The effect of corrugation on the quantum dynamics of dissociative and diffractive scattering of H2 from Pt(111)

Abstract

We present results of two dimensional ͑2D͒ and three dimensional ͑3D͒ calculations for dissociative and diffractive scattering of H 2 from Pt͑111͒, using a potential energy surface obtained from density functional theory ͑DFT͒ employing the generalized gradient approximation ͑GGA͒ in conjunction with a slab representation of the metal surface. The present study is motivated by the importance of Pt as a hydrogenation catalyst, and by a paradox regarding the amount of corrugation of the H 2 ϩPt͑111͒ potential energy surface ͑PES͒. Molecular beam experiments on dissociation of D 2 from a Pt͑111͒ surface suggest a rather corrugated PES, which is at odds with results from molecular beam experiments on rotationally inelastic diffraction of HD from Pt͑111͒, where only very little diffraction is found, suggesting a weakly corrugated PES. Results of our 3D calculations for off-normal incidence show that the present 3D model does not obey normal energy scaling, and that parallel motion inhibits dissociation at low collision energies, in agreement with the dissociation experiment. On the other hand, substantial diffraction is found, where the diffraction experiment found almost none. For each impact site considered in the 2D calculations, the computed dynamical barrier height, E 0 , is substantially lower than the barrier height in the PES, E b , at that site. Both the 2D and the 3D calculations show a large vibrational enhancement of reaction. These effects are not due to a reduced mass effect, the barrier to dissociation being early, but to a decrease in the force constant of the H 2 vibration upon approaching the barrier to dissociative adsorption from the gas phase. The vibrational enhancement computed for H 2 ϩPt͑111͒ was not observed in seeded beam experiments on D 2 ϩPt͑111͒ ͓A. C. Luntz, J. K. Brown, and M. D. Williams, J. Chem. Phys. 93, 5240 ͑1990͔͒. However, an analysis performed here strongly suggests that seeded beam experiments will be unable to observe vibrational enhancement if the dissociation of the molecule in ϭ0 proceeds without an energetic threshold, as is the case for H 2 ϩPt͑111͒.

Diffractive and reactive scattering of (v=0, j=0) HD from Pt(111): Six-dimensional quantum dynamics compared with experiment

“…2 Out-of-plane diffractive scattering may well account for much of the ''lost flux'' observed in their experiments. 2 Like previous studies, [31][32][33] the present calculations indicate that experiments only looking at in-plane diffraction are not well suited for probing the corrugation of the molecule-surface PES.…”

“…This controversy has been addressed in several theoretical studies [31][32][33] on H 2 scattering from Pt͑111͒. In a study treating all six molecular degrees of freedom quantum mechanically 33 and employing a PES based on density functional theory ͑DFT͒, 34,35 it was found that reaction does not obey normal energy scaling, and that the diffraction is substantial, supporting the conclusion of Luntz et al 12 It was suggested that the experiments by Cowin et al 1,2 failed to find proof of the corrugation of the surface because they measured only in-plane diffraction and did not consider diffraction out of the plane of incidence ͑the out-of-plane diffraction was predicted to be substantial by the theory͒.…”

Constructing accurate potential energy surfaces for a diatomic molecule interacting with a solid surface: H2+Pt(111) and H2+Cu(100)

“…For H 2 ϩPt(111), vibrational energy release is due to a decrease of the force constant associated with the H 2 vibration as the molecule approaches the barrier. 1 The same mechanism is responsible for the vibrational enhancement of reaction in the early barrier system H 2 ϩPd(100). 15 The same mechanism is also responsible for the efficient reaction of vϭ0 H 2 at low energies.…”

“…This controversy was also addressed in a previous paper 1 on H 2 ϩPt(111) where results of two-dimensional ͑2D͒ and three-dimensional ͑3D͒ calculations were presented. In the 3D calculations a model was employed in which the molecular degrees of freedom were the center-of-mass distance to the surface Z, the internuclear distance r, and one translational degree of freedom parallel to the surface x.…”

“…However, as stated before, we expect that diffraction will be less efficient due to the smaller surface lattice constant in the 4D model. 1 In the 3D model the surface lattice constant L was equal to the separation of the two top sites that are furthest apart in the diamond shaped surface unit cell ͑9.08 bohr͒. In the 4D model the correct surface lattice constant is used, given by the smallest distance between two top sites in the ͑111͒ face of Pt ͑5.24 bohr͒.…”