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J. Phys. Chem. C 2009, 113, 21314–21318
Structural and Electronic Properties of Finite Carbon Chains Encapsulated into Carbon Nanotubes B. Xu Department of Physics, National UniVersity of Singapore, 2 Science DriVe 3, Singapore 117542, Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833, and College of Physics and Communication Electronics, Jiangxi Normal UniVersity, Nanchang, Jiangxi, People’s Republic of China 330022
J. Y. Lin and S. H. Lim Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833
Y. P. Feng* Department of Physics, National UniVersity of Singapore, 2 Science DriVe 3, Singapore 117542 ReceiVed: July 22, 2009; ReVised Manuscript ReceiVed: NoVember 02, 2009
Finite carbon chains encapsulated into carbon nanotubes are investigated by using first-principles calculations based on spin density functional theory. Dimerization is observed in carbon chains formed by an even number of carbon atoms, but not in carbon chains containing an odd number of carbon atoms. All carbon chains inside the carbon nanotubes are spin-polarized due to spin-split energy levels around the Fermi level. By comparing the results of carbon chains inside the carbon nanotubes and isolated charged carbon chains, we found that the charge transfer from the carbon nanotubes to the carbon chains leads to the structure transformation and the spin-polarization of the carbon chains when encapsulated inside the carbon nanotubes, whereas the orbital hybridization removes the degeneracy of energy levels around the Fermi levels. Our results provide a deep understanding on the interaction between the carbon chains and the carbon nanotubes. I. Introduction In addition to the well-known stable allotropic forms of carbon that possess sp2 and sp3 bond hybridization, possible occurrence of linear carbon chains with sp hybridization has been reported and discussed both experimentally and theoretically in the past years,1-6 due to their interesting nonlinear optical and electronic transport properties. Generally, sp chains can be stabilized by isolation in rare gas or inorganic matrices7,8 or by terminating the chain ends with proper functional groups.2,9 Isolated infinite sp carbon species are linear structures with either alternating single and triple bonds, called polyynes, or identical double bonds, called cumulenes.7 Calculations on infinite carbon chains indicate that polyynes are energetically more stable than cumulenes due to Peierls distortion.10 However, for finite length linear chain Cn (n is an integer), particularly for a linear chain formed by less than 20 carbon atoms, the situation is more complicated. Interesting oscillatory phenomena have been observed in these materials. Furthermore, carbon chains in contact with metal leads exhibit interesting transport features such as even-odd conductance11 and even-odd thermopower behavior.12 Earlier studies indicate that the origins of the even-odd behaviors are more or less related to the electronic structures. It is known that a free n-atom chain has (n - 1)/2 fully occupied π orbitals if n is odd, but when n is even, (n/2) - 1 π orbitals are fully occupied and the two additional electrons occupy the next higher orbital. Consequently, Cn chains possess a singlet ground state when n is odd, but a triplet ground state * To whom correspondence
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when n is even, with the only exception of C2, which has a singlet ground state. Recently, linear carbon chains were observed inside multiwalled carbon nanotubes after arc discharge of carbon electrodes, using high-resolution transmission electron microscopy (HRTEM) in combination with Raman spectroscopy.13,14 This discovery of carbon chain inside carbon nanotube triggered a renewed interest in these linear carbon chain species and their hybrid structures with carbon nanotubes.15-20 One of the key issues is the interaction between the linear chains and the nanotubes that affects the properties of the carbon chain such as its geometric and electronic structures. For a periodic infinite carbon chain in a single-walled carbon nanotube (SWCNT), if the density of the encapsulated one-dimensional (1D) carbon chain is not too high the ferromagnetic ground state is more stable than the antiferromagnetic one, which is due to the weak coupling between the 1D carbon chain and the SWCNT.15 Furthermore, it was found that the interaction between the chain and the tube, which includes charge transfer and chain-tube orbital hybridization, suppresses the Peierls dimerization.16 The situation is more complicated when a finite length carbon chain is encapsulated in a single-walled nanotube, and studies on such hybrid structures have been limited. Liu et al.17 carried out a density functional theory (DFT) study on energies, structures, and vibration frequencies of carbon chains, as well as other species, inside single-walled carbon nanotubes and concluded that carbon chains can be inserted coaxially into nanotubes with a diameter of 0.7 nm. Their calculation, however, was limited to the nonspin-polarized case. Another DFT calculation was carried out recently by Kertesz et al.18 to investigate the structures and the energies of linear carbon chains. However,
10.1021/jp906980y 2009 American Chemical Society Published on Web 11/25/2009
Finite Carbon Chains Encapsulated into Carbon Nanotubes only a one-dimensional restricted environment was considered and the carbon nanotube was not explicitly included in their calculations. Motivated by these works as well as their limitations, we carried out spin-polarized DFT calculations on short carbon chains encapsulated inside carbon nanotubes, to study the effect of the carbon nanotube on the structure and properties of the carbon chain, and in particular to probe whether a finite carbon chain encapsulated in a carbon nanotube (CNT) also exhibits the even-odd oscillatory behavior observed for isolated finite carbon chains. Our studies reveal interesting behaviors of the carbon chains encapsulated in CNTs. Carbon chains formed by an even number of carbon atoms exhibit dimerization but those containing an odd number of carbon atoms do not. All of the inserted carbon chains are spin-polarized and the energy bands around the Fermi level are nondegenerate. These totally different behaviors compared to isolated finite carbon chains are due to the interaction with the CNTs. Our studies provide a deep understanding on the interaction between CNT and coaxial carbon chain.
J. Phys. Chem. C, Vol. 113, No. 51, 2009 21315 TABLE 1: C-C Bond Lengths (Å) in Isolated Carbon Chain Cn (n ) 2-7), Carbon Chain Encapsulated in the (5,5) SWCNT and Charged Cn Systema model
bond
C2 C3 C4
C1-C2 C1-C2 C1-C2 C2-C3 C1-C2 C2-C3 C1-C2 C2-C3 C3-C4 C1-C2 C2-C3 C3-C4
C5 C6 C7
isolated encapsulated 1.331 1.317 1.338 1.308 1.315 1.303 1.328 1.306 1.296 1.312 1.307 1.294
1.287 1.319 1.298 1.352 1.308 1.312 1.294 1.344 1.273 1.303 1.321 1.295
∆1
charged
∆2
-0.044 0.002 -0.040 0.044 -0.007 0.009 -0.034 0.038 -0.023 -0.009 0.014 -0.001
1.292 1.320 1.303 1.348 1.310 1.313 1.300 1.339 1.278 1.305 1.319 1.295
0.005 0.001 0.005 -0.004 0.002 0.001 0.006 -0.005 0.005 0.002 -0.002 0.000
a C1, C2, C3, and C4 label carbon atoms from the end to the center of Cn. ∆1 is the change of the bond length due to encapsulation (difference between column 4 and column 3), and ∆2 is the change of the bond length of the charged carbon chains with respect to the carbon chains encapsulated into the tube (difference between column 6 and column 4).
II. Computational Details Calculations were performed with the SIESTA package21 with the generalized gradient approximation (GGA) proposed by Perdew, Burke, and Ernzerhof (PBE) for exchange-correlation functional.22 Additional calculations at the local density approximation (LDA) level lead to very similar results. We use a standard double-ζ polarized (DZP) basis set for carbon atoms. Spin polarization is considered in all of our calculations. We choose the armchair (5,5) SWCNT in our model of the carbon chain and SWCNT hybrid structure because its diameter is the closest to that of the innermost tube observed in the experiment.13 A linear carbon chain made of n carbon atoms (Cn, n ) 2-7) is initially placed at the center of the tube, but the relative position between the carbon chain and the CNT along the axial direction is arbitrary. A supercell geometry is adopted and a periodic boundary condition is applied, with a large lateral separation (45 Å) between tube centers to minimize interaction between the SWCNT-Cn structure and its images in neighboring cells. Along the tube axial direction, the supercell includes nine unit cells of the (5,5) SWCNT (180 carbon atoms), with a periodicity of 22.14 Å. The long period is used to ensure that the separation between the longest carbon chain studied here (7 atoms) and its images in neighboring cells is at least 10 Å, to minimize interaction between them. The Brillouin zone of the supercell is sampled by a (1,1,10) k-point mesh within the Monkhorst-Pack scheme.23 The structure is fully relaxed until the interatomic forces are less than 0.05 eV/Å. III. Results and Discussions A. Isolated Neutral Finite Carbon Chains Cn (n ) 2-7). To serve as a reference for finite carbon chain encapsulated in nanotubes, we first determined the geometries and calculated the electronic structures of isolated neutral finite carbon chains Cn for n ) 2-7. The C-C bond lengths of the optimized carbon chains are listed in the third column of Table 1. All structures were found symmetric with respect to their centers. Therefore, only data for half of the carbon chain are presented. In Table 1, C1, C2, C3, and C4 label the carbon atoms from an end to the center of a carbon chain. Basically, besides the C1-C2 bond at the end of the carbon chains that is relative long, all the other C-C bonds have lengths of about 1.30 Å. Therefore, no obvious dimerization can be found in these isolated carbon chains, regardless if the number of carbon atoms in the chain is even
or odd. Our results are in good agreement with those obtained by Kertesz et al.24 using DFT at the B3LYP/6-31G* theoretical level, even though the C-C bond lengths obtained in our calculations are somewhat larger due to the GGA used in our calculations. Furthermore, the ground states of the carbon chains Cn (n ) 3-7), namely a singlet ground state when n is odd and a triplet ground state when n is even, are correctly predicted in our calculations. The ground states of carbon chains with an even number of carbon atoms are spin-polarized, whereas those with an odd number of carbon atoms favor nonspin-polarized ground states. The only exception is the ground state of C2 for which a triplet ground state is predicted. We noted, however, other DFT calculations had the same problem and multiconfiguration reference methods or coupled cluster methods are required to correctly predict the ground state of C2.25,26 This exception in ground state prediction does not significantly affect other calculated properties of C2. B. Finite Carbon Chains Cn (n ) 2-7) Encapsulated in Single-Walled Carbon Nanotube. Next, we discuss the structure and properties of the hybrid SWCNT-Cn system formed by a finite carbon chain Cn (n ) 2-7) encapsulated in the armchair (5,5) SWCNT. It is noted that the geometries of the SWCNT are essentially not changed during the structural optimization. Therefore, we focus our discussion on the encapsulated carbon chains. The C-C bond lengths in the optimized SWCNT-Cn structure are listed in the fourth column of Table 1, and the change from the corresponding bond lengths of the isolated carbon chains is also shown in the fifth column in Table 1. It is interesting to note that the bond lengths vary alternately from the end to the center for both even and odd numbered carbon chains. The lengths of the bonds at the end of all the carbon chains (C1-C2) contract except for C3. Besides this similarity, a significant difference also exists between carbon chains with even and odd numbers of carbon atoms. First of all, the changes in bond lengths in carbon chains with an even number of atoms are much larger (>0.023 Å) than those in carbon chains with an odd number of atoms (
