  The hybrid halide perovskite CH3NH3PbI3 exhibits a complex structural
behaviour, with successive transitions between orthorhombic, tetragonal and
cubic polymorphs at ca. 165 K and 327 K. Herein we report first-principles
lattice dynamics (phonon spectrum) for each phase of CH3NH3PbI3. The
equilibrium structures compare well to solutions of temperature-dependent
powder neutron diffraction. By following the normal modes we calculate infrared
and Raman intensities of the vibrations, and compare them to the measurement of
a single crystal where the Raman laser is controlled to avoid degradation of
the sample. Despite a clear separation in energy between low frequency modes
associated with the inorganic PbI3 network and high-frequency modes of the
organic CH3NH3+ cation, significant coupling between them is found, which
emphasises the interplay between molecular orientation and the corner-sharing
octahedral networks in the structural transformations. Soft modes are found at
the boundary of the Brillouin zone of the cubic phase, consistent with
displacive instabilities and anharmonicity involving tilting of the PbI6
octahedra around room temperature.
