Application of symmetry coupling coefficients in zero-field splitting of d5 ion complexes

Symmetry coupling coefficients and symmetry reduced matrix elements are used in calculating the minimum required matrix elements required to determine the analytical expressions for the three ⁶ A ₁ ground-state energy levels for a d⁵ ion in a weak crystal field of tetragonal symmetry. Expressions for the spin hamiltonian parameters a, D, F and G are derived, from which the effect of spin-orbit coupling and the tetragonal component of the crystal field are examined. The parameters describe the form of the hamiltonian and consequently the spin eigenfunctions and eigenvalues of the ground state where a is a measure of the isotropic component whereas D, F and G measure the tetragonal component of the interaction giving rise to the zero-field splitting. Some experimental results are examined.