  We have used the locally self-consistent Green's function (LSGF) method in
supercell calculations to establish the distribution of the net charges
assigned to the atomic spheres of the alloy components in metallic alloys with
different compositions and degrees of order. This allows us to determine the
Madelung potential energy of a random alloy in the single-site mean field
approximation which makes the conventional single-site density-functional-
theory coherent potential approximation (SS-DFT-CPA) method practically
identical to the supercell LSGF method with a single-site local interaction
zone that yields an exact solution of the DFT problem. We demonstrate that the
basic mechanism which governs the charge distribution is the screening of the
net charges of the alloy components that makes the direct Coulomb interactions
short-ranged. In the atomic sphere approximation, this screening appears to be
almost independent of the alloy composition, lattice spacing, and crystal
structure. A formalism which allows a consistent treatment of the screened
Coulomb interactions within the single-site mean-filed approximation is
outlined. We also derive the contribution of the screened Coulomb interactions
to the S2 formalism and the generalized perturbation method.
