  The physical properties of the transitional metals from the bulk to the
nanoparticles cannot be calculated accurately using a tight-binding
approximation restricted to a simple d-band. The investigations on this
approximation show the limitations, leading to a wrong cohesive energy compared
to an all-electron tight-binding basis calculation. These investigations
through the second moment approximation, the charge neutrality and the Stoner
model allow us to derive the appropriate corrections to these inconsistencies.
