Theory of high-spin d(4) complexes: An angular-overlap model parametrization of the ligand field in vibronic-coupling calculations

A new theoretical approach for the calculation of the electronic and molecular structures of octahedrally-coordinated high-spin d4 complexes is described. A prescription for the construction of an effective 3T1 + 5E (O) Hamiltonian from the ligand-field matrices of a complex with general trigonal symmetry is given, where the ligand field is parametrized in terms of the angular-overlap model (AOM). The Jahn–Teller matrices for the 3T1 + (5Ee) vibronic Hamiltonian are constructed and the lowest eigenvalues are calculated by a numerical method. The model obviates the need to assume a temperature dependence of bonding parameters, inherent to the conventional ligand-field-theory approach and is applicable over the whole range of vibronic-coupling strengths, as demonstrated by example calculations on the [Mn(OD2)6]3+ cation and MgO:Cr2+