Dynamics on Six-Dimensional Potential Energy Surfaces for H₂/Cu(111): Corrugation Reducing Procedure versus Modified Shepard Interpolation Method and PW91 versus RPBE

Abstract

We have constructed first principle based six-dimensional (6D) potential energy surfaces (PESs) describing the interaction of H 2 with Cu(111) obtained by interpolation of a set of density functional theory (DFT) total energy data. The DFT calculations have been performed within the generalized gradient approximation (GGA) framework. In applying the GGA we have tested the two exchange-correlation (XC) functionals most popular in surface science, i.e., the PW91 and RPBE functionals. The interpolation of the PW91 PES has been performed using two different methods, the corrugation reducing procedure (CRP), which has been proven to be one of the most successful interpolation methods to build 6D PESs, and the modified Shepard (MS) interpolation method, a very promising method to build high dimensional (nD) PESs, which is computationally cheaper than the CRP. We show that, in spite of the difference between the CRP-PES and the MS-PES and the inaccuracies found in the latter, quantum and classical reaction and scattering probabilities obtained for both PESs are very similar. We also show that PW91 predicts higher reactivity than RPBE, due to the presence of lower energy dissociation barriers in the PW91-PES. The differences between the PW91-PES and the RPBE-PES are also reflected in the vibrational excitation and rotational excitation probabilities, and the diffraction patterns.

Vibrational deexcitation and rotational excitation of H2 and D2 scattered from Cu(111): Adiabatic versus non-adiabatic dynamics

“…Note that the top site is not the site with the minimum reaction barrier, in fact, the minimum energy reaction barrier for H 2 /Cu(111) is located at the bridge site. 49 Thus, Figs. 9 and 10 show that vibrationally excited molecules getting closer to surface do not follow the minimum energy reaction path.…”

“…Our analysis allows us to understand, first, the reason why vibrational deexcitation is more efficient for the PW91-PES than for the SRP-PES. Although the energetic and the geometric corrugation are similar for the two PESs, 49 the PW91-PES presents lower barriers. Therefore, for the same incidence conditions, the molecules get closer to the surface on the PW91-PES (see Fig.…”

“…This phenomenon has been already described for dissociative adsorption of vibrationally excited H 2 molecules on Cu(100). 68 The top site reaction path for H 2 /Cu(111), as in the case for H 2 /Cu(100), 43 presents a large curvature in front of the barrier, 49 which promotes vibrationally inelastic scattering. 41,42 Thus, the higher the number of molecules closely approaching the surface and scattered close to the top site, the more vibrational inelastic scattering is expected.…”

“…The 6D potential energy surface (PES) (Ref. 49) was obtained by applying the corrugation reducing procedure (CRP) method 50 to a set of density functional theory/generalized gradient approximation (DFT/GGA) data points, sampled throughout the configuration space. In performing the DFT/GGA calculations, we have used the exchange-correlation functional PW91, 51 which yields a semi-quantitative description of the H 2 /Cu(111) system.…”

Modified Shepard interpolation of gas-surface potential energy surfaces with strict plane group symmetry and translational periodicity

“…Building on the success of modified Shepard interpolation for building the PESs for gas phase reactions in an algorithm often called Grow, [45][46][47][48][49][50][51] modified Shepard interpolation has been used to represent the PES in gas-surface reactions. 44,[52][53][54][55] This approach has several advantages, including being able to treat polyatomic adsorbates, simple and seamless treatment of reactive or nonreactive collisions, physisorption, chemisorption and surface catalysed reactions, and strict interpolation of known energies. While the formalism that has been used to date has been successful, 16,44,[52][53][54][55][56][57] it has a number of weaknesses.…”