Equivalent orbitals in molecules of known symmetry

Abstract The paper aims at providing a connecting link between the theory of molecular orbitals and the theory of localized bonds. An examination is made of the fundamental equations which must be satisfied by molecular orbitals in fields of known symmetry, particularly in molecules of the type XYn. It is shown by the methods of the group theory that these equations can be transformed to others which involve sets of equivalent functions. These are associated with equivalent orbitals which have the property of being identical as regards distribution in space and differ only in their orientation. It is shown that under certain conditions these can be regarded as localized orbitals associated with particular bonds. General formulae are obtained and applied to the particular cases of molecules of trigonal, tetrahedral and octahedral symmetry.