Ligand-field theory for five-co-ordinate molecules. Part III. The magnetic properties of trigonal bipyramidal molecules with A ground terms

Abstract

The energy levels for transition metal ions with the electronic configurations d², d⁴, d⁷, and d⁹, under the combined action of spin–orbit coupling and a crystal field of trigonal bipyramidal geometry have been deduced and the magnetic properties, expected for such systems of levels, evaluated. For metal ions with these electronic configurations, and which have orbital singlet ground states in a crystal field of D_3h symmetry, it is shown that the contributions to the ground-state eigenfunctions from higher lying, orbitally degenerate crystal-field states, affect only one of the principal molar susceptibilities, thus leading to anisotropic magnetic properties. The general formula for the magnetic moments of powder samples can be summarised as µ_eff=µ_8·0. (1 –nλ/E) where n= 4 for the d² and d⁷ configurations (assuming only the ^xE″ excited state from the ^xF state being mixed in) and n= 2 for the d⁴ and d⁹ configurations, and E is the energy between the A₂′ and E″ or the A₁′ and E″ crystal-field states respectively.

The magnetic properties of some compounds of basically trigonal bipyramidal geometry are considered and using the experimental data for the complex VBr₃(NMe₃)₂, a value for the spin–orbit coupling constant for the metal ion close to the free-ion value has been evaluated. In addition the magnetic properties of some complexes of C_3v and lower symmetry are discussed in the light of the predicted behaviour, and for the d⁷ configuration the observed magnetic moments are larger than given by the model.