As powerful as the concept of the band structure model proved to be in describing metallic bonding, it has the drawback of remaining a one-electron approximation of a many-body problem. In other words, the energy states of each electron are described as if all the other electrons simply form a homogeneous background. Researchers such as Mott and Hubbard realized that this was perhaps appropriate for strongly delocalized s- and p-electrons; but for d-electrons, and even more for f-electrons, the interaction with electrons (and atomic displacements) in the local environment may become stronger than the delocalization that leads to broad bands. Thus, the transition from localized unpaired electrons to itinerant ones partaking in metallic bonding became more comprehensible.
