In a recent publication , we presented results of electronic-structure calculations on Σ5 grain boundaries in Cu. These calculations were performed using the real-space multiplescattering theory (RSMST), a first-principles method which does not rely on translational invariance and Bloch's theorem [2, 3], and hence avoids the problems associated with treating interfaces in a periodic repeating slab geometry. A brief summary of this method follows.
The RSMST is based on the concept of semi-infinite periodicity (SIP), defined as the regular repetition along a given direction of a scattering unit (atom, planes of atoms, etc.), or a set of such units. Systems with SIP possess the property of removal invariance, which states that the scattering properties (scattering matrices) of any such system remain invariant when an integral number of scattering units is removed from, or added to, the free end of the system. Using this property in conjunction with multiple-scattering theory, one can determine the electronic Green function, and hence all one-particle quantities such as the density of states (DOS), directly in real space.
The essence of the method consists in a prescription for the proper renormalization of the scattering properties of the boundary sites of a cluster of atoms. Unrenormalized or “bare” sites in the interior of the cluster describe the region of interest, such as a grain boundary, while the renormalized boundary sites represent the infinite medium surrounding the cluster. This “dressing up” of the cluster is done independently for each part of a system that is characterized by its own SIP, so that grain boundaries between essentially arbitrary crystal structures can be treated.
The calculations described previously  used given atomistic configurations and electronic one-particle potentials and computed the local DOS at atoms of interest within the grain boundaries. We are currently extending our method to incorporate charge self-consistency and total-energy capabilities. In connection with this, we have implemented four different methods of expressing mathematically the invariance properties of semi-infinite systems, and are evaluating them for optimal rates of convergence and computational efficiency. Calculations on Cu (100) monolayers will be used to illustrate these methods.