  Phonon anharmonicity plays a crucial role in determining the stability and
vibrational properties of high-pressure hydrides. Furthermore, strong
anharmonicity can render phonon quasiparticle picture obsolete questioning
standard approaches for modeling superconductivity in these material systems.
In this work, we show the effects of non-Lorentzian phonon lineshapes on the
superconductivity of high-pressure solid hydrogen. We calculate the
superconducting critical temperature T$_\mathrm{C}$ \emph{ab initio}
considering the full phonon spectral function and show that it overall enhances
the T$_\mathrm{C}$ estimate. The anharmonicity-induced phonon softening
exhibited in spectral functions increases the estimate of the critical
temperature, while the broadening of phonon lines due to phonon-phonon
interaction decreases it. Our calculations also reveal that superconductivity
emerges in hydrogen in the $Cmca-12$ molecular phase VI at pressures between
450 and 500 GPa and explain the disagreement between the previous theoretical
results and experiments.
