A semiempirical PM3 quantum computational method has been used to generate the electronic and optimized geometrical structure of SWNT of zigzag and armchair types. We shed light on the electronic structures of SWNT with various diameters and lengths of the tube. Particularly, the calculated HOMO, LUMO and band-gap of SWNT are not monotonic but exhibit a well-defined oscillation, which depends on the tubular diameter and the tubular length. Calculated HOMO, LUMO and band-gap of the zigzag SWNTs have oscillated with tubular diameter as they contain an odd or even number of benzenoids in the circular plane of the carbon nanotube. The zigzag SWNTs with an odd number of benzenoids have a higher band-gap than those of SWNTs with an even number of benzenoids in the circular plane of the carbon nanotube. Calculated results also reveal that the tubular length in the zigzag SWNTs influences the band-gaps very little. For the armchair SWNT, calculated HOMO, LUMO and band-gap contained the oscillate depending on the number of carbon sections in the tubular length axis. Their repeat sections are 3n-1, 3n and 3n+1. The armchair SWNT with 3n+1 sections has a high band-gap while the SWNTs with 3n-1 sections have a low band-gap. The tubular diameters of armchair SWNT influence the HOMO, LUMO and band gap very little.
Journal of the Chinese Chemical Society=中國化學會會誌 50(5), pp.939-945