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Bending Deformation on the electronic structure of the (3,3), (4,4), (5,0) and (6,0) single-wall carbon nanotubes

In this work we investigate the effect of bending defect on the electronic and structural properties of the (3,3), (4,4), (5,0) and (6,0) single-wall carbon nanotubes (SWCNTs) using density functional theory (DFT) within Becke three parameter Lee–Yang–Parr (B3LYP) functional using 6-31 basis set. Our result revealed that as the bending angle increases, the deformation of atomic structure of the tube increases, particularly in the centralized zone of the tube. The obtained outcomes revealed that the bandgap fluctuates with the bending angle of CNTs and the cohesive energy, the highest occupied (EHOMO) and the lowest unoccupied molecular orbitals energies (ELUMO) decrease (in magnitude) as the CNTs bending increases. On the other hand, the electron affinity and the ionization potential increases with the bending angle of CNTs, while the Fermi energy decreases with the bending angle of CNTs, with a fluctuation of Fermi energy with the bending for (4,4) tube. Finally, in the presence of bending deformation, the highest number of density of states in the valence and conduction bands decrease with increasing the bending angle of CNTs.


INTRODUCTION
Investigation into carbon nanotubes (CNTs) properties has become one of the greatest active fields of present research. Though early research concentrated on growth and characterization, these interesting properties have led to increasing the number of investigations focused on application development in the past 5 years 1-3 .
The breadth of applications of CNTs is indeed wide-ranging field emission devices, nanoelectronics, composites, quantum wire interconnects, biosensors, chemical sensors, detectors, etc.
In the last decades, computer simulations have emerged as a fundamental and powerful new tool for condensed matter research. Simulations not only make 2nd International Scientific Conference of Al-Ayen University (ISCAU-2020) IOP Conf. Series: Materials Science and Engineering 928 (2020) 072032 IOP Publishing doi: 10.1088/1757-899X/928/7/072032 2 conceivable the comprehensive explanation of experimental outcomes, especially in the atomic scale, but in most cases, they provide predictions of properties and processes not yet observed in the laboratory. Various defects in CNTs are widely observed in experiments 4,5 . CNTs were found to be not as perfect as it seems. Defects can be existing in as prepared CNTs. These defects can significantly change the electrical, thermal, electronic and mechanical properties of CNTs 6 . Regardless of these extensive properties, but it is very infrequent for imperfection control to be perilous to a specific application. Becke three parameter Lee-Yang-Parr (B3LYP) functional 10 using 6-31G basis set, have been applied in the calculations, where B3LYP is one of the often-utilized hybrids functional that used in studies of nanotubes.

COMPUTATIONAL METHODS
All the computational studies were carried out using DFT implemented in the Gaussian 09 programs running and visualized by GaussView 5.08 program 9 . The calculated properties of nanotubes have been calculated via DFT with 6-31G basis sets, the calculations in DFT were executed in the B3LYP hybrid functional. B3LYP is one of the most active hybrids functional used in studies of nanotubes. The optimized structure for a nanotube at which the nanotubes have the lowest energy; and can be achieved by discovery the first derivative of energy with respect to the distance between different atoms, known as the gradient. In Figure 1       The results in Figure 4 show that the cohesive energy (in magnitude) slightly decreases as the CNTs bending increase for both zigzag ((5, 0) and (6, 0)) and armchair ((3, 3) and (4, 4)) tubes. The system with larger E coh is more stable. Thus, the pristine CNTs are energetically more stable than bending CNTs.

Conclusions
Ab-initio calculations based on density functional theory (DFT) have been performed to study the electronic structure of of (3, 3), (4,4), (5,0) and (6, 0) single-wall carbon nanotubes. We have built models with bending angles of The cohesive energy, total energy, band gap, Fermi energy, ionization potential, electron affinity, highest occupied and lowest unoccupied molecular orbital, and density of state were studied in details. The results indicated that the cohesive energy and total energy increase (in magnitude) with increasing number of atoms. The bent carbon nanotubes present smaller cohesive energy than those of the pristine ones. The Fermi energy of carbon nanotubes vary when the bending is introduced into the nanotubes due to the change in size that produces different surfaces with different properties. It has been found that the bending cause significant changes in energy gap, with fluctuating of band gap according to the bending angle of carbon nanotubes. In general, ionization potential and electron affinity increase as bending defects are introduced into the nanotubes. In addition, presence of defects in nanotube causes some distribution of charge along the length of tube. It is also found that the bending defects in tubes decreasing the height of peaks; the highest number of DOS in the valence and conduction bands are less.