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We introduced the inter-site electron-electron correlation to the Hubbard IIIapproximation. This correlation was excluded in the Hubbard III approximationand also in the equivalent coherent potential approximation. Including itbrings two spin dependent effects: the bandwidth correction and the bandshiftcorrection, which both stimulate the ferromagnetic ground state. The bandshiftcorrection factor causes an exchange splitting between the spin-up andspin-down spectrum, and its role is similar to the exchange interaction in theclassic Stoner model. The spin dependent bandwidth correction lowers thekinetic energy of electrons by decreasing the majority spin bandwidth for someelectron occupations with respect to the minority spin bandwidth. In certainconditions it can lead to ferromagnetic alignment. A gain in the kinetic energyachieved in this way is the opposite extreme to the effect of a gain inpotential energy due to exchange splitting. The bandshift factor is a dominantforce behind the ferromagnetism. The influence of the bandwidth factor is tooweak to create ferromagnetism and the only result is the correction to theclassic coherent potential approximation in favor of ferromagnetism.

Hubbard Model with Inter-Site Kinetic Correlations