Basic exchange model: Comparison of Anderson and valence bond configuration interaction approaches and an alternative exchange expression

The application of the Anderson [Phys. Rev. 115, 2 (1959)] and valence bond configuration interaction (VBCI) methods on a basic exchange model is investigated to assess their ability to calculate the exchange energy under a variety of physical situations, represented by the model parameters. The model comprises two metal orbitals and a central ligand orbital. We show that the validity of the Anderson method is not restricted to cases in which U⪡Δ if the ``repulsion assisted transfer'' term is included in the exchange expressions. We discuss the influence of the Coulomb repulsion in the metal and ligand orbitals on the Anderson method, pointing out some deficiencies of the Anderson orbitals. In cases of strong metal-ligand covalency, the VBCI method fails due to its perturbational character. The modified Anderson exchange performs better in some of these cases, depending on the specific situation. Based on the concept of a strict separation of covalent and exchange effects, we derive an exchange expression that overcomes all the discussed difficulties of the Anderson and VBCI methods.