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基于杂化轨道的定域轨道与基于群轨道的离域轨道之间的互逆性

吕东梅1, 吴超2,3   

  1. 1 西安交通大学化学学院, 陕西 西安 710049;
    2 西安交通大学前沿科学技术研究院, 陕西 西安 712046;
    3 西安交通大学前沿科学技术学科交叉中心, 陕西 西安 712046
  • 收稿日期:2026-01-22 修回日期:2026-04-14
  • 通讯作者: 吴超 E-mail:chaowu@xjtu.edu.cn Chao Wu
  • 基金资助:
    西安交通大学2024年研究生教学改革专项(XJG2024068)

The reciprocity between hybrid orbital-based localized orbitals and ligand group orbital (SALCs)-based delocalized orbitals

Dongmei Lu1, Chao Wu2,3   

  1. 1 School of Chemistry, Xi'an Jiaotong University, Xi'an 710049, Shaanxi Province, China;
    2 Frontier Institute of Science and Technology, Xi'an Jiaotong University, Xi'an 712046, Shaanxi Province, China;
    3 Interdisciplinary Research Center of Frontier Science and Technology, Xi'an Jiaotong University, Xi'an 712046, Shaanxi Province, China
  • Received:2026-01-22 Revised:2026-04-14
  • Contact: Chao Wu E-mail:chaowu@xjtu.edu.cn

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摘要： 教科书中对基于杂化轨道理论的定域轨道(localized orbital， LO)和基于群轨道(即对称性匹配的原子轨道线性组合， SALCs)的离域轨道(delocalized orbital， DO)之间的互相转化关系进行了不同程度的描述，但是这些描述往往不够系统和简洁。本文通过一系列典型分子为例说明，其spn杂化轨道的系数与群轨道的系数各自构成的矩阵互为逆矩阵，即展示了两种理论操作的互逆性。对于“中心原子的杂化轨道+配体的原子轨道”构成的定域轨道，乘以群轨道的系数矩阵，就转化为“中心原子的原子轨道+群轨道”的离域化的正则分子轨道。同理，正则分子轨道乘以杂化轨道系数矩阵，可以得到基于杂化轨道理论的定域轨道。

关键词: 杂化轨道理论, 群轨道, 分子轨道理论, 定域轨道, 离域轨道

Abstract: Textbooks describe to various degrees the inter-conversion between localized orbital (LO) based on hybrid orbitals and delocalized orbital (DO) based on ligand group orbitals or SALCs (symmetryadapted linear combinations of atomic orbitals), but the descriptions are often not systematic and clear enough. This paper demonstrates through a series of representative molecules that the coefficients of the spn hybrid orbitals and the coefficients of the ligand group orbitals correspondingly form a pair of inverse matrices, thereby showing the reciprocity of the operations based on the two theories. For the localized orbitals composed of the hybrid orbitals of the central atom and the atomic orbitals of the ligands, multiplying the coefficient matrix of the ligand group orbitals transforms them into delocalized orbitals composed of the atomic orbitals of the central atom and the ligand group orbitals, that is, canonical molecular orbitals. Similarly, multiplying canonical molecular orbitals by the hybrid orbital coefficient matrix can yield localized orbitals that are based on the hybrid orbitals.

Key words: Hybrid orbital theory, Ligand group orbitals, Molecular orbital theory, Localized orbital, Delocalized orbital