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