A first-principles potential energy surface for Eley–Rideal reaction dynamics of H atoms on Cu(111)

Automatic Feature Selection for Atom-Centered Neural Network Potentials Using a Gradient Boosting Decision Algorithm

Atom-centered neural network (ANN) potentials have shown high accuracy and computational efficiency in modeling atomic systems. A crucial step in developing reliable ANN potentials is the proper selection of atom-centered symmetry functions (ACSFs), also known as atomic features, to describe atomic environments. Inappropriate selection of ACSFs can lead to poor-quality ANN potentials. Here, we propose a gradient boosting decision tree (GBDT)-based framework for the automatic selection of optimal ACSFs. This framework takes uniformly distributed sets of ACSFs as input and evaluates their relative importance. The ACSFs with high average importance scores are selected and used to train an ANN potential. We applied this method to the Ge system, resulting in an ANN potential with root-mean-square errors (RMSE) of 10.2 meV/atom for energy and 84.8 meV/Å for force predictions, utilizing only 18 ACSFs to achieve a balance between accuracy and computational efficiency. The framework is validated using the grid searching method, demonstrating that ACSFs selected with our framework are in the optimal region. Furthermore, we also compared our method with commonly used feature selection algorithms. The results show that our algorithm outperforms the others in terms of effectiveness and accuracy. This study highlights the significance of the ACSF parameter effect on the ANN performance and presents a promising method for automatic ACSF selection, facilitating the development of machine learning potentials.

Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111)

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

Dynamics in reactions on metal surfaces: A theoretical perspective

Recent advances in theoretical characterization of reaction dynamics on metal surfaces are reviewed. It is shown that the widely available density functional theory of metals and their interactions with molecules have enabled first principles theoretical models for treating surface reaction dynamics. The new theoretical tools include methods to construct high-dimensional adiabatic potential energy surfaces, to characterize nonadiabatic processes within the electronic friction models, and to describe dynamics both quantum mechanically and classically. Three prototypical surface reactions, namely, dissociative chemisorption, Eley-Rideal reactions, and recombinative desorption, are surveyed with a focus on some representative examples. While principles governing gas phase reaction dynamics may still be applicable, the presence of the surface introduces a higher level of complexity due to strong interaction between the molecular species and metal substrate. Furthermore, most of these reactive processes are impacted by energy exchange with surface phonons and/or electron-hole pair excitations. These theoretical studies help to interpret and rationalize experimental observations and, in some cases, guide experimental explorations. Knowledge acquired in these fundamental studies is expected to impact many practical problems in a wide range of interfacial processes.

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.

SIX-DIMENSIONAL DYNAMICS OF DISSOCIATIVE CHEMISORPTION OF H2 ON METAL SURFACES

The theory of time-dependent quantum dynamics of dissociative chemisorption of hydrogen on metal surfaces is reviewed, in the framework of electronically adiabatic scattering from static surfaces. Four implementations of the time-dependent wave packet (TDWP) method are discussed. In the direct product pseudo-spectral and the spherical harmonics pseudo-spectral methods, no use is made of the symmetry associated with the surface unit cell. This symmetry is exploited by the symmetry adapted wave packet and the symmetry adapted pseudo-spectral (SAPS) method, which are efficient for scattering at normal incidence. The SAPS method can be employed for potential energy surfaces of general form.

Comparison to experiment shows that the TDWP method yields good, but not yet excellent, quantitative accuracy for dissociation of (ν = 0, j = 0) H 2 if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecule's vibration (rotation) is well (reasonably well) described. The theory does not yet yield quantitatively accurate results for rovibrationally inelastic scattering. The theory has helped with the interpretation of existing experimental results, for instance, by solving a parodox regarding the corrugation of Pt(111) as seen by reacting and scattering H 2. The theory has also provided some exciting new predictions, for instance, concerning where on the surface of Cu(100) H2 reacts depending on its vibrational state. Future theoretical studies of H 2 reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H 2 with complex metal surfaces.

H(D) → D(H) + Cu(111) collision system: molecular dynamics study of surface temperature effects

All the channels of the reaction dynamics of gas-phase H (or D) atoms with D (or H) atoms adsorbed onto a Cu(111) surface have been studied by quasiclassical constant energy molecular dynamics simulations. The surface is flexible and is prepared at different temperature values, such as 30 K, 94 K, and 160 K. The adsorbates were distributed randomly on the surface to create 0.18 ML, 0.28 ML, and 0.50 ML of coverages. The multi-layer slab is mimicked by a many-body embedded-atom potential energy function. The slab atoms can move according to the exerted external forces. Treating the slab atoms non-rigid has an important effect on the dynamics of the projectile atom and adsorbates. Significant energy transfer from the projectile atom to the surface lattice atoms takes place especially during the first impact that modifies significantly the details of the dynamics of the collisions. Effects of the different temperatures of the slab are investigated in this study. Interaction between the surface atoms and the adsorbates is modeled by a modified London-Eyring-Polanyi-Sato (LEPS) function. The LEPS parameters are determined by using the total energy values which were calculated by a density functional theory and a generalized gradient approximation for an exchange-correlation energy for many different orientations, and locations of one- and two-hydrogen atoms on the Cu(111) surface. The rms value of the fitting procedure is about 0.16 eV. Many different channels of the processes on the surface have been examined, such as inelastic reflection of the incident hydrogen, subsurface penetration of the incident projectile and adsorbates, sticking of the incident atom on the surface. In addition, hot-atom and Eley-Rideal direct processes are investigated. The hot-atom process is found to be more significant than the Eley-Rideal process. Furthermore, the rate of subsurface penetration is larger than the sticking rate on the surface. In addition, these results are compared and analyzed as a function of the surface temperatures.

Dynamics simulation of N(2) scattering onto W(100,110) surfaces: A stringent test for the recently developed flexible periodic London-Eyring-Polanyi-Sato potential energy surface

An efficient method to construct the six dimensional global potential energy surface (PES) for two atoms interacting with a periodic rigid surface, the flexible periodic London-Eyring-Polanyi-Sato model, has been proposed recently. The main advantages of this model, compared to state-of-the-art interpolated ab initio PESs developed in the past, reside in its global nature along with the small number of electronic structure calculations required for its construction. In this work, we investigate to which extent this global representation is able to reproduce the fine details of the scattering dynamics of N(2) onto W(100,110) surfaces reported in previous dynamics simulations based on locally interpolated PESs. The N(2)/W(100) and N(2)/W(110) systems are chosen as benchmarks as they exhibit very unusual and distinct dissociative adsorption dynamics although chemically similar. The reaction pathways as well as the role of dynamic trapping are scrutinized. Besides, elastic/inelastic scattering dynamics including internal state and angular distributions of reflected molecules are also investigated. The results are shown to be in fair agreement with previous theoretical predictions.

Dissociative chemisorption of H2 on the Cu(110) surface: a quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.

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.

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).

Relaxation of hot atoms following H2 dissociation on a Pd(111) surface

We study the relaxation of hot H atoms produced by dissociation of H2 molecules on the Pd111 surface. Ab initio density-functional theory calculations and the "corrugation reducing procedure" are used to determine the interaction potential for a H atom in front of a rigid surface as well as its modification under surface-atom vibrations. A slab of 80 Pd atoms is used to model the surface together with "generalized Langevin oscillators" to account for energy dissipation to the bulk. We show that the energy relaxation is fast, about 75% of the available energy being lost by the hot atoms after 0.5 ps. As a consequence, the hot atoms do not travel more than a few angstroms along the surface before being trapped into the potential well located over the hollow site.

Six-dimensional quantum dynamics of (v=0,j=0)D2 and of (v=1,j=0)H2 scattering from Cu(111)

We report six-dimensional quantum dynamics calculations of the dissociative scattering of molecular hydrogen from the copper111 surface. Two potential energy surfaces are investigated and the results are compared with experiment. Our study completes the preliminary work of Somers et al. [Chem. Phys. Lett. 360, 390 (2002)] and focuses on the role of initial vibrational excitation and on isotopic effects. None of the two investigated potential energy surfaces is found satisfactory: the use of neither potential yields reaction and vibrational excitation probabilities and vibrational efficacies that are in close agreement with experiment. In addition to showing the shortcomings of existing potential energy surfaces we point out an inconsistency in the experimental fits for D2.

Quasiclassical study of Eley–Rideal and hot atom reactions of H atoms with Cl adsorbed on a Au(111) surface

Using quasiclassical methods and a potential energy surface based on total energy calculations, we have found that H atoms react with Cl atoms adsorbed onto a Au(111) surface to produce HCl via Eley-Rideal (ER), hot atom (HA), and Langmuir-Hinschelwood (LH) pathways. We observe two ER mechanisms. At small normal incidence energies reaction results from a more or less direct collision with Cl, leading to a large amount of product vibration (nu=8), and relatively cold rotation and translation. In the second mechanism, more dominant at near-normal incidence and/or large incident energies, the H atom passes near Cl, recoils from the metal, and is pulled into orbit about Cl. This leads to broader product state distributions, and a more even distribution of the 3.0 eV of available energy among the product degrees of freedom, similar to products formed via the HA pathway. Overall, ER processes tend to contribute less than 10% to the reactivity, and most of the HCl is formed via HA processes. There is an increase in HCl formation with surface temperature for both the ER and HA mechanisms, but this increase is relatively weak. We observe typically about 12% H atom sticking, which would lead to HCl formation via a LH process in the experiments, above 140 K. We observe a weak forward scattering due to the direct ER component, as in the experiments. However, unlike the experiments, we observe a dip in our product angular distributions about thetaf=0 degrees, which we ascribe to our quasiclassical approximation. While we tend to see more energy in the hot products than in the experiments, our product translational, rotational, and vibrational distributions are in relatively reasonable agreement with those measured. One major disagreement with experiment is that there is apparently a significant sticking of the H atom at low temperatures, leading to a large LH component. In addition, the ER and HA components increase much more strongly with temperature than in the calculations. It is possible that electon-hole pair excitations in the metal strongly relax both the H atom and the excited HCl molecules formed.

A first-principles potential energy surface and vibrational states for hydrogen on Cu(100)

Density-functional theory calculations based on plane-wave expansion and pseudopotential treatment were carried out for atomic hydrogen on a rigid Cu(100) surface. A global potential energy surface was then obtained by using a three-dimensional spline interpolation. It is found that the minimum of the potential is located at the fourfold hollow site with a diffusion barrier of 88 meV at the bridge site. The vibrational states of atomic hydrogen and deuterium on the Cu(100) surface were calculated on the potential surface. Our calculations show that the vibrational states A(1) (0), A(1) (1), E(1), and B(2) (1) of H/Cu(100) exhibit strong localized character and very narrow band widths, whereas other excited vibrational states have considerable delocalized character and broad band widths. The vibrational frequency of 71.2 (51.5) meV for H(D) in the perpendicular direction obtained in this study is in good agreement with the experimentally observed value of 70 (52) meV.

Hot-atom versus Eley–Rideal dynamics in hydrogen recombination on Ni(100). I. The single-adsorbate case

We compare the efficiency of the Eley-Rideal (ER) reaction with the formation of hot-atom (HA) species in the simplest case, i.e., the scattering of a projectile off a single adsorbate, considering the Hydrogen and Hydrogen-on-Ni(100) system. We use classical mechanics and the accurate embedded diatomics-in-molecules potential to study the collision system over a wide range of collision energies (0.10-1.50 eV), both with a rigid and a nonrigid Ni substrate and for impact on the occupied and neighboring empty cells. In the rigid model metastable and truly bound hot-atoms occur and we find that the cross section for the formation of bound hot-atoms is considerably higher than that for the ER reaction over the whole range of collision energies examined. Metastable hot-atoms form because of the inefficient energy transfer to the adsorbate and have lifetimes of the order 0.1-0.7 ps, depending on the collision energy. When considering the effects of lattice vibrations we find, on average, a consistent energy transfer to the substrate, say 0.1-0.2 eV, which forced us to devise a two-step dynamical model to get rid of the problems associated with the use of periodic boundary conditions. Results for long-lived HA formation due to scattering on the occupied cell at a surface temperature of 120 K agree well with those of the rigid model, suggesting that in the above process the substrate plays only a secondary role and further calculations at surface temperatures of 50 and 300 K are in line with these findings. However, considerably high cross sections for formation of long-lived hot-atoms result also from scattering off the neighboring cells where the energy transfer to the lattice cannot be neglected. Metastable hot-atoms are reduced in number and have usually lifetimes shorter than those of the rigid-model, say less than 0.3 ps. In addition, ER cross sections are only slightly affected by the lattice motion and show a little temperature dependence. Finally, we find also that absorption and reflection strongly depend on the correct consideration of lattice vibrations and the occurrence of trapping.

Application of the modified Shepard interpolation method to the determination of the potential energy surface for a molecule–surface reaction: H2+Pt(111)

We have used a modified Shepard (MS) interpolation method, initially developed for gas phase reactions, to build a potential energy surface (PES) for studying the dissociative chemisorption of H2 on Pt(111). The aim was to study the efficiency and the accuracy of this interpolation method for an activated multidimensional molecule-surface reactive problem. The strategy used is based on previous applications of the MS method to gas phase reactions, but modified to take into account special features of molecule-surface reactions, like the presence of many similar reaction pathways which vary only slightly with surface site. The efficiency of the interpolation method was tested by using an already existing PES to provide the input data required for the construction of the new PES. The construction of the new PES required half as many ab initio data points as the construction of the old PES, and the comparison of the two PESs shows that the method is able to reproduce with good accuracy the most important features of the H2 + Pt(111) interaction potential. Finally, accuracy tests were done by comparing the results of dynamics simulations using the two different PESs. The good agreement obtained for reaction probabilities and probabilities for rotationally and diffractionally inelastic scattering shows clearly that the MS interpolation method can be used efficiently to yield accurate PESs for activated molecule-surface reactions.

Efficient Eley-Rideal reactions of H atoms with single Cl adsorbates on Au(111)

Density functional theory is used to construct an interaction model for H atoms with Cl over Au(111). Single-adsorbate Eley-Rideal reactions are investigated with quantum and quasiclassical methods. The reaction cross sections, amounting to 2-3 A(2), are much larger than for HD recombinations on metals. This can be traced to the adsorbed Cl being relatively far above the surface, the H-Cl interaction prevailing over the H-substrate attraction for a sizable range of impact parameters.

Laminar growth of ultrathin metal films on metal oxides: Co on hydroxylated alpha-Al2O3(0001)

Metals deposited in vacuum on metal oxides such as alumina normally grow as three-dimensional clusters because of weak adatom-substrate interactions. This tendency hinders our ability to form interfaces of ultrathin, laminar metal films on oxides for use in microelectronics and other technologies where nanostructural control is desired. We present experimental and theoretical results showing that room temperature Co deposition on fully hydroxylated clean sapphire (alpha-Al2O3) produces a surface chemical reaction that leads to laminar growth, despite a large mismatch in lattice constants. This process should be applicable to a wide range of metals and metal oxides.