We investigated the electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) with different tube diameters using density functional theory (DFT) and molecular dynamics (MD) simulation, respectively. The carbon nanotubes’ electronic properties were derived from the index number ( n 1 , n 2 ), lattice vectors, and the rolled graphene sheet orientation. For (6,1) SWCNT, ( n 1-n 2)/3 is non-integer, so the expected characteristic is semiconducting. We have considered (6,1) Chiral SWCNT with different diameters ‘d’ (4.68 Å, 4.90 Å, 5.14 Å, 5.32 Å, 5.53 Å) corresponds to respective bond lengths ‘  ’ (1.32 Å, 1.38 Å, 1.45 Å, 1.50 Å and 1.56 Å) and then analyze the electronic properties from the Linear Combination of Atomic Orbitals (LCAO) based on DFT. We have used both the DFT-1/2 and GGA exchange energy correlation approximations for our calculation and compared the results. In both cases, the energy bandgap is decreasing order with the increase in bond lengths. The lowest value of formation energy was obtained at the bond length  = 1.45 Å ( d = 5.14 Å). For the mechanical properties, we have calculated Young’s modulus using molecular dynamics (MD) simulations. From our calculation, we have found that the (6,1) SWCNT with bond length 1.45 Å ( d = 5.14 Å) has Young’s modulus value of 1.553 TPa.

We report the comparative study of electronic and optical properties of (6,1) SWCNT from GGA and DFT-1/2 methods. (6,1) SWCNT is a low-bandgap semiconductor, which falls within ( n1 − n2)/3≠ integer. The calculated bandgaps are 0.371 eV and 0.462 eV from GGA and DFT-1/2, respectively. Thus, DFT-1/2 enhanced the electronic bandgap by 24.52%. From both GGA and DFT-1/2 approaches (6,1) SWCNT exhibits an indirect bandgap along Γ − Δ symmetry. However, the percentage change in direct–indirect bandgap is negligibly small, i.e., 4.1% and 3.7% from GGA and DFT-1/2, respectively. The refractive index measured along x-axis ( n x ) approaches unity, indicating transparent behaviour, while that along z-axis ( n z ) goes as high as ∼3.82 for photon energy 0.0 − 0.15 eV, exhibiting opaque behaviour. Again, the value of n z drops below unity at photon energy ∼0.18 eV and again approaches ∼ 1 for higher energy ranges. The optical absorption is highly anisotropic and active within the infrared region.