Real-space multiple-scattering theory and the electronic structure of systems with full or reduced symmetry

We present a new real-space multiple-scattering-theory method for the solution of the Schr{umlt o}dinger equation and the calculation of the electronic structure of solid materials with full or reduced symmetry. The method is based on the concept of semi-infinite periodicity (SIP), rather than translational invariance, and on the property of removal invariance of the scattering matrix of systems with SIP. This latter property allows one to replace the usual Brillouin-zone integrals in reciprocal space by a self-consistency equation for the {ital t} matrix, which is sufficient for the determination of the Green function and related properties. Because it is developed entirely in direct space, the method provides a unified treatment of the electronic structure of bulk materials, surfaces, interfaces and grain boundaries (coherent or incoherent), impurities of interstitial or substitutional kinds, and can be easily extended to treat concentrated, substitutionally disordered alloys. One of its advantages over methods based on Bloch's theorem and reciprocal space is the great simplicity of setting up and running the associated computer codes even for complex structures, and structures with reduced or no symmetry that lie outside the realm of applicability of conventional methods. We present the results of model calculations for one-dimensional and three-dimensional model systems as well as for three-dimensional realistic materials. Where appropriate, these results are compared with those obtained through conventional techniques, and give an indication of the method's flexibility and reliability. Our applications of this method to this point are discussed, and our plans for future development are presented.