Lattice dynamics and vibrational spectra of the orthorhombic, tetragonal, and cubic phases of methylammonium lead iodide

The hybrid halide perovskite ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$ exhibits a complex structural behavior, with successive transitions between orthorhombic, tetragonal, and cubic polymorphs around 165 and 327 K. Herein we report first-principles lattice dynamics (phonon spectrum) for each phase of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$. The equilibrium structures compare well to solutions of temperature-dependent powder neutron diffraction. By following the norma