利用全始算方法及密度泛函數理論搭配週期性邊界模型，模擬計算奈米管無限長時幾何結構與電子性質。在本研究中我們分別計算碳與硼氮奈米管其鋸齒、單臂與螺旋形之各種管徑大小結構，並探討其結構變化與HOCO、LUCO 和能隙的關係，在奈米碳管部分，鋸齒與單臂形經計算後，隨著直徑增加顯示出兩種碳-碳鍵長收斂至與二維石墨鍵長相同，將石墨、鋸齒與單臂形使用均一鍵長，計算其能階變化，在HOCO部分石墨與鋸齒形出現能量簡併(degeneracy)，而在單臂形則沒有出現，由此得知石墨與鋸齒形當較大直徑時，產生楊-泰勒效應，在螺旋形單層奈米碳管隨著直徑小與螺旋角度小，將造成結構扭曲增大，而接近n = 2m情況下結構變異最小，在奈米硼氮管的計算顯示隨著直徑增大其能隙值，將收斂至5.03 eV，奈米硼氮管其半導體性質與直徑大小無關，在鋸齒形奈米硼氮管當直徑大於18 (Å)時其能隙出現與鋸齒形奈米碳管相似，呈現三個為一組週期之震盪現象。 The detailed geometrical structures of zigzag, armchair and chiral type single-walled carbon nanotubes (SWCNTs) and boron-nitride Nanotubes (SWBNTs) with infinite tubular length were investigated using localized Gaussian type orbital-periodic boundary condition-density functional theory (LGTO-PBC-DFT) method. It was found that the optimized structures of the zigzag, armchair type SWCNTs showed two C-C bond lengths that decrease with an increase in the tubular diameter. We found degeneracy in the highest occupied crystal orbitals if identical bond lengths were employed for the zigzag SWCNTs and the two-dimensional graphite sheet. This implies that the two different bond lengths found in the zigzag SWCNTs and the two-dimensional graphite sheet are probably due to the Jahn-Teller effect. The diameter decreasing and dwindling with the chiral angle of the chiral type single-walled carbon nanotubes cause the greatest structure to twist. The calculations of boron-nitride nanotubes reveal that the calculated Eg (band gap between HOCO and LUCO) increases with increasing tubular diameter and eventually converge to 5.03 eV for BN nanotubes of larger tubular diameter. According to the calculated Eg, the BN nanotubes are semiconductors and their conductivities are not sensitive to the tubular diameter. The calculated results also indicate that zigzag BN nanotubes with the tubular diameter larger than 18 Å display 3n properties in the calculated Eg, which is also obtained for zigzag carbon nanotubes.