A magnetic tight-binding model : the origin and the effects of the exchange-correlation hole in transition metals

Abstract

The accuracy of a method solving an electronic many-body problem lies in the estimation of the exact exchange-correlation term. Many approximations are formulated for some special situations and how to tackle the correlations, leading to overestimated or underestimated physical properties. It is possible to understand and evaluate the exact exchange-correlation in a semi-empirical model by understanding the charge distribution and a screening effect of a delocalized s state. A quantitative calculation in a simple tight-binding + U model is performed, which describes quite accurately some physical properties as the magnetism and the gap in transition metal oxides. Unifying several approaches of the band structure theory, explaining some disagreements in theoretical physics and some experimental results. We found 1.3 eV in the Iron BCC, 1.55 eV in the Cobalt FCC and 2.2 eV in the Nickel for the exchange-correlation energies per orbital and a good estimation of the Curie temperature