Activation energies for quantum diffusion of hydrogen in metals and on metal surfaces using delocalized nuclei within the density-functional theory

The quantum diffusion of hydrogen on the Cu(001) and in bulk Nb and Ta was studied using first-principles electronic-structure calculations. 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 was also performed. A direct comparison can be made with nuclear magnetic resonance data for the two bulk systems. The results show an excellent agreement for both the coincidence energy and the tunneling matrix element.