Study Of Orbital Hybridization And Electron Property In Single-Walled Carbon Nanotubes

Since carbon nanotubes were discovered in 1991, they have attracted the physicists, the chemists and the material scientists' widespread interests because of unique nanometer scale tubular geometry structure, the outstanding physical and chemical properties, astonishing stiffness, strength and elastic force properties. They become one of the study foci of condensed matter physics and material science in the recent ten years. Single-walled carbon nanotubes (SWCNTs) are one kind of limiting conditions of carbon nanotubes.Because of curvature effects, π orbitals in single-walled carbon nanotubes are not normal to their surfaces, but have a small slanting angle deviation(π orbitals have the second hybridization) . They have been observed through STM on the experiments. In this paper, based on the geometrical structure of the tubes, the inclined angles of π orbitals for zigzag, armchair, and chiral tubes are given and are obviously different in their expressions. After comparing the results with the results in Reference[64] by the same approximate expression, our results can reflect the differences of π orbitals' inclined angles of different tubes.Based on inclined angles of π orbitals, the hybridization orbitals' analytical expressions in SWCNTs are given according to the hybridization theory of orbitals. The result shows that for the zigzag tubes (n < 40), the armchair tubes (n < 20), and thechiral tubes (n < 30,m < n), the s-orbital components are larger. These cases cannot beregarded as the sp~2 hybridization in calculation of the electronic structure. So the influences which are caused by curvature effects to hybridization orbitals can't be neglected.The lattice atom wave functions are not orthonormal basis functions in single-walled carbon nanotubes. According to the rehybridization orbitals, the...