C <sub> 60 </ Sub> Ring, C <sub> 36 </ Sub> Ring, The Nature Of The Small-diameter Carbon Nanotubes And Fullerene New Structure Theory Research

This study work is mainly composed of three parts:1 The structures and stabilities of C60 and C36-ringsFor the first time, the C60 and C36-rings are classified systematically. The concept of "bonding-belts" are proposed for constructing and naming the rings with n folded principal axis and composed of n cages. Their geometry structures and electronic properties are studied using MNDO (C60-rings) and AM1 (C36-rings) method.The results show that the stabilities of Dnh and Cnv C60-rings are mainly affected by three factors: (1)the change of strain energies due to the distortion of C60 balls, (2) the number of double bonds introduced into the pentagons on C60 balls and (3) the number of covalent bonds formed between neighbor C60 molecules. We proposed A strain-associated factor σ, which can be used to predict the strain energy changes of the C60-rings due to the distortion. All these 3 factors can be determined by the structure of an undistorted C60 molecule and the linking-patterns. A semi-quantitative formula then be derived to express the different interaction energies of Ceo-rings. Then the relative stabilities of the C60-rings can be predicted before taking quantum calculations.Formation of ring structures is favorable to stabilization of the C36 systems. The strain-associated factor σ can also be used to estimate the strain energy changes in the C36-rings due to cage distortion, including ellipsoid shaped carbon cages. Several interaction factors are concerned with stabilities of the C36-rings, such as the change of strain energies due to the distortion of C36 cages, the type of the bonded carbon atoms, the size of retained aromatic domains and the number of shared pentagon-pentagon double bonds. The situation is complicated than Ceo-rings.2 The band structures of small diameter carbon nanotubesThe band structures of 19 small single walled carbon nanotubes with diameter ranging from 0.1842⁰.7910 nm are studied using B3LYP method on 321G and 6-31G* level. Zigzag nanotubes (3. 0)^{6, 0} is metallic. The increasing curvature, the phase of the wave function of a1 state and the interaction between opposite walls of the tube result in the semiconductor-metallic transition of these zigzag nanotubes.