  Shifting the Fermi energy in solids by doping, defect formation or gating
generally results in changes in the charge density distribution, which reflect
the ability of the bonding pattern in solids to adjust to such external
perturbations. In the ionic limit, such changes are described by the formal
oxidation states (FOS) whereby a single atom type is presumed to absorb the
full burden of the perturbation (change in charge) of the whole compound. In
this picture, when the solar absorber CsSnI3 loses 50 % of its Sn atoms thereby
forming the ordered vacancy compound Cs2SnI6, the Sn is said to change from
Sn2+ to Sn4+. In reality, the charge redistribution is more complex. To
understand the electronic properties of these two groups and to gauge the
trends in s-electron charge on the nucleus, we studied the 113/216 compound
pairs CsSnCl3/Cs2SnCl6; CsSnBr3/Cs2SnBr6, and CsSnI3/Cs2SnI6. We have
calculated the electronic structure of these three compound pairs,
complementing them by CsSnF3/Cs2SnF6 in the hypothetical cubic structure for
completing the chemical trends. These materials were also synthesized by
chemical routes and characterized by X-ray diffraction, Mossbauer spectroscopy
and K-edge X-ray Absorption Spectroscopy. We find that in going from 113 to 216
there 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 downshift
of the otherwise unoccupied p level, an effect that tends to replenish much of
the lost s charge. This effect is theoretically explained as a self-regulating
response [H. Raebiger, S. Lany, and A. Zunger, Nature 453, 763 (2008)] whereby
the system re-hybridizes to minimize the effect of the charge perturbation
created by vacancy formation. Our work clarifies the relation between FOS and
charge transfer that can be applied to a wide variety of materials.
