Pair modes of organic cations in hybrid perovskites: Insight from first-principles calculations of supercell models

We have studied the properties of the prototype hybrid organic-inorganic perovskite CH3NH3PbI3 using relativistic density functional theory (DFT). For our analysis we introduce the concept of CH3NH + 3 “pair modes”, that is, characteristic relative orientations of two neighboring CH3NH + 3 cations. In our previous work [Phys. Rev. B 94, 045201(2016)] we identified two preferential orientations that a single CH3NH+3 cation adopts in a unit cell. The total number of relevant pairs can be reduced from the resulting 196 combinations to only 25 by applying symmetry operations. DFT results of several 2×2×2 supercell models reveal the dependence of the total energy, band gap and band structure on the distribution of CH3NH + 3 cations and the pair modes. We have then analyzed the pair-mode distribution of a series of 3×3×3 supercell models with disordered CH3NH+3 cations. Our results show that diagonally-oriented CH3NH + 3 cations are rare in optimized CH3NH3PbI3 supercell structures. The prevailing pair modes are advantageous for the formation of linear domains. Our pair-mode concept provides combined atomistic-statistical insight to understand the disordered structures in bulk hybrid perovskite materials.