We review the application of the finite element (FE) method to ab initio electronic structure calculations in solids. The FE method is a general approach for the solution of differential and integral equations which uses a strictly local, piecewise-polynomial basis. Because the basis is composed of polynomials, the method is completely general and its accuracy is systematically improvable. Because the basis is strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited for parallel implementation. The method thus combines significant advantages of both real-space-grid and basis-oriented approaches, and so is well suited for large, accurate ab initio calculations. We review the construction and properties of the required FE bases and their use in the self-consistent solution of the Kohn–Sham equations of density functional theory.

An overview of PURGATORIO, a new implementation of the INFERNO 1 equation of state model, is presented. The new algorithm emphasizes a novel decimation scheme for automatically resolving the structure of the continuum density of states, circumventing limitations of the pseudo-R matrix algorithm previously utilized.

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We report on recent developments with the Purgatorio code, a new implementation of Liberman's Inferno model. This fully relativistic average atom code uses phase shift tracking and an efficient refinement scheme to provide an accurate description of continuum states. The resulting equations of state accurately represent the atomic shell-related features which are absent in Thomas-Fermi-based approaches. We discuss various representations of the exchange potential and some of the ambiguities in the choice of the effective charge Z * in average atom models, both of which affect predictions of electrical conductivities and radiative properties.

The free volume of metallic glasses has a significant effect on atomic relaxation processes, although a detailed understanding of the nature and distribution of free volume sites is currently lacking. Positron annihilation spectroscopy was employed to study free volume in a Zr-Ti-Ni-Cu-Be bulk metallic glass following plastic straining and cathodic charging with atomic hydrogen. Multiple techniques were used to show that strained samples had more open volume, while moderate hydrogen charging resulted in a free volume decrease. It was also shown that the free volume is associated with zirconium and titanium at the expense of nickel, copper, and beryllium. Plastic straining led to a slight chemical reordering.