Quantum Dynamics of Dissociative Chemisorption of H₂ on the Stepped Cu(211) Surface

Abstract

Reactions on stepped surfaces are relevant to heterogeneous catalysis, in which a reaction often takes place at the edges of nanoparticles where the edges resemble steps on single-crystal stepped surfaces. Previous results on H2 + Cu(211) showed that, in this system, steps do not enhance the reactivity and raised the question of whether this effect could be, in any way, related to the neglect of quantum dynamical effects in the theory. To investigate this, we present full quantum dynamical molecular beam simulations of sticking of H2 on Cu(211), in which all important rovibrational states populated in a molecular beam experiment are taken into account. We find that the reaction of H2 with Cu(211) is very well described with quasi-classical dynamics when simulating molecular beam sticking experiments, in which averaging takes place over a large number of rovibrational states and over translational energy distributions. Our results show that the stepped Cu(211) surface is distinct from its component Cu(111) terraces and Cu(100) steps and cannot be described as a combination of its component parts with respect to the reaction dynamics when considering the orientational dependence. Specifically, we present evidence that, at translational energies close to the reaction threshold, vibrationally excited molecules show a negative rotational quadrupole alignment parameter on Cu(211), which is not found on Cu(111) and Cu(100). The effect arises because these molecules react with a site-specific reaction mechanism at the step, that is, inelastic rotational enhancement, which is only effective for molecules with a small absolute value of the magnetic rotation quantum number. From a comparison to recent associative desorption experiments as well as Born–Oppenheimer molecular dynamics calculations, it follows that the effects of surface atom motion and electron–hole pair excitation on the reactivity fall within chemical accuracy, that is, modeling these effect shifts extracted reaction probability curves by less than 1 kcal/mol translational energy. We found no evidence in our fully state-resolved calculations for the “slow” reaction channel that was recently reported for associative desorption of H2 from Cu(111) and Cu(211), but our results for the fast channel are in good agreement with the experiments on H2 + Cu(211).

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)

“…Figures 6a,b show that for narrow low average translational energy molecular beams 51 the QD method predicts slightly larger sticking probabilities compared to QCT sticking probabilities calculated from the same set of rovibrational states. This small gap between QD and QCT sticking probabilities based on the same set of rovibrational states is slightly bigger then what was obtained for H 2 + Cu(211) when using the SRP48 DF 36 . Though this suggests that quantum effects might play a small role in the dynamics, it is also possible that the slightly higher sticking probability predicted by QD is due to the underlying reaction probability curves for specific included rovibrational states showing more structure than for H 2 + Cu(211) 36 .…”

“…This small gap between QD and QCT sticking probabilities based on the same set of rovibrational states is slightly bigger then what was obtained for H 2 + Cu(211) when using the SRP48 DF 36 . Though this suggests that quantum effects might play a small role in the dynamics, it is also possible that the slightly higher sticking probability predicted by QD is due to the underlying reaction probability curves for specific included rovibrational states showing more structure than for H 2 + Cu(211) 36 . Since the molecular beam sticking probabilities are very small in figures 6a,b, they could be very sensitive to increased structure (and noise) in the underlying reaction probability curves.…”

“…Due to the computational expense of calculating molecular beam sticking probabilities using the QD method we only carried out QD molecular beam simulations for H 2 + Cu(111) for the B86SRP68-DF2 DF (figures 4e,f and 5). We have used the same methodology to carry out QD molecular beam simulations as in our previous work on Cu(211) 36 . Overall, for the four experiments considered with both methods, the MAD value obtained with the the B86SRP68-DF2 DF increases from a QCT value of 1.3 kJ/mol to 1.6 kJ/mol for QD.…”

“…We have also carried out a full quantum mechanical molecular beam simulation by carrying out a large number of fully initial-state resolved quantum dynamical (QD) 66,67 calculations for the H 2 + Cu (111) system. This is important because the inclusion of a Van der Waals well in the PES might lead to discrepancies between quasi-classical trajec-tory (QCT) 68 and QD results compared to the good agreement that was obtained for these two methods for the H + Cu(211) system 36 using the SRP48 DF 10,62 , which does not employ nonlocal correlation.…”

Chiral Surface Characterisation and Reactivity Toward H–D Exchange of a Curved Platinum Crystal

“…The lower symmetry of these unit cells make them more challenging to study with accurate theoretical methods. Nonetheless, the dynamics of molecule-surface collisions with vicinal surfaces have been subject of several theoretical and experimental studies, some even including rovibrational state-selection of the incident molecule [17][18][19][20][21][22][23].…”