The electronic structure and its theoretical simulation of carbon nanotube with finite length. Part II: the energy gap and its oscillation properties of short armchair nanotubes

On the basis of optimized geometric structure at B3LYP/6-31G level, the energy gaps, Eg, of three types of short armchair carbon nanotubes with various lengths have been calculated at PM3 and also B3LYP/6-31G levels, respectively. The results found that a regular oscillation with period 3a/2 appeared on the Eg, and the Eg are reduced gradually and have the least at Ns=3ma/2 along with increasing the tube length Ns. The Eg calculated values are also consistent with those reckoned from STM and AFM experiments. The theoretical simulated method developed in this Letter reproduced successfully the results obtained from above-mentioned complicated calculations and SPM technique. The simulated method proved that the periodic boundary condition is also suitable for the axial direction of short armchair nanotubes but then the variation Δk induced by finite tube length must be considered. According to the modified boundary condition, an unified condition suited to the vectors of carbon nanotube axial and its radial directions was obtained and the essence correlated with Eg periodic variance was revealed.