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Shifting the Fermi energy in solids by doping, defect formation or gatinggenerally results in changes in the charge density distribution, which reflectthe ability of the bonding pattern in solids to adjust to such externalperturbations. In the ionic limit, such changes are described by the formaloxidation states (FOS) whereby a single atom type is presumed to absorb thefull burden of the perturbation (change in charge) of the whole compound. Inthis picture, when the solar absorber CsSnI3 loses 50 % of its Sn atoms therebyforming the ordered vacancy compound Cs2SnI6, the Sn is said to change fromSn2+ to Sn4+. In reality, the charge redistribution is more complex. Tounderstand the electronic properties of these two groups and to gauge thetrends in s-electron charge on the nucleus, we studied the 113/216 compoundpairs CsSnCl3/Cs2SnCl6; CsSnBr3/Cs2SnBr6, and CsSnI3/Cs2SnI6. We havecalculated the electronic structure of these three compound pairs,complementing them by CsSnF3/Cs2SnF6 in the hypothetical cubic structure forcompleting the chemical trends. These materials were also synthesized bychemical routes and characterized by X-ray diffraction, Mossbauer spectroscopyand K-edge X-ray Absorption Spectroscopy. We find that in going from 113 to 216there is a decrease in the s charge on Sn, in agreement with the FOS picture.However, at the same time, we observe an increase of the p charge via downshiftof the otherwise unoccupied p level, an effect that tends to replenish much ofthe lost s charge. This effect is theoretically explained as a self-regulatingresponse [H. Raebiger, S. Lany, and A. Zunger, Nature 453, 763 (2008)] wherebythe system re-hybridizes to minimize the effect of the charge perturbationcreated by vacancy formation. Our work clarifies the relation between FOS andcharge transfer that can be applied to a wide variety of materials.

Changes in charge density vs changes in formal oxidation states: The case of Sn halide perovskites and their ordered vacancy analogues