  We introduced the inter-site electron-electron correlation to the Hubbard III
approximation. This correlation was excluded in the Hubbard III approximation
and also in the equivalent coherent potential approximation. Including it
brings two spin dependent effects: the bandwidth correction and the bandshift
correction, which both stimulate the ferromagnetic ground state. The bandshift
correction factor causes an exchange splitting between the spin-up and
spin-down spectrum, and its role is similar to the exchange interaction in the
classic Stoner model. The spin dependent bandwidth correction lowers the
kinetic energy of electrons by decreasing the majority spin bandwidth for some
electron occupations with respect to the minority spin bandwidth. In certain
conditions it can lead to ferromagnetic alignment. A gain in the kinetic energy
achieved in this way is the opposite extreme to the effect of a gain in
potential energy due to exchange splitting. The bandshift factor is a dominant
force behind the ferromagnetism. The influence of the bandwidth factor is too
weak to create ferromagnetism and the only result is the correction to the
classic coherent potential approximation in favor of ferromagnetism.
