Activation Energies for Quantum Diffusion of Hydrogen in Metals and on Metal Surfaces using Delocalized Nuclei within the Density-Functional Theory

Hydrogen diffusion on the Cu(001) surface and in bulk Nb and Ta is studied in the quantum regime using first-principles electronic-structure calculations. We present, for the first time, a direct density-functional calculation of the activation energy required to establish the quantum-mechanically delocalized hydrogen coincidence configuration and of the corresponding tunneling matrix element. For the two bulk systems a direct comparison can be made with nuclear magnetic resonance data, and we find excellent agreement for both the coincidence energy and the tunneling matrix element.