Classical and quantum-mechanical methods were used to calculate the site-to-site hopping rate of H in crystalline material. The calculations involved a parametrized version of a potential surface which had been calculated by using density functional methods. The hopping rate was deduced from the time integral of a flux correlation function which was evaluated by using molecular dynamics and real-time path integral techniques. The results indicated that quantum-mechanical tunnelling played an important role in the diffusion process; even above room temperature. Moreover, the calculated diffusion rate exhibited a reverse isotope effect in the domain between activated and tunnelling dynamics. This arose from the zero-point energy of the H atom in the direction perpendicular to the line which connected 2 stable minima.

K.M.Forsythe, N.Makri: Journal of Chemical Physics, 1998, 108[16], 6819-28