Anharmonic phonons in high-pressure hydrogen and hydrogen-rich materials.*

Hydrogen-rich materials are characterized by the presence of large quantum fluctuations affecting hydrogen motion. While the impact of nuclear quantum effects (NQEs) on the behaviour of these systems is substantial, from the theoretical sides understanding how NQEs modify their vibrational properties still represents a challenge. In this work, we introduce a framework to compute accurate phonons in atomic[1] and molecular[2] crystals even in case of strong quantum anharmonicity. This method is based on the evaluation of the static limit of the exact Matsubara phononic Green’s function. It is fully ab initio, as we obtain this quantity within density functional theory coupled with path integral molecular dynamics. We show that, by means of our approach, one can reach converged phonon frequencies at much lower computational cost and at higher precision than previously reported in literature. As application, we compute the vibrons modes of phase III and IV of high-pressure solid molecular hydrogen with unprecedented accuracy, by characterizing their nature. Finally, we show the major role played by NQEs in the phonon dispersion of the high-temperature superconducting H₃S, by coupling these results with quantum Monte Carlo calculations for the electronic part.