Comparison Study on the Electronic Structure of Smallest (2, 2) Carbon Nanotube by Ultra-Soft Pseudo-Potential and All-Electron Methods

A detailed comparison between the results of ultra-soft pseudo-potential and all-electron approaches on the structure, total energy and electronic property of the smallest (2, 2) single walled carbon nanotube is performed. It is found that each approach can reach a second energy minimum if exchanging the used methods during the geometrical relaxation. One corresponds to the relaxed lattice constant c = 2.560 Å, another corresponds to the relaxed lattice constant c = 2.450 Å, but they are in different energy order. For (2, 2) single walled carbon nanotube with lattice constant c = 2.560 Å, band structures obtained from two methods both indicate a small energy gap existing near the Fermi level. However, both pseudo-potential and all-electron calculations indicate the vanishing of energy gap in the case of lattice constant c = 2.45 Å. Charge density analysis shows that different distribution in charge density along the tube axis and perpendicular to it conducts to the semiconductor and metallic behaviour.