We introduce the Korringa-Kohn-Rostocker nonlocal coherent-potential approximation ͑KKR-NLCPA͒ for describing the electronic structure of disordered systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used KKR-CPA approach and includes nonlocal correlations in the disorder configurations by means of a self-consistently embedded cluster. The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalization of the KKR-CPA; it remains fully causal, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated. In particular, it is suitable for combination with electronic density-functional theory to give an ab initio description of disordered systems. Future applications to charge correlation and lattice displacement effects in alloys, and spin fluctuations in magnets amongst others, are very promising. We illustrate the method by application to a simple one-dimensional model.

For many years, density-functional-based calculations for the total energies of substitutionally disordered alloys have been based upon the Korringa-Kohn-Rostoker coherent-potential approximation ͑KKR-CPA͒. However, as a result of the single-site nature of the KKR-CPA, such calculations do not take into account important local environmental effects such as charge correlations ͑the Madelung energy͒ and chemical shortrange order ͑SRO͒. Here the above approach is generalized by combining the recently developed Korringa-Kohn-Rostoker nonlocal coherent-potential approximation with density functional theory, showing how these effects may be systematically taken into account. As a first application of the theory, total energy calculations for the bcc Cu 50 Zn 50 solid solution are presented, showing how the total energy varies as a function of SRO. The fcc Cu 60 Pd 40 and Cu 77 Ni 23 systems are also investigated.

For many years the Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA) has been widely used to describe the electronic structure of disordered systems based upon a firstprinciples description of the crystal potential. However, as a single-site theory the KKR-CPA is unable to account for important environmental effects such as short-range order (SRO) in alloys and spin fluctuations in magnets, amongst others. Using the recently devised KKR-NLCPA (where NL stands for nonlocal), we show how to remedy this by presenting explicit calculations for the effects of SRO on the electronic structure of the bcc Cu50Zn50 solid solution.

Progress has recently been made within the effective medium approach to describing substitutionally disordered systems through the development of the nonlocal coherent-potential approximation (NLCPA). The NLCPA generalizes the widely used CPA approach and is capable of including a description of important environmental effects neglected by the CPA. As a currently developing field with much potential future application, the aim of this review is to clarify the ideas underlying the existing theory in relation to other known methods using both simple models and first-principles calculations. In addition to demonstrating the appealing aspects of the theory, this review also aims to highlight the theoretical issues which need to be addressed.