Motts Justification of Hubbard

John Hubbard was the first person to note the inconsistency between theoretical band calculation and experimental conductivity data in the case of transition metal oxides. Without much ado, he simply added a band gap of the size U at the Fermi level. With U = 2 eV, the electronic transitions start at 2 eV instead of 0 eV, which, as it turns out, is a considerable improvement of the previous theoretical numbers. 

Mott (later Sir Neville Mott) was rightly concerned and tried to justify Hubbard U. He came up with a model where the energy U is the energy needed to transfer one electron from one site to an equivalent site (thereby, in fact, assnming that the system is localized). It should cost in energy to move an electron to an eqnivalent site. In chemical terms, the reaction is as follows for NiO  

The nearby Ni ions change their configuration from 3d to 3d and 3d . Mott considered that U essentially consists of the energy U = (3d l/ri2 3d), the electronic 

If AG is too large for thermal transition between the phases, optical transitions may take place between the spin-coupled states and the charged states. As Equation 

2 shows, Hubbard transitions are, at the same time, intervalence transitions. 

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