  We perform a thorough structural search with the minima hopping method (MHM)
to explore low-energy structures of methylammonium lead iodide. By combining
the MHM with a forcefield, we efficiently screen vast portions of the
configurational space with large simulation cells containing up to 96 atoms.
Our search reveals two structures of methylammonium iodide perovskite (MAPI)
that are substantially lower in energy than the well-studied experimentally
observed low-temperature $Pnma$ orthorhombic phase according to density
functional calculations. Both structures have not yet been reported in the
literature for MAPI, but our results show that they could emerge as
thermodynamically stable phases via compression at low temperatures. In terms
of the electronic properties, the two phases exhibit larger band gaps than the
standard perovskite-type structures. Hence, pressure induced phase selection at
technologically achievable pressures (i.e., via thin-film strain) is a route
towards the synthesis of several MAPI polymorph with variable band gaps.
