A recently developed ab initio approach to the electronic structure of substitutionally disordered alloys and their surfaces is reviewed. It is based on (i) the tight-binding linear muffin-tin orbital (TB-LMTO) method in the atomic sphere approximation which provides a physically transparent solution of the one-electron problem in metallic materials, (ii) the coherent potential approximation (CPA) for a mean- field treatment of the substitutional randomness, and (iii) the surface Green functions for a proper description of the true semi-infinite geometry of surfaces and interfaces. Theoretical formulation of fundamental electronic quantities, both site-diagonal (charge densities, densities of states) and site non-diagonal (the Bloch spectral functions) is presented. Transformation properties of the LMTO-CPA theory as well as specific problems of application of the local density approximation to random alloys are briefly discussed and basic algorithms employed in the numerical implementation of the formalism are described.
Turek, I., Kudrnovský, J., & Drchal, V. (2007). Disordered Alloys and Their Surfaces: The Coherent Potential Approximation. In Electronic Structure and Physical Properies of Solids (pp. 349–378). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-46437-9_10