The relation between zero-field splittings and distortions along the normal coordinates in transition metal complexes

Abstract

A systematic approach is developed for the ZFS (zero-field splitting) parameters D and E in slightly distorted tetrahedral and octahedral complexes with spatially non-degenerate ground states. This approach is illustrated by treatment of the normal coordinate system. The ZFS part of a spin Hamiltonian is expressed in terms of the distortion along normal coordinates and the coefficients characteristic of a metal-ligand combination. This expression for a spin Hamiltonian clarifies the relation between the ZFS and the distortions of the coordination geometry from T_d and O_h symmetries, and is particularly useful in the calculation of the ZFS under non-axial distortions. Some of the coefficients are derived for the ground A₂ state (tetrahedral d⁷ and octahedral d³) ions in terms of the e ^σ and e ^π parameters of the angular overlap model. Satisfactory agreement is obtained in the application of the approach to Cs₃CoCl₅, Cs₂CoCl₄ and ruby.