Simple Ligand-Field Theory of d4 and d6 Transition Metal Complexes with a C3 Symmetry Axis

There have been a number of recent studies reporting high-spin d(4,6) complexes with three- and four-coordinate geometry, which exhibit roughly trigonal symmetry. These include complexes of Fe(II) with general formula L3FeX, where L = thioether or dialkylphosphine donors of a tripodal chelating ligand and X is a monodentate ligand on the C-3 axis. In these systems, there is unquenched orbital angular momentum, which has significant consequences on the electronic/magnetic properties of the complexes, including magnetic susceptibility, EPR spectra, and magnetic Mossbauer spectra. We describe here a simple model using a description of the d orbitals with trigonal symmetry that along with the application of the spin orbit interaction successfully explains the magnetic properties of such systems. These d orbitals with 3-fold symmetry are complex orbitals with a parameter, a, that is determined by the bond angle, alpha, of LFeX. We demonstrate that the E symmetry states in such systems with S > 1/2 cannot be properly simulated by or be represented by the Zeeman and second-order zero-field spin Hamiltonian alone because by definition the parameters D and E are second-order terms. One must include the first-order spin orbit interaction. We also find these systems to be very anisotropic in all their magnetic properties. For example, the perpendicular values of g and the hyperfine interaction parameter are essentially zero for the ground-state doublet. For illustrative purposes, the discussion focuses primarily on two specific Fe(II) complexes: one with the bond angle alpha greater than tetrahedral and another with the bond angle alpha less than tetrahedral. The nature of the EPR spectra and hyperfine interaction of Fe-57 are discussed.