First-principles pseudopotential calculations for hydrogen in 4d transition metals. II. Vibrational states for interstitial hydrogen isotopes

In this second part of our first-principles study of hydrogen in transition metals within the framework of the Born-Oppenheimer and the local density-functional approximations, the mixed-basis pseudopotential method, which was outlined in the first part, is applied to calculate total energies and internal forces in Pd(n)H supercells with n less-than-or-equal-to 32 and Nb(n)H supercells with n less-than-or-equal-to 4. Adiabatic potentials for H in PdH and NbH are determined and the influence of lattice relaxations is discussed. Analytic model potentials are fitted to the first-principles results, and the importance of anharmonicity for vibrational states of interstitial H isotopes is investigated. By comparing our calculated vibrational energies with results from neutron-scattering experiments, we find that for NbH the anharmonicity is weak and the results obtained in harmonic approximation or via perturbation theory are in good agreement with experiment. For PdH the harmonic approximation as well as the perturbation theory are insufficient. The anharmonicity and the periodicity of the adiabatic potential need to be represented carefully by a Fourier series. Then the agreement with experiment is found to be as good as for NbH and even allows us to propose a reinterpretation of the experimental data.