  The Shirley reduced basis (SRB) represents the periodic parts of Bloch
functions as linear combi- nations of eigenvectors taken from a coarse sample
of the Brillouin zone, orthogonalized and reduced through proper orthogonal
decomposition. We describe a novel transformation of the self-consistent
density functional theory eigenproblem from a plane-wave basis with ultra-soft
pseudopotentials to the SRB that is independent of the k-point. In particular,
the number of operations over the space of plane-waves is independent of the
number of k-points. The parameter space of the transformation is explored and
suitable defaults are proposed. The SRB is shown to converge to the plane-wave
solution. For reduced dimensional systems, reductions in computational cost,
compared to the plane-wave calculations, exceed 5x. Performance on bulk systems
improves by 1.67x in molecular dynamics-like contexts. This robust technique is
well-suited to efficient study of systems with strin- gent requirements on
numerical accuracy related to subtle details in the electronic band structure,
such as topological insulators, Dirac semi-metals, metal surfaces and
nanostructures, and charge transfer at interfaces with any of these systems.
The techniques used to achieve a k-independent transformation could be applied
to other computationally expensive matrix elements, such as those found in
density functional perturbation theory and many-body perturbation theory.
