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

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.