Real-space formulation of the mixed-basis pseudopotential method: Bulk structural properties of elemental copper

We present a formulation of the mixed-basis expansion for electronic structure calculations, which allows calculations on systems in which there is a strongly localized component of the valence charge density. As in the conventional mixed-basis expansion, a small plane-wave basis is augmented with a set of auxiliary functions to describe the localized component of the wave functions. Unlike the conventional mixed-basis scheme, however, a fixed set of optimized nonoverlapping auxiliary functions are employed, so that matrix elements involving this set are calculable by very fast and accurate one-dimensional k-independent quadrature. The method is applied to study the electronic structure and bulk structural properties of Cu. The electronic structure, based on the pseudopotential of Bachelet, Hamann, and Schl\"uter, compares well with that obtained from other self-consistent state-of-the-art all-electron methods. The total energies for Cu in the fcc and bcc crystal structures are calculated and compared. We find that the fcc structure is favored at all densities, although the bcc exhibits an unusually stable high-density structure. A number of technical points relating to the use of these optimized local basis functions in band-structure calculations are discussed.