Mott–Hubbard condition for electron localization in the Hartree–Fock band theory

The relative stabilities of the delocalized and the localized states of a half-filled band were examined in terms of the Hartree–Fock band theory. The electron localization condition thus obtained is very similar to that derived by Hubbard considering the dynamics of electrons in a narrow band. The relative stability problem of the delocalized vs the localized state in a crystalline chain was also compared with that of the low-spin vs the high-spin state in a weakly interacting metal dimer complex.