  Koopmans-compliant functionals have been shown to provide accurate spectral
properties for molecular systems; this accuracy is driven by the generalized
linearization condition imposed on each charged excitation - i.e. on changing
the occupation of any orbital in the system, while accounting for screening and
relaxation from all other electrons. In this work we discuss the theoretical
formulation and the practical implementation of this formalism to the case of
extended systems, where a third condition, the localization of Koopmans'
orbitals, proves crucial to reach seamlessly the thermodynamic limit. We
illustrate the formalism by first studying one-dimensional molecular systems of
increasing length. Then, we consider the band gaps of 30 paradigmatic
solid-state test cases, for which accurate experimental and computational
results are available. The results are found to be comparable with the
state-of-the-art in diagrammatic techniques (self-consistent many-body
perturbation theory with vertex corrections), notably using just a functional
formulation for spectral properties and the physics of the generalized-gradient
approximation; when ionization potentials are compared, the results are roughly
twice as accurate.
