First-principles calculations of phonon frequencies, lifetimes, and spectral functions from weak to strong anharmonicity: The example of palladium hydrides

The variational stochastic self-consistent harmonic approximation is combined with the calculation of third-order anharmonic coefficients within density functional perturbation theory and the 2n + 1 theorem to calculate anharmonic properties of crystals. It is demonstrated that in the perturbative limit, the combination of these two methods yields the perturbative phonon linewidth and frequency shift in a very efficient way, avoiding the explicit calculation of fourth-order anharmonic coefficients. Moreover, it also allows calculating phonon lifetimes and inelastic neutron-scattering spectra in solids where the harmonic approximation breaks down and a nonperturbative approach is required to deal with anharmonicity. To validate our approach, we calculate the anharmonic phonon linewidth in the strongly anharmonic palladium hydrides. We show that due to the large anharmonicity of hydrogen optical modes, the inelastic neutron-scattering spectra are not characterized by a Lorentzian line shape, but by a complex structure including satellite peaks.