Qualitative Considerations on Transition Metal Compounds
In many semi quantitative considerations on transition metal compounds, the Coulomb interaction between two electrons at one atom is represented by the so-called “Hubbard U”. U is also the energy necessary for charge transfer, i.e. the energy of the chemical reaction M(dn) + M(dn) → M(dn+1) + M(dn-1). For a reaction between free ions Uat = In+1 - In, where In is the ionization energy of an ion M(dn). For free ions In+1 > In, so that U > 0. In a solid (or liquid) the interaction between two electrons on the same atom is screened: U = Uat + ΔUscr., due to at scr. interaction with the surroundings. This screening is a result of the polarization of the neighbouring atoms, and has contributions from vibronic and electronic polarization. The screening leads to a lowering of U, so that U < Uat. This screening effect is generally quite large, and ΔUscr. is usually of the same order as Uat. It is even possible that the net effect of screening is so large that U < 0 (overscreening). If this is the case, charge transfer dn + dn → dn+1 + dn-1 will occur spontaneously, and the state dn+1 + dn-1 is the more stable one.
KeywordsAuger Haas Disproportionation
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