Theoretical Studies Of Adsorption And Vibrational Properties Of Hydrogen On Rh(111)

Since hydrogen is presumably a key intermediate in many important catalytic reactions and rhodium is one of the most important materials for heterogeneous catalyst for hydrogenation reactions, a detailed knowledge on the adsorption and vibrational properties for the hydrogen atom on the rhodium surface is of great interest for exploring the hydrogenation reaction mechanisms and understanding the nature of the adsorption states and the dynamics of surface processes. Recently, periodic density functional theory (DFT) calculations using a slab model have become a powerful approach for studying the adsorption of atoms and small polyatomic molecules on the metal surface. In this study, we used the plane wave based DFT method to study the adsorption of hydrogen on the Rh(111) surface for three surface cells (2×2), ( 3×3) and (1×1). Geometrical structures were optimized to determine the chemisorption energies. The fcc hollow site was found to be most stable. The difference of the adsorption energies between two 3-fold hollow sites was found to decrease when hydrogen coverage is increased. On the other hand, the adsorption energy is related to the number of hydrogen coordination. Surface relaxation did not significantly affect the adsorption. Only small changes in the surfaces interlayer spacing were observed and the adsorption energies were only slightly affected. The activation energy for diffusion has also been calculated. To fully explore the possible diffusion pathways we have investigated three different pathways: fcc to hcp (via the bridge site), hcp to fcc(via the top site), and fcc to an equivalent neighbor one. Our results showed that diffusion on the Rh(111) surface will be through the bridge site. For coverage of 0.25 ML/0.33 ML/1 ML, the barrier height was found to be 0.13 eV/0.12 eV/0.14 eV. In order to give a detailed understanding of the nature of the chemisorbed hydrogen and the vibrational states of H/Rh(111), we have carried out density functional theory calculations to generate the full three-dimensional potential energy surface of H/Rh(111) surface for a coverage of 1 ML. The global potential is then obtained by using the three-dimensional spline interpolation. In order to calculate the energy levels and wave functions for the vibrational states of hydrogen on the metal surface, we proposed a theoretical procedure based on the discrete variable representation and Lanczos algorithm. Since the potential is periodic in two dimensions parallel to the surface, Bloch theorem was applied for the wave function in the plane of the surface. The energy eigenstates are characterized by a band index and a two-dimensional wave vector. The width of the energy bands can be obtained by evaluating the difference in the eigenstate energy at the center (Γpoint) and the boundary (M point) of the Brillouin zone. It was found that the wave function for the ground vibrational state is localized at the preferred hollow site. Higher excited states are of delocalized nature and mixed parallel and perpendicular character. Therefore, the local model could be used to explain the behavior of the ground vibrational state for the adsorbed hydrogen on the Rh(111) surface at high coverage. The calculated fundamental frequencies (63and 145 meV) for the parallel and perpendicular vibrations are in good agreement with the experimentally observed value of 56 and 136 meV.