  Hydrogen-rich superhydrides are promising high-Tc superconductors, with
superconductivity experimentally observed near room temperature, as shown in
recently discovered lanthanide superhydrides at very high pressures, e.g. LaH10
at 170 GPa and CeH9 at 150 GPa. Superconductivity is believed to be closely
related with the high vibrational modes of the bound hydrogen ions. Here we
study the limit of extreme pressures (above 200 GPa) where lanthanide hydrides
with large hydrogen content have been reported. We focus on LaH16 and CeH16,
two prototype candidates for achieving a large electronic contribution from
hydrogen in the electron-phonon coupling. In this work, we propose a first
principles calculation platform with the inclusion of many-body corrections to
evaluate the detailed physical properties of the Ce-H and La-H systems and to
understand the structure, stability and superconductivity of these systems at
ultra-high pressure. We provide a practical approach to further investigate
conventional superconductivity in hydrogen rich superhydrides. We report that
density functional theory provides accurate structure and phonon frequencies,
but many-body corrections lead to an increase of the critical temperature, that
is associated with spectral weight transfer of the f-states.
