Ground-State Structures of Ice at High-Pressures

\textit{Ab initio} random structure searching based on density functional theory is used to determine the ground-state structures of ice at high pressures. Including estimates of lattice zero-point energies, ice is found to adopt three novel crystal phases. The underlying sub-lattice of O atoms remains similar among them, and the transitions can be characterized by reorganizations of the hydrogen bonds. The symmetric hydrogen bonds of ice X and $Pbcm$ are initially lost as ice transforms to structures with symmetries $Pmc2_1$ (800 - 950 GPa) and $P2_1$ (1.17 TPa), but they are eventually regained at 5.62 TPa in a layered structure $C2/m$. The $P2_1 \rightarrow C2/m$ transformation also marks the insulator-to-metal transition in ice, which occurs at a significantly higher pressure than recently predicted.