## Abstract

The correct prediction of elementary processes occurring when
H_{2} scatters from a metal surface is one of the main
challenges of surface science. In the field, the scattering of
H_{2} from Cu(111) has been considered a prototype system
for activated dissociative chemisorption. Experimental and
theoretical work suggested that a proper description of some
scattering experiments on this system might require going
beyond the static surface approximation, to consider how the
motion of the Cu atoms affects the scattering event. Previous
work suggested that important effects of phonons on the
dynamics can be incorporated in the Potential Energy Surface
(PES) by including four degrees of freedom, that have
approximately additive couplings with the hydrogen molecule:
the 3 dimensional motion of the nearest 1^{st} layer
copper atom and the displacement of the nearest
2^{nd} layer copper atom along the direction
perpendicular to the surface [3]. In the
present work, we extend the 6D dynamical model by including
the perpendicular motion of the 2^{nd} layer surface
atom and we study this novel dynamical model with two
techniques: an approximate method based on the Phonon Sudden
Approximation (PSA) and an exact description using 7D
wavepacket quantum dynamics. We consider how the inclusion and
the excitation of the lattice degree of freedom affect some
relevant processes: dissociative chemisorption, vibrational
excitation of H_{2} and state-to-state scattering
probabilities fully resolved with respect to the vibrational
states of the surface. We show that the PSA works in an
excellent way for the system, thereby suggesting that this
might be a viable way to study higher dimensional quantum
models, incorporating four surface degrees of freedom that
appear to be most relevant for H_{2} scattering.

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