Editing Electronic band structure (section)

=== Dynamical mean-field theory ===
{{Main|Dynamical mean-field theory}}
Although the nearly free electron approximation is able to describe many properties of electron band structures, one consequence of this theory is that it predicts the same number of electrons in each unit cell. If the number of electrons is odd, we would then expect that there is an unpaired electron in each unit cell, and thus that the valence band is not fully occupied, making the material a conductor. However, materials such as [[Cobalt(II) oxide|CoO]] that have an odd number of electrons per unit cell are insulators, in direct conflict with this result. This kind of material is known as a [[Mott insulator]], and requires inclusion of detailed electron-electron interactions (treated only as an averaged effect on the crystal potential in band theory) to explain the discrepancy. The [[Hubbard model]] is an approximate theory that can include these interactions. It can be treated non-perturbatively within the so-called [[dynamical mean-field theory]], which attempts to bridge the gap between the nearly free electron approximation and the atomic limit. Formally, however, the states are not non-interacting in this case and the concept of a band structure is not adequate to describe these cases.