[en] Highlights: • A quantum mechanical model determined cations substituted problem. • Only nine kinds of cations can be all substituted into Pb sites. • The first principle identified the nine kinds of structural stability. • Nine kinds of cations substituted can control the band gap. -- Abstract: 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.