  We present a new implementation of the k-space interpolation scheme for
electronic structure presented by E. L. Shirley, Phys. Rev. B 54, 16464 (1996).
The method permits the construction of a compact k-dependent Hamiltonian using
a numerically optimal basis derived from a coarse-grained set of effective
single-particle electronic structure calculations (based on density functional
theory in this work). We provide some generalizations of the initial approach
which reduce the number of required initial electronic structure calculations,
enabling accurate interpolation over the entire Brillouin zone based on
calculations at the zone-center only for large systems. We also generalize the
representation of non-local Hamiltonians, leading to a more efficient
implementation which permits the use of both norm-conserving and ultrasoft
pseudopotentials in the input calculations. Numerically interpolated electronic
eigenvalues with accuracy that is within 0.01 eV can be produced at very little
computational cost. Furthermore, accurate eigenfunctions - expressed in the
optimal basis - provide easy access to useful matrix elements for simulating
spectroscopy and we provide details for computing optical transition
amplitudes. The approach is also applicable to other theoretical frameworks
such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter
equation for optical responses.
