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The adsorption and diffusion of hydrogen atoms on Cu(001) are studied using first-principles calculations. By taking into account the contribution of zero-point energy (ZPE), the originally identical barriers are shown to be different for H and D, which are respectively calculated to be ~ 158 meV and ~ 139 meV in height. Using the transfer matrix method (TMM), we are able to calculate the accurate probability of transmission across the barriers. The crucial role of quantum tunneling is clearly demonstrated at low-temperature region. By introducing a temperature-dependent attempting frequency prefactor, the rate constants and diffusion coefficients are calculated. The results are in agreement with the experimental measurements at temperatures from ~ 50 K to 80 K.

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The activation and dissociation of H2 molecules on Cu(001) surface is studied theoretically. The activation barrier for the dissociation of H2 on Cu(001) is determined by first-principles calculations to be ~0.59 eV in height. Electron transfer from the substrate Cu to H2 plays a key role in the activation, breaking of the H-H bond and the formation of the Cu-H bonds. At around the critical height of bond breaking, two stationary states are identified, which correspond respectively to the molecular and dissociative state. Using the transfer matrix method, we are able to study the role of quantum tunneling in the dissociation process along the minimum energy pathway (MEP), which is found to be significant at room temperature and below. At given temperatures, the tunneling contributions from the translational and vibrational motions of H2 are quantified for the dissociation process. Within a wide range of temperatures, the effects of quantum tunneling on the effective barriers of dissociation and the rate constants are revealed. The deduced energetic parameters associated with thermal equilibrium and non-equilibrium (molecular beam) conditions are comparable with experimental data. In the low-temperature region, crossover from classical to quantum regime is identified.