Why cannot all divalent cations completely substitute the Pb cations of CH3NH3PbI3 perovskite?

Organic-inorganic hybrid CH3NH3PbI3 perovskite has a great potential for applications in low-cost photovoltaic devices. However, the doped and substitution of Pb sites in CH3NH3PbI3 has not been widely reported. In this article, a quantum mechanical model was applied to determine why all divalent cations cannot substitute the Pb cations of CH3NH3PbI3 perovskite. The evaluation was performed by comparison the model with experimental results. On this basis, we carefully examined 42 types of cations and identified only nine kinds of cations including Ca2+, Sr2+, Sc2+, Ti2+, V2+, Y2+, Zr2+, Nb2+ and Sn2+ for doped into Pb sites. In these cases, it is expected that the corresponding compound would be single phase. Finally, an analysis was performed based on first principle, and the results indicate that divalent cations substituting the Pb sites modify the band structure and influence the performance of perovskite-based photostatics.