7D Quantum Dynamics of H₂Scattering from Cu(111): The Accuracy of the Phonon Sudden Approximation

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.

Performance of Made Simple Meta-GGA Functionals with rVV10 Nonlocal Correlation for H2 + Cu(111), D2 + Ag(111), H2 + Au(111), and D2 + Pt(111)

“…Furthermore, incorporating surface motion in the dynamics calculations would lead to a broadening of the reaction probability curves. 21 , 50 , 51 , 54 In view of the procedure used to calculate E 1/2 (ν, J ) parameters, an increase of reactivity at low translational energies has the potential to lower the E 1/2 (ν, J ) parameters. 14 We also note that our calculations have been carried out employing an unreconstructed Au(111) surface.…”

“… 49 − 53 Calculations that incorporate surface motion show that the impact of surface atom motion (phonons) can be neglected due to the effect on the reaction probability being small for the low-surface-temperature experiments considered here. 19 , 21 , 51 , 54 It is also justified to neglect the effect of electron–hole pair excitation on the reaction probability, as its effect on sticking has previously been shown to be small in calculations on H 2 + Cu(111), 55 − 57 Ag(111), 58 − 60 and Ru(0001). 61 Previous research has also shown that for highly activated dissociation of H 2 on cold metals, the difference between quantum dynamics (QD) and QCT calculations is marginal, 14 , 62 , 63 and there is also some evidence that the same observation holds for the nonactivated reaction of D 2 + Pt(111) for all but the lowest translational energies.…”

The effect of the exchange-correlation functional on H2 dissociation on Ru(0001)

“…Recently quantum dynamics calculations have been performed for H 2 dissociation on Cu(111) where 1 surface degree has been taken into account either completely (7D) or using a phonon sudden approximation (6+1D). 97 Such calculations, or calculations taking into account even more degrees of freedom, could help clarify to what extent such a DW model holds.…”

Possible effect of static surface disorder on diffractive scattering of H2 from Ru(0001): Comparison between theory and experiment

“…Presumably, this could be done with quantum dynamics calculations in which at least the motion of first layer (and possibly second layer) surface atoms perpendicular to the surface is modeled, in seven-dimensional (7D) (or eight-dimensional) quantum dynamics calculations also accurately describing the motion in all six molecular degrees of freedom, as has been done in 7D H 2 + Cu(111) calculations. 51 Alternatively, one might try to model the attenuating effect of phonons in 6D quantum dynamics calculations using a static surface approximation through the presence of a suitably chosen optical potential. 52 In yet another approach, in calculations on diffractive scattering one would "remove" the van der Waals well from the PES in a clever way and perform static surface calculations comparing with DW extrapolated measured probabilities, which is to some extent analogous to using a GGA PES.…”