Rigorous definition of oxidation states of ions in solids
  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. 
Lai Jiang, Sergey V. Levchenko, and Andrew M. Rappe
cond-mat.mtrl-sci