Static surface temperature effects on the dissociation of H2 and D2 on Cu(111)

Abstract

A model for taking into account surface temperature effects in molecule-surface reactions is reported and applied to the dissociation of H(2) and D(2) on Cu(111). In contrast to many models developed before, the model constructed here takes into account the effects of static corrugation of the potential energy surface rather than energy exchange between the impinging hydrogen molecule and the surface. Such an approximation is a vibrational sudden approximation. The quality of the model is assessed by comparison to a recent density functional theory study. It is shown that the model gives a reasonable agreement with recently performed ab initio molecular dynamics calculations, in which the surface atoms were allowed to move. The observed broadening of the reaction probability curve with increasing surface temperature is attributed to the displacement of surface atoms, whereas the effect of thermal expansion is found to be primarily a shift of the curve to lower energies. It is also found that the rotational quadrupole alignment parameter is generally lowered at low energies, whereas it remains approximately constant at high energies. Finally, it is shown that the approximation of an ideal static surface works well for low surface temperatures, in particular for the molecular beams for this system (T(s) = 120 K). Nonetheless, for the state-resolved reaction probability at this surface temperature, some broadening is found.

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

“…No large non-adiabatic effects were found in these dynamics calculations, suggesting that the BornOppenheimer approximation works well for these systems. The validity of the static surface approximation has been tested recently for H 2 dissociation on Cu(111) using ab initio molecular dynamics (AIMD) calculations, 39 in which surface atoms in 3 layers of a 2 × 2 unit cell were allowed to move, and static corrugation model (SCM) calculations, 40 which excluded energy exchange with the surface but included the displacement of surface atoms and surface expansion effects. In these studies, good agreement was found between static surface calculations and calculations at the experimental surface temperature (T s = 120 K).…”

“…The surface temperature used in the experiments, T s = 180 K, 31 is rather low. In ab initio molecular dynamics calculations 39 and static corrugation model calculations, 40 almost no effects were found for H 2 dissociating on Cu(111) at a surface temperature T s = 120 K. While the surface temperature for the molecular beam experiments on H 2 dissociation on Ru(0001) was slightly higher, the experimentalists did not find surface temperature effects down to T s = 140 K. 31 Furthermore, the lowest barriers in the H 2 on Ru(0001) system are further away from the surface than was the case for H 2 on Cu(111), suggesting a weaker coupling between H 2 and surface degrees of freedom. Finally, energy exchange is not expected to be important for this system due to the large mass mismatch between a H 2 molecule and a ruthenium atom.…”

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

“…We immediately note that the effect of surface temperature predicted by our model seems to be extremely small, clearly less than suggested by experiments [37,40] and by predictions of other theoretical models [41,62]. There are at least three problems that should be considered, that can explain the inadequacy of our model in reproducing the experimental results.…”

“…From the analysis of the energetic coupling, we pointed out in previous work that at least the motion of a first layer atom should be considered, both in the parallel and perpendicular direction. Furthermore, we cannot fully exclude the importance of non-additive couplings between the lattice degrees of freedom, even if they seem to be on a smaller energy scale [3] and even if the work by Wijzenbroek et al showed that a qualitatively consistent model for surface temperature can be built by simply considering uncoupled lattice atoms [62].…”

“…By means of Ab Initio Molecular Dynamics (AIMD), Nattino et al proved that the inclusion of surface temperature effects allows a better prediction of the rotational quadrupole alignment parameter [41]. Furthermore, Wijzenbroek and Somers pointed out the importance of the temperature of the lattice even at a level at which energy transfer to surface phonons is not allowed, via a simplified molecular dynamics study on the system [62]. Finally, Sahoo et al addressed the problem with an effective hamiltonian derived from a meanfield approximation to the phonon modes and showed the importance of the surface modes directed along the Z-axis [55,56].…”