Effects of Finite Carbon Nanotube Length on Sidewall Addition of

Chemically reactive species remain alive inside carbon nanotubes: a density functional theory study. Takashi Yumura. Phys. Chem. Chem. Phys. 2011 13, ...
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ORGANIC LETTERS

Effects of Finite Carbon Nanotube Length on Sidewall Addition of Fluorine Atom and Methylene

2004 Vol. 6, No. 5 731-734

Holger F. Bettinger* Lehrstuhl fu¨r Organische Chemie 2, Ruhr-UniVersita¨t Bochum, 44780 Bochum, Germany [email protected] Received December 9, 2003

ABSTRACT

Density functional computations (PBE and B3LYP) in conjunction with 3-21G and 6-31G* basis sets are used to determine the energy of fluorine atom and CH2 addition to the sidewall of (5,5) C30+10nH20 (n ) 0, 1, 2...18) carbon nanotube slabs. A pronounced oscillation of the addition energy is found for fluorine atom addition, while oscillations are significantly damped for carbene addition due to the insertion into CC bonds.

Fluorination1 of single-walled carbon nanotubes2 (SWNT) provides an efficient method for modification of the properties of these hollow filaments. Theoretical studies3 of fluorinated single-walled carbon nanotubes give some important insights into the properties of this novel carbonfluorine material. However, a key aspect of nanotube fluorination, the strength of the bond between a SWNT and a single fluorine atom, remains unclear to date. Using a twolayered ONIOM4 approach (B3LYP/4-31G:UFF) with a

coronene unit as a high-level area, Bauschlicher3a arrived at a binding energy of 26 kcal mol-1, while Jaffe3h obtained 38 kcal mol-1 (B3LYP/4-31G) for a C78H20 model of a (5,5) SWNT. Larger binding energies were obtained in density functional investigations on finite-length (5,5) armchair slabs, but a strong dependence on the nanotube length is observed: 45 kcal mol-1 (B3LYP/6-31G*) for a C50H20 (5,5) tube;3g 68 kcal mol-1 (PBE/6-31G*) for a C90H20 (5,5) tube.3d Even though attack of fluorine during the fluorination reac-

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tion is expected to be more facile at (closed or open) ends, at defect sites, and in close proximity to a carbon atom already fluorinated,3a,h,i a principal understanding of the factors governing the C-F bond dissociation energy is desirable. Another example of addition to nanotube sidewalls is the reaction with carbenes, which has been demonstrated experimentally.5 But as density functional theory computations based on polycyclic aromatic hydrocarbon (PAH), curved as in a (10,10) SWNT suggested that the binding energy is small, some of the earlier experiments have been questioned.6 One drawback of theoretical investigations in the study of nanotube reactivity is their need to rely on small models in order to limit the computational expense. However, truncation of a nanotube to finite length results in a finite HOMO-LUMO energy gap, while (n,n) armchair tubes are metallic and (n,0) zigzag tubes are semiconducting or semimetallic (if n is divisible by 3) at infinite length. The HOMO-LUMO gap (or a weighted version thereof) is commonly used as a qualitative measure of kinetic stability of extended π systems.7 Applied to nanotube chemistry, this would suggest that metallic tubes should be more reactive than semiconducting ones, as has been demonstrated very recently for the diazotation in aqueous medium by Strano et al.8 Accordingly, it seems reasonable to assume that the artificial generation of an energy gap by truncation of an otherwise (semi)metallic SWNT should result in reduced reactivity. In addition, edge effects are recognizable for nanotubes,9-11 in analogy to their planar PAH cousins.12 Matsuo et al.,10 for example, linked the oscillations of structure, frontier orbital energies, and gaps to Clar13 valence bond structures and found agreement with nucleus-indepen(5) (a) Chen, Y.; Haddon, R. C.; Fang, S.; Rao, A. M.; Eklund, P. C.; Lee, W. H.; Dickey, E. C.; Grulke, E. A.; Pendergrass, J. C.; Chavan, A.; Haley, B. E.; Smalley, R. E. J. Mater. Res. 1998, 13, 2423. (b) Chen, J.; Hamon, M. A.; Hu, H.; Chen, Y.; Rao, A. M.; Eklund, P. C.; Haddon, R. C. Science 1998, 282, 95. (c) Holzinger, M.; Vostrowsky, O.; Hirsch, A.; Hennrich, F.; Kappes, M.; Weiss, R.; Jellen, F. Angew. Chem. 2001, 113, 4132; Angew. Chem., Int. Ed. Engl. 2001, 40, 4002. (d) Holzinger, M.; Abraham, J.; Whelan, P.; Graupner, R.; Ley, L.; Hennrich, F.; Kappes, M.; Hirsch, A. J. Am. Chem. Soc. 2003, 125, 8566. (e) Niyogi, S.; Hamon, M. A.; Hu, H.; Zhao, B.; Bhowmik, P.; Sen, R.; Itkis, M. E.; Haddon, R. C. Acc. Chem. Res. 2002, 35, 1105. (f) Kamaras, K.; Itkis, M. E.; Hu, H.; Zhao, B.; Haddon, R. C. Science 2003, 301, 1501. (g) Hu, H.; Zhao, B.; Hamon, M. A.; Kamaras, K.; Itkis, M. E.; Haddon, R. C. J. Am. Chem. Soc. 2003, 125, 14893. (h) Hirsch, A. Angew. Chem. 2002, 114, 1933; Angew. Chem., Int. Ed. 2002, 41, 1853. (6) Jaffe, R. L. Proc. Electrochem. Soc. 1999, 12, 153. (7) (a) Hess, B. A.; Schaad, L. J. J. Am. Chem. Soc. 1971, 93, 2413. (b) Haddon, R. C.; Fukunaga, T. Tetrahedron Lett. 1980, 21, 1191. (c) Schmalz, T. G.; Seitz, W. A.; Klein, D. J.; Hite, G. E. J. Am. Chem. Soc. 1988, 110, 1113. (d) Zhou, Z.; Parr, R. G. J. Am. Chem. Soc. 1989, 111, 7371. (e) Diener, M. D.; Alford, J. M. Nature (London) 1998, 393, 668. (f) Manolopoulos, D. E.; May, J. C.; Down, S. E. Chem. Phys. Lett. 1991, 181, 105. (g) Liu, X.; Schmalz, T. G.; Klein, D. J. Chem. Phys. Lett. 1992, 188, 550. (h) Yoshida, M.; Aihara, J. Phys. Chem. Chem. Phys. 1999, 1, 227. (i) Aihara, J. Phys. Chem. Chem. Phys. 2000, 2, 3121, (8) Strano, M. S.; Dyke, C. A.; Usrey, M. L.; Barone, P. W.; Allen, M. J.; Shan, H.; Kittrell, C.; Hauge, R. H.; Tour, J. M.; Smalley, R. E. Science 2003, 301, 1519. (9) (a) Rochefort, A.; Salahub, D. R.; Avouris, P. J. Phys. Chem. B 1999, 103, 641. (b) Liu, L.; Jayanthi, C. S.; Guo, H.; Wu, S. Y. Phys. ReV. B 2001, 64, 033414. (c) Venema, L. C.; Wildo¨er, J. W. G.; Janssen, J. W.; Tans, S. J.; Tuinstra, H. L. J. T.; Kouwenhoven, L. P.; Dekker, C. Science 1999, 283, 52. (10) Matsuo, Y.; Tahara, K.; Nakamura, E. Org. Lett. 2003, 5, 3181. (11) (a) Andriotis, A. N.; Menon, M.; Chernozatonskii, L. Nano Lett. 2003, 3, 131. (b) Liang, W.; Wang, X. J.; Yokojima, S.; Chen, G. J. Am. Chem. Soc. 2000, 122, 11129. 732

dent chemical shift (NICS)14 analyses. Among the three possible cases, the structures with a “fully benzenoid” arrangement of electron sextets were found to have the highest-lying HOMO, lowest-lying LUMO, and smallest band gap, and thus should have the highest reactivity.10 In contrast, it is known for planar PAHs that the fully benzenoid members have the largest band gap and the lowest reactivity.12b,c,13a Although Matsuo et al.10 concluded that there must be a dependence of reactivity on the length of the tubes, this has not been studied explicitly. We report here the results of a computational investigation of the dependence of the reaction energy of fluorine atom and methylene (CH2) addition on the length of a (5,5) armchair tube. To our knowledge, a systematic investigation has not been reported previously, even though the extensive use of very small nanotube models in computational investigations of sidewall reactivity clearly demands such an analysis. We have investigated 19 individual (5,5) SWNT segments starting with C30H20 and increasing in length by increments of 10 carbon atoms until C210H20, i.e., C30+10nH20, n ) 0, 1...18. The hydrogen atoms were added at the open ends to avoid dangling bonds. Geometry optimizations were performed within the general gradient approximation using the Perdew-Burke-Ernzerhof15 (PBE) functional in conjunction with a 3-21G basis set. Final energies were obtained with Becke’s16 three-parameter hybrid functional as implemented17 in the Gaussian program,18 the Lee-Yang-Parr19 exchangecorrelation functional (B3LYP), and the 6-31G* basis set. All energies mentioned in the text were obtained at the (U)B3LYP/6-31G*//(U)PBE/3-21G level of theory (see Supporting Information for further details). Isomers with n ) 2k (k ) 0, 1...) have a symmetry plane (σyz) orthogonal to the tube axis (x direction), whereas those with n ) 2k + 1 (k ) 0, 1...) do not have this symmetry element (Figure 1). The fluorine atom is added to a carbon atom in the center of (12) (a) Klein, D. J.; Bytautas, L. J. Phys. Chem. A 1999, 103, 5196. (b) Stein, S. E.; Brown, R. L. J. Am. Chem. Soc. 1987, 109, 3721. (c) Moran, D.; Stahl, F.; Bettinger, H. F.; Schaefer, H. F.; Schleyer, P. v. R. J. Am. Chem. Soc. 2003, 125, 6746. (d) Yoshizawa, K.; Yahara, K.; Tanaka, K.; Yamabe, T. J. Phys. Chem. B 1998, 102, 498. (13) (a) Clar, E. Polycyclic Hydrocarbons; Academic Press: New York, 1964. (b) Clar, E. The Aromatic Sextet; Wiley: London, 1972. (14) (a) Schleyer, P. v. R.; Maerker, C.; Dransfeld, A.; Jiao, H.; van Eikema Hommes, N. J. R. J. Am. Chem. Soc. 1996, 118, 6317. (b) Schleyer, P. v. R.; Manoharan, M.; Wang, Z.-X.; Kiran, B.; Jiao, H.; Puchta, R.; van Eikema Hommes, N. J. R. Org. Lett. 2001, 3, 2465. (15) (a) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (b) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1997, 78, 1396(E). (16) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (17) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.11; Gaussian, Inc.: Pittsburgh, PA, 1998. (19) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. Org. Lett., Vol. 6, No. 5, 2004

Figure 1. Structural models of (5,5) armchair single-walled carbon nanotubes C30+10nH20 with even n (left) and odd n (right). The black arrows indicate the carbon atoms to which fluorine is added.

the SWNT slabs as far away from the nanotube edges as possible. Among the isomers with even n values, those with n ) 0, 6, 12, and 18 are fully benzenoid, while in the odd series, n ) 3, 9, and 15 characterizes fully benzenoid members. Based on C-C bond lengths and on NICS values, Matsuo et al.10 termed the members with n ) 1, 4, 7, 10, 13, and 16 as “Kekule´”, while those with n ) 2, 5, 8, 11, 14, and 17 are of the “incomplete Clar” type. We observe similar HOMOLUMO level and band gap oscillations as reported by Matsuo et al. (Figure 2).10

Figure 2. Dependence of HOMO (squares) and LUMO (diamonds) energies (in eV) and band gaps (filled triangles, in eV) for (5,5) SWNTs of C30+10nH20 composition and band gaps (open triangles, in eV) for corresponding methylene adducts on n as computed at the PBE/3-21G level of theory.

We furthermore observe a strong oscillation of the C-F bond dissociation energy (Figure 3a) ranging from 43 to about 68 kcal mol-1. The oscillation of the addition energy is larger for the shorter members (∆E ) 25 kcal mol-1), while for the longer ones (n ) 13-18) the energy varies between 47 and 58 kcal mol-1. The strain of the carbon backbone associated with addition of a fluorine atom3h is Org. Lett., Vol. 6, No. 5, 2004

Figure 3. Reaction energies (in kcal mol-1) for the addition to (5,5) single-walled carbon nanotube models C30+10nH20 as computed at the (U)B3LYP/6-31G*//(U)PBE/3-21G level of theory. (A) Fluorine atom; (B) triplet methylene (n ) 2k) addition mode A (Figure 4).

most easily minimized in the most flexible SWNT models (n ) 0, 1), for which consequently the fluorination reactions have exceptionally large exothermicities compared to the slabs with n ) 2, 3. The 43 kcal mol-1 obtained here for n ) 2 is in good agreement with the 45 kcal mol-1 obtained previously3g by B3LYP/6-31G* geometry optimization. The energy oscillation is periodic with peaks at the fully benzenoid members, in agreement with their smallest band gaps. The even n members of the fully benzenoid series have the strongest C-F bonds with very similar energies close to 60 kcal mol-1. The computation of still longer fully benzenoid SWNT slabs is most probably troublesome with the cluster approach adopted here due to a further decrease in the band gap. The carbon atom carrying the fluorine substituent is transformed from (formally) sp2 to sp3. The corresponding C-C bond distances range between 1.507 and 1.516 Å (for bonds along the tube axis, see Figure 4) and 1.521-1.555 Å (for perpendicular bonds). As expected, the extreme values are obtained for the more flexible shorter tubes. The C-F distances vary between 1.438 Å (n ) 0) and 1.455 Å (n ) 9). We have selected methylene as a prototype carbene for investigation of the length dependence of the addition energy (Figure 3b). There are a number of differences compared to 733

Figure 4. (5,5) SWNT slab with n ) 6 (C90H20) with rings symbolizing the aromatic sextets in the fully benzenoid Clar structure. The black arrows indicate the bonds to which the carbene is added in “perpendicular” mode (A) and “along the tube axis” (B).

the fluorine atom addition: the oscillation is dramatically damped for the larger members (n g 6; E ) -93 to -89 kcal mol-1), while the addition reaction is significantly more exothermic for the short members (in particular for n ) 0). An explanation of this opposing behavior of (5,5) SWNT slabs in carbene addition compared to fluorine atom addition can be found when considering the geometric and electronic structures of the SWNT reactants and addition products. Most remarkably, the latter do not have the typical three-membered rings associated with carbene addition to double bonds, but rather the CC bond is broken (C-C distances range from 2.439 Å (n ) 0) to 2.163 Å (n ) 3) and are close to 2.20 Å for the longest tubes). The breaking of the C-C bond can be ascribed to the strain exerted on these bonds in the tubular structures. This strain can be reduced by insertion of a flexible methylene bridge, which is particularly effective for the more flexible short members of the series (n ) 0, 2). Furthermore, insertion of the CH2 unit into the central CC bond does not change the topology of the π system (see Figure 4), as the number of conjugated carbon atoms remains the same as in the SWNT model.20 Electronically similar systems are therefore compared on the left- and right-hand sides of the SWNT + CH2 f CH2-SWNT equation, and hence edge effects are reduced. Accordingly, the HOMOLUMO gaps in CH2-SWNT parallel those of the pristine tubes (Figure 2). In contrast, fluorine addition transforms one (formally) sp2 carbon into an sp3 carbon, thereby changing the topology of the π system. Formation of a three-membered ring is observed upon carbene addition to a bond that is oriented along the tube axis (B in Figure 4, n = 6), but this cyclopropane derivative is less favorable than the CC-insertion product by 29 kcal (20) In this sense, the π systems of methylene adducts are related to those of the pristine nanotubes by homoconjugation. See, e.g.: Stahl, F.; Schleyer, P. v. R.; Jiao, H.; Schaefer, H. F.; Chen, K.-H.; Allinger, N. L. J. Org. Chem. 2002, 67, 6599.

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mol-1. The open structure is also more favorable (by 12 kcal mol-1) for the (10,10) analogue of the (5,5) n ) 6 slab, indicating that the perpendicular bonds are significantly strained also in larger diameter nanotubes. In summary, we have shown that the energy for addition of fluorine to the nanotube sidewall depends strongly on the length of the nanotube. Fully benzenoid nanotubes have the smallest band gap and the largest addition energy, in agreement with frontier orbital expectations as expressed by Matsuo et al.10 The pronounced length dependence needs to be taken into account when probing the viability of sidewall functionalization computationally. As the infinite-length armchair nanotubes have zero band gaps, we suggest focusing on fully benzenoid slabs when the binding energy of a radical to an armchair tube is of interest.3d,g Reaction of methylene, CH2, differs as insertion into the strained perpendicular CC bonds preserves the topologies of the delocalized π systems and reduces edge effects. Addition of CH2 to the CC bonds oriented along the tube axis is significantly less favorable. Taking into account the BellEvans-Polyani principle, which connects reaction energies to barrier heights, it could be speculated that the barrier for carbene addition to the perpendicular bonds should be lower. Note that the opening of the armchair nanotube sidewalls by carbene addition was not found in two-layer ONIOM calculations (B3LYP/6-31G*:AM1) with a pyrene-like C16 high-level layer. 21d In view of our results, we stress that a careful selection of layers is crucial for application3a,21 of the ONIOM method for the investigation of nanotube sidewall functionalization.22 Acknowledgment. I thank the Fonds der chemischen Industrie for continued support through a Liebig Fellowship, Professor Sander for encouragement, and Chen et al. (ref 22) for providing a preprint of their work and unpublished B3LYP/6-31G* data. This work was supported by the BMBF through the SONNE project. Supporting Information Available: Computational details, absolute energies, and Cartesian coordinates for structures considered in this work. This material is available free of charge via the Internet at http://pubs.acs.org. OL0363974 (21) (a) Lu, X.; Yuan, Q.; Zhang, Q. Org. Lett. 2003, 5, 3527. (b) Lu, X.; Tian, F.; Xu, X.; Wang, N.; Zhang, Q. J. Am. Chem. Soc. 2003, 125, 10459. (c) Lu, X.; Tian, F.; Zhang, Q. J. Phys. Chem. B 2003, 107, 8388. (d) Long, L.; Lu, X.; Tian, F.; Zhang, Q. J. Org. Chem. 2003, 68, 4495. (e) Lu, X.; Tian, F.; Wang, N.; Zhang, L. Org. Lett. 2002, 4, 4313. (f) Lu, X.; Zhang, L.; Xu, X.; Wang, N.; Zhang, Q. J. Phys. Chem. B 2002, 106, 2136. (g) Bauschlicher, C. W. Nano Lett. 2001, 1, 223. (h) Froudakis, G. E. Nano Lett. 2001, 1, 179. (i) Bauschlicher, C. W.; So, C. R. Nano Lett. 2002, 2, 337. (22) Failure of some ONIOM calculations in describing the addition of divalent species, in particular the sidewall opening, has recently been analyzed in detail by: Chen, Z.; Nagase, S.; Hirsch, A.; Haddon, R. C.; Thiel, W.; Schleyer, P. v. R. Angew. Chem., Int. Ed.. In press.

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