Simultaneous Deep Tunneling and Classical Hopping for Hydrogen Diffusion on Metals

Hydrogen diffusion on metals exhibits rich quantum behavior, which is not yet fully understood. Using simulations, we show that many hydrogen diffusion barriers can be categorized into those with parabolic-tops and those with broad-tops. With parabolic-top barriers, hydrogen diffusion evolves gradually from classical hopping to shallow tunneling to deep tunneling as the temperature decreases, and noticeable quantum effects persist at moderate temperatures. In contrast, with broad-top barriers quantum effects become important only at low temperatures and the classical to quantum transition is sharp, at which classical hopping and deep tunneling both occur. This coexistence indicates that more than one mechanism contributes to the quantum reaction rate. The conventional definition of the classical to quantum crossover temperature is invalid for the broad-tops, and we give a new definition. Extending this we propose a model to predict the transition temperature for broad-top diffusion, providing a general guide for theory and experiment.