【摘要】 采用密度泛函M06-2X方法，对C₆₀和包裹了Li⁺的C₆₀与巴氏碗（素馨烯）及其同系物的弱相互作用进行了系统的研究.在优化的几何构型基础上，对4种化合物进行了前线分子轨道成分分析；在考虑基组重叠误差下，对相互作用能进行分析，并利用约化梯度模型得到了它们的约化梯度密度散点图.结果表明4种化合物的弱相互作用强弱顺序为：C₁₈O₃H₆/Li⁺@C₆₀<C₂₁H₁₂@C₆₀<C₁₈N₃H₆/Li⁺@C₆₀<C₂₁H₁₂/Li⁺@C₆₀.巴氏碗碗沿的—CH₂基团被—NH和O原子取代后，掺杂了杂原子的素馨烯导致分子间的静电相互作用增大.通过几何构型和约化梯度模型分析表明，掺杂了杂原子的素馨烯与C₆₀之间的距离增大，π-π堆积的色散作用减小，相互作用能降低.对于素馨烯与Li⁺@C₆₀之间的弱相互作用需要同时考虑静电和色散作用.更多还原

【Abstract】 In the work, density functional M06-2X method and 6-31+G（d） basis set were used to optimize C₆₀ and sumanene or Li⁺ at C₆₀(Li⁺@C₆₀) and sumanene(namely: C₂₁H₁₂@C₆₀, C₂₁H₁₂/Li⁺@C₆₀, C₁₈N₃H₉/Li⁺@C₆₀, C₁₈O₃H₆/Li⁺@C₆₀). Based on the optimized structure, composition of frontier molecular orbitals, basis-set superposition error and reduced density gra-dient isosurface, weak intermolecular interactions are investigated. Results indicate that the weak interactions follow the order of C₁₈O₃H₆/Li⁺@C₆₀<C₂₁H₁₂@C₆₀<C₁₈N₃H₆/Li⁺@C₆₀<C₂₁H₁₂/Li⁺@C₆₀. Based on the frontier molecular orbital analysis, the HOMOs component of C₂₁H₁₂@C₆₀ molecule is distributed in the sumanene and C₆₀ objects, which reduces the electrostatic interaction. However, after encapsulating Li⁺ in C₆₀, HOMOs and LUMOs of three molecules were located on sumanene and C₆₀, respectively. By analyzing the frontier molecular orbitals, the electrostatic interaction between sumanene and C₆₀ will be increased while adding the doped atoms N and O into the bowl conjugated molecule sumanene. On the other hand, we can also prove it by the dihedral angle formed by the bottom of the bowl and the edge of the bowl. The larger the dihedral angle, the more concave the bowl-shaped conjugate molecule, and the greater the depth, the farther the distance from C₆₀. Encapsulating a Li⁺ into a fullerene, distance between C₆₀ and sumanene will be reduced. While —CH₂ groups were replaced by —NH and O at the sumanene, the distance between Li⁺@C₆₀ and sumanene will be increased. At the same time, the intramolecular and intermolecular weak interactions were further studied by using the independent gradient model（IGM）. The reduced density gradient（RDG） scatter plots of the four complexes were obtained by using the IGM. δg can be divided into δg^intra and δg^inter, and the δg^intra in the description fragment is obtained by subtracting δg^inter from δg. The red is the weak intermolecular interaction, and the black is the interatomic interaction within the molecule. By comparing the size of the red region, it is qualitatively demonstrated that the weak interaction between C₂₁H₁₂/Li⁺@C₆₀ molecules is the largest, and the weak interaction between C₁₈O₃H₆/Li⁺@C₆₀ molecules is the least, which is consistent with the results obtained by our quantitative calculation through basis set superposition error（BSSE）. Finally, for the weak interaction between sumanene and Li⁺@C₆₀, both electrostatic and dispersion effects should be considered更多还原