  We present justification and rigorous procedure for electron partitioning
among atoms in extended systems. The method is based on wavefunction topology
and the modern theory of polarization, rather than charge density partitioning
or wavefunction projection, and, as such, re-formulates the concept of
oxidation state without assuming real-space charge transfer between atoms. This
formulation provides rigorous electrostatics of finite extent solids, including
films and nanowires.
