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.
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