Seven-dimensional microcanonical treatment of hydrogen dissociation dynamics on Cu(111): Clarifying the essential role of surface phonons

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A simple picture of the hydrogen dissociation/associative desorption dynamics on Cu(111) emerges from a two-parameter, full dimensionality microcanonical unimolecular rate theory (MURT) model of the gas-surface reactivity. Vibrational frequencies for the reactive transition state were taken from density functional theory calculations of a six-dimensional potential energy surface [Hammer et al., Phys. Rev. Lett. 73, 1400 (1994)]. The two remaining parameters required by the MURT were fixed by simulation of experiments. These parameters are the dissociation threshold energy, E(0)=79 kJmol, and the number of surface oscillators involved in the localized H(2)Cu(111) collision complex, s=1. The two-parameter MURT quantitatively predicts much of the varied behavior observed for the H(2) and D(2)Cu(111) reactive systems, including the temperature-dependent associative desorption angular distributions, mean translational energies of the associatively desorbing hydrogen as a function of rovibrational eigenstate, etc. The divergence of the statistical theory's predictions from experimental results at low rotational quantum numbers, J < or approximately 5, suggests that either (i) rotational steering is important to the dissociation dynamics at low J, an effect that washes out at high J, or (ii) molecular rotation is approximately a spectator degree of freedom to the dissociation dynamics for these low J states, the states that dominate the thermal reactivity. Surface vibrations are predicted to provide approximately 30% of the energy required to surmount the activation barrier to H(2) dissociation under thermal equilibrium conditions. The MURT with s=1 is used to analytically confirm the experimental finding that partial differential "E(a)(T(s))" partial differential E(t)= -1 for eigenstate-resolved dissociative sticking at translational energies E(t)<E(0)-E(v)-E(r). Explicit treatment of the surface motion (i.e., surface not frozen at T(s)=0 K) is a relatively novel aspect of the MURT theoretical approach.