Density Functional Study of the 13C NMR Chemical Shifts in Single

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Density Functional Study of the 13C NMR Chemical Shifts in Single-Walled Carbon Nanotubes with Stone-Wales Defects Eva Zurek,† Chris J. Pickard,‡ and Jochen Autschbach*,§ Max-Planck-Institut fu¨r Festko¨rperforschung, Heisenbergstrasse 1, 70569, Stuttgart, Germany, School of Physics & Astronomy, UniVersity of St Andrews, St Andrews KY16 9SS, Scotland, Department of Chemistry, State UniVersity of New York at Buffalo, Buffalo, New York 14260-30000 ReceiVed: April 12, 2008; ReVised Manuscript ReceiVed: May 13, 2008

The 13C NMR chemical shifts of (7,0), (8,0), (9,0), and (10,0) single-walled carbon nanotubes (SWNTs) with Stone-Wales (SW) defects have been studied computationally using a gauge-including projector-augmented plane-wave (GIPAW) density functional theory (DFT) method. A SW-defect substantially broadens the NMR signal of a particular tube, however, in general the average shift of the non-defect carbons does not differ greatly from that of the pristine species. “Parallel” orientations of the defect site yields shifts at around 150-160 ppm from atoms in the defect site which are separated from the rest of the NMR signal. Therefore, the results indicate that 13C NMR might be able to detect the presence of, and perhaps even quantify the concentration of SW defects found in SWNTs. Differences in the NMR obtained for two defect orientations are analyzed by comparing the shifts of the defect atoms with those of planar and bent structures of the azupyrene molecule. Representative visualizations for the shielding tensors of the (8,0) SWNT with and without defects are also reported. I. Introduction Presently much research activity is directed toward singlewalled carbon nanotubes (SWNTs) due to their potential applications. For example, it has been proposed that SWNTs may be used as Schottky diodes,1 electron field emitters,2 magnetic tips for magnetic scanning probe microscopy,3 or as gas,4,5 DNA,6 and protein7 sensors. Chemical functionalization of these systems can render them soluble in aqueous media and therefore potentially useful in biotechnology and biomedical applications.8,9 However, SWNTs are rarely “perfect”.10,11 Defects such as single or double vacancies and pentagon-heptagon pairs may drasticallychangetheelectronicstructure,12–14chemicalreactivity,12–17 mechanical18 and transport19,20 properties of these systems. To understand the influence of defects on the aforementioned properties it is necessary to develop standard, easily applicable methods in order to qualify the type, and quantify the amount of defects present in a given sample. Currently, high-resolution transmission electron microscopy (HR-TEM),21 scanning tunneling microscopy (STM),22 and Raman spectroscopy23 are primarily employed. A combination of resonant photoabsorption and vibration spectroscopy with STM has also been used.24 The advantage, but also a drawback, of the microscopic techniques is that one can observe the local structure in specific nanotubes and even study a single defect. Unfortunately, the microscopic techniques do not yield information about large heterogeneous samples. On the other hand, Raman vibrational spectroscopy which is generally a very versatile tool for nanotube sample characterization lacks the resolution to directly identify defects at low concentrations in otherwise mainly pristine material.25 Recently, it has been proposed that selective electrochemical * To whom correspondence should be addressed. E-mail: jochena@ buffalo.edu. † Max-Planck-Institut fu ¨ r Festko¨rperforschung. E-mail: [email protected]. ‡ University of St Andrews. § State University of New York at Buffalo.

deposition (SED)10 or monitoring the physiorption of H2 by cryogenic thermal-desorption spectroscopy (cryo-TDS)26 can be employed to study the defects present in a bulk sample. Unfortunately, it is not possible to determine the chemical nature of the defects using these techniques.10 One of the most versatile experimental tools to study the local geometry and electronic structure of molecules and solids is nuclear magnetic resonance (NMR). Over the past few years, an increasing amount of experimental and theoretical NMR data for SWNTs are becoming available; see refs 27–32 and references therein. For example, experimental advances in sample purification have yielded NMR spectra with line widths of only 9-10 ppm,33–35 characterization of SWNT samples functionalized with diamine-terminated oligomeric polyethylene glycol36 and fluorine37 have been performed, the change of the NMR spectra upon protonation35 has been examined, evidence of the spatial proximity of the nanotubes and the functional group has been provided,33 and related structures such as carbon nanohorns have been characterized via NMR.38 Barron et al. have recently advocated using NMR preferentially over other experimental techniques to investigate functionalization of SWNTs.37 Recently our first-principles computations showed that the NMR of functionalized SWNTs is potentially very rich in information.28–30 The 13C nuclear magnetic shielding, which probes local aspects of the electronic structure, appears promising as a probe for the functionalized sites if the resolution of the experiments can be increased further. That is, direct observation of the NMR signals of functionalized sidewall carbons might be observable in NMR experiments of nanotubes with a high degree of functionalization. For the same reason that NMR is a good probe for functionalized sites in SWNT sidewalls, it might also yield detailed information about the local electronic structure of defect sites. Herein, we provide the first theoretical results for the chemical shifts of SWNTs with defects obtained from first-principles calculations on isolated, infinite periodic systems. We focus on

10.1021/jp803180v CCC: $40.75  2008 American Chemical Society Published on Web 07/11/2008

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TABLE 1: The Geometry Optimizations, Band Gap, and NMR Shielding Tensor Calculations were carried out using a Monkhorst-Pack Grid of Dimension (1,1, m)a defect type/SWNTb

(7,0)

(8,0)

(9,0)

(10,0)

P-SW defect, two unit cells D-SW defect, two unit cells P-SW defect, three unit cells D-SW defect, three unit cells

18/19 16 16/17 9

12 16

17 19/20 12 10

15/16 16

a If two values are given, the reported chemical shifts were calculated from an average obtained from both (1, 1, m) k-grids. b The heptagon-heptagon bond in the SW defect may be oriented either parallel (P) or diagonal (D) to the tube axis. See Figure 1b,c. Systems with one defect per two unit or three unit cells of the pristine SWNT were considered.

the Stone-Wales (SW) or 5/7/7/5 defect39 since it is considered to be the lowest energy defect in a SWNT.18 For low defect concentrations, direct measurements of NMR peaks of defectsite carbons will probably remain a challenge for quite some time. However, it is important to predict the chemical shift positions and patterns, as well as the general influence of defects on the NMR spectra of SWNTs, to help with the assignment of future NMR spectra that may contain telltale signals from defectsite atoms. Our results indicate that there are indeed characteristic NMR signals that can be associated with SW defects, and these are somewhat dependent upon the defect orientation. In each of the systems studied, the presence of the defects led to pronounced geometry distortions with a concomitant broadening of the simulated NMR spectra. However, the average chemical shifts for carbons that are not part of the defect site are similar to those in pristine SWNTs, analagous to what we found previously for covalently sidewall functionalized SWNTs.30 II. Methodology, Computational Details The computations employed a plane-wave density functional theory (PAW DFT) first-principles method with ultrasoft pseudopotentials as implemented in a developer’s version of the Castep code.40,41 We have used the Perdew-Burke-Ernzerhof (PBE)42 nonhybrid density functional, and a plane-wave basis energy cutoff of 420 eV along with ultrasoft pseudopotentials.43 Isolated infinite SWNTs were calculated by using a hexagonal unit cell of appropriate size in the a, b -direction to ensure an intertube separation of at least 8 Å, as described previously.31 NMR shielding tensors were calculated using a “gaugeincluding” projector-augmented plane-wave (GIPAW) approach extended to ultrasoft pseudopotentials.44,45 The computational settings were carefully benchmarked in Ref. 31 and are described extensively in Refs. 30 and 31. The reciprocal space grids (“kgrids”) necessary to obtain converged chemical shifts are provided in Table 1. Band gaps, binding energies and geometrical parameters converge with fewer k-points. If the shielding constants obtained for a (1,1, m) and a (1,1, m+1) k-grid differed by more than 0.5 ppm for any of the atoms in the unit cell, an average from the two k-grids was used. In most cases, the supercell consisted of a single defect per two unit cells of the parent (n, 0) SWNT, as listed in Tab. 1. For these systems, the number of carbon atoms in the supercell is 8n, i.e. 56, 64, 72, and 80, for the (7,0), (8,0), (9,0), and (10,0) systems, respectively. The dimension of the supercell in the direction of the SWNT axis is given below in Tab. 5. However, in order to study how the defect concentration affects the results we have also considered a single defect per three unit cells for the (7,0) and (9,0) SWNTs (i.e. with 12n atoms per supercell). A cell of dimension (20,20,10) Å and one k-point was used for calcula-

tions on the azupyrene molecule. All structures were fully optimized except for the bent azupyrene structures. The chemical shifts reported here are referenced to tetramethylsilane (TMS) by using benzene as a reference compound for the computational data and adding to the result the experimental chemical shift of benzene with respect to TMS.31 In this way, results may be directly compared between those obtained for finite SWNTs32 and other molecular systems and infinite periodic pristine SWNTS.31 III. Results and Discussion A. Geometrical Parameters, Bonding Energies, and Band Gaps. A SW defect (Figure 1a) is conceptually obtained by a 90° rotation of a C-C bond connecting two hexagons in a perfect SWNT or fullerene structure.39 In a SWNT, this transforms four connected hexagonal rings into two pentagons and heptagons and is therefore also called a 5/7/7/5 defect. For a zigzag SWNT, the rotation may occur about a C-C bond diagonal (D) or parallel (P) to the tube axis. This gives rise to two different systems which we label P-SW and D-SW, as illustrated in Figure 1, panels b and c, respectively. For the P-SW defect in a zigzag SWNT, the defect bonds 2/3, 4/5, 7/8, and 9/10 as labeled in Figure 1a are symmetry equivalent. The molecular homologue of the defect site, azupyrene (dicyclopenta[ef,kl]heptalene), has the same carbon framework as in Figure 1a, with hydrogens saturating the dangling σ bonds at the perimeter. The optimized bond lengths for azupyrene, as well as for the different bonds in the P-SW and D-SW defect sites are given in Table 2. The optimized bond 1 in azupyrene, 1.384 Å, agrees reasonably well with the 1.333 Å reported for a single crystal X-ray structure46 of this molecule. The agreement for bonds 2 and 3 (calculated: 1.470, X-ray structure: 1.494) is also reasonable. Some deviations should be expected due to crystal packing effects. For all of the zigzag SWNT with P-SW defects, the optimized length of bond 1 was found to be quite close to that in azupyrene, whereas for the D-SW defect bond 1 was between ∼0.03-0.04 Å shorter than in the corresponding P-SW system. For bonds 2, 3 we can also note pronounced differences between the P-SW and the D-SW structures, with the bond in the P-SW systems being longer, and the bonds in the D-SW systems being shorter than the corresponding bonds of the planar azupyrene system. It is seen that the local structure of the defect site is noticeably influenced by the curvature of the SWNT sidewall and that the orientation of the defect site in the zigzag nanotubes plays an important role. A number of studies have addressed the question as to weather the SW defect sites are more reactive than bonds in pristine SWNTs and identified the most reactive bonds.12,15,16 Previous work has also found that the defect formation energies (∆ESW) are dependent upon the tube curvature, chirality and defect orientation.47–49 Our results, collected in Table 3, indicate that, although the formation energy for the P-SW defect is lower than D-SW for tubes with smaller radii, it increases rapidly with diameter. Thus, the energies of the high-curvature SWNTs in their pristine state are comparatively closer to those with P-SW, as opposed to D-SW defects. For the D-SW defect ∆ESW is nearly radius independent. The comparison of the formation energies of the P-SW defect in the systems with two- and threeunit supercells show that for P-SW ∆ESW decreases significantly as the defect concentration decreases. The SW defect induces a quite substantial geometry rearrangement in each system. Given the close proximity of SW defects in the 2-unit supercell systems it is not surprising that a significant stabilization is obtained when the defects are somewhat further apart. [Due to the fact

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TABLE 2: Optimized Bond Lengths within a SW Defect Site in (n, 0) (7 e n e 10) SWNTsa bond

(7,0)-P

(7,0)-D

1 2 3 4 5 6 7 8 9 10

1.383 1.521

1.341 1.436 1.437 1.397 1.402 1.447 1.450 1.441 1.418 1.448

1.425 1.420 1.457 1.483

(7,0)-P

b

(8,0)-P

(8,0)-D

(9,0)-P

(9,0)-D

1.390 1.507

1.378 1.519

1.372 1.519

1.422

1.422

1.416 1.446

1.422 1.463

1.466

1.480

1.338 1.437 1.440 1.399 1.391 1.442 1.441 1.443 1.448 1.418

1.342 1.433 1.433 1.398 1.403 1.431 1.432 1.436 1.428 1.444

1.420 1.424 1.465 1.479

b

(10,0)-P

(10,0)-D

C16H10c

1.379 1.503

1.370 1.515

1.384 1.470

1.420

1.414

1.415 1.450

1.427 1.474

1.466

1.474

1.337 1.435 1.438 1.401 1.393 1.428 1.436 1.431 1.445 1.427

(9,0)-P

1.426 1.382 1.397 1.395

a The bond numbering is shown in Figure 1. Unless otherwise noted, the supercell consisted of one SW defect per two unit cells of the pristine tube. The SW defect was oriented either parallel (P) or diagonal (D) to the tube axis as shown in Figure 1. b Three unit cells. c Azupyrene molecule.

Figure 1. SW, or 5/7/7/5, defects in zigzag SWNTs. a) local defect pattern and C-C bond labeling. (b) P-SW defect obtained from rotating a C-C bond pair parallel to the SWNT axis. (c) D-SW defect obtained from rotating a diagonal C-C bond pair. The SW defect site is highlighted by thick lines. For panels b and c the tube axis is horizontal.

TABLE 3: SW Defect Formation Energy (∆ESWa) in kcal/mol defect type/SWNT

b

P-SW defect, two unit cells D-SW defect, two unit cells P-SW defect, three unit cells D-SW defect, three unit cells

(7,0)

(8,0)

(9,0)

(10,0)

56.69 80.71 48.64 73.29

65.70 85.72

71.28 83.17 62.39 77.63

79.27 85.19

a ∆ESW ) ESW - Epristine for super cell size as indicated, containing a single defect. b Supercell size with respect to unit cell of pristine system.

that fewer symmetry elements could be applied in the calculations of the D-SW defect SWNTs we had to forego NMR computations with larger supercells for these systems.] For the double unit-cell systems, the formation energy for the P-SW is lower than for the D-SW defect. However, the computational data indicate that for increasing tube radii the ∆ESW values will eventually converge. One might expect such a trend for a SWNT sidewall with decreasing curvature. Already, a large decrease in the difference of the formation energies for the two sites is evident in going from the (7,0) tube (24.02 kcal/mol difference) to the (10,0) tube (5.92 kcal/mol difference). Examination of Table 4 reveals that the introduction of SW defects at the moderate to high concentrations investigated here has a substantial influence on the band gaps of SWNTs. It is therefore important to understand the role and detect the presence of defects for effective band gap engineering applications. Our results indicate that both the defect concentration, as well as the orientation can change the band gap significantly. Moreover, for the (7,0)-P, (9,0)-D, and (10,0)-D SWNTs containing one defect per double unit cell, an indirect band gap is observed. The band structures for these systems, as well as their pristine counterparts, are given in Figure 2. Introduction of the defect breaks the symmetry of the pristine tube, resulting in the splitting of degenerate bands. The indirect band gap is only slightly smaller than the gap at Γ. For all three cases, the

Figure 2. Band structures for selected pristine SWNTs and those with SW defects (one SW defect per double unit cell). See Figure 1 for definitions of P-SW and D-SW. The arrows indicate the location of the indirect band gap. The Fermi level has been set to zero.

TABLE 4: Unscaled Calculated Band Gaps in eV for Pristine SWNTs and SWNTs with SW Defects defect type/SWNT

(7,0)

(8,0)

(9,0)

(10,0)

pristine P-SW defect, two unit cells D-SW defect, two unit cells P-SW defect, three unit cells

0.200 0.170a 0.386 0.024

0.575 0.708 0.493

0.102 0.309 0.124a 0.249

0.747 0.269 0.728a

a Band gap given at the Γ point. These systems possess a slightly smaller, indirect band gap.

minimum energy in the conduction band is shifted by about 0.2-0.25 (Γ-Z) relative to the maximum in the valence band. The bands of the (10,0) D-SW system can be compared to those of the (10,0) P-SW SWNT calculated in ref 13. In both cases, the defect gives rise to the lowest lying unoccupied band. However, the P-SW system does not afford an indirect band gap. Our results suggest that an indirect gap might be more prevalent for the D-SW systems but more systematic data would be needed to confirm this. Inspection of the data in Table 4 and Figure 2 shows the profound impact of the defects on the band structure. Therefore, when considering the known strong sensitivity of NMR parameters to band gaps, the nature of low-lying electronic

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Figure 4. Cross section of an optimized (8,0) SWNT with a P-SW defect. The defect site is on the right-hand side of the SWNT.

Figure 3. Calculated histograms of the 13C NMR chemical shifts of zigzag (7 e n e 10) SWNTs with one “parallel” SW (P-SW) defect per double unit cell of the pristine SWNT. See also Figure 1b). The shifts of carbons within the defect site are color coded. The “Average Shift” does not include the shifts of the defect atoms.

states, and other features of the electronic structure, sizable differences of the chemical shifts compared to the pristine SWNTs should be expected. We will show in the next section that this is indeed the case. B. 13C NMR Chemical Shifts of SWNTs with SW Defects. We will discuss the P-SW defects first. Histograms of the calculated 13C NMR chemical shifts with P-SW defects are shown in Figure 3. The defect not only introduces a substantial broadening of the spectrum similar to what we found recently for functionalized SWNTs30 but it also yields individual peaks from the defect site which are quite well separated from the

rest of the spectrum. Most notably, in all cases we calculate a signal around 150-160 ppm arising from the two carbons in the bond connecting the two heptagons (bond 1 in Figure 1a). For comparison, in the planar azupyrene molecule the shifts of these carbons were calculated to be significantly lower at 139.8 ppm. In azupyrene the only other carbons which are not bonded to hydrogen correspond to the carbons highlighted in orange in Figure 3 (i.e., the carbons adjacent to bond 1). Here, the shifts in the molecule (133.6 ppm) are somewhat closer to those found within the SWNT defect site (129-136 ppm). Given the large shift differences for the bond-1 carbons, it is clear that the planar azupyrene molecule is not a particularly good model for the nonplanar P-SW defects in narrow to medium-diameter SWNTs. For all of the tubes studied, the highest chemical shift arises from the carbons in bond 1 (color-coded in red in Figure 3), the next largest from bond 6 (blue) and the third largest from the carbons at the heptagon tips (purple). The shifts from the green and orange color-coded carbons, the remaining heptagon carbons, are the lowest. Due to the fact that the shifts of most of the carbons belonging to the defect are separated from those corresponding to the rest of the carbons within the tube, we also list the average shift of the remaining bulk of the carbons in each subfigure. With the exception of the small diameter (7,0) system this average differs by only 1.3 to 2.6 ppm from those of the pristine species. This indicates that SW-defects should lead to a broadening of the NMR signal of the bulk carbons, however the average of this signal will not differ substantially from that of the pristine tubes. This result is qualitatively similar to what we found recently for functionalized SWNTs.30 In ref 30, we noted that upon covalent functionalization the SWNTs cross sections became slightly oval and that much of the predicted NMR peak broadening can be attributed to curvature changes along the SWNT circumference. This assignment was made with the help of a calculation on a distorted (8,0) SWNT without the functional group, to separate geometrydistortion effects from the direct electronic influences by the functional group. It turned out that the shifts of the carbons at the functionalization site were very high, around 172 ppm. Visual inspection of the functionalized SWNT cross section (Figure 4 in ref 30) shows that the curvature at the functionalization site is highest. In comparison, in the present work the defect-site SWNTs also exhibit some “ovality” of the SWNT cross section which is therefore analogous to the functionalization situation. An example is shown in Figure 4 for the P-SW defect in the (8,0) SWNT. We cannot easily perform a calculation without the defect site to isolate the structural effects from the bulk of the carbons but it appears reasonable to assume that also for the SW defect SWNT much of the predicted NMR signal broadening is due to curvature changes along the tube’s circumference. As we have

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TABLE 5: Optimized c Axes of the Supercell (Double Unit Cell of the Pristine SWNT) for Pristine Zig-Zag (n, 0) Tubes and Those with P-SW and D-SW Defects (in Angstrom) n

pristine

P-SW

D-SW

7 8 9 10

8.544 8.537 8.542 8.548

8.400 8.416 8.431 8.449

8.634 8.618 8.620 8.609

seen, the P-SW defect sites also afford several high-shift carbons in these high-curvature areas. Another structural effect from the defect is a noticeable contraction of the cell dimension in the direction of the SWNT axis (the c axis in our calculations) when the P-SW defect is considered. For the D-SW defect, the opposite trend is found, namely a slight elongation of the unit cell. The optimized lengths of c are given in Table 5. The elongation of a zigzag SWNT upon introducing a D-SW defect was previously predicted by Zhang et al.50 based on tight-binding calculations. Our firstprinciples computations confirm this result. To summarize the chemical shift data for the P-SW defect: For moderate defect concentrations, our results suggest that it may be possible to identify the presence of SW-defects, and perhaps even quantify the defect concentration, by the presence of weak NMR signals around 150-160 ppm. It would be important that these signals are not obscured by low-frequency NMR signals originating from metallic SWNTs. One may, for instance, separate metallic from semiconducting tubes prior to NMR studies. Figure 5 shows the 13C NMR chemical shift histograms for a triple unit cell containing a single P-SW defect. Once again, we note the presence of a peak well separated from the rest of the signal, corresponding to the carbons in the heptagonheptagon bond. Comparison with Figure 3 shows that decreasing

Figure 6. Same as Figure 3 but for the “diagonal” SW defect (DSW). See also Figure 1c. Average shifts include all atoms, and do not exclude the defect-site carbons as in Figures 3 and 5.

Figure 5. Calculated histograms of the 13C NMR shifts of (7,0) and (9,0) SWNTs with one P-SW defect per triple unit cell of the pristine SWNT. Otherwise same as Figure 3. The “Average Shift” does not include the shifts of the defect atoms.

the defect concentration has a slight influence on the location of the peak. This suggests that signals in this range should be detected for all zigzag SWNTs irrespective of the defect concentration and may therefore be used to identify the presence of SW-defects. A substantial broadening remains. For the (7,0) system, upon lowering the defect concentration, the average shift of the carbons not in the defect is now also very close to that of the pristine tube. Figure 6 shows the computed NMR histograms for the D-SW defect SWNTs for supercells consisting of two unit cells of the pristine SWNTs (compare with Figure 3 for the P-SW defect). Investigation of the individual shifts in the defect site reveals that the D-SW systems do not exhibit quite as large characteristic

SWNTs with Stone-Wales Defects

Figure 7. The carbons in the D-SW systems with the highest NMR shifts are those belonging to bond 6 in Figure 1a that, if connected by a line, have a larger angle with the SWNT axis (straight line and squares).

deshielded bond-1 signals as seen in the P-SW defects. The computed shifts for bond 1 are explicitly listed in the histograms, along with the average shifts of all atoms in the supercells. It becomes apparent that bond-1 carbons are among the most deshielded but not consistently the most deshielded carbons in the D-SW zigzag SWNTs. The highest chemical shifts in the D-SW systems result from two carbons that are part of the defect site. In each case, these are one of the carbons in bond 6 and its partner atom on the opposite side of the defect, as shown by the squares in Figure 7. We attribute this different behavior to the fact that the curvature-induced strain on the bonding pattern of the P-SW and the D-SW defect is very different. See also Zhang et al.50 Compared to the P-SW systems, we also notice that the highest shifts are not as well separated from the remaining shifts, although for the larger-diameter (10,0) system the effects from the P-SW and D-SW defects seem to become more comparable (which goes along with more comparable energies for the defects). Overall, apart from the bond-1 signal, the influence from the D-SW defect on the SWNT NMR is quite similar to the P-SW defect: there is a substantial broadening of the NMR shifts in the defect systems, with strongly deshielded signals found for the carbons inside the defect site. To further investigate the effect from the tube curvature on the shifts at the defect sites, and to characterize the differences between P-SW and D-SW defects, we calculated the shifts of the carbons in bond 1 in a bent azupyrene molecule. In order to generate structures that allow for direct comparison with the SWNT defects, the optimized defect including the carbons surrounding the defect site was cut out from a (7,0) P-SW and D-SW supercell, respectively. The surrounding carbons were then replaced by hydrogens with C-H distances adjusted to 1.09 Å to obtain a bent azupyrene structure that resembles the defect in the SWNT. For the P-SW azupyrene model, the computed shifts for the carbons of bond 1 were 156.0 ppm,

J. Phys. Chem. C, Vol. 112, No. 31, 2008 11749 and for the D-SW azupyrene model we obtained 137.8 ppm. In comparison, for the (7,0) nanotubes with defects the computed shifts of bond 1 carbons were 153.9 and 149.4 ppm for P-SW and D-SW, respectively. The azupyrene molecule’s shift trend in bond 1 upon bending is overestimated compared to the corresponding shifts in the defect SWNTs. Nonetheless, the comparison shows that, at least for the P-SW defect, the high shifts of the bond-1 carbons are likely to be a direct result of the geometrical curvature-induced distortion. For the D-SW defect, the comparison between SWNT and molecule is not as conclusive. However, the trend of decreasing shifts (i.e., increased shielding) in bond 1 when changing a P-SW into a D-SW defect is well reproduced. The isotropic shifts reported here represent the average of the shielding tensors’ principal components. Differences in the isotropic shifts of defect and nondefect sites may be due to a combination of changes in the individual shielding components. Therefore, we also report some representative shielding tensor data in this work. Figure 8 graphically displays selected shielding tensors of the (8,0) SWNT for the pristine and the two defect systems in form of polar plots. Consider a function f(r) ) Σij rirjσijA centered at carbon atom A, with shielding tensor elements σijA and r ) (r1, r2, r3) ) (x, y, z). This function is then written in polar coordinates as r2g(φ, θ). The plots show the angular dependence of g(φ, θ) for each tensor as a polar plot, i.e., r ) g(φ, θ), with a separate surface for positive and negative g. An isotropic tensor would be represented by a sphere. It is seen that the shielding tensors are strongly anisotropic. The tensor orientation for the pristine (8,0) tube is the same as what we reported previously for a finite (9,0) SWNT32 and for an infinite (9,0) SWNT:31 We see a large positive principal component perpendicular to the SWNT sidewall (the radial component), and negative components tangential to the tube’s surface (the ortho-radial and axial components. The axial component is in the direction of the SWNT axis.). For the defect systems, the shielding tensor of one of the bond-1 carbons and the shielding tensor of an atom at the periphery of the defect are plotted. Since lower shielding means higher shifts, we see that the particularly high shifts of the P-SW bond-1 atoms are caused by a reduction of the positive radial component along with the occurrence of a significant negative axial tensor component. The selected carbon at the periphery of the P-SW defect also has larger negative tangential shielding tensor components compared to the pristine system. The tensors for the D-SW defect are quite different: we see that the selected bond-1 atom does not have the very large axial deshielding component as the one in the P-SW defect. Instead, one of the atoms at the periphery has the lowest shielding in this system (see Figure 3), which is seen to

Figure 8. Shielding tensors of the pristine,and the P-SW and D-SW defect (8,0) SWNTs. The tensors are represented as polar plots of functions Σij rirjσijA centered at carbon atom A, with shielding tensor elements σijA and Cartesian position vectors r ) (r1,r2,r3). See text for details. The plots show the tensor orientation as well as the relative magnitude and sign of the principal components (blue/orange)positive/negative).

11750 J. Phys. Chem. C, Vol. 112, No. 31, 2008 result from a large negative tangential shielding tensor component which is roughly at a 45 degree angle with respect to the SWNT axis. IV. Conclusions Computations of the chemical shifts in infinite periodic zigzag SWNTs with SW defects have shown the following: (i) The presence of a defect leads to a substantial NMR signal broadening. The overall influence on the NMR spectrum will, of course, be dependent upon the defect concentration. Aside from the shifts of the atoms belonging to the defect site itself, the effects from the presence of SW defects are qualitatively similar to those obtained for functionalized SWNTs in ref 30. That is, a substantial peak broadening occurs which is at least partially due to the overall change of the SWNT geometry. For example, in Figure 4, we illustrate how geometry relaxation due to the presence of a SW defect introduces a deviation from a circular SWNT cross section. (ii) For the atoms that are part of the defect site, large chemical shifts are predicted (up to ∼150-160 ppm). For systems with high concentrations of SW defects it may be possible to identify the defects by these characteristically high shifts, provided that they are not obscured by shifts arising from metallic species. (iii) Comparison with the molecule azupyrene, which has the same carbon connectivity as the SW defect site, in planar and bent geometries has shown that the SWNT curvature plays an important role for the generally high chemical shifts of the carbons in bond 1, the central C-C bond in the SW defect. The molecular model of the P-SW defect exhibits bond-1 shifts that are in good agreement with those in the defect SWNT. The azupyrene calculations have also shown that the relatively lower chemical shift of the bond-1 carbons for D-SW defects is to some degree a geometric effect, although the less good agreement between molecule and defect SWNT indicate that for the D-SW defect electronic effects beyond those induced by the bending may play a significant role. Acknowledgment. We thank Thao Vo and Catherine Johnson for assistance with a subset of the computations which were performed as part of their undergraduate research projects at SUNY Buffalo. J.A. acknowledges support from the Center of Computational Research at SUNY Buffalo and is grateful for financial support of his research from the CAREER program of the National Science Foundation (Grant No. CHE-0447321).1,1 Supporting Information Available: Shielding tensor data used to generate Figure 8. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Manohara, H. M.; Wong, E. W.; Schlecht, E.; Hunt, B. D.; Siegel, P. H. Nano Lett. 2005, 5, 1469–1474. (2) Zhou, O.; Shimoda, H.; Gao, B.; Oh, S.; Fleming, L.; Yue, G. Acc. Chem. Res. 2002, 35, 1045–1053. (3) Kim, Y.-H.; Choi, J.; Chang, K. J.; Toma´nek, D. Phys. ReV. B 2003, 68, 125420–4. (4) Snow, E. S.; Perkins, F. K.; Houser, E. J.; Badescu, S. C.; Reinecke, T. L. Science 2005, 307, 1942–1945. (5) Qi, P.; Vermesh, O.; Grecu, M.; Javey, A.; Wang, Q.; Dai, H.; Peng, S.; Cho, K. J. Nano Lett. 2003, 3, 347–351. (6) Tang, X.; Bansaruntip, S.; Nakayama, N.; Yenilmez, E.; Chang, Y.-I.; Wang, Q. Nano Lett. 2006, 6, 1632–1636. (7) Chen, R. J.; Choi, H. C.; Bangsaruntip, S.; Yenilmez, E.; Tang, X.; Wang, Q.; Chang, Y.-L.; Dai, H. J. Am. Chem. Soc. 2004, 126, 1563–1568. (8) Lin, Y.; Taylor, S.; Li, H.; Shiral Fernando, K. A.; Qu, L.; Wang, W.; Gu, L.; Zhou, B.; Sun, Y.-P. J. Mater. Chem. 2004, 14, 527–541. (9) Tasis, D.; Tagmatarchis, N.; Bianco, A.; Prato, M. Chem. ReV. 2006, 106, 1105–1136.

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