Electronic Structure of the Finite-Sized Single-Walled Carbon Nanotubes (original) (raw)
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Current Applied Physics, 2009
We have investigated the geometrical and electronic structures of open-end single-walled carbon nanotubes (SWNTs) having chemically modified tips, using semi-empirical AM1 and density functional theory methods. The hydroxyl (-OH), carboxyl (-COOH) and amide (-CONH 2 ) functional groups were used to saturate the open-ends of nanotubes. The effects of functional groups were studied by comparison with the pristine tubes, of which the tubular lengths vary from two to ten unit-cells (40 Å ). The results show that the C-C bond lengths of all model tubes are only slightly different, and the behavior of converging bond lengths in COOH-and CONH 2 -SWNTs is very similar to the pristine tube. Tip functionalization alters the frontier orbitals of the pristine tube, but these effects seem to rapidly decrease as the tubule becomes longer. In general, it can be concluded that the geometrical and electronic structures of pristine tubes after tube-end ''full" functionalization will be preserved, hence supporting that more real-world ''partially" functionalized SWNTs can be used in the same way as the pristine version in most application areas.
On the basis of density functional theory, we study the electronic structures of (3,3), (4,4), (5, 0) and (6, 0) SWCNTs. The results show that the cohesive energy of armchair tubes are larger than those of zigzag ones. The calculated band gap of (4,4) is smaller than those of other tubes. Moreover, the band gap for armchair tubes are smaller than those of zigzag. The variation of ionization potential, electron affinity, and Fermi energy level as the number of atoms in the tube grows up. This curve fluctuates strongly because of the change in size that produce different surfaces with different properties. The IP is larger than the EA, as is the normal situation for molecules. The highest number of degenerate states in the conduction and valence bands are about as follow: 7, 9, 9, and 7 for (3,3), (4,4), (5,0) and (6,0) CNTs, respectively.
Effects of Finite Length on the Electronic Structure of Carbon Nanotubes
The Journal of Physical Chemistry B, 1999
The electronic structure of finite-length armchair carbon nanotubes has been studied using several ab-initio and semi-empirical quantum computational techniques. The additional confinement of the electrons along the tube axis leads to the opening of a band-gap in short armchair tubes. The value of the band-gap decreases with increasing tube length, however, the decrease is not monotonic but shows a well defined oscillation in short tubes. This oscillation can be explained in terms of periodic changes in the bonding characteristics of the HOMO and LUMO orbitals of the tubes. Finite size graphene sheets are also found to have a finite band-gap, but no clear oscillation is observed. As the length of the tube increases the density of states (DOS) spectrum evolves from that characteristic of a zero-dimensional (0-D) system to that characteristic of a delocalized one-dimensional (1-D)
Electronic properties of open-ended single wall carbon nanotubes
Journal of Molecular Structure: THEOCHEM, 2002
We have investigated the electrostatic, charge and orbital properties of open-ended single-wall carbon nanotubes in zigzag geometry. The calculations were performed by using the AM1-RHF semiempirical molecular orbital method. It has been found that the tubes with smaller radius behave like a metallic solid whereas the tubes with larger radius behave like a metallic hollow cylinder.
International Journal of Quantum Chemistry, 2019
Density functional theory and molecular dynamics (MD) calculations were used to evaluate electronic structure properties in a series of nanotubes with smallest possible diameters (both types: armchair and zigzag), and the corresponding chiral nanotubes (8,m) for 0 ≤ m ≤ 8. The calculations were performed considering a length of 16.5 Å. We evaluated a set of 26 combinations of dual nanotubes (armchair/armchair, zigzag/zigzag, armchair/zigzag, and zigzag/armchair), where the first label corresponds to the outer tube. We extended our study with nine additional systems of double-walled carbon nanotubes (DWCNT) with semiconductor nature. In this regard, we gave insight into the semiconductive or metallic nature inherited to the dual tubes. DWCNT systems were possible to construct by maintaining a radial distance of 3.392 Å for the armchair/armchair arrangement and 3.526 Å for the zigzag/zigzag type. It was considered as a reference, the interplanar distance of graphite (3.350 Å). Electronic transport calculations were also performed on selected DWCNT systems in order to understand the role played by the different symmetries under study. It was evidenced that the electronic structure nature of the systems rules the ability to transport electrons through the DWCNT interface.
Analytical Study of Unit Cell and Molecular Structures of Single Walled Carbon Nanotubes
International journal of computational engineering research, 2012
Recently it has been experimentally confirmed that the chirality of a nanotube controls the speed of its growth, and the armchair nanotube should grow the fastest. Therefore, chirality is an important parameter in designing a carbon nanotube (CNT) and needs to be investigated for the role it plays in the structure of a CNT. In this paper, we have analytically analyzed the unit cell and molecular structures of various single walled carbon nanotubes (SWCNTs) at different values of chirality combinations. The results suggest that total number of unit cells, carbon atoms and hexagons in each structure of SWCNTs are being changed by changing its chirality. A simple and step by step approach has been followed in describing the analytical expressions of overall unit cell structure, molecular structure, chiral angle and diameter of SWCNTs. The analytical formulations have been verified by simulating different SWCNTs at various chirality values. The simulated results match very well with the mathematical results thus validating, both the simulations as well as analytical expressions.
The Electronic Structure of Short Carbon Nanotubes: The Effects of Correlation
Advances in Condensed Matter Physics, 2015
This paper presents atight bindingandab initiostudy of finite zig-zag nanotubes of various diameters and lengths. The vertical energy spectra of such nanotubes are presented, as well as their spin multiplicities. The calculations performed using thetight bindingapproach show the existence of quasi-degenerate orbitals located around the Fermi level, thus suggesting the importance of high-qualityab initiomethods, capable of a correct description of the nondynamical correlation. Such approaches (Complete Active Space SCF and Multireference Perturbation Theory calculations) were used in order to get accurate ground and nearest excited-state energies, along with the corresponding spin multiplicities.
Band theory and electronic structures of carbon nanotubes
Synthetic Metals, 1997
A band structure model for carbon nanotubes taking into account the deformation potential characterizing the conformal mapping of graphene to tubules is presented and overlap is introduced in theT band calculations. This model corresponds to the study of aone-dimensional ( ID) system and is not simply the limit of a 2D system becoming quasi-1D. While development is explicitly made for the zigzag tubules, the method itself can also be applied to the armchair and chiral configurations by modifying the structure factor and boundary conditions. 0 1997 Elsevier Science S.A.
Electronic structure of carbon nanotubes
1998
A study of the electronic structure of carbon nanoparticles has been carried out using the methods of quantum chemistry and X-ray emission spectroscopy. Fragments of (n, 0) tubes with n = 6, ... ,11 and of (5,5)-(10,0) tubes were calculated using PM3 method. The dependence of the electronic structure of the fragment on length and symmetry was investigated. The structure of the frontier orbitals was shown to change regularly depending on the tube chirality. Band structure of (n,O) and (5,5) tubes was studied by the tight-binding method. A comparison of the basic blocks of the molecular orbitals (MOs) of the fragment and bands of (6,0) and (5,5) tubes was carried out. Experimental CKo spectra. for single-wall and multiwall carbon nanotubules were obtained. These spectra agree satisfactorily with the theoretical spectra plotted as the results of cluster calculations. The structure of the valence zone for the central hexagons of the nanotube fragments keeps the basic features in the ser...