First-principles Study And Symmetry Properties Of Single-walled Carbon Nanotubes

The study on physical properties of carbon nanotubes(CNTs) is a hot topic in material fields.In principle most basic physical properties of solid can be illustrated and explained by the band theory and symmetry properties of CNTs is closely related to its special geometric structure,thus it is significant to carry out the subject" First-principles Study and Symmetry properties of Single-walled Carbon Nanotubes"First-Principles calculation has some obvious advantages relative to the semiempirical method.Because it can obtain the total energy and electron structure of microcosmic system using quantum mechanics method without knowing any other experiential or stimulant parameter.In Recent years,First-Principles calculation based on Density Functional Theory(DFT) has make a breakthrough in many aspects such as the design, synthesis and simulated calculations of material.It has become the basis and kemel of the calculation of materials.Here the band structures and density of states(DOS) of four types of single-walled carbon nanotubes(SWNTs) with small diameters(5,5),(6,6),(4,0)and(5,0)are calculated and their conductivities are predicted.The results show that SWNTs(5,5),(6,6),(4, 0)and(5,0)are all metallic.While the results in tight binding approximation show SWNTs(4,0)and(5,0)are semiconductors.This is due to the fact that,the hybridization betweenσ^* andπ^* orbitals exists near Femi surface,leading to the overlap between conduction band and valence band for the tubes of small diameters on account of predominant curvature effect.This gives an innovative result.The length of bond C-C is calculated with LDA and GGA respectively.The value is 1.42 A in LDA and 1.43(?) in GGA.Comparing the results with the experimental reference value1.44(?),the error is 0.6% showing this plan is feasible.The relationship between group theory and Physics is particularly close.Application of group theory method to the problem is more concise and more easily reveals the symmetry inherent of physical phenomena.The point groups the achiral single-walled carbon naontubes(n,O)and(n,n)belong to,D_nh(n = 2j)and D_nd(n = 2j + 1),are discussed.This provides reference in theory for the study on symmetry of achiral SWNTs.