  The report on the near-ambient superconductivity in a nitrogen-doped lutetium
hydride has stimulated great interest in this material (Dasenbrock-Gammon et
al. 2023). While its superconductivity is still a subject of debate, the
structure of the claimed cubic phase remains uncertain. In this work, we study
the effect of nitrogen doping and pressure on the energetic and dynamic
stability of cubic LuH3. Our findings indicate that both pressure and nitrogen
doping can enhance the stability of the cubic LuH3 phase. We propose a Lu8H21N
structure that exhibits stable phonon, reasonable thermodynamic stability at 1
GPa, and a similar XRD pattern to the experimental data. However, we do not
observe electron-phonon coupling in the zone-center phonon modes of these
crystal structures.
