Apparent failure of the Born–Oppenheimer static surface model for vibrational excitation of molecular hydrogen on copper

Abstract

The accuracy of dynamical models for reactive scattering of molecular hydrogen, H 2 , from metal surfaces is relevant to the validation of first principles electronic structure methods for molecules interacting with metal surfaces. The ability to validate such methods is important to progress in modeling heterogeneous catalysis. Here, we study vibrational excitation of H 2 on Cu(111) using the Born-Oppenheimer static surface model. The potential energy surface (PES) used was validated previously by calculations that reproduced experimental data on reaction and rotationally inelastic scattering in this system with chemical accuracy to within errors ≤ 1 kcal∕mol ≈ 4.2 kJ∕mol [Díaz C, et al. (2009) Science 326:832-834]. Using the same PES and model, our dynamics calculations underestimate the contribution of vibrational excitation to previously measured time-of-flight spectra of H 2 scattered from Cu(111) by a factor 3. Given the accuracy of the PES for the experiments for which the Born-Oppenheimer static surface model is expected to hold, we argue that modeling the effect of the surface degrees of freedom will be necessary to describe vibrational excitation with similar high accuracy.Born-Oppenheimer approximation | dissociative chemisorption | molecule-surface scattering R eactions of molecules with metal surfaces are of tremendous importance, as the production of most man-made chemicals involves heterogeneous catalysis by a metal surface. One of the achievements recognized by the 2007 Nobel Prize in Chemistry, awarded to G. Ertl, was the detailed description of the sequence of elementary molecule-surface reactions by which ammonia is produced (1). In such reaction sequences, the dissociative chemisorption of molecules often plays a prominent role.In the present state of the art, theoretical calculations can reproduce overall rates of heterogeneously catalyzed reactions like ammonia production to within an order of magnitude (2). Achieving greater precision has been hampered by the lack of accuracy inherent in the density functional theory (DFT) used to calculate the interactions of molecules with metal surfaces.Because dissociative chemisorption involves stretching bonds until they rupture, reactivity of molecules on surfaces is closely related to transfer of energy to and from the vibrational degrees of freedom (3). Thus vibrationally inelastic scattering can be a sensitive probe of the barrier region of the potential energy surface (PES), and experiments (4, 5) and theory (6, 7) suggest that this process is governed by the same region of the PES as dissociative chemisorption: The picture of vibrational excitation occurring in competition with dissociative chemisorption is that it results from a stretching of the molecule as it approaches the transition state (4, 5). In principle, experiments on this competition may reveal much interesting information. For instance, comparison of data on vibrationally inelastic scattering and reaction on a surface has been suggested to provide information on whether these pro...

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

“…On the other hand, Sitz and co. 46 have found that a significant amount of energy in H 2 is lost to the surface upon scattering from Cu(100). Recently, 47 it has been hypothesized, based on an exhaustive analysis of experimental data, that phonons may play a significant role in promoting vibrational excitation.…”

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

“…In the case of scattering of (v = 0, J = 0) H 2 , our results predict that the vibrationally excited molecules have transfered less than 3 meV to the surface, in the range of E inc considered (0.6-1.2 eV). This amount of energy is far below what can be reasonably expected for this kind of experiment, which is around 30% of the incidence energy [34]. This analysis indicates that other surface degrees of freedom with a more efficient energy transfer should be considered to achieve a better description of the vibrationally inelastic scattering experiments [51] than obtained so far [34].…”

“…In [34] it is suggested that this discrepancy could be reduced by taking into account the thermal motion of the surface. In fact, the intensity of the TOF signal reflects not only the probability of scattering to the (v = 1, J = 3) state, but also the energy loss to the surface (including loss to surface phonons), since molecules which have lost part of their incidence energy travel more slowly in the detection zone and thereby increase the detection signal [34,51]. Díaz et al showed that the most important contribution to the (v = 1, J = 3) TOF signal comes from the (v = 0, J = 5) initial state [16].…”

“…At the beginning, theoretical studies were performed with a limited number of H 2 degrees of freedom with the aim of clarifying the mechanisms underlying reactive scattering [10][11][12][13][14][15]22,58]. Next, quantum dynamics calculations based on DFT potential energy surfaces including all degrees of freedom of H 2 [7,28,47] became feasible and were used for a qualitative and quantitative comparison with experiments [7,9,[16][17][18]34,44,59]. More recently, chemical accuracy was achieved by Díaz et al [16,18] by means of the Specific Reaction Parameter (SRP) approach to Density Functional Theory (DFT) [6].…”

“…Firstly, the associative desorption experiments that were used to measure the rotational quadrupole alignment parameter [32] were performed at high surface temperature (T S = 925 K). Secondly, the comparison between calculations and experiments on vibrational excitation of H 2 scattering from Cu(111) [51] suggests that an accurate description of this process requires the inclusion of surface motion [34].…”