NANO LETTERS
Periodic Graphene Nanobuds
2009 Vol. 9, No. 1 250-256
Xiaojun Wu and Xiao Cheng Zeng* Department of Chemistry and Nebraska Center for Materials and Nanoscience, UniVersity of NebraskasLincoln, Lincoln, Nebraska 68588 Received September 17, 2008; Revised Manuscript Received November 19, 2008
ABSTRACT Periodic graphene nanobuds (PGNBs) can be engineered by attaching C60 buckyballs onto a graphene monolayer, where C60 molecules form a periodic lattice structure. Structural and electronic properties of two prototype PGNBs are investigated for the first time by using the first-principles methods. In type I PGNB, C60 buckyballs are covalently bonded to a graphene monolayer, while in type II the fragmented buckyballs are fused onto the graphene monolayer. It is found that type I PGNBs can be either semiconducting or semimetallic, depending on the pattern of chemical bonding between C60 and graphene. Type II PGNBs are generally semimetallic. In particular, one hallmark electronic structure of the graphene monolayer, i.e., conic Dirac points, is still preserved in type II PGNBs except for the “ripped” graphene monolayer. The diversity in electronic structures renders PGNB a promising carbon material for applications in nanoelectronics and cold electron field emission. Furthermore, multilayer PGNBs form a porous network structure with surface areas greater than 2000 m2/g, which can be exploited for gas storage.
Introduction. Prototype low-dimensional carbon nanostructures such as buckminsterfullerene C60, carbon nanotubes (CNTs), and graphene carbon nanostructures have attracted intense research interest owing to their potential applications in nanoelectronics, sensors, and gas storage.1-10 Manifestation of quantum-confinement effect in these low-dimensional structures endows them with unique electronic, magnetic, and optical properties. For example, a single-walled CNT can be either metallic or semiconducting, depending on its helicity. A graphene monolayer is a semimetal with exactly zero band gap. Its charge carriers’ velocity is constant throughout the band edge, including the Dirac point where the top and the valence band overlaps with the bottom of the conduction band. Recently, it is reported that “buckyballs” C60 under certain conditions are capable of conducting electricity like metal atoms.11 Over the past few years, research effort has also been made to fabricate hybrid carbon nanostructures to seek new carbon materials with novel properties. The first hybrid carbon nanostructure fabricated in the laboratory is the carbon nanopeapod, in which a chain of C60 buckyballs are assembled within a carbon nanotube.10,12-14 Another hybrid carbon nanostructure reported recently is the so-called carbon nanobuds, in which C60 buckyballs are covalently attached to the sidewall of a single-walled CNT.15 Both experimental and theoretical studies suggest that carbon nanobuds (CNBs) can entail certain advantages of both C60 and CNT. As such, CNBs may be utilized as a new building block in nanoelectronic devices or for field emission.16-19 In this Letter, we report computer-aided materials design of a new series of * Corresponding author. E-mail:
[email protected]. 10.1021/nl802832m CCC: $40.75 Published on Web 12/10/2008
2009 American Chemical Society
hybrid carbon nanostructures, namely, periodic graphene nanobuds (PGNBs). A PGNB is a hybrid zero-dimensional and two-dimensional carbon material in which C60 buckyballs are covalently attached to a graphene monolayer or fragmented buckyballs are fused onto the graphene monolayer, forming a periodic lattice on the monolayer. We have studied structural, electronic, and field-emission properties of PGNBs by using the first-principles methods. Computational Methods. The first-principles calculations were carried out using the linear combination of atomic orbital density-functional theory (DFT) methods implemented in the DMol3 package.20-22 The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form and an all-electron double numerical basis set augmented with polarized function (DNP basis set) were chosen for the spin-restricted DFT calculations.23 Test calculation with a spin-unrestricted method gave the same results. The real-space global cutoff radius was set to be 3.70 Å. After geometric optimization, the forces on all atoms were less than 0.05 eV Å-1. A tetragonal supercell with dimension 24.7 × 24.7 × 40 Å3 (10 periodic lengths of graphene layer in both the a and b directions) was adopted in the DFT calculations (see Figure 1). The nearest distance between two neighbor nanobuds is greater than 17 Å. Only the Γ point was considered in the Brilliouin zone for the geometric optimization. For calculation of electronic properties of PGNBs, the Brilliouin zone was sampled by 10 × 10 × 1 k-points using the Monkhorst-Pack scheme.24 The ab initio molecular dynamic simulation in the Born-Oppenheimer scheme was performed using a constant temperature and constant volume (NVT) ensemble.25 The temperature (800 K) was controlled using the Nose´-Hoover
Figure 1. Optimized structures of (a) a single C60 molecule, (b) the supercell of graphene monolayer, the supercell of (c) 22-hp, (d) 22-hh, and (e) 66 PGNBs. The binding region between C60 and graphene is highlighted in yellow.
method, in which the kinetic energy fluctuation is controlled by coupling it to another thermostat variable.26 The time step was set to be 1 fs, and the total simulation time is 5 ps for each PGNB system. To speed up the simulation, the minimal basis set was used and the real-space global cutoff radius was reduced to 3.0 Å. Results and Discussion. A C60 molecule is composed of 60 sp2-hybrid carbon atoms that form a spherical cage with 20 hexagonal and 12 pentagonal rings. Two types of C-C bonds can be identified in C60, one intervening between a hexagonal and pentagonal ring and another between two hexagonal rings (labeled by hp and hh in Figure 1a). In a graphene monolayer, all sp2-hybrid carbon atoms are in the same plane, giving rise to the honeycomb structure as shown in Figure 1b. We have designed two prototype PGNBs based on hybrid C60 molecules and a graphene monolayer. The first type of PGNB (hereafter named as type I PGNB) is akin to the experimentally fabricated carbon nanobuds where C60 molecules are covalently attached to the “substrate” via cycloaddition reaction. Here, two possible ways of chemical bonding can arise: (1) two parallel C-C bonds are formed between C60 and graphene through the [2 + 2] cycloaddition, which give rise to a quadrilateral ring, and (2) a hexagonal ring of C60 is connected to a hexagonal ring of graphene through the [6 + 6] cycloaddition, which gives rise to six C-C bonds. More specifically, three conformers can be produced through the cycloaddition reactions: (i) 22-hp PGNB, in which chemical bonds are formed between the hp ring of C60 and graphene (Figure 1c), (ii) 22-hh PGNB, in which chemical bonds are formed between the hh ring of C60 and graphene (Figure 1d), and (iii) 66 PGNB, which solely arises from the [6 + 6] cycloaddition reaction (Figure 1e). We performed geometric optimization for all three conformers (see Methods). Clearly, some carbon atoms in Nano Lett., Vol. 9, No. 1, 2009
Table 1. Binding Energy (Eb), Average Bond Length of Newly Forming C-C Bonds (dcc), and Charge Transfer from C60 to Graphene 22-hp PGNB 22-hh PGNB 66 PGNB
Eb (eV)
dcc (Å)
C(e)
3.506 2.802 7.829
1.641 1.636 1.595
-0.011 -0.011 0.087
the graphene monolayer are pulled out of the graphene plane due to the formation of covalent bonds with C60 molecules. The binding energy, average bond length of newly formed C-C bonds between C60 and graphene, and the charge transfer from C60 to graphene computed using the Hirshfeld analysis method27 are summarized in Table 1. Here, the binding energy of C60 to graphene is defined as Eb(bud) ) E(bud) - E(C60) - E(graphene), where E(system) is the total energy of the system per supercell. As shown in Table 1, the 22-hh PGNB is more stable than the other two PGNBs since it requires the least binding energy (2.802 eV). Note that a positive value of binding energy refers to the endothermic binding process. The 22-hp PGNB is less stable than 22-hh PGNB as reflected in the longer average bond length between C60 and graphene. The less stability of 22hp PGNB can be understood from the bonding character involved in the cycloaddition reaction, that is, the hh bond entails more π-bond character than the hp bond in the C60 molecule.16 The 66 PGNB has the highest binding energy due to larger distortion, even though the average bond distance between C60 and graphene is the least among the three PGNBs. Charge analysis suggests that the charge transfer between C60 and graphene is miniscule in the formation of type I PGNB. The second type of PGNB (hereafter named as type II PGNB) involves fragmented C60 and a defective graphene monolayer, which can bring to bear more diverse struc251
Figure 2. A full or fragmented C60 molecules is fused with a graphene monolayer within the supercell. (a) A full C60 molecule shares a single hexagonal ring with graphene (C254). (b-e) A fragmented C60 molecule is fused with the defective graphene monolayer where the supercell contains 248, 224, 218, and 200 C atoms, respectively. The region of fusion is highlighted in yellow.
Table 2. Average Formation Energy (Eformation) of Five Type II PGNBs Eformation (eV/atom)
C254
C248
C224
C218
C200
0.114
0.121
0.093
0.071
0.071
tures than type I PGNB. In type II PGNB, full or fragmented C60 molecules are fused with the defective graphene monolayer, resulting in nonhexagonal carbon rings. We note that previous theoretical and experimental studies have explored many forms of structural defects that may exist in CNTs or graphene monolayers.28-35 Among others, the formation of pentagonal or heptagonal rings is quite common in the synthesis of low-dimensional carbon nanomaterials. With some of these structural defects, a change of local curvature may occur and give rise to unusual structures such as carbon nanocones, nonclassical fullerenes, and z-type CNTs. We have considered five model systems for the type II PGNB: (1) a full C60 molecule shares a hexagonal ring with the graphene monolayer, where the supercell contains 254 C atoms (C254, Figure 2a); (2) a large-sized C60 fragment is fused with a defective graphene and forms three heptagonal and octagonal rings, where the supercell contains 248 C atoms (C248, Figure 2b); (3) a midsized C60 fragment is fused with the defective graphene and forms three pentagonal and six heptagonal rings, where the supercell contains 224 C atoms (C224, Figure 2c); (4) a small-sized C60 fragment is fused with the defective graphene and forms three heptagonal rings, where the supercell contains 218 C atoms (C218, Figure 2d), and (5) a small C60 cap is fused with the defective graphene and forms three 5-7-7-5 Stone-Wales defects, where the supercell contains 200 C atoms (C200, Figure 2e). In all five model systems, full or fragmented C60 252
Figure 3. The minimum energy path (MEP) for the formation of 22-hh PGNB (product state) from separated C60 and graphene monolayer (reactant state). The distances are in Å.
molecules distribute periodically on the graphene monolayer. The optimized model structures are displayed in Figure 2, where the region of fusion is highlighted in yellow. The “nanobud” in the C254, C248, C224, C218, and C200 PGNB has 60, 54, 48, 42, and 21 C atoms per supercell, respectively. Note that the C200 PGNB is structurally very similar to the periodic “ripped” graphene monolayer recently fabricated in the laboratory.36 The average formation energies per carbon atom for all type II PGNBs were computed based on the formula Eformation ) EPGNB ⁄ n - µC
where EPGNB is the total energy per supercell of PGNB, n is the number of C atoms in the supercell, and µC is the chemical potential of the C atom, obtained based on the Nano Lett., Vol. 9, No. 1, 2009
Figure 4. (a) Electronic band structure of a graphene monolayer (with 10 × 10 supercell size) and molecular obitals of a C60 molecule. (b-d) Electronic band structures and projected DOS of three conformers (22-hp, 22-hh, and 66) of type I PGNB. Red dashed lines denote the Fermi level, black solid lines the total DOS, red and blue solid lines the projected DOS on nanobuds and graphene, respectively. G ) (0, 0, 0), K ) (-1/3, 2/3, 0), and M ) (0, 1/2, 0) in the Brillouin zone. G represents the Γ point.
perfect graphene monolayer. The calculated Eformation values for five type II PGNBs are summarized in Table 2. Positive values of Eformation indicate that the type II PGNBs are less stable than the pristine graphene monolayer. Among the five model systems, C218 and C200 PGNBs have the least values of Eformation, while C248 PGNB has the largest one. The relative stability may be understood from the defect structures in the fusion region. The Stone-Wales defect is easier to form compared to other types of defects in carbon materials because of smaller (positive) formation energy. C218 PGNB involves only three heptagonal rings and, thus, the associated formation energy is also relatively small. The octagonal ring is less stable than either the pentagonal or heptagonal ring so that C248 PGNB has the largest (positive) formation energy. To gain more insights into the type I PGNB, we evaluated the minimum energy pathway (MEP) for the formation of type I PGNB from separated C60 molecule and graphene monolayer. The nudged elastic bands (NEB) method was employed, which has been widely used to search for MEP and transition state of reaction on surface.37,38 Here, we present only the MEP for the formation of 22-hh PGNB, as shown in Figure 3. Physisorption of a C60 molecule on graphene monolayer was chosen as the reactant state while the 22-hh PGNB was the product state. The calculated MEP (Figure 3) suggests that the energy barrier for the formation of 22-hh PGNB is 3.51 eV, while it is 0.71 eV for the dissociation of 22-hh PGNB. At the transition state, the nearest distance between C60 and graphene is about 2.0 Å. Thus, sufficient initial energy is required to overcome the energy barrier for the formation of 22-hh PGNB. Once
Figure 5. Electronic band structures and DOS of type II PGNB (a) C254, (b) C248, (c) C224, (d) C218, and (e) C200. Red dashed lines denote the Fermi level; red solid lines denote the projected DOS on “nanobuds”. Nano Lett., Vol. 9, No. 1, 2009
253
Figure 6. Profiles of HOS and LUS at the Γ point for (a) type I 22-hh and (b) type II C218 PGNB. The isosurface value is (0.01 (distinguished by blue/yellow) in atomic unit (a.u./bohr3).
Scheme 1. PGNB or Periodic “Ripped” Graphene Monolayer with Periodic Ripples
formed, the 22-hh PGNB is expected to be stable at room temperature due to the 0.71 eV energy barrier for the dissociation. As shown in Figure 3, the interaction energy is relatively small in the reactant state and it entails larger error since local or semilocal functionals in DFT generally give poor description of weak interaction. Additionally, the calculation of the interaction energy is also susceptible to the basis set superposition error, especially in the reactant state. However, this error is expected to be much less significant to the interaction energy at the transition state due to the high value of energy barrier. In view of diverse forms of type II PGNB, we studied their thermal stability by performing ab initio molecular dynamic (AIMD) simulation at 800 K (see Methods). During the 5 ps AIMD simulation for each system, no event of bond breaking or making was observed, suggesting that type II PGNBs should be quite stable even at the elevated temperature. High thermal stability of carbon nanostructures is essential for their application in electronic devices. Recently, Lusk et al. constructed a similar PGNB structure, named as C200, by introducing an inverse Stone-Wales defect in a graphene monolayer.33
Their theoretical calculation shows that the reaction barrier for PGNB formation is quite low in the vicinity of vacancies. This PGNB structure may be produced through thermal reconstruction of carbon atoms. In Figure 4, the electronic band structures and the density of states (DOS) of graphene monolayer and three conformers of type I PGNBs are presented, including the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of C60. The valence band edge (VBE) was chosen to be the Fermi level. Our DFT calculation reproduces known results such as the graphene monolayer is semimetallic and the HOMO-LUMO gap of C60 is 1.67 eV. It is also known that DFT tends to underestimate the band gap of semiconductors. But this theoretical deficiency will not affect qualitative analysis of the electronic properties of PGNB. DFT calculations show that electronic properties of type I PGNBs depend on the covalent bonding configuration between C60 and graphene. The 22-hp and 22-hh PGNBs are semiconducting with a narrow band gap of 0.068 and 0.159 eV, respectively, whereas 66 PGNB is semimetallic. Clearly, with C60 covalently bonded to the graphene,
Table 3. Calculated Work Function (WF) of PGNBs and Stand-Alone Graphene Monolayer, as Well as the Ionization Potential (IP) of the C60 Molecule graphene WF (eV) IP (eV) 254
C60
4.480
22-hp
22-hh
66
C254
C248
C224
C218
C200
4.670
4.625
4.497
4.607
4.662
4.513
4.531
4.497
7.44 Nano Lett., Vol. 9, No. 1, 2009
Figure 7. Optimized structure of multilayer 22-hh PGNBs. The interlayer distance is about 12.5 Å.
energy band degeneracy of pristine graphene is removed while concomitant impurity states arise. In general, the impurity states near the Fermi level are due to hybridization of the frontier orbitals of C60 with electronic bands of pristine graphene. As shown from the projected DOS (red solid lines in Figure 4), most impurity states near the Fermi level are above the Fermi level and thus are unoccupied. These unoccupied impurity states due to the attachment of C60 provide additional possibilities for chemical functionalization of PGNB with other molecular groups or for doping PGNB with other elements so that electronic structures of PGNB can be tailored. It is also worthy of noting that for the 66 PGNB, the chemical attachment of C60 has little effect on the conic Dirac points despite a large number of induced impurity states. Type II PGNB exhibits quite different electronic structures compared to type I PGNB (see Figure 5). All five model PGNBs are semimetallic regardless of the size of fragmented C60 molecules. Moreover, the band structures near the Fermi level bear resemblance to that of stand-alone graphene monolayer (Figure 4a) with the exception of C200 PGNB (also called “ripped” graphene monolayer36) whose band structure has a partially occupied impurity state nearly overlapping with the Fermi level (Figure 5e). The projected DOS on nanobuds (red solid lines in Figure 4) for PGNB with smaller nanobuds or “ripples” is broader and flatter compared to that for PGNB with larger nanobuds whose total DOS shows sharper and separated peaks. Because of their diverse electronic properties, hybrid carbon nanostructures like PGNBs hold the promise for nanoelectronic application. Another potential application is the cold-electron field emission for which highly curved nanobuds may become ideal sites for the field emission. To explore this possibility, the work function (WF) of PGNB was computed. Note that the WF of bulk metal is defined as Φ - EF, where Φ is the electrostatic potential change across the dipole layer due to the “spilling out of electrons at the metal surface” and EF is the Fermi energy.39,40 Previous Nano Lett., Vol. 9, No. 1, 2009
studies have shown that Φ is much less than EF for carbon nanomaterials, and thus the WF can be estimated by EF, i.e. WF ≈ -EF.39,40 The calculated WFs of PGNBs and standalone graphene monolayer based on this approximation are summarized in Table 3. The WFs of PGNBs (ranging from 4.497 to 4.670 eV) are slightly larger than the WF of the stand-alone graphene monolayer (4.480 eV). Obviously, all the WF values are much less than the ionization potential (IP) ∼7.44 eV of C60 calculated at the same level of theory. Hence, the highly curved structure of nanobuds combined with descreased WF render the hybrid PGNB a promising field-emission material. The highest occupied state (HOS) and lowest unoccupied state (LUS) at Γ point for PGNBs are shown in Figure S1 (Supporting Information). In Figure 6, we plot the electronic profiles of the HOS and LUS of type I 22-hh and type II C218 PGNB. The HOS of type I PGNB is mainly contributed by the graphene as well as by a few carbon atoms of C60 that form covalent bonds with the graphene; the LUS is predominantly contributed by the C60 but also has a little projection on the carbon atoms of graphene in the fusion region. Thus, for type I PGNB, the electrons may be emitted from the top of C60 region after electrons are pumped from HOS to LUS. Since type I PGNB can be either semimetallic or semiconducting with a narrow band gap, this pumping process can be realized at room temperature. In stark contrast, the HOS and LUS of type II PGNB are broadly dispersed over the hybrid structure. Thus, electrons can be easily emitted from the top of nanobuds without going through the pumping process. Moreover, PGNBs may be more easily controlled as field-emission components because of their array structure as shown in Scheme 1. In CNT-based field emitter, arrays of highly aligned CNTs are required in order to achieve similar field-emission intensity.41,42 Another potential application of PGNB is for gas storage. In Figure 7, we display an optimized structure of multilayer 22-hh PGNB. Here, the interlayer distance is about 12.5 Å, compared to the interlayer distance 3.67 Å in the graphite 255
(computed at the same level). Still, the interlayer interaction is van der Walls type as in graphite, and this interlayer distance is an estimated value because of a limitation of DFT methods in describing weak interaction. Unlike graphite, however, multilayer PGNBs are a porous network structure. The surface area for the 22-hh PGNB system shown in Figure 7 is estimated to be 2346 m2/g. The much enhanced interlayer distance (∼4-fold) due to the nanobuds allows a large amount of gases such as methane or hydrogen to be physisorbed within the slit pores at low temperature or under high external pressure. We note that a multilayer carbon nanostructure has been proposed and studied previously.43 This nonbonding multilayer nanostructure is constructed by inserting C60 buckyballs between graphite layers (but without covalent bonding between C60 and the graphene). In PGNB, however, the covalent bonding between C60 and graphene allows the network structure to be more intact since aggregation of C60 buckyballs is prevented. Conclusion. In conclusion, we propose a computer-aided materials design of a series of hybrid carbon nanostructuressthe periodic graphene nanobuds. Two prototype PGNBs have been studied: In type I PGNB, C60 buckyballs are covalently bonded to a graphene monolayer whereas in type II, fragmented buckyballs are fused onto a defective graphene monolayer. In both cases, the C60 molecules form a periodic lattice on the graphene monolayer. We have studied structural, electronic, and field-emission properties of PGNB by using the first-principles DFT methods. We have shown that various forms of PGNB are all thermally stable at an elevated temperature (∼800 K). Type I PGNB can be either semiconducting or semimetallic, depending on the pattern of chemical bonding between C60 and graphene. Type II PGNB is generally semimetallic. A hallmark electronic structure of the graphene monolayer, i.e., the conic Dirac points, is still preserved in type II PGNB except for the ripped graphene monolayer. Finally, multilayer PGNBs are a porous network structure and may be exploited for gas storage. The much enhanced interlayer distance due to the nanobuds allows gases such as methane or hydrogen to be physisorbed within the slit pores at low temperature or under high external pressure. Acknowledgment. We are grateful to valuable discussions with Professor Y. F. Lu. This work is supported by grants from NSF (CHE-0427746, CHE-0701540, CMMI-0709333, and MRSEC DMR-0820521), Office of Naval Research, the Nebraska Research Initiative, NSFC (#20628304), and by theResearchComputingFacilityatUniversityofNebraskasLincoln and Holland Superomputing Center at University of NebraskasOmaha. Supporting Information Available: Profiles of electronic HOS and LUS for various model systems of periodic graphene nanobuds. This material is available free of charge via the Internet at http://pubs.acs.org. References (1) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of Fullerences and Carbon Nanotubes; Academic Press: New York, 1996. (2) Kroto, H. W.; Heath, J. R.; O‘Brien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162–163. 256
(3) Iijima, S. Nature 1991, 354, 56–58. (4) Beghune, D. S.; Kiang, C. H.; Vries, M. S. de.; Gorman, G.; Savoy, R.; Vazquez, J.; Beyers, R. Nature 1993, 363, 605–607. (5) Louie, S. G. Top. Appl. Phys. 2001, 80, 113–145. (6) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature 2005, 438, 197–200. (7) Zhang, Y. B.; Tan, Y. W.; Stormer, H. L.; Kim, P. Nature 2005, 438, 201–204. (8) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183–191. (9) Novoselov, K. S.; McCann, E.; Morozov, S. V.; Fal’ko, V. I.; Katsnelson, M. I.; Zeitler, U.; Jiang, D.; Schedin, F.; Geim, A. K. Nat. Phys. 2006, 2, 177–180. (10) Novoselov, K. S.; Jiang, Z.; Zhang, Y.; Morozov, S. V.; Stormer, H. L.; Zeitler, U.; Maan, J. C.; Boebinger, G. S.; Kim, P.; Geim, A. K. Science 2007, 315, 1379. (11) Feng, M.; Zhao, J.; Petek, H. Science 2008, 320, 359–362. (12) Lee, J.; Kim, H.; Kahng, S. J.; Kim, G.; Son, Y. W.; Ihm, J.; Kato, H.; Wang, Z. W.; Okazaki, T.; Shinohara, H.; Kuk, Y. Nature 2002, 415, 1005–1008. (13) Hornbaker, D. J.; Kahng, S. J.; Misra, S.; Smith, B. W.; Johnson, A. T.; Mele, E. J.; Luzzi, D. E.; Yazdani, A. Science 2002, 295, 828– 831. (14) Okada, S.; Saito, S.; Oshiyama, A. Phys. ReV. Lett. 2001, 86 3835. (15) Nasibulin, A. G.; Pikhitsa, P. V.; Jiang, H.; Brown, D. P.; Krasheninnikov, A. V.; Anisimov, A. S.; Queipo, P.; Moisala, A.; Gonzalez, D.; Lientschnig, G.; Hassanien, A.; Shandakov, S. D.; Lolli, G.; Resasco, D. E.; Choi, M.; Toma´nek, D.; Kauppinen, E. I. Nat. Nanotechnol. 2007, 2, 156–161. (16) Wu, X. J.; Zeng, X. C. Acs Nano 2008, 2, 1459–1465. (17) Li, X. L.; Liu, L. Q.; Qin, Y. J.; Wu, W.; Guo, Z. X.; Dai, L. M.; Zhu, D. B. Chem. Phys. Lett. 2003, 377, 32–36. (18) Nasibulin, A. G.; Anisimov, A. S.; Pikhitsa, P. V.; Jiang, H.; Brown, D. P.; Choi, M.; Kauppinen, E. I. Chem. Phys. Lett. 2007, 446, 109– 114. (19) Meng, T. Z.; Wang, C. Y.; Wang, S. Y. Phys. ReV. B 2007, 77, 033415. (20) Delley, B. J. Chem. Phys. 1990, 92, 508–517. (21) Delley, B. J. Chem. Phys. 2003, 113, 7756–7764. (22) DMol3 is a density functional theory quantum mechanical package available from Accelrys Software, Inc. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (24) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (25) Nose´, S. Mol. Phys. 1984, 52, 255–268. (26) Tuckerman, M. E.; Liu, Y.; Ciccotti, G.; Martyna, G. J. J. Chem. Phys. 2001, 115, 1678–1702. (27) Hirshfeld, F. L. Theor. Chim. Acta B 1977, 44, 129–138. (28) Crespi, V. H.; Cohen, M. L.; Rubio, A. Phys. ReV. Lett. 1997, 79, 2093–2096. (29) Lee, G. D.; Wang, C. Z.; Yoon, E.; Hwang, N. M.; Kim, D. Y.; Ho, K. M. Phys. ReV. Lett. 2005, 95, 205501. (30) Charlier, J. C. Acc. Chem. Res. 2002, 35, 1063–1069. (31) Chico, L.; Crespi, V. H.; Benedict, L. X.; Louie, S. G.; Cohen, M. L. Phys. ReV. Lett. 1996, 76, 971–974. (32) Yao, Z.; Postma, H. W. Ch.; Balents, L.; Dekker, C. Nature 1999, 402, 273–276. (33) Lusk, M. T.; Xarr, L. D. Phys. ReV. Lett. 2008, 100, 175503. (34) Meyer, J. X.; Kisielowski, C.; Erni, R.; Rossell, M. D.; Crommie, M. F.; Zettl, A. Nano Lett. 2008, 8, 3582. (35) Hashimoto, A.; Suenaga, K.; Gloter, A.; Urita, K.; Iijima, S. Nature 2004, 430870–873. (36) Va´zquez de Parga, A. L.; Calleja, F.; Borca, B.; Passeggi, M. C. G., Jr.; Hinarejos, J. J.; Guinea, F.; Miranda, R. Phys. ReV. Lett. 2008, 100, 056807. (37) Henkelman, G.; Jo´sson, H. J. Chem. Phys. 2000, 113, 9978–9985. (38) Olsen, R. A.; Kroes, G. J.; Henkelman, G.; Arnaldsson, A.; Jo´sson, H. J. Chem. Phys. 2004, 121, 9776–9792. (39) Lang, N. D.; Kohn, W. Phys. ReV. B 1971, 3, 1215. (40) Skriver, H. L.; Rosengaard, N. M. Phys. ReV. B 1992, 46, 7157–7168. (41) Zhou, G.; Duan, W. H.; Gu, B. L. Phys. ReV. Lett. 2001, 87, 095504. (42) Suzuki, S.; Bower, C.; Watanabe, Y.; Zhou, O. Appl. Phys. Lett. 2000, 76, 4007–4009. (43) Kuc, A.; Zhechkov, L.; Patchkovskii, S.; Seifert, G.; Heine, T. Nano Lett. 2007, 7, 1–5.
NL802832M Nano Lett., Vol. 9, No. 1, 2009
