhibit higher chemical reactivities than the C2-C58 structures. The defect regions of the C1-C59 structures are analogous to the interstitial-vacancy pairs formed in irradiated graphite.33 Thus, we focus on the highly reactive C1-C59(A) species with the five-membered ring as a defected C60 cage in next sections. Conversion of the C60 Cage into the C1-C59 Defect. First we discuss the formation of the C1-C59(A) defect with the fivemembered ring to confirm whether the C1-C59 defect can be formed from the C60(Ih) cage. Optimized geometries of reaction intermediates and a transition state during the reaction are given in Figure 2, where bond lengths are given in Å and energies relative to the C60 cage in the singlet state are given in eV. As shown in Figure 2, the conversion of the C60 cage into the C1C59 defect proceeds via a transition state with a protruding C atom from the C60 cage. According to DFT calculations at the B3LYP/6-31G* level, the defect intermediate in the singlet state is by 0.74 eV (17.1 kcal/mol) more stable relative to the triplet state intermediate, although the transition state in the singlet state is comparable in energy to the triplet state transition state. Thus, we confine our discussion to the defect formation in the singlet state in this paper. Figure 2 shows that the formation of the C1-C59(A) defect requires an activation energy of 8.37 eV (193.0 kcal/mol). In the transition state, two bonds (C1C2 and C3C1) cleave in the C60 cage, and one new bond (C2C3) is formed. At the transition state, the imaginary mode of vibration (210i cm-1) indicates that the C1 atom moves from C60(Ih) to C1-C59(A), as expected. After the transition state, the defected C60 cage is formed, and its relative energy is calculated to be 7.05 eV (162.6 kcal/mol). Table 1 shows relative energies for the transition state and the C1-C59(A) defect at B3LYP/3-21G, B3LYP6-31G*//B3LYP/ 3-21G, and B3LYP/6-31G* levels of theory. According to Table 1, the B3LYP/6-31G* relative energies are similar to those at the more approximate B3LYP6-31G*//B3LYP/3-21G level of theory. In refs 7 and 8, the TEM observations were under electron irradiation at 120 keV. The barrier of 8.37 eV (193.0

kcal/mol) can be easily overcome under these conditions.9 The barrier is smaller than the activation energies for the defect formation in graphite (10.1-10.8 eV (232.9-249.1 kcal/mol))33 and for the “Stone-Wales” rearrangement in graphite (∼10 eV (∼230.6 kcal/mol)).34,35 The reaction pathway for the formation of the C1-C59(A) defect was analyzed in detail using intrinsic reaction coordinate (IRC) calculations. An IRC is traced using a mass-weighted Cartesian coordinate s from the transition state between reactant and product as the steepest descent path.36,37 Figure 3 shows the potential energy surface for the reaction from C60(Ih) (s < 0) to C1-C59(A) (s > 0) via the transition state (s ) 0), together with the concomitant geometrical changes. During the reaction, there are two qualitative changes; one is a displacement of C1 from its original position in the cage, and the other is a formation of a new five-membered ring. As shown in Figure 3a, the potential energy increases considerably by s ) ∼ -6.0. At this point, C1 (indicated by green in Figure 3) is displaced substantially from its original position in the cage. As the C1 atom protrudes from the cage, the C1C3 bond breaks first at around s ) -6.0. Then a neighboring five-membered ring is strained and the C2C4 and C2C5 bonds lengthen significantly. Because of the significant geometrical changes, the sharp energy increase is understandable. The two-coordinated C3 atom, created by cleaving the C1C3 bond, binds to C2 to form a new C2C3 bond at around s ) -4.0. The rearrangement creates a highly strained five-membered ring in which the C2C4 and C2C5 bond lengths are respectively 1.575 and 1.646 Å at s ) -4.0. At this point, however, the C2C3 bond is almost completely formed and the C1 and C2 atoms start to part each other. Then the coordinatively unsaturated C1 atom in the C60 cage gradually protrudes from the cage to form the transition state. Beyond the transition state, the C1C2 and C1C3 bonds split completely and the strains in the five-membered ring are relieved; the C2C4 bond is shortened and the C2C5 bond is lengthened. These relaxations in the five-membered ring correspond to decreases in energy after s ) ∼1.0. The IRC calculations show that the C1-C59(A) defect is formed from the C60(Ih) cage by the protruding of C1 atom without an intermediate. It is interesting to elucidate how the initially formed C1-C59(A) defect interacts with a SWNT and how the interactions modify the SWNT structure. Defected C60 Cage inside SWNT. Here we discuss effects of the highly reactive defected C60, C1-C59(A), on the inside of the (10,10) armchair nanotube on properties of SWNTs with a focus on the formation of the new bonds between the guest and the host. Figure 4 summarizes structural information on the guest-host system of C60 and the finite-length C420H40 segment of the (10,10) nanotube at the B3LYP/3-21G level. Figure 4a shows that the optimized structure of the C60(Ih)@C420H40 nanopeapod, where the defect free C60(Ih) is encapsulated inside the finite-length C420H40 nanotube. Detailed information on the optimized geometries of C420H40 and C60(Ih)@C420H40 is given in Figures S1 and S2 (Supporting

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Figure 3. (a) Potential energy diagram for the C1-C59 (A) defect formation using B3LYP/6-31G* intrinsic reaction coordinate (IRC) calculations. Potential energy surface is given as a function of the reaction coordinate s; the transition state corresponds to s ) 0 (red dot), and the reactant (C60(Ih)) and product (C1-C59(A)) directions correspond to s < 0 and s > 0, respectively. (b) Changes in bond lengths of C1C2, C1C3, and C2C3 bonds in the cage along the IRC. (c) Changes in bond lengths of C2C4, C2C5, C3C6, and C3C7 bonds in the cage along the IRC.

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Figure 4. Optimized geometries of the (a) C60(Ih)@C420H40 nanopeapod and (b-d) three C1-C59(A)@C420H40 nanopeapods (B3LYP/3-21G). (b) C1-C59(A)@C420H40 does not have coupling between the C1-C59 cage and the inner SWNT surface (NOB). The two other C1-C59(A)@C420H40 have couplings where the protruding carbon atom (green) from the cage attaches into the blue CdC bond orthogonal O or slanted S to the axis of the tube, which are given by (c) or (d), respectively. Bond lengths are in Å.

Information). In the C60(Ih)@C420H40 nanopeapod, the shortest spacing between the C60(Ih) cage and the inner C420H40 surface is 3.34 Å, a value close to the van der Waals distance. Figures S1 and S2 show that the CC bond lengths of the SWNT in the C60(Ih)@C420H40 nanopeapod remain nearly unchanged relative to those in the empty C420H40 SWNT. On the SWNT surface, except for the edges, the optimized CC bond lengths range from 1.420 to 1.432 Å, which are very close to those calculated for the corresponding infinite-length nanotube.38 Whether new CC bonds are formed between the C1-C59(A) cage and the SWNT depends on orientation of the protruding C atom of the fullerene inside the SWNT; if the protruding C atom is close to the tube axis, direct coupling between the

TABLE 2: Energetics of C1-C59(A)@C420H40 Nanopeapods NOB, O, and S Relative to the Defect-Free C60(Ih)@C420H40 Nanopeapoda nanopeapod

B3LYP/3-21G

B3LYP/6-31G*// B3LYP/3-21G

C1-C59(A)@C420H40 (NOB) C1-C59(A)@C420H40 (O) C1-C59(A)@C420H40 (S)

7.27 (167.7) 7.00 (161.4) 7.17 (165.3)

7.04 (162.3) 6.91 (159.3) 7.14 (164.7)

a Relative energies in eV, values in kcal/mol are also given in parentheses.

reactive site of the cage and the SWNT is not possible, whereas if the protruding C atom is near the SWNT, new CC bonds can be formed. We obtained three types of optimized geometries

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Figure 5. CC bond lengths (Å) near the binding site in the three C1-C59(A)@C420H40 nanopeapods (B3LYP/3-21G). Red and blue lines indicate C-C bonds whose lengths increase and decrease by at least 0.01 Å, respectively, relative to those in the C60(Ih)@C420H40 nanopeapod. Bold lines on the surface correspond to the binding site. (a)-(c) correspond to the structures shown in Figure 4b-d, respectively. Dotted lines indicate continuation of the nanotubes.

of the C1-C59(A)@C420H40 nanopeapods. One is a defected nanopeapod without coupling between the C1-C59(A) cage and C420H40 SWNT, which is termed as “not-bonded” (NOB) and is shown in Figure 4b, in which the protruding C1 atom points along the tube axis. In the NOB structure, C1 is not sufficiently close to the tube surface to create new bonds. In the other two structures, the C1-C59(A)@C420H40 nanopeapods form new CC bonds between the defected cage and the SWNT (Figure 4c,d). We can distinguish two scenarios, depending on whether the C-C bond on the SWNT (blue), into which the C1 atom of the C1-C59(A) defect (green) binds, is orthogonal (O) or slanted

(S) relative to the tube axis. These two orientations of the attachment are denoted as O (Figure 4c) or S (Figure 4d). The binding of the coordinatively unsaturated C1 atom to the SWNT creates a three-membered ring, similar to carbene additions into nanotubes.24,39,40 The two new CC bonds (yellow bonds in Figure 4c,d) are about ∼1.48 Å long. At the same time, the CdC bond of the tube (blue bonds in Figure 4c,d) at the binding site is lengthened to ∼1.53 (∼1.57) Å, accompanied by sagging toward to the tube axis. The energetics of C1-C59(A)@C420H40 relative to C60(Ih)@ C420H40 is given in Table 2. Measuring their relative energies

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Figure 6. Clar valence bond (VB) representations for the addition of the C1-C59 defect into (a) an orthogonal CC bond and (b) a slanted CC bond on the inner nanotube surface. The purple dots represent binding sites for the C1-C59 defect. Aromatic sextes are indicated by circles. The tubes are presented as planar projections; only the vicinity of the addition site is shown.

by the DFT calculations, in which the error of van der Waals components are largely compensated, is realistic, because of the uncertainty in the van der Waals energy and the lack of such a term in DFT.41 Table 2 shows that the three C1-C59(A)@C420H40 nanopeapods lie close in energy, although two covalent bonds, whose lengths are between typical lengths of single and double CC bonds, are formed in the O and S C1-C59(A)@C420H40 nanopeapods. Within the three C1-C59(A)@C420H40 nanopeapods, orientation O is the most stable in energy and the relative energies increase in the order O < NOB < S. In addition to the bond formation in O and S,

tube deformations should also play an important role in the energetics. Moreover the energy difference between the defected nanopeapods O and S is 0.23 eV (5.3 kcal/mol), suggesting that the site preference of the C1-C59 defect into the inner nanotube is not as significant as in the case of carbene additions.24,39,40 Changes in the CC bonding of the SWNTs. Next we turn to the changes on the SWNT structures caused by the new bond formation. As shown in Figure 5, the two new CC bonds formed with the C1-C59(A) cage cause significant changes relative to the C60(Ih)@C420H40 nanopeapod (Figure 5a). In conjunction

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Figure 7. Bond length alternation near the binding site in the circumferential direction of the C1-C59(A)@C420H40 nanopeapods O and S as a function of Sn and Ln where n is integer. The S (L) character indicates short (long) CC bonds within the bond length alternation patterns.

with the formation of the two new covalent bonds in the C1C59(A)@C420H40 (O) nanopeapod, the CC bonds on the surface change near the binding site, as shown in Figure 5b, where red and blue lines indicate a CC bond whose length increases and decreases by at least 0.01 Å relative to that in the C60(Ih)@C420H40 nanopeapod, respectively. For example, CC bonds adjacent to the binding site along the tube axis become longer (∼1.47 Å). As shown in Figure 5b, the local environment is reminiscent of a bisnorcaradiene-like framework.42,43 Also we can see bond-length alternation patterns with substantial decreases in orthogonal CC bond lengths and increases in slanted CC bond lengths in the circumferential direction near the binding site, whose short and long CC bonds are, respectively, given by blue and red in Figure 5b. Similar local changes can be seen on the nanotube in the C1-C59(A)@C420H40 (S) nanopeapod (Figure 5c). The geometrical changes are explainable qualitatively, considering the addition of the C1-C59(A) defect into the inner surface from a viewpoint of Clar valence bond (VB) representations. Clar’s concept44 was applied to π networks in finite-length nanotubes by Matsuo, Tahara, and Nakamura20 and to infinitelength nanotubes by Ormsby and King.45 In these VB representations, all π-electrons on the rolled-up graphene of the (10,10) nanotube can be assigned to “aromatic sextets” (sixelectron π cycles).20,45 The VB representations should aid a qualitative interpretation of the geometrical changes due to the addition of the C1-C59(A) defect in which two π-electrons are removed from the delocalized π-electron system of the SWNT.

As shown in Figure 6, there are three representations, which can explain the optimized geometries for the inner addition, B, B′, and Q. In Figure 6, the aromatic sextets are represented by circles. On the basis of the VB representations, two degenerate butadiene-like patterns (B and B′) are formed by the binding of the defected cage into the SWNT, in addition to a quinonoidpattern (Q). The three patterns are independent of the sites into which the C1-C59(A) defect binds, although their orientations with respect to the tube axis can be either orthogonal (O) or slanted (S). These patterns can be observed locally near the binding sites in the optimized geometries of the C1-C59(A)@C420H40 nanopeapods in both O and S orientations. Figure 7 shows the bond-length alternation in the circumferential direction for these two kinds of binding sites. They follow the Q pattern, but the alternation is only significant near the binding site. Frontier Orbitals of Defected Nanopeapods. To increase our understanding of the role of the defected C60 cage in forming the local modifications on the SWNT structures, we turn our attention to differences in frontier orbitals of the C1-C59(A)@C420H40 (O) and (NOB) nanopeapods, especially fullerene-based orbitals, as shown in Figure 8. Since there is no significant mixing between the defected C60 cage and the inner nanotube surface in the “not-bonded” C1-C59(A)@C420H40 (NOB) nanopeapod, their frontier orbitals are categorized into nanotube-based and fullerene-based orbitals, which are given by red and blue, respectively, in Figure 8a. The nanotube-based orbitals have some degeneracies, similar to those in the C420H40

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Figure 8. Orbital energies in the frontier orbital regions in (a) the not-bonded C1-C59(A)@C420H40 (NOB) nanopeapod and (b) the C1-C59(A)@C420H40 (O) nanopeapod (B3LYP/3-21G). The blue (red) lines present energy levels whose orbitals come from the C60 cage (SWNT). Orbital amplitudes in representative orbitals (the HOMO in NOB and the HOMO-2 in O) are given in Figure 9.

CHART 1: Bonding Interactions between the Defected C60 Cage and the Inner SWNT Surface

SWNT.16b The nanotube-based orbitals are delocalized throughout the nanotube in the C1-C59(A)@C420H40 (NOB) nanopeapod. This can be seen in a representative occupied orbital (the highest occupied molecular orbital (HOMO) in Figure 8a) in Figure 9a. The orbitals are delocalized in the C1-C59(A)@C420H40 (NOB) nanopeapod to the same extent as those of the C60(Ih)@C420H40 nanopeapod and the empty C420H40 SWNT. It should be worth noting that nanotube-based orbitals have two types of orbital patterns, antisymmetric orbitals with respect to the σv plane and symmetric orbitals.16 The orbital symmetries should be responsible for interactions between the defected cage and the inner SWNT surface. With respect to the fullerene-based orbitals, the unoccupied t1u(C60) orbitals at ∼-3.0 eV are split to -2.93, -3.10, and -3.70 eV and the

occupied hu(C60) orbitals at ∼-5.9 eV are split to -5.57, -5.80, -5.94, -6.00, and -6.20 eV, due to the formation of C1-C59(A). In contrast, the C1-C59(A)@C420H40 (O) nanopeapod has substantial orbital interactions between the C1-C59 cage and the C420H40 SWNT. Because of the interactions, degeneracies of their frontier orbitals are lifted, as shown in Figure 8b. Figure 9b shows that the HOMO-2 lying at -4.92 eV has significant amplitudes on the encapsulated fullerene molecule. The HOMO-2 is characteristic for the C1-C59(A)@C420H40 (O) nanopeapod, because the frontier orbitals based on the C1-C59(A) cage do not lie in the -3.7 ∼ -5.6 eV range. As given schematically in Chart 1, the key bonding interaction comes from the in-phase interactions between the p orbital of the terminal C1 atom of the C1-C59(A) cage and an antisymmetric orbital of the C420H40 SWNT with respect to the σv plane. Because of the bonding interactions, orbital amplitudes on the SWNT in the occupied orbital are localized, especially at the binding site. Such localization cannot be seen in the not-bonded C1-C59(A)@C420H40 (NOB) nanopeapod, as expected. In the characteristic occupied orbital, orbital combinations highlighted by a red box in Figure 9b are consistent with the formation of the bisnorcaradiene-like deformation on the SWNT, as expected by the VB diagrams of B and B′. Thus, the in-phase interactions are one of the key factors in leading to local deformations on the SWNT. Similar discussions can be applied to the frontier orbitals of the C1-C59(A)@C420H40 (S) nanopeapod; the p orbital in the defected cage interacts with a symmetric orbital with respect to the σv plane of the SWNT, lying at -5.04 eV.

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Figure 9. Orbital amplitudes of representative occupied orbitals: (a) HOMO in the C1-C59(A)@C420H40 (NOB) nanopeapod; (b) HOMO-2 in the C1-C59(A)@C420H40 (O) nanopeapod). In (b) orbital combinations highlighted by a red box are consistent with the formation of the bisnorcaradienelike strain on the SWNT.

These DFT calculations demonstrate that the defected C60 cage binds with the inner SWNT surface through their orbital interactions and the covalent bond formations cause local modifications on the SWNT. These local modifications of the SWNT in nanopeapods, which might be reflected in the TEM observations,7,8 are important in terms of functionalizations of the SWNTs,10 because local perturbations should be formed on seamless SWNT surfaces, which should be responsible for formations of specific addition patterns.40

C1-C59(A)@C420H40 nanopeapods are energetically comparable. Because of the direct couplings between the defected C60 and the inner surface of the SWNT, the carbon network of the tube is locally modified near the binding site. According to DFT calculations together with Clar valence bond representations and molecular orbital analysis, the modified network has a pair of butadiene-like framework in the axial direction and a quinonoid pattern in the circumferential direction whose bond-length alternations are only significant near the binding site.

Conclusions

Acknowledgment. Support by the Japan Society for the Promotion of Science (JSPS) for a postdoctral fellowship for T.Y. is gratefully acknowledged. Computational support from the National Center for Supercomputing Applications (NCSA) and NSF Grant No. DMR-0331710 is gratefully acknowledged. We thank Dr. K. Suenaga and Dr. Y. Sato for valuable discussion on nanopeapods using TEM observations.

We have analyzed at the B3LYP DFT level of theory properties of defected nanopeapods in which a defected C60 cage, C1-C59(A), is encapsulated inside a finite-length (10,10) nanotube C420H40. Intrinsic reaction coordinate (IRC) analyses show that a defected C60 structure with topology of C1-C59 is initially formed from the C60(Ih) cage via a transition state with a protruding C atom from the cage, requiring a high activation energy (8.37 eV (193.0 kcal/mol)). Since the C1-C59 defect has a coordinatively unsaturated C atom, it is reactive toward the inner surface of the host carbon nanotubes. Orientation of the C1-C59 defect inside the (10,10) nanotube determines whether CC bonds are formed between the C1-C59 defect and the (10,10) nanotube or not. When the protruding C atom points along the tube axis, the C1-C59 defect does not bind into the inner nanotube surface, whereas when the protruding C atom is in the vicinity of the SWNT, two CC bonds can be formed between the defected C60 cage and the SWNT. There are two types of opportunities: the C1-C59 defected fullerene can bind into a CC bond orthogonal (O) or slanted (S) relative to the tube axis. DFT calculations show that the three

Supporting Information Available: Cartesian coordinates of all optimized geometries of Figures 1, 2, and 4 (Tables 1-3), full author lists for ref 12, and CC bond lengths for the nanotubes of C420H40 (Figure S1) and C60(Ih)@C420H40 (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Iijima, S. Nature 1991, 354, 56. (2) Iijima, S.; Ichihashi, T. Nature 1993, 363, 603. (3) (a) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, R. C. Science of Fullerenes and Carbon Nanotubes; Academic Press: New York, 1996. (b) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998.

Local Modifications of Single-Wall Carbon Nanotubes (4) (a) Smith, B. W.; Monthioux, M.; Luzzi, D. E. Nature (London) 1998, 396, 323. (b) Burteaux, B.; Claye, A.; Smith, B. W.; Monthioux, M.; Luzzi, D. E.; Fischer, J. E. Chem. Phys. Lett. 1999, 310, 21. (c) Smith, B. W.; Monthioux, M.; Luzzi, D. E. Chem. Phys. Lett. 1999, 315, 31. (d) Smith, B. W.; Luzzi, D. E. Chem. Phys. Lett. 2000, 321, 169. (5) (a) Bandow, S.; Takizawa, M.; Hirahara, K.; Yudasaka, M.; Iijima, S. Chem. Phys. Lett. 2001, 337, 48. (b) Bandow, S.; Takizawa, M.; Kato, H.; Okazaki, T.; Shinohara, H.; Iijima, S. Chem. Phys. Lett. 2001, 347, 23. (c) Bandow, S.; Hiraoka, T.; Yumura, T.; Hirahara, K.; Iijima, S. Chem. Phys. Lett. 2003, 384, 320. (6) (a) Okada, S.; Saito, S.; Oshiyama, A. Phys. ReV. Lett. 2001, 86, 3835. (b) Berber, S.; Kwon, Y.-K.; Toma´nek, D. Phys. ReV. Lett. 2002, 88, 185502. (c) Kane, C. L.; Mele, E. J.; Johnson, A. T.; Luzzi, D. E.; Smith, B. W.; Hornbaker, D. J.; Yazdani, A. Phys. ReV. B 2002, 66, 235423. (d) Ulbricht, H.; Moos, G.; Hertel, T. Phys. ReV. Lett. 2003, 90, 095501. (e) Cho, Y.; Han, S.; Kim, G.; Lee, H.; Ihm, J. Phys. ReV. Lett. 2003, 90, 106402. (f) Lu, J.; Nagase, S.; Zhang, S.; Peng, L. Phys. ReV. B 2003, 68, 121402. (g) Dubay, O.; Kresse, G. Phys. ReV. B 2004, 70, 165424. (h) Yoon, M.; Berber, S.; Toma´nek, D. Phys. ReV. B 2005, 71, 155406. (7) Urita, K.; Sato, Y.; Suenaga, K.; Gloter, A.; Hashimoto, A.; Ishida, M.; Shimada, T.; Shinohara, H.; Iijima, S. Nano Lett. 2004, 4, 2451. (8) Sato, Y.; Yumura, T.; Urita, K.; Suenaga, K.; Kataura, H.; Kodama, T.; Shinohara, H.; Iijima, S. Phys. ReV. B 2006, 73, 233409. (9) Banhart, F. Rep. Prog. Phys. 1999, 62, 1181. (10) Yumura, T.; Sato, Y.; Suenaga, K.; Urita, K.; Iijima, S. Nano Lett. 2006, 6, 1389. (11) Hirsch, A. Angew. Chem., Int. Ed. 2002, 41, 1853. (12) Frisch, M. J.; et al. Gaussian 03; Gaussian, Inc.: Pittsburgh, PA, 2003. (13) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (b) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (c) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (14) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (15) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (16) (a) Yumura, T.; Hirahara, K.; Bandow, S.; Yoshizawa, K.; Iijima, S. Chem. Phys. Lett. 2004, 386, 38. (b) Yumura, T.; Bandow, S.; Yoshizawa, K.; Iijima, S. J. Phys. Chem. B 2004, 108, 11426. (c) Yumura, T.; Nozaki, D.; Bandow, S.; Yoshizawa, K.; Iijima, S. J. Am. Chem. Soc. 2005, 127, 11769. (d) Yumura, T.; Sato, Y.; Suenaga, K.; Iijima, S. J. Phys. Chem. B 2005, 109, 20251. (e) Yumura, T.; Nozaki, D.; Hirahara, K.; Bandow, S.; Iijima, S.; Yoshizawa, K. Annu. Rep. Prog. Chem., Sect. C: Phys. Chem. 2006, 102, 71. (17) (a) Sun, G.; Kertesz, M. New J. Chem. 2000, 24, 741. (b) Sun, G.; Kertesz, M. Chem. Phys. Lett. 2000, 328, 387. (c) Sun, G.; Kertesz, M. J. Phys. Chem. A 2000, 104, 7398. (d) Sun, G.; Kertesz, M. J. Phys. Chem. A 2001, 105, 5212. (e) Sun, G.; Kertesz, M. J. Phys. Chem. A 2001, 105, 5468. (f) Sun, G.; Kertesz, M. Chem. Phys. 2002, 276, 107. (18) Cioslowski, J.; Rao, N.; Moncrieff, D. J. Am. Chem. Soc. 2002, 124, 8485. (19) Rochefort, A.; Salahub, D. R.; Avouris, P. J. Phys. Chem. B 1999, 103, 641. (20) Matsuo, Y.; Tahara, K.; Nakamura, E. Org. Lett. 2003, 5, 3181. (21) (a) Zhou, Z.; Steigerwald, M.; Hybertsen, M.; Brus, L.; Friesner, R. J. Am. Chem. Soc. 2004, 126, 3597. (b) Zurek, E.; Autschbach, J. J. Am. Chem. Soc. 2004, 126, 13079.

J. Phys. Chem. B, Vol. 111, No. 5, 2007 1109 (22) Feng, X.; Irle, S.; Witek, H.; Morokuma, K.; Vidic, R.; Borguet, E. J. Am. Chem. Soc. 2005, 127, 10533. (23) Bettinger, H. F.; Yakobson, B. I.; Scuseria, G. E. J. Am. Chem. Soc. 2003, 125, 5572. (24) Bettinger, H. F. Chem.sEur. J. 2006, 12, 4372. (25) (a) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. (b) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (26) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. (27) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939. (b) Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J. Am. Chem. Soc. 1982, 104, 2797. (c) Pietro, W. J.; Francl, M. M.; Gordon, M. S.; Hehre, W. J.; Defrees, D. J.; Pople, J. A.; Binkley, J. S. J. Am. Chem. Soc. 1982, 104, 5039. (d) Dobbs, K. D.; Hehre, W. J. J. Comput. Chem. 1986, 7, 359. (e) Dobbs, K. D.; Hehre, W. J. J. Comput. Chem. 1987, 8, 861. (e) Dobbs, K. D.; Hehre, W. J. J. Comput. Chem. 1987, 8, 880. (28) Murry, R. L.; Strout, D. L.; Odom, G. K.; Scuseria, G. E. Nature 1993, 366, 665. (29) Patchkovskii, S.; Thiel, W. J. Am. Chem. Soc. 1996, 118, 7164. (30) Yi, J.-I.; Bernholc, J. J. Chem. Phys. 1992, 96, 8634. (31) Eggen, B. R.; Heggie, M. I.; Jungnickel, G.; Latham, C. D.; Jones, R.; Briddon, P. R. Science 1996, 272, 87. (32) Honda, K.; Osawa, E. Fullerene Sci. Technol. 1996, 4, 925. (33) Ewels, C. P.; Telling, R. H.; El-Barbary, A. A.; Heggie, M. I.; Briddon, P. R. Phys. ReV. Lett. 2003, 91, 025505. (34) Kaxiras, E.; Pandey, K. C. Phys. ReV. Lett. 1988, 61, 2693. (35) Xu, C. H.; Fu, C. L.; Pedraza, D. F. Phys. ReV. B 1993, 48, 13273. (36) (a) Fukui, K. J. Phys. Chem. 1970, 74, 4161. (b) Fukui, K. Acc. Chem. Res. 1981, 14, 363. (37) (a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523. (38) (a) Sun, G.; Ku¨rti, J.; Kertesz, M.; Baughman, R. H. J. Am. Chem. Soc. 2002, 124, 15076. (b) Sun, G.; Ku¨rti, J.; Kertesz, M.; Baughman, R. H. J. Phys. Chem. B 2003, 107, 6924. (39) Lee, Y.-S.; Marzari, N. Phys. ReV. Lett. 2006, 97, 11680. (40) Yumura, T.; Kertesz, M. Chem. Mater., in press. (41) On the basis of local density approximation (LDA) calculations in ref 6, the calculated attractive binding energies in C60@(10,10) nanotubes have a wide range of -0.5 to -2.0 eV/C60(Ih). Our B3LYP/6-31.G*// B3LYP3-21.G calculation estimates this interaction in C60(Ih)@C420H40 as a repulsive energy of +0.5 eV/C60(Ih). As is well-known, the standard DFT methods, such as B3LYP method, omit weak intermolecular dispersion forces and cannot provide consistent and accurate calculations for these interactions. For a leading reference for this problem, see the following: Rydberg, H.; Jacobson, N.; Hyldgarrd, P.; Simak, S. I.; Lundqvist, B. I.; Langreth, D. C. Surf. Sci. 2003, 532, 606. (42) Vogel, E.; Roth, H. D. Angew. Chem., Int. Ed 1964, 3, 228. (43) Choi, C. H.; Kertesz, M. J. Phys. Chem. A 1998, 102, 3429. (44) (a) Clar, E. Polycyclic Hydrocarbons; Academic Press: New York, 1964. (b) Clar, E. The Aromatic Sextet; Wiley: London, 1972. (c) For a recent confirmation, see the following: Maksi, Z. B.; Bari, D.; Mu¨ller, T. J. Phys. Chem. A 2006, 110, 10135. (45) Ormsby, J. L.; King, B. T. J. Org. Chem. 2004, 69, 4287.