Anharmonicity and the inverse isotope effect in the palladium-hydrogen system

We have used the full-potential linearized-augmented-plane-wave (LAPW) method to perform electronic-structure calculations for the palladium-hydrogen system in the rocksalt structure for the static lattice and for the cases of hydrogen displacements in the 〈100〉, 〈110〉, and 〈111〉 directions. Utilizing the LAPW total energies, and the approximation of an isotropic anharmonic oscillator, we have determined the zone-center optic modes for PdH, PdD, and PdT and find very good agreement with experiment. Using our lattice-dynamics results and our calculations of the electron-phonon interaction in the rigid-muffin-tin approximation, we have determined the superconducting coupling parameter λ and ${\mathit{T}}_{\mathit{c}}$ for these three hydrides. We find that the inverse isotope effect is semiquantitatively accounted for by the anharmonic lattice dynamics, without assuming an explicit dependence of the electron-phonon interaction on hydrogen isotope, in agreement with earlier calculations. However, there is a significant quantitative variation of the isotope effect with the value of the Coulomb pseudopotential parameter ${\mathrm{\mu }}^{\mathrm{*}}$, which must be estimated. We also estimate the effect of pressure on ${\mathit{T}}_{\mathit{c}}$ and on the isotope effect.