In hybrid perovskite materials like CH 3 NH 3 PbI 3 , methylammonium (MA) lead iodide (MAPI), the orientation of the MA + cations and their ordering can significantly affect the structure of the inorganic framework. Although the states near the band edges are known to be primarily derived from the Pb and halogen orbitals rather than from the organic ion, the latter may have an indirect effect through their impact on the structural relaxation. In this work, we investigate both the structural relaxation effects of the inorganic framework in response to the MA + orientation and their impact on the electronic structure near the band edges. Calculations are performed for MA(Pb,Sn) X 3 with ( X = I, Br, and Cl) materials for both Pb- and Sn-based compounds. The work focuses on the high-temperature α-phase, which is nominally cubic if averaged over all possible MA orientations and in which no alternating rotations of the octahedral occur, so that the unit cell is the smallest possible. The effects of van der Waals (vdW) corrections to density functional theory on the structural relaxation are investigated. Our results reveal that the vdW interactions between the MA + cation and the inorganic framework can strongly affect the optimized orientation and position of the molecule and the resulting distortion of the inorganic framework. Consequently, it also affects the electronic properties of the materials and specifically can change the band structure from direct to indirect band gaps. The robustness of this result is studied by comparing hybrid functional calculations and quasiparticle self-consistent GW calculations as well as spin–orbit coupling.

The mechanical properties of perovskite oxides depend on two metal oxide lattices that are intercalated. This provides an opportunity for separate tuning of hardness, Poisson's ratio (transverse expansion in response to the compression), and shear strength. The elastic constants of series of perovskite oxides were studied by first principles approach. Both A-site and B-site cations were systematically varied in order to see their effects on the elastic parameters. To study the effects of A-site cations, we studied the elastic properties of perovskite ATiO3 for A being Be, Mg, Ca, Sr, or Ba, one at a time. Similarly, for B-site cations, we studied the elastic properties of PbBO3 for B being Ti, Zr, or Hf, one at a time. The density functional first principles calculations with local density approximation (LDA) and generalized gradient approximation (GGA) were employed. It is found that the maximum C11 elastic constant is achieved when the atomic size of the cations at A-site and B-site are comparable. We also found that C12 elastic constant is sensitive to B-site cations while C44 elastic constant is more sensitive to A-site cations. Details and explanations for such dependencies are discussed.