Interactions of Aromatics on the Surface of Single-Wall Carbon

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Noncovalent π-π Stacking and CH---π Interactions of Aromatics on the Surface of Single-Wall Carbon Nanotubes: An MP2 Study Tapas Kar,*,† Holger F. Bettinger,‡ Steve Scheiner,† and Ajit K. Roy§ Department of Chemistry and Biochemistry, Utah State UniVersity, Logan, Utah 84322-0300, Organic Chemistry II, Ruhr-UniVersity Bochum, 44780 Bochum, Germany, and Air Force Research Laboratory, AFRL/MLBCM, Bldg 654, 2941 Hobson Way, Wright-Patterson AFB, Ohio 45433-7750 ReceiVed: September 03, 2008

The magnitude and nature of interactions between small aromatic systems (benzene and naphthalene) and various single-wall carbon nanotubes are examined by MP2 theory. π-π stacking configurations are more strongly bound than CH---π analogues. There is a small preference for placement of the aromatic directly above a CdC bond center in the nanotube. All of these complexes are dominated by dispersion forces. Mobility of adsorbed benzene on the tube surface is considered in terms of rotating, tilting, and sliding. As noted previously for covalent modification of nanotubes, the computationally efficient same level different basis set protocol is reliable for studying noncovalent interactions. Previously reported DFT (LDA or GGA) binding energies for π-π stacking arrangements are underestimated, whereas dispersion-corrected methods overestimate these binding energies. Introduction Chemical modifications of carbon nanotubes at their surfaces and tips via covalent and noncovalent functionalizations are essential to use this fascinating material in wider applications, such as composite materials and biosensors, than their pristine forms. Such chemical and physical modifications make nanotubes soluble in various solvents and thus also open possibilities of separating them into sets of semiconducting and metallic tubes. Recent developments in the functionalization of nanotubes and associated changes in solubility have been summarized in several recent review articles.1-9 Attachment of molecules at the surface by covalent bonding deforms the structure10 and thus somewhat alters the intrinsic properties of single-wall nanotubes (SWNTs). The extent of structural deformation depends upon the reaction sites and density of functionalized groups,11 an area which is not yet fully understood and warrants further systematic exploration. On the other hand, thermodynamically controlled noncovalent functionalizations offer the possibility of attaching molecules using much weaker van der Waals or π-π stacking forces with only minor perturbations of the electronic network of the tube.12 The recent literature encompasses extensive experimental studies on such noncovalently modified carbon nanotubes, and the list of guest molecules includes various species of polymers,13,14 polynuclear aromatic compounds,15-17 surfactants,18,19 and biomolecules.9,19-21 One of the most important sorts of functional groups that interact directly with the tube is aromatics. It appears that an aromatic moiety, such as phenyl, acts principally as an anchor to the surface of nanotubes. Despite experimental progress, relatively little is known about the magnitude (binding or adsorption energy) and nature (chirality and site selectivity) of the interactions between adsorbed molecules and the surface of nanotubes, nor about the details of any changes in electronic * Corresponding author. Fax: 435-797-3390. E-mail: [email protected]. † Utah State University. ‡ Ruhr-University Bochum. § Wright-Patterson AFB.

structure that accompany this weak attachment. The current work begins to address this lack of information through the use of quantum chemical calculations. To date, prior calculations22-25 of this phenomenon have consisted primarily of density functional theory (DFT), including the recently developed dispersion-corrected DFT (DFT-D) and semiempirical PM3 (PM3-D)26 methods. Reported studies, summarized in Table 1, predict a wide range of binding energy (between 2 and 11 kcal/mol) for the adsorption of a benzene molecule on the outer wall of various nanotubes. Although the binding energy is highly sensitive to the particular method, one conclusion that seems common to all procedures is that the benzene molecule has little to no preference for the chirality of the tube, and also that the most stable structure places the benzene directly above a bridging CdC bond of SWNT. There also remains a lingering controversy in that a stronger interaction between some planar organic molecules with metallic tubes over semiconducting counterpart predicted by local density approximation (LDA)24 was contradicted by a recent PM-D investigation.26 From a theoretical perspective, weak interactions such as these typically require a highly correlated quantum mechanical method, such as MP2,27 and lower level calculations such as DFT and PM3 cannot necessarily be trusted. The benzene dimer is a typical example of such an interaction28 where MP2 theory was found to be essential for an appropriate description of the π-π interaction. In the present investigation, MP2 theory is employed to estimate the binding energy of benzene and naphthalene molecules at the outer surface of different nanotubes, in an attempt to provide a more reliable and accurate accounting of the forces involved. It is hoped further that the results here may serve as a benchmark for calculations carried out at lower levels. Computational Methods All calculations were performed at the correlated MP2 level27 (inner shells excluded from the correlation), using the Gaussian03 code.29 A split-valence double-ζ quality 6-31G(d) basis

10.1021/jp807809u CCC: $40.75  2008 American Chemical Society Published on Web 11/21/2008

π-π Stacking and CH---π Interactions on SWCNTs

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TABLE 1: Summary of Previous Studies on Benzene SWNTs modela (m,n)

site-#C

methodb

∆E (kcal/ mol)c

Rd (Å)

ref (code used)

(10,0) (5,5) (10,0) (6,6) (10,0) (8,0)

B-C80 B-C80 B-C60 B-C96 B-C120 B-C96 S-C96 B-C280H20 B-C84H24 B-C80H20

PBC, GGA-WP, DZ+P PBC, LDA-PZ, DZ+P+3s for C, CP

-2.37 -4.45 -4.52 -2.31 -2.54 -6.00 -3.48 -10.32 (-14.69) -10.56 (-15.12) -7.4

3.7 3.26 3.21 3.28 3.16 3.12 3.22 3.192 3.248 3.192

22 (DMOL) 23 (SIESTA)

(10,0) (6,6) (10,0)

PBC, LDA, DZ, full-opt PBC, LDA PM3-D, full-opt BLYP-D, TZV(2d,2p), PM3-D 0pt

a

24 (CASTEP) 25 (VASP) 26 (Gaussian03) 26 (Gaussian03)

b

B - Bridge bond, S - Stacking (see Figure 1 for description). PBC - periodic boundary condition, GGA - generalized gradient approximation, LDA - local density approximation, WP - Wang and Perdew, PZ - Perdew and Zunger, DZ - double ζ basis, P - additional polarization functions, full-opt - fully optimized geometries, CP - counterpoise BSSE correction. BLYP-D and PM3-D - dispersion-corrected BLYP and PM3 theory, respectively, TZV - triple ζ basis set. c Binding/interaction energy. Negative quantities refer to attractive binding. Dispersion energies are in parenthesis. d Closest C-C distance.

Figure 1. Molecular models used in the present study. Different adsorption sites (S, B, BB, and T) are shown by black dots. Carbon atoms, within the box, of SWCNTs are considered for the SLDB method. See text for the definition of arrows.

set was used for all calculations, including Cartesian dpolarization for carbon atoms. Specific nanotube molecular models considered in the present study are armchair (a) (5,5) and zigzag (z) (10,0) tubes terminated with hydrogen atoms on both ends. As may be noted in Figure 1, these configurations differ in that the long axis of each hexagon is parallel to the tube axis in the zigzag structure, whereas this hexagon axis is rotated by 90° in the armchair. Detailed calculations are mostly performed with 80-carbon tubes (a80 and z80); 120-carbon tubes (a120 and z120) are also included in the list so as to estimate the effect of length on the results. In all cases, the benzene molecule is placed on the surface of each tube in one of the positions depicted in Figure 1. The π-π stacking arrangement, denoted S, places the benzene directly above a tube hexagon. If the benzene is slid so that its center is directly above an axial CdC bond (parallel to tube axis), this “bridge” configuration is denoted by B. The bridgebis (BB) configuration also places the benzene center above a CdC bond, but in this case the bond makes an angle of 30° to the tube axis. The T-shaped (T) structure rotates the benzene so that it is perpendicular to the tube, with one C-H bond approaching the π cloud, forming what is sometimes termed a CH · · · π H-bond.

Kar and co-workers10,30,31 recently showed the advantages of using a same level different basis (SLDB) protocol over other procedures, such as the widely used ONIOM,32,33 for studying chemical modifications of SWNTs at their side walls and tips. In this approach, atoms in defined active sites are provided with larger sets of basis functions, while smaller sets are applied to the remaining atoms. To assess the reliability of this technique for noncovalent interactions here, MP2 computations with a 6-31G* basis set for all atoms are compared with results obtained using MP2-SLDB, in which 6-31G* basis functions are applied to benzene and six (for S and T) to 10 (for B and BB) carbons of NTs as indicated by the rectangles in Figure 1. The remaining atoms are treated with a smaller split-valence double-ζ (3-21G) basis set. This combination reduces the number of basis functions and hence the computational time within the context of a full MP2/6-31G* calculation. In general, MP2-SLDB saves computational time by about 60-70% on the correlation calculation step, at the cost of less than (0.5 kcal/ mol for 80-carbon tubes (see below). Since such weak physical interactions have little effect on the structures of interacting species (also confirmed by optimization using different methods23,24,26), the geometries of approaching benzene and host SWNTs are held fixed during the calculations, in the structures optimized as isolated systems. Interaction energies (∆E), obtained as the energy difference E(benzene · · · SWNT) - [E(SWNT) + E(benzene)], are corrected for basis set superposition error (BSSE) by the counterpoise procedure of Boys and Bernardi.34 Results and Discussion Binding energies, with and without BSSE correction, estimated using MP2/6-31G* and MP2-SLDB (6C/10C-6-31G*+321G) theory are summarized in Table 2. Correlation energies refer to the difference in BSSE-corrected binding energy between the MP2 and SCF levels, reported in Table 2 as E(Corr). Dispersion is a phenomenon associated with electron correlation, and so it is contained within the correlation contribution to the interaction energy. Uncorrected MP2 energies reported in the first two columns of Table 2 clearly support previous findings that the B configuration, with the benzene stacked above an axial CdC bond, represents the preferred site of attachment, whether one is considering either a z- or a-type tube. This preference remains after counterpoise correction, albeit not as pronounced. For the S or B arrangements of the benzene, there seems to be a slight

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Kar et al.

TABLE 2: MP2 Binding Energies (∆E),a Dispersion Contributions E(Corr), and Interaction Distances (R) of Benzene on (10,0) and (5,5) SWCNTs ∆E (kcal/mol)

BSSE-corrected ∆E (kcal/mol)

R (Å)c

E(Corr) kcal/mol

modelb

6-31G*

SLDB

6-31G*

SLDB

6-31G*

SLDB

C-C/X---H

R(X-X′)

q(me)d NPA

S-z80 S-a80 B-z80 B-a80 BB-z80 BB-a80 T-z80 T-a80 S-z120 S-a120 B-z120 B-a120

-9.71 -9.82 -13.03 -11.99 -11.13 -11.15 -6.62 -5.91

-9.51 -9.58 -12.98 -11.84 -11.46 -10.93 -6.72 -5.94 -10.47 -10.50 -13.76 -12.77

-4.37 -3.68 -5.69 -4.89 -3.55 -4.68 -2.69 -2.79

-3.82 -3.16 -5.13 -4.56 -3.59 -4.18 -2.36 -2.57 -4.63 -4.07 -5.85 -5.42

-14.92 -15.90 -19.09 -17.69 -16.23 -16.74 -8.16 -6.83

-13.91 -14.45 -18.03 -16.88 -16.16 -15.71 -8.36 -6.78 -14.51 -15.01 -18.27 -17.58

3.21 3.20 3.08 3.17 3.18 3.17 2.30 2.20 3.21 3.20 3.08 3.17

3.40 3.20 3.00 3.10 3.10 3.10 4.79 4.69 3.40 3.20 3.00 3.10

+2.5 +2.6 +7.8 +3.0 +5.3 +8.5 -3.8 -4.2 +2.9 +3.1 +10.8 +1.0

a Negative quantities refer to attractive binding. b S, B, BB, and T stand for stacking, bridge, bridge-bis, and T-structure (C-H---π H-bonded), respectively, as shown in Figure 1. a and z stand for (5,5) armchair and (10,0) zigzag SWCNT, respectively. c Closest intermolecular C---C/X---H distances, where X is the center of the hexagon at the tube surface (black dot in Figure 1). X′ is the center of the benzene ring. d Changes in natural charges (in millielectrons) of benzene upon complex formation. Positive (negative) value indicates loss (gain) of electron density.

preference for a z over an a tube, and the opposite is noted for BB. The T-shaped arrangement is consistently less stable than any of the stacked structures. It may be recalled that, for the simple benzene dimer, the T-shape π-hydrogen-bonded structure is isoenergetic or slightly more stable28,35 than the paralleldisplaced structure (similar to the B arrangement here) representing one significant difference between the small and larger complexes. With respect to full 6-31G* vs the more efficient SLDB, as in the cases of covalent modifications at the tips and side walls of SWCNTs,10,30,31 the computationally efficient mixed basis set protocol is quite reliable for studying noncovalent interactions: the SLDB interaction energies mimic the trends in the full 6-31G* data in most cases. The maximum deviation of the MP2-SLDB energy is only 0.003 kcal/mol per carbon atom from MP2/6-31G* values. Comparing previous results summarized in Table 1 and MP2 values for the most stable B configuration of the same kind of tube, it is clear that DFT (LDA or GGA) underestimates the binding energy, with the exception of BSSE-corrected LDA for B-C80-(5,5).23 However, this same method underestimates the ∆E value by 1.2 kcal/mol for the (10,0) tube. For the (10,0) case, DFT-D energy26 is overestimated by about 2 kcal/mol, whereas this difference is almost doubled at the PM3-D level of calculation. According to reported DFT-LDA studies,23,24 binding energy difference between benzene and semiconducting (10,0) and metallic (5,5) tubes is negligible (the former being preferred by only 0.1 to 0.2 kcal/mol), and thus no conclusion can be drawn on the preference of benzene adsorption. The corresponding MP2 difference is slightly higher; the zigzag (10,0) tube is preferred by about 0.7 kcal/mol per benzene molecule. In reality, nanotubes are much longer than those considered in these studies, and certainly many benzene molecules may anchor at the surface. If binding energies are additive, then the difference will increase correspondingly. To verify such a scenario, two benzene molecules were placed at opposite sides of the wall (both at B site) of the 80-carbon tubes. The BSSEcorrected MP2-SLDB values are -10.3 and -9.1 kcal/mol for (10,0) and (5,5), respectively. These values are exactly double the corresponding values obtained for a single benzene. This result suggests that even a small preference in binding of a single molecule will be appropriately magnified by the number of such benzenes that may attach to the nanotube.

The effect of terminating the tube at a given length is considered by using longer z120 and a120 molecular models, an increment of length by about 0.4 and 0.5 nm, respectively, compared to their smaller 80-carbon cousins. MP2-SLDB binding energies are displayed in the lower part of Table 2. The interaction energy of benzene with both kinds of tube is enhanced by less than 1.0 kcal/mol by this lengthening, regardless of the attachment site. One might anticipate that this increment will diminish with further elongations of the tube, leading to a rapid convergence of binding energies. Because of the nature of the interacting species, it is expected that a large portion of the binding energy will arise from dispersion energy. As indicated above, this quantity is contained within the correlation portion of the interaction energy. The other major contributor to the correlation energy arises from the changes induced in the electrostatic energy that are associated with the correlation-induced modifications in the electron distributions within each monomer.36 The latter term would appear to be quite small in these cases. This conclusion is drawn by a comparison of SCF with MP2 multipole moments of the individual species. It was found that the diagonal elements of the quadrupole moment tensors, the highest-order nonzero moments of these symmetric benzene and nanotube species, were changed by less than 3% when the level of calculation was raised from SCF to MP2. For this reason, the correlation energies of the various complexes can be considered to serve as a reasonably accurate measure of the dispersion component. As noted from the large negative values of the correlation energies reported in Table 2, the dispersion energy is quite attractive: between 15 and 20 kcal/mol for the stacked arrangements. It would be fair to categorize these complexes as dispersion-dominated as the interaction energies at the MP2 geometry are repulsive at the SCF level. The largest correlation energies are associated with the B arrangements (these quantities are about 4-5 kcal/mol larger than predicted by PM3-D). The magnitude of the dispersion energy is cut in half when the benzene is rotated 90° into the T-shaped complexes. It may be worth mentioning that, in the case of π-stacked benzene dimer, MP2 interaction energy is slightly overestimated compared to that of CCSD(T) energies.28 It is hoped that the correlation energies reported here may be utilized for in the continued development of dispersion-corrected DFT, or other economical methods, for dealing with nanotubes and related systems.

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Figure 3. Variation of energies with tilt angle.

Figure 2. Tilting directions of benzene on a (10,0) tube.

The penultimate column of Table 2 lists the optimized distances between the benzene and nanotube centers. In the stacked geometries, the two entities are much closer together than in the more weakly bound T-shaped structures. The shortest intermolecular distance occurs for B-z80, wherein the benzene lies directly above a CdC bond of the zigzag nanotube. On the other hand, there is little to distinguish one stacked structure from another on this score, as the distances are comparable for all. The preceding column lists an alternate parameter in the same structures, the separation between the relevant CdC bond of the nanotube and the nearest C (or H for T-shape) atom of the benzene. (This quantity is listed primarily for purposes of comparison with other calculations, as those reported in Table 1.) The group charge acquired by the benzene molecule upon complexation in each of the complexes is displayed in the final column of Table 2, in millielectron units. The benzene acquires a slight positive charge (loses electron density) for the stacked geometries, with the reverse occurring if the benzene approaches with its plane perpendicular to the nanotube axis. The latter acquisition of negative charge by the benzene is consistent with the normal pattern of electron transfer from the proton acceptor (nanotube) to the donor (benzene) upon formation of a hydrogen bond.37 Thus, depending on the arrangements of guest at the surface, nanotubes can act as electron acceptor or donor. Benzene is considered here as modeling the part of a larger molecule that is noncovalently attached to the surface of SWNTs. Substituents may cause the aromatic structure to deviate or dislocate from its optimal location, determined and discussed above. To examine how such deviations might affect the energetics, the benzene molecule was rotated and tilted relative to the nanotube. The intermolecular distances were held fixed at their optimized values listed in Table 2, and then for both S and B arrangements the benzene was pivoted as a rigid unit, as illustrated in Figure 2. For both S and B arrangements, it appears that benzene can freely rotate on the surface, as the

energy (MP2-SLDB) change is less than 0.2 kcal/mol on successive rotation by 10° from the original position. A similar result was also reported by Tournus and Charlier23 using the LDA method. The first mode of tilting benzene rotates its molecular plane so as to make a tilt angle with the axis of the nanotube, designated as “ax”, indicated on the left side of Figure 2. The “circumferential” (cir) deformation, shown on the right side of the figure, rotates the benzene perpendicularly to the nanotube axis. The destabilization of the MP2-SLDB energy with respect to tilt angle is displayed in Figure 3 (because of SCF convergence problems, B-z80-ax and S-z80-ax results could not be included for comparison). These energy increments are fairly small, less than 1 kcal/mol for deviations of less than 10°. A similar result was reported by Tournus and Charlier23 using the LDA method. However, larger deformations result in an escalating destabilization, up to as much as 6 kcal/mol for the B structure when θ ) 20°. The S arrangement is least susceptible to distortion energy, and the zigzag tube least of all. The circumferential distortion requires less energy than does the axial deformation. In addition to tilting, benzene may also slide along the tube surface: such a translation could again be along the axial or circumferential directions. Because of orientational differences of hexagons in zigzag and armchair tubes, sliding from stacking (S) configuration to CdC double bond sites (B) (designated by arrow in S-z120 of Figure 1) of the (10,0) tube, along the circumferential direction, appears more facile (costs only 1.3 kcal/mol) than that along the axial direction. On the basis of the same reasoning, translation along the axial direction seems easier for armchair tubes. Tournus and Charlier23 had earlier studied the translation of benzene on the (9,0) nanotube surface. The LDA energy difference between S and B sites is about 2 kcal/mol, slightly higher than the MP2 value of 1.3 kcal/mol for the (10,0) tube. The present investigation was extended beyond the benzene paradigm by considering naphthalene as a larger representative aromatic molecule. Sample results are presented in Figure 4, where part of the tube is included for clarity. Two possibilities of attachment were evaluated via the MP2-SLDB method, where the naphthalene lies parallel to the circumferential (cir) and axial (ax) directions on 120 C tubes (previous studies denoted these structures, respectively, as perpendicular and parallel). For

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Figure 4. Naphthalene on top of (10,0) and (5,5) tubes. Energies are in kilocalories per mole, and charges (q) of naphthalene are in millielectrons. Positive means loss of electron density.

N-z120-cir and N-a120-ax, the 14 C atoms forming three hexagons (like anthracene) and 13 carbons of N-z120-ax and N-a120-cir (like 1H-phenalene) directly facing the guest are represented by the larger 6-31G* basis set, in addition to all carbons of naphthalene. The smaller 3-21G basis was used for the remaining atoms of the SWCNT. Single-point MP2-SLDB calculations were performed, holding intermolecular distances fixed at the values obtained for the most stable B-z80 (3.08 Å) and B-a80 (3.17 Å) structures. Because of different arrangements of hexagons of zigzag and armchair nanotubes, the guest’s two planar hexagons face SWCNTs in different ways. In the case of N-z120-cir, both naphthalene rings are above the bridge sites, one somewhat closer (3.08 Å) to the tube. Both hexagon centers are located at the same distance from the nanotube in the N-a120-ax configuration. In the axial structure of zigzag tube (N-z120-ax), both B and S sites are involved, as is also the case for N-a120-cir. A previous DFT-LDA24 study indicated that naphthalene prefers metallic (6,6) tube at cir-(perpendicular) orientation compared to a semiconducting tube at ax- or parallel position; the energy difference is slightly more than 2.0 kcal/mol. However, a recent PM3-D study by Hillier and co-workers26 did not support such a large difference. The latter calculation indicated that all four structures are nearly isoenergetic: ax orientations are more stable by only 0.5 kcal/mol. It may be noted that geometries were fully optimized in both LDA and PM3-D studies, whereas C-C distances considered in the present MP2 calculations were fixed and fell close to the optimized values. In comparison to the present BSSE-corrected MP2-SLDB energies, the LDA method underestimated the interaction energies, almost half that of MP2 for armchair tubes, and onethird for zigzag tubes. PM3-D, on the other hand, overestimated this quantity by 5-6 kcal/mol. It is worth mentioning that the two latter calculations did not correct superposition error. Such a correction would further reduce the interaction energies. On the basis of the binding energies of benzene to the nanotubes, one might suppose that the strongest interaction between naphthalene and a (5,5) tube would occur at an axial site (N-a120-ax) where each ring of the guest lies above a CdC

Kar et al. double bond (B sites) and resides at a similar intermolecular distance. In the comparable arrangement in N-z120-cir, one hexagon is far from the second CdC double bond in the circumferential direction and hence may contribute less to the total binding energy. However, the present study does not support such a prediction. According to the present MP2 investigation, the most stable structure is N-z120-ax (∆E ) -11.06 kcal/mol) followed by N-z120-cir (-10.44 kcal/mol) and N-a120-ax (-9.96 kcal/mol), and the least stable of the four is N-a120-cir (-9.79 kcal/mol). Therefore, for both tubes, the ax orientation is preferred, probably because of the large contact area. The difference between ax and cir naphthalene armchair tubes is only 0.2 kcal/mol, and the corresponding value is 0.6 kcal/mol for a (10,0) tube. As discussed in the case of benzene, if one thinks of a high density of guest molecules on the surface of much longer SWCNTs, then this difference will rise proportionately (multiplied by the number of guests), which may lead to a preferred interaction with a zigzag tube. Again, the dispersion contribution to binding is significant, and those values are close to PM3-D for cir arrangements, but the latter theory underestimated this quantity by 7-9 kcal/mol for ax orientations. Natural charge analyses indicate that nanotubes are accepting electron density from naphthalene to a larger amount than occurs for benzene. Conclusions Electron-correlated quantum mechanical MP2 method, necessary for accurate description of weakly bound systems, has been used to understand the magnitude and nature of noncovalent interaction between aromatic molecules (benzene and naphthalene) with various nanotubes. Depending on the sites of adsorption, MP2 binding energies are 2.5-6.0 kcal/mol per benzene molecule, and π-π stacking interactions are considerably stronger than C-H---π H-bonded arrangement. The configuration where benzene lies on top of a CdC double bond of the SWCNT is the most stable structure, followed by hexagon-hexagon stacking. Benzene prefers a zigzag (10,0) tube over the isoelectronic armchair (5,5) by about 1.3 kcal/ mol, and this difference grows roughly proportionately with the number of adsorbent molecules. However, this conclusion is based on the comparison between (10,0) and (5,5) tubes only and may not be capable of gross generalization. Lengthening of tube model increases the binding energy. While benzene can rotate freely on the active site, tilting is more costly in energy. With regard to a larger aromatic, the strongest interaction is found between naphthalene and the (10,0) tube in an axial orientation. DFT theory underestimates the interaction, and dispersioncorrected methods (DFT-D and PM3-D) overestimate the binding energies. Like for covalent interactions, the computationally efficient SLDB method is found to be reliable for studying noncovalent chemistry of carbon nanotubes. Since nanotubes are not easily separable and synthetic methods have yet to be developed to produce nanotubes based on their chirality and dimensions, the present MP2 results may be considered as a possible benchmark for further development of efficient methods, such as dispersion-corrected DFT or PM3, to study noncovalent interactions of large nanotubes. Acknowledgment. This work was supported by the Alexander von Humboldt-Stiftung and the Deutsche Forschungsgemeinschaft. We thank the MSRC personnel for their support in using the ASC/HP computational resources.

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