Spherical box model and reduction of Coulomb interactions in the crystal field theory of 3dn ions

Abstract

With an accuracy of 0.1 eV, all the electron transitions in any 3d transition element and in the corresponding ions, isolated or inside a crystal, can be obtained with the Hartree–Fock model by using hydrogen d orbitals with suitable effective charges ζ. When the ion is embedded in a crystal, the value of ζ is generally weaker than that in the isolated state. For a given ion, the value of the reduction factor depends on the nature of the crystal. This phenomenon is explained by the boundaries imposed on the ion by the presence of the first neighboring ions (box effect). The application to some crystals (oxides and carbonates) corroborates this interpretation. An empirical relationship between the size of the ion and that of the cavity in which it is confined is proposed.