Abstract: For a quantized subgroup of the symmetry group of Hamiltonian of a molecule, a site projection operator is defined to produce symmetry-adapted wave functions from the functions with the symmetry of the subgroup. Based on site projection operator, a systematic method is proposed to factorize the single-particle π Hamiltonian into irreducible representations of the maximal symmetry of the molecule. This method has been used to calculate electronic structures of the icosahedral, tetrahedral and dihedral fullerenes and some stability rules are obtained.

Key words: quantization of subgroup, site projection operator, fullerenes

摘要： 对于哈密顿的对称群的量子化子群，可以定义一个位置投影算子，来从具有该子群对称性的轨道产生完全的对称性匹配轨道。基于位置投影算子，提出了一个系统的方法，用来按照分子的最大对称群，彻底地分解π电子共轭体系的哈密顿。这种方法已经用于系统地研究具有二十面体群、四面体群和二面体群对称性的各富勒烯同系列，并且得到规律性的结果。

关键词: 子群量子化, 位置投影算子, 富勒烯