利用原子軌道線性疊加方法，選擇一個單位細胞有兩個原子，每各原子有四各軌道，所以我們有 漢米爾頓矩陣。在小半徑奈米碳管裡，我們考慮曲率造成的混成效應及考慮到第三鄰近原子的交互作用力來計算奈米碳管的能帶結構。我們發現曲率效應的確影響電子特性以及第三鄰近原子的交互作用力降低了能隙大小。我們的數值計算結果顯示 (4,0) 和 (6,0) 奈米碳管在費米能階上沒有能隙 ，所以呈現金屬性質，而且此結果和第一原理的計算結果相符合。在這篇論文裡，我們將呈現考慮到第三鄰近原子的交互作用力的重要性。

Based on LCAO calculations, there are four atomic orbitals ( ) per atom. We thus have eight Bloch orbitals in the two atoms in a unit cell. We have constructed the Hamiltonian matrix., including 2s and 2p orbitals to take into account the mixing effect of σ and π orbitals due to the curvature of tubes with small radii, and we calculate the band structure of carbon nanotubes including up to third-nearest neighbors interactions numerically. We find tube curvature may significantly affect the electronic properties and the third-neighbor interactions reduce the energy gap. Our results show that the (4,0) and (6,0) tubes have no energy gap at the Fermi level and are in good agreement with first-principles calculations, and with decreasing radius, the effect of third-neighbor interactions on the gap becomes more important. We show the importance of calculations including up to third-nearest neighbors interactions.

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