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We present justification and a rigorous procedure for electron partitioning among atoms in extended systems. The method is based on wave-function topology and the modern theory of polarization, rather than charge density partitioning or wave-function projection, and, as such, reformulates 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.
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