Mechanisms of H2 dissociative adsorption on the Pt(211) stepped surface

Alignment and impact angular dependence to O2 sticking and dissociation on Pt(111) and close-packed steps

Oxygen's interaction with Pt surfaces serves as a model system in the development of an accurate theoretical description of reaction mechanisms that involve multiple precursor states. To benchmark the influence of surface structure on the dynamics of this interaction, we report absolute values of the initial sticking probability of O₂ onto Pt(111) and two vicinal surfaces for state-selected and rotationally-aligned O₂ molecules. Sticking probabilities vary significantly for helicoptering and cartwheeling molecules. Our data can be understood if normal energy scaling holds for all molecular orientations relative to the surface. Vicinal surfaces are much more reactive than Pt(111) with little to no dependence on the molecule's alignment and a more complex angular dependence. At low incident energies, sticking probabilities are highest for incidence into step facets. The weak alignment dependence points toward predominant scattering into a physisorbed state preceding chemisorbed states over a wide angular range.

Quantum effects in thermal reaction rates at metal surfaces

There is wide interest in developing accurate theories for predicting rates of chemical reactions that occur at metal surfaces, especially for applications in industrial catalysis. Conventional methods contain many approximations that lack experimental validation. In practice, there are few reactions where sufficiently accurate experimental data exist to even allow meaningful comparisons to theory. Here, we present experimentally derived thermal rate constants for hydrogen atom recombination on platinum single-crystal surfaces, which are accurate enough to test established theoretical approximations. A quantum rate model is also presented, making possible a direct evaluation of the accuracy of commonly used approximations to adsorbate entropy. We find that neglecting the wave nature of adsorbed hydrogen atoms and their electronic spin degeneracy leads to a 10× to 1000× overestimation of the rate constant for temperatures relevant to heterogeneous catalysis. These quantum effects are also found to be important for nanoparticle catalysts.

Accurate Simulations of the Reaction of H2 on a Curved Pt Crystal through Machine Learning

Theoretical studies on molecule-metal surface reactions have so far been limited to small surface unit cells due to computational costs. Here, for the first time molecular dynamics simulations on very large surface unit cells at the level of density functional theory are performed, allowing a direct comparison to experiments performed on a curved crystal. Specifically, the reaction of D2 on a curved Pt crystal is investigated with a neural network potential (NNP). The developed NNP is also accurate for surface unit cells considerably larger than those that have been included in the training data, allowing dynamical simulations on very large surface unit cells that otherwise would have been intractable. Important and complex aspects of the reaction mechanism are discovered such as diffusion and a shadow effect of the step. Furthermore, conclusions from simulations on smaller surface unit cells cannot always be transfered to larger surface unit cells, limiting the applicability of theoretical studies of smaller surface unit cells to heterogeneous catalysts with small defect densities.

Towards bridging the structure gap in heterogeneous catalysis: the impact of defects in dissociative chemisorption of methane on Ir surfaces

The negatively activated region in CH₄ dissociation is attributed to a precursor-mediated mechanism involving surface defects.

Scaling Platinum-Catalyzed Hydrogen Dissociation on Corrugated Surfaces

We determine absolute reactivities for dissociation at low coordinated Pt sites. Two curved Pt(111) single-crystal surfaces allow us to probe either straight or highly kinked step edges with molecules impinging at a low impact energy. A model extracts the average reactivity of inner and outer kink atoms, which is compared to the reactivity of straight A- and B-type steps. Local surface coordination numbers do not adequately capture reactivity trends for H2 dissociation. We utilize the increase of reactivity with step density to determine the area over which a step causes increased dissociation. This step-type specific reactive area extends beyond the step edge onto the (111) terrace. It defines the reaction cross-section for H2 dissociation at the step, bypassing assumptions about contributions of individual types of surface atoms. Our results stress the non-local nature of H2 interaction with a surface and provide insight into reactivity differences for nearly identical step sites.

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

Understanding heterogeneous catalysis at the atomic level requires detailed knowledge of the reactivity of different surface sites toward specific bond breaking and bond making events. We illustrate a new method in such investigations. We use a macroscopically curved Pt single crystal containing a large variation in density of highly kinked steps of two different chiralities. Scanning tunneling microscopy maps the entire range of surface structures present on the 31° section surrounding the Pt(111) apex. Whereas most of the surface shows the expected characteristic arrays of parallel steps, hexagonally-shaped, single-atom deep pits remain after cleaning procedures near the apex. Their orientation is indicative of the different chiralities present on the two sides of the crystal’s apex. These unintended defects locally raise the surface defect concentration, but are of little consequence to subsequent reactivity measurements for $$\text {D}_2$$ D 2 dissociation and H–D exchange as probed by supersonic molecular beam techniques. We quantify absolute elementary dissociation and relative isotopic exchange rates across the surface with high spatial resolution. At low incident energies, elementary dissociation of the homonuclear isotoplogues is dominated by the kinked steps. H–D exchange kinetics depend also mostly linearly on step density. The changing ratio of D2 dissociation to H–D formation, however, suggests that anisotropic diffusion of H(D) atoms is of influence to the measured HD production rate.

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

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).

Transferability of the Specific Reaction Parameter Density Functional for H2 + Pt(111) to H2 + Pt(211)

The accurate description of heterogeneously catalyzed reactions may require chemically accurate evaluation of barriers for reactions of molecules at the edges of metal nanoparticles. It was recently shown that a semiempirical density functional describing the interaction of a molecule dissociating on a flat metal surface (CHD₃ + Pt(111)) is transferable to the same molecule reacting on a stepped surface of the same metal (Pt(211)). However, validation of the method for additional systems is desirable. To address the question whether the specific reaction parameter (SRP) functional that describes H₂ + Pt(111) with chemical accuracy is also capable of accurately describing H₂ + Pt(211), we have performed molecular beam simulations with the quasi-classical trajectory (QCT) method, using the SRP functional developed for H₂ + Pt(111). Our calculations used the Born-Oppenheimer static surface model. The accuracy of the QCT method was assessed by comparison with quantum dynamics results for reaction of the ro-vibrational ground state of H₂. The theoretical results for sticking of H₂ and D₂ on Pt(211) are in quite good agreement with the experiment, but uncertainties remain because of a lack of accuracy of the QCT simulations at low incidence energies and possible inaccuracies in the reported experimental incidence energies at high energies. We also investigated the nonadiabatic effect of electron-hole pair excitation on the reactivity using the molecular dynamics with the electron friction (MDEF) method, employing the local density friction approximation (LDFA). Only small effects of electron-hole pair excitation on sticking are found.

Site-specific reactivity of molecules with surface defects—the case of H2 dissociation on Pt

The classic system that describes weakly activated dissociation in heterogeneous catalysis has been explained by two dynamical models that are fundamentally at odds. Whereas one model for hydrogen dissociation on platinum(111) invokes a preequilibrium and diffusion toward defects, the other is based on direct and local reaction. We resolve this dispute by quantifying site-specific reactivity using a curved platinum single-crystal surface. Reactivity is step-type dependent and varies linearly with step density. Only the model that relies on localized dissociation is consistent with our results. Our approach provides absolute, site-specific reaction cross sections.

Anomalous Dependence of the Reactivity on the Presence of Steps: Dissociation of D2 on Cu(211)

Stepped metal surfaces are usually assumed to exhibit an increased catalytic activity for bond cleavage of small molecules over their flat single-crystal counterparts. We present experimental and theoretical data on the dissociative adsorption of molecular hydrogen on copper that contradicts this notion. We observe hydrogen molecules to be more reactive on the flat Cu(111) than on the stepped Cu(211) surface. We suggest that this exceptional behavior is due to a geometric effect, that is, that bond cleavage on the flat surface does not occur preferentially over a top site.

Dissociation mechanism of H2 molecule on the Li2O/hydrogenated-Li2O (111) surface from first principles calculations

Hydrogen molecules in a purge gas are known to enhance the release of tritium from lithium ceramic materials, which has been demonstrated in numerous in-pile experiments.

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

State-of-the-art theoretical models allow nowadays an accurate description of H₂/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.

Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.

Dynamical pruning of static localized basis sets in time-dependent quantum dynamics

We investigate the viability of dynamical pruning of localized basis sets in time-dependent quantum wave packet methods. Basis functions that have a very small population at any given time are removed from the active set. The basis functions themselves are time independent, but the set of active functions changes in time. Two different types of localized basis functions are tested: discrete variable representation (DVR) functions, which are localized in position space, and phase-space localized (PSL) functions, which are localized in both position and momentum. The number of functions active at each point in time can be as much as an order of magnitude less for dynamical pruning than for static pruning, in reactive scattering calculations of H2 on the Pt(211) stepped surface. Scaling of the dynamically pruned PSL (DP-PSL) bases with dimension is considerably more favorable than for either the primitive (direct product) or DVR bases, and the DP-PSL basis set is predicted to be three orders of magnitude smaller than the primitive basis set in the current state-of-the-art six-dimensional reactive scattering calculations.

Dynamics of the Dissociation of Hydrogen on Stepped Platinum Surfaces Using the ReaxFF Reactive Force Field

The dissociation of hydrogen on eight platinum surfaces, Pt(111), Pt(100), Pt(110), Pt(211), Pt(311), Pt(331), Pt(332), and Pt(533), has been studied using molecular dynamics and the reactive force field, ReaxFF. The force field, which includes the degrees of freedom of the atoms in the platinum substrate, was used unmodified with potential parameters determined from previous calculations performed on a training set exclusive of the surfaces considered in this work. The energetics of the eight surfaces in the absence of hydrogen at 0 K were first compared to previous density functional theory (DFT) calculations and found to underestimate excess surface energy. However, taking Pt(111) as a reference state, we found that the trend between surfaces was adequately predicted to justify a relative comparison between the various stepped surfaces. To assess the strengths and weaknesses of the force field, we performed detailed simulations on two stepped surfaces, Pt(533) and Pt(211), and compared our findings to published experimental and theoretical results. In general, the absolute magnitude of reaction rate predictions was low, a result of the force field's tendency to underpredict surface energy. However, when normalized, the simulations show the correct linear scaling with incident energy and angular dependence at collision energies where a direct dissociation mechanism is observed. Because ReaxFF includes all degrees of freedom in the substrate, we carried out simulations aimed at understanding surface-temperature effects on Pt(533). On the basis of the results on Pt(533)/Pt(211), we studied the reaction of hydrogen at normal incidence on all eight surfaces in a range of energies where we anticipated the force field to give reasonable qualitative trends. These results were subsequently fit to a simple linear model that predicts the enhanced reactivity of surfaces containing 111-type atomic steps versus 100-type atomic steps. This model provides a simple framework for predicting high-energy/high-temperature kinetics of complex surfaces not vicinal to Pt(111).

Rotational effects in the dissociative adsorption of H2 on the Pt211 stepped surface

Rotational effects in the dissociative adsorption of H2 on the Pt211 stepped surface have been studied using classical trajectory calculations on a six-dimensional, density-functional theory potential-energy surface. Reaction of rotating molecules via an indirect trapping mechanism exhibits an unexpected nonmonotonic dependence on the initial rotational quantum number J. Indirect reaction is first quenched with increasing J but is enhanced again for high J initial states. The quenching is attributed to rotational-to-translational energy transfer, which facilitates escape from the chemisorption wells responsible for molecular trapping. For high J, rotational and translational motions decouple, and the energy transfer is no longer possible, which leads again to trapping. Degeneracy-resolved calculations show that for high initial J, molecules rotating in a "cartwheel" fashion (mJ=0) are more likely to become trapped and react indirectly than "helicoptering" molecules (mJ=J). Experimental confirmation of this finding would lend strong support to the existence of the chemisorption wells that trap molecules prior to reaction.