  Koopmans spectral functionals aim to describe simultaneously ground state
properties and charged excitations of atoms, molecules, nanostructures and
periodic crystals. This is achieved by augmenting standard density functionals
with simple but physically motivated orbital-density-dependent corrections.
These corrections act on a set of localized orbitals that, in periodic systems,
resemble maximally localized Wannier functions. At variance with the original,
direct supercell implementation [Phys. Rev. X 8, 021051 (2018)], we discuss
here i) the complex but efficient formalism required for a periodic-boundary
code using explicit Brillouin zone sampling, and ii) the calculation of the
screened Koopmans corrections with density-functional perturbation theory. In
addition to delivering improved scaling with system size, the present
development makes the calculation of band structures with Koopmans functionals
straightforward. The implementation in the open-source Quantum ESPRESSO
distribution and the application to prototypical insulating and semiconducting
systems are presented and discussed.
