A practical method for performing self-consistent electronic structure calculations based upon full-potential multiple-scattering theory is presented. Solutions to the single site Schroedinger equation are obtained by solving coupled channel integral equations for a potential which is analytically continued out to the circumscribing sphere. This potential coincides with the full cell potential inside each atomic cell. Scattering matrices and wavefunctions for the full cell potential are obtained from surface Wronskian relations. The charge density is obtained from the single particle Green's function. This Green's function is computed using the cell scattering matrices and wavefunctions using the layer multiple scattering theory. Self consistent solutions require a solution at each iteration to the Poisson equation. The Poisson equation is solved using a variational cellular method. In the approach a local solution to each cell is augmented by adding a series of regular harmonics (solutions to Laplace's equation). Minimizing the coulomb energy, subject to continuity of the potential across all cell boundary provides an expression for the coefficients of the regular harmonics. This method is applied to BCC Nb. Calculated properties converge well in angular momentum and show comparable accuracy to full potential linearized muffin-tin orbital calculations.

A description of general techniques for solving linear partial differential equations by dividing space into regions to which the equations are independently applied and then assembling a global solution from the partial ones. Intended for researchers and graduates involved in calculations of the electronic structure of materials, this will also be of interest to workers in quantum chemistry, electron microscopy, acoustics, optics, and other fields. The book begins with an intuitive approach to scattering theory and then turns to partial waves and a formal development of multiple scattering theory, with applications to the solid state. The authors then present a variational derivation of the formalism and an augmented version of the theory, concluding with a discussion of the relativistic formalism and a discussion of the Poisson equation. Appendices discuss Green's functions, spherical functions, Moller operators and the Lippmann-Schwinger equation, irregular solutions, and singularities in Green's functions.

This edited book, based on material presented at the EU Spec Training School on Multiple Scattering Codes and the following MSNano Conference, is divided into two distinct parts. The first part, subtitled “basic knowledge”, provides the basics of the multiple scattering description in spectroscopies, enabling readers to understand the physics behind the various multiple scattering codes available for modelling spectroscopies. The second part, “extended knowledge”, presents “state- of-the-art” short chapters on specific subjects associated with improving of the actual description of spectroscopies within the multiple scattering formalism, such as inelastic processes, or precise examples of modelling.

In 1947, it was discovered that multiple scattering theory (MST) can be used to solve the Schröedinger equation for the stationary states of electrons in a solid. Written by experts in the field, J S Faulkner, G Malcolm Stocks and Yang Wang, this book collates the results of numerous studies in the field of MST and provides a comprehensive, systematic approach to it. For many scientists, students and engineers working with multiple scattering programmes, this will be a useful guide to help expand the existing knowledge of MST as well as understanding its future implications.

The MRS Symposium Proceeding series is an internationally recognised reference suitable for researchers and practitioners.