Quantum instanton evaluations of surface diffusion, interior migration, and surface-subsurface transport for H/Ni

The quantum instanton approximation is extended to investigate dynamical processes of hydrogen on surface, from surface to subsurface, and between interior sites in nickel lattice. The path integral Monte Carlo and adaptive umbrella sampling techniques are employed to manipulate the quantum instanton formula. The free energy profiles along reaction paths, temperature dependence of free energies, and rates as well as diffusion coefficients are calculated for each process. The results manifest that the motions of nickel atoms beneath the surface have little effect on the hydrogen diffusion on Ni(111), and the hydrogen at the fcc binding site is much easier to get into bulk nickel than the one at the hcp site. The temperature dependence of free energy profiles also reveals that the hydrogen in the subsurface octahedral vacancy and interior tetrahedral vacancy becomes unstable at low temperatures, which proposes a temperature dependence of reaction mechanism. In addition, the relaxations of the lattices dramatically lower the free energy barriers except for the process of the hydrogen diffusion on Ni(111). The quantum motions of the lattice atoms affect the free energies little at 300 K, but they hinder the rates by 20%-40% compared with the classical motions of lattice atoms.