Assessment of Two Problems of Specific Reaction Parameter Density Functional Theory: Sticking and Diffraction of H₂ on Pt(111)

Abstract

It is important that theory is able to accurately describe dissociative chemisorption reactions on metal surfaces, as such reactions are often rate-controlling in heterogeneously catalyzed processes. Chemically accurate theoretical descriptions have recently been obtained on the basis of the specific reaction parameter (SRP) approach to density functional (DF) theory (DFT), allowing reaction barriers to be obtained with chemical accuracy. However, being semiempirical, this approach suffers from two basic problems. The first is that sticking probabilities (to which SRP density functionals (DFs) are usually fitted) might show differences across experiments, of which the origins are not always clear. The second is that it has proven hard to use experiments on diffractive scattering of H2 from metals for validation purposes, as dynamics calculations using a SRP-DF may yield a rather poor description of the measured data, especially if the potential used contains a van der Waals well. We address the first problem by performing dynamics calculations on three sets of molecular beam experiments on D2 + Pt(111), using four sets of molecular beam parameters to obtain sticking probabilities, and the SRP-DF recently fitted to one set of experiments on D2 + Pt(111). It is possible to reproduce all three sets of experiments with chemical accuracy with the aid of two sets of molecular beam parameters. The theoretical simulations with the four different sets of beam parameters allow one to determine for which range of incidence conditions the experiments should agree well and for which conditions they should show specific differences. This allows one to arrive at conclusions about the quality of the experiments and about problems that might affect the experiments. Our calculations on diffraction of H2 scattering from Pt(111) show both quantitative and qualitative differences with previously measured diffraction probabilities, which were Debye–Waller (DW)-extrapolated to 0 K. We suggest that DW extrapolation, which is appropriate for direct scattering, might fail if the scattering is affected by the presence of a van der Waals well and that theory should attempt to model surface atom motion for reproducing diffraction experiments performed for surface temperatures of 500 K and higher.

Designing new SRP density functionals including non-local vdW-DF2 correlation for H2 + Cu(111) and their transferability to H2 + Ag(111), Au(111) and Pt(111)

“…The molecular beam experiments of Cao et al 60 are not as well described by the B86SRP68-DF2 DF, as can be seen in figure S7. However we note that the increase of the MAD value in going from figure 8a to figure S7a is similar in size to what was reported for the PBEα57-DF2 DF 65 (see table S9). Earlier work from our group has shown that the experimental results of Luntz et al 64 and Cao et al 63 are in good agreement with each other for the lower incidence energies but somewhat diverge for the higher incidence energies 65 .…”

“…The reason for taking this approach, instead of fitting the DF to best reproduce experiments on all systems shown in the results section, is that numerous experimental results are available for the reaction of H 2 and D 2 on Cu(111) [45][46][47][48][49][50][51][52][53][54][55] . For the non-copper systems discussed in this work experimental results are sparse 17,70 , and there is discussion about the validity of the available parameters describing the molecular beams used in the experiments on H 2 (D 2 ) + Ag (111) and Pt(111) 19,60,64,65 .…”

“…The possible origins of the discrepancy between these two sets of experimental data are discussed in ref. 65 . Here it was surmised that at high average incidence energies the reaction probabilities of Cao et al 63 are most likely somewhat underestimated compared to the results of Luntz et al 64 because the average incidence energies are somewhat underestimated in the experiment of Cao et al 60 .…”

“…For both the activated and non-activated reactions of H 2 on transitions metals there is now only a single well studied system, namely H 2 + Cu(111) (and maybe H 2 + Pt(111) 65 ). What we mean by well studied is that there should be different kinds of well described experiments.…”

“…Apart from the H 2 + Cu(111) system we will consider such experiments for the the H 2 + Pt(111) system 63,64 and the H 2 + Ag(111) system 54 . For the latter two systems there exists some uncertainty about the validity of the molecular beam parameters describing the experiments 19,65 . We however feel that, although there are some uncertainties in the parameters describing the experiments, nevertheless valuable insights on transferability can be derived by analysing the predicted reactivity of the SRP-DFs considered here.…”