Abstract: A group of complete, strong-field-energy matrices for the perturbed Hamiltonian H' of the d⁵ ion system are constructed by using the Oh group representation strong field scheme. From this, we have successfully obtained a unified theoretical explanation of the spectrum and the cubic zero-field splitting of the ground state of Mn²⁺ions in eight-ligand system (CaF₂) and six-ligand system (KZnF₃. RbCdF₃) for the first time. The calculated values are in good agreement with the observed result.

Key words: Cubic zero-field splitting, Complete energy matrices, O_kgroup representation