  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.
