Investigation in the L.C.A.O.-M.O. Framework of the overlap and covalency contribution to the zero field splitting of S state ions

Using the L.C.A.O.-M.O. scheme, we review the different stages of the calculation of the overlap and covalency contribution to the zero-field splitting of ⁶S state ions. We calculate general molecular integrals involved in the non-local spin-spin contribution and derive analytic functions of the metal-ligand distance to fit numerical results of integral calculations for Mn²⁺---F^?, Mn²⁺---O^2?, Fe³⁺---F^?and Fe³⁺---O^2? bonds. We use these results to calculate the zero-field splitting of Mn²⁺ and Fe³⁺ ions at Ca²⁺ or Zn²⁺ crystal sites of tetragonal or trigonal symmetry in diamagnetic host lattices (RbCaF₃ and KZnF₃).