Electronic structure of random binary alloys : an augmented space formulation in reciprocal space

We present here a reciprocal space formulation of the Augmented space recursion (ASR) which uses the lattice translation symmetry in the full augmented space to produce configuration averaged quantities, such as spectral functions and complex band structures. Since the real space part is taken into account {\sl exactly} and there is no truncation of this in the recursion, the results are more accurate than recursions in real space. We have also described the Brillouin zone integration procedure to obtain the configuration averaged density of states. We apply the technique to Ni$_{50}$Pt$_{50}$ alloy in conjunction with the tight-binding linearized muffin-tin orbital basis. These developments in the theoretical basis were necessitated by our future application to obtain optical conductivity in random systems.