First-principles prediction of a stable hexagonal phase of CH$_{\mathrm{3}}$NH$_{\mathrm{3}}$PbI$_{\mathrm{3}}$

Methylammonium lead iodide (CH$_{\mathrm{3}}$NH$_{\mathrm{3}}$PbI$_{\mathrm{3}}$ or MAPbI$_{\mathrm{3}})$ is a promising photovoltaic material with high power conversion efficiency. However, its experimental perovskite phases show poor thermodynamic stability. Using first-principles density functional theory, we predict a hexagonal (\textit{2H}) phase with $P63mc$ space-group symmetry to be the thermodynamically most stable phase. The \textit{2H}-phase consists of infinite chains of face-shared PbI$_{\mathrm{6}}$ octahedra with organic MA cations taking up the space between the chains, which is in contrast to the corner-connected octahedra observed in the experimental orthorhombic, tetragonal, and cubic phases. It has a negative formation enthalpy, independent of the choice of exchange correlation functional used in the calculations. The absence of soft-phonon modes in the \textit{2H}-phase demonstrates its dynamical stability. The \textit{2H}-phase has an indirect band gap of 2.6 eV, which is \textasciitilde 1 eV larger than the direct band gap of orthorhombic phase. The change in octahedral connectivity favors strongly anisotropic charge transport. Overall, the \textit{2H}-phase presents a new route to overcome the stability issues in MAPbI$_{\mathrm{3}}$.