Structures of hydrogen at terapascal pressures

Stable structures of atomic phases of hydrogen are investigated up to about 9 TPa by using ab initio calculations, where the zero-point energy of protons is estimated with the use of the self-consistent harmonic approximation (SCHA). In addition to the structures so far proposed, random structure searches find a relatively isotropic structure of $Cmcm$ symmetry with two atoms in the primitive cell, which is called $Cmcm\text{\ensuremath{-}}2$ here. The analysis with the SCHA predicts the low-enthalpy structures as follows: Cs-IV $\ensuremath{-}(1.4\phantom{\rule{0.16em}{0ex}}\mathrm{TPa})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}C{222}_{1} \ensuremath{-}(3.7\phantom{\rule{0.16em}{0ex}}\mathrm{TPa})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}I\overline{4}3d$. However, above $\ensuremath{\sim}4$ TPa, several isotropic structures turn out to have quite close enthalpies owing to anharmonicity, which are the $I\overline{4}3d$, hcp, $Cmcm\text{\ensuremath{-}}2$, and fcc structures. It may also be possible that the bcc structure is added to this group above 5.8 TPa, for the bcc structure is stabilized dynamically above 5.8 TPa in the SCHA, while imaginary-frequency phonons exist up to about 233 TPa in the harmonic approximation.