Vibrational states for hydrogen in palladium

Vibrational potentials for hydrogen isotopes in PdH and ${\mathrm{Pd}}_4$H are determined from first-principles total-energy calculations. The strong anharmonicity of the potential for H around octahedral sites must be taken into account beyond perturbation theory. For PdH good quantitative agreement of our calculated vibration energies with inelastic-neutron-scattering (INS) results is achieved, allowing a reinterpretation of the INS spectra. For lower H concentrations (${\mathrm{Pd}}_{\mathit{n}}$H, n=4, 8, 16, and 32) the influence of local lattice relaxations on the vibration potentials and energies is important. Furthermore, metastable states confined to tetrahedral sites in Pd are found for the heavier isotopes ${}_{}{}^2{}_{}{}^{}\mathrm{D}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{T}$.