  We present a new theory for partitioning simulations of periodic and
solid-state systems into physically sound atomic contributions at the level of
Kohn-Sham density functional theory. Our theory is based on spatially localized
linear combinations of crystalline Gaussian-type orbitals and, as such, capable
of exposing local features within periodic electronic structures in a more
intuitive and robust manner than alternatives based on the spatial distribution
of atomic basis functions alone. Early decomposed cohesive energies of both
molecular polymers and different crystalline polymorphs demonstrate how the
atomic properties yielded by our theory convincingly align with the expected
charge polarization in these systems, also whenever partial charges and
Madelung energies may lend themselves somewhat ambiguous to interpretation.
