The locally self-consistent Green's function (LSGF) method is an order
-N method for calculation of the electronic structure of systems with
an arbitrary distribution of atoms of different kinds on an underlying
crystal lattice. For each atom Dyson's equation is used to solve the
electronic multiple scattering problem in a local interaction zone (LI
Z) embedded in an effective medium judiciously chosen to minimize the
size of the, LIZ. The excellent real-space convergence of the LSGF cal
culations and the reliability of its results are demonstrated for a br
oad spectrum of metallic alloys with different degree of order. The re
lation of the convergence of our method to fundamental properties of t
he system, that is, the effective cluster interactions, is discussed.