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Relations between different cubic ligand field parameters Δ are derived in the framework of LCAO theory on the basis of group theory. From the symmetry of the ligand system and the transformation properties of the d-orbitals, the values of the Δ parameters are related to the octahedral parameter. These ratios Δ/Δ Oh  , partially including π- and δ-antibonding effects, are — ⁴⁄₉ for the tetrahedron, — ⁸⁄₉ for the cube, — ½ for the tetradecahedron, + ⁸⁄₉ for the tetrakishexahedron and triakisoctahedron when equal central atom ligand distances are considered. The proposed procedure, including also lower symmetries, is compared with the Ξ-method of JØRGENSEN, PAPPALARDO and SCHMIDTKE  1 , giving it a more developed physical significance.

Die Relationen zwischen den kubischen Ligandenfeldparametern und ihre Ableitung auf gruppentheoretischer Grundlage