An improved static corrugation model.

Accurately describing surface temperature effects for the dissociation of H2 on Cu(111) remains challenging. While Ab initio Molecular Dynamics (AIMD), the current state-of-the-art method for modelling such systems, can produce accurate results, it is computationally very expensive to use for extensive testing of, for example, density functionals. A chemically accurate static corrugation model for H2 and D2 on Cu(111) dissociation was made by introducing effective three-body interactions as well as an H2-bond dependence and fitting the model to density functional theory energies for 15 113 different configurations. Reaction probabilities and rovibrational (in)elastic scattering probabilities were computed and compared to experiments and other calculations. Theoretical and experimental results are in good agreement, except for the reaction of (v = 0, J = 0) H2 where both AIMD and the newly developed static corrugation model, both based on the same underlying density functional, predict a similar deviation from the experiment.

An ab initio molecular dynamics study of D2 dissociation on CO-precovered Ru(0001).

In dynamics calculations of H2 dissociating on metal surfaces often clean, high-symmetry surfaces are used. Few such dynamics studies have been performed on surfaces with pre-adsorbed molecules, especially when also the motion of the surface and the adsorbate are considered. In this study, the dissociation of H2 on a carbon monoxide-covered Ru(0001) surface is considered. Ab initio molecular dynamics (AIMD) calculations are performed on this system using the PBE-vdW-DF2 functional, which accurately describes the reaction probability for H2 on Ru(0001). Using this functional, the reaction probability of H2 on the CO-covered Ru(0001) surface is found to be too low when compared to experiments. This suggests that exchange-correlation functionals that can describe the reaction of H2 on a bare metal surface are not in general able to describe the reaction of H2 on a CO-precovered surface of the same metal, with the same accuracy. However, it cannot be ruled out that the discrepancy between theory and experiment is partly due to an inhomogeneous coverage of the surface by CO in the experiments. The incorporation of the motion of the surface has only a small effect on the reaction probability. It is found that when including surface motion for this system, the size of the simulation cell can be important. Upon collision, a considerable amount of energy is transferred to the surface, causing the adsorbed CO molecules to move apart, which opens the surface for reaction. In order to obtain converged reaction probabilities with respect to the size of the simulation cell, at least a 3 × 3 simulation cell is needed, because in the smaller cell the CO molecules cannot be pushed apart as only a single independent CO molecule is present, also leading to less energy exchange with the surface.

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

The specific reaction parameter (SRP) approach to density functional theory (DFT) has enabled a chemically accurate description of reactive scattering experiments for activated H2-metal systems (H2 + Cu(111) and Cu(100)), but its application has not yet resulted in a similarly accurate description of non-activated or weakly activated H2-metal systems. In this study, the effect of the choice of the exchange-correlation functional in DFT on the potential energy surface and dynamics of H2 dissociation on Ru(0001), a weakly activated system, is investigated. In total, full potential energy surfaces were calculated for over 20 different functionals. The functionals investigated include functionals incorporating an approximate description of the van der Waals dispersion in the correlation functional (vdW-DF and vdW-DF2 functionals), as well as the revTPSS meta-GGA. With two of the functionals investigated here, which include vdW-DF and vdW-DF2 correlation, it has been possible to accurately reproduce molecular beam experiments on sticking of H2 and D2, as these functionals yield a reaction probability curve with an appropriate energy width. Diffraction probabilities computed with these two functionals are however too high compared to experimental diffraction probabilities, which are extrapolated from surface temperatures (Ts) ⩾ 500 K to 0 K using a Debye-Waller model. Further research is needed to establish whether this constitutes a failure of the two candidate SRP functionals or a failure of the Debye-Waller model, the use of which can perhaps in future be avoided by performing calculations that include the effect of surface atom displacement or motion, and thereby of the experimental Ts.

Reactive scattering of H2 from Cu(100): comparison of dynamics calculations based on the specific reaction parameter approach to density functional theory with experiment.

We present new experimental and theoretical results for reactive scattering of dihydrogen from Cu(100). In the new experiments, the associative desorption of H(2) is studied in a velocity resolved and final rovibrational state selected manner, using time-of-flight techniques in combination with resonance-enhanced multi-photon ionization laser detection. Average desorption energies and rotational quadrupole alignment parameters were obtained in this way for a number of (v = 0, 1) rotational states, v being the vibrational quantum number. Results of quantum dynamics calculations based on a potential energy surface computed with a specific reaction parameter (SRP) density functional, which was derived earlier for dihydrogen interacting with Cu(111), are compared with the results of the new experiments and with the results of previous molecular beam experiments on sticking of H(2) and on rovibrationally elastic and inelastic scattering of H(2) and D(2) from Cu(100). The calculations use the Born-Oppenheimer and static surface approximations. With the functional derived semi-empirically for dihydrogen + Cu(111), a chemically accurate description is obtained of the molecular beam experiments on sticking of H(2) on Cu(100), and a highly accurate description is obtained of rovibrationally elastic and inelastic scattering of D(2) from Cu(100) and of the orientational dependence of the reaction of (v = 1, j = 2 - 4) H(2) on Cu(100). This suggests that a SRP density functional derived for H(2) interacting with a specific low index face of a metal will yield accurate results for H(2) reactively scattering from another low index face of the same metal, and that it may also yield accurate results for H(2) interacting with a defected (e.g., stepped) surface of that same metal, in a system of catalytic interest. However, the description that was obtained of the average desorption energies, of rovibrationally elastic and inelastic scattering of H(2) from Cu(100), and of the orientational dependence of reaction of (v = 0, j = 3 - 5, 8) H(2) on Cu(100) compares less well with the available experiments. More research is needed to establish whether more accurate SRP-density functional theory dynamics results can be obtained for these observables if surface atom motion is added to the dynamical model. The experimentally and theoretically found dependence of the rotational quadrupole alignment parameter on the rotational quantum number provides evidence for rotational enhancement of reaction at low translational energies.

Towards a specific reaction parameter density functional for reactive scattering of H2 from Pd(111).

Recently, an implementation of the specific reaction parameter (SRP) approach to density functional theory (DFT) was used to study several reactive scattering experiments of H2 on Cu(111). It was possible to obtain chemical accuracy (1 kcal/mol ≈ 4.2 kJ/mol), and therefore, accurately model this paradigmatic example of activated H2 dissociation on a metal surface. In this work, the SRP-DFT methodology is applied to the dissociation of hydrogen on a Pd(111) surface, in order to test whether the SRP-DFT approach is also applicable to non-activated H2-metal systems. In the calculations, the Born-Oppenheimer static surface approximations are used. A comparison to molecular beam sticking experiments, performed at incidence energies ≥125 meV, on H2 + Pd(111) suggested the PBE-vdW [where the Perdew, Burke, and Ernzerhof (PBE) correlation is replaced by van der Waals correlation] functional as a candidate SRP density functional describing the reactive scattering of H2 on Pd(111). Unfortunately, quantum dynamics calculations are not able to reproduce the molecular beam sticking results for incidence energies <125 meV. From a comparison to initial state-resolved (degeneracy averaged) sticking probabilities it seems clear that for H2 + Pd(111) dynamic trapping and steering effects are important, and that these effects are not yet well modeled with the potential energy surfaces considered here. Applying the SRP-DFT method to systems where H2 dissociation is non-activated remains difficult. It is suggested that a density functional that yields a broader barrier distribution and has more non-activated pathways than PBE-vdW (i.e., non-activated dissociation at some sites but similarly high barriers at the high energy end of the spectrum) should allow a more accurate description of the available experiments. Finally, it is suggested that new and better characterized molecular beam sticking experiments be done on H2 + Pd(111), to facilitate the development of a more accurate theoretical description of this system.

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

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.