摘要采用密度泛函理论(Density functional theory, DFT)中的杂化密度泛函（B3LYP）方法，在6-31G基组水平上对C20四聚体和C80纳米管进行了几何参数全优化，得到了基态构型,并对其稳定性、电子结构、极化率和芳香性进行了计算研究。主要结论如下：86520

(1) C20四聚体是具有C1对称性的平面结构，它由两个共用一条边的三角形（三角顶点为C20碳笼）组成。碳笼以[2+2]加成方式结合形成C20四聚体，进行加成反应后碳笼体积稍稍增大，碳笼相互结合部位的C-C键的键长更大，说明其比较容易断裂。C80纳米管是标准碳纳米管，主体部分由30个碳六元环构成，两端各由半个富勒烯球（六个碳五元环）封顶。

(2) C20聚合物中随着碳笼数的增加，加成反应的反应热和能隙都逐渐变大，说明它的热力学和化学稳定性逐渐增强。和C20四聚体相比，C80纳米管的反应热更大，但能隙更小，表明C80纳米管的热力学稳定性和化学活性最强。

(3) C20四聚体和C80纳米管的NBO分布相近，每个碳原子的2s轨道上有约1个电子转移到了2p轨道上，但C80纳米管发生的电荷转移要比C20四聚体明显。C原子内以sp2的方式杂化，原子之间有微量的电荷转移。

(4) C20四聚体和C80纳米管的红外光谱（IR光谱）和Raman光谱都有很多的振动峰。其中C20四聚体IR光谱的最强振。动峰位于频率867。84 cm-1  处，对应着四个碳笼的呼吸振动，Raman光谱最强的振动峰位于波数1365。99 cm-1处，该处的振动模式为碳笼的呼吸振动。C80纳米管的IR光谱的最强的峰位于频率1334。47 cm-1处，该处振动模式为C80纳米管中一系列碳碳键的伸缩运动；Raman光谱的最强峰位于频率1527。36 cm -1 处，其对应的振动模式也是纳米管中一系列碳碳键的伸缩振动。 

(5) C20聚合物的极化率张量的平均值。随着碳笼数的增加而逐渐增大，说明团簇中原子间的成键。相互作用渐渐增强。C20四聚体极化率张量的平均值最大，即原子间成键的相互作用最强。而C80纳米管的极化率张量的平均值比C20四聚体小，说明其原子间成键的相互作用较弱。

(6) C20四聚体和C80纳米管均具有芳香性，但C20四聚体芳香性较强。C20四聚体和C80纳米管的反应。都是放热反应，二者的热力学稳定性较好。

毕业论文关键词：富勒烯C20四聚体   C80纳米管   结构与性能   密度泛函理论

Abstract The possible geometrical and electronic structures of C20 tetramer and C80 carbon nano-tube (CNTs) are optimized by using the density functional theory（DFT） at B3LYP/6-31G level。 The stability of the ground state structure has been studied, and its stability properties, natural bond orbits (NBO), the spectrum, the polarizability and the aromatic characteristics are analyzed。 Results are as follows:

   （1）C20 tetramer，Having C1 point group symmetry，may be synthesized by [2+2] addition reaction of C20 carbon cages，which is a planar structure consists of two triangles that share an edge。 After the polymerization reaction, slight swelling occurred, bonding sites C-C bonds have a larger bond length which make the bonds more prone to breakage。 C80 carbon nanotube is composed of thirty six-membered rings constituting a hollow tube and each of ends capped by half carbon cage (six five-membered rings)。 

(2) The heat of addition reaction and energy gap were both increased with increasing number of carbon cages, this means thermodynamic and chemical stability gradually increased。 The heat of reaction of C80 carbon nanotube is largest and the energy gap is smallest, it show that the heat of reaction and energy gap of C80 carbon nanotube is the strongest。

(3) The NBO of C20 tetramer and C80 carbon nanotube are similar, about one electron of 2s orbital transferred to 2p orbital, carbon atoms in clusters are in sp2 hybridization and these atoms happen to have charge transfer。 But the charge transfer of C80 carbon nanotube significantly higher than the C20 tetramer。