Superexchange in Magnetic Insulators:  An Interpretation of the Metal−Metal Charge Transfer Energy in the Anderson Theory

The superexchange interactions in four three-center model systems A-L-B, for A and B being paramagnetic centers and L a diamagnetic bridging ligand, are analyzed by valence bond configuration interaction models in combination with fourth-order perturbation theory. We analyze the four distinct cases where a bridging ligand orbital simultaneously interacts with half-filled orbitals localized on A and B (case i), a half-filled orbital localized on A and an empty orbital localized on B (case ii), a full orbital localized on A and a half-filled orbital localized on B (case iii), and finally a full orbital localized on A and an empty orbital localized on B (case iv). In all four cases we compare our new results using localized orbitals with the equivalent results obtained using the Anderson ansatz of delocalized (magnetic) orbitals. The effective metal-to-metal electron transfer energy Ueff in the old formalism with delocalized orbitals is expressed in terms of the metal-to-metal electron transfer energy U and the ligand-to-metal electron transfer energy delta using localized orbitals. We find that the old formalism containing only Ueff is in general not sufficient. For cases i and ii we show that Ueff can be regarded as an effective U strongly reduced with respect to the free ion as a result of hybridization effects, whereas the same reduction of U for the cases iii and iv is not possible. The relevance and applicability of our theoretical results is demonstrated on magnetochemical data from the literature.