Gas-surface Dynamics Research Articles

Benchmarking of machine learning interatomic potentials for reactive hydrogen dynamics at metal surfaces

Simulations of chemical reaction probabilities in gas surface dynamics require the calculation of ensemble averages over many tens of thousands of reaction events to predict dynamical observables that can be compared to experiments. At the same time, the energy landscapes need to be accurately mapped, as small errors in barriers can lead to large deviations in reaction probabilities. This brings a particularly interesting challenge for machine learning interatomic potentials, which are becoming well-established tools to accelerate molecular dynamics simulations. We compare state-of-the-art machine learning interatomic potentials with a particular focus on their inference performance on CPUs and suitability for high throughput simulation of reactive chemistry at surfaces. The considered models include polarizable atom interaction neural networks (PaiNN), recursively embedded atom neural networks (REANN), the MACE equivariant graph neural network, and atomic cluster expansion potentials (ACE). The models are applied to a dataset on reactive molecular hydrogen scattering on low-index surface facets of copper. All models are assessed for their accuracy, time-to-solution, and ability to simulate reactive sticking probabilities as a function of the rovibrational initial state and kinetic incidence energy of the molecule. REANN and MACE models provide the best balance between accuracy and time-to-solution and can be considered the current state-of-the-art in gas-surface dynamics. PaiNN models require many features for the best accuracy, which causes significant losses in computational efficiency. ACE models provide the fastest time-to-solution, however, models trained on the existing dataset were not able to achieve sufficiently accurate predictions in all cases.

Effect of growth conditions and reactor configuration on the growth uniformity of large-scale graphene by chemical vapor deposition

Chemical vapor deposition (CVD) is an affordable method for the preparation of large-scale and high-quality graphene. With the increase in CVD reactor size, gas mass transfer, flow state, and gas phase dynamics become more complicated. In this study, computational fluid dynamics is used to investigate factors affecting the uniformity of large-scale graphene growth under different growth conditions and reactor configurations. The dimensionless number defined in this paper and the Grashof number are utilized to distinguish the species transfer patterns and the flow states, respectively. A gas-surface dynamics model is established to simulate the graphene growth. Results reveal that the graphene growth rate uniformity is the highest at very low pressure and flow rate due to the flow symmetry and diffusion-dominated species transfer. At an increased pressure of 20 Torr, the uniformity of the graphene growth rate becomes higher axially and lower circumferentially with an increasing inlet mass flow rate. When the flow rate is fixed at 1500 SCCM and pressure is reduced from 20 to 2 Torr, graphene growth uniformity first increases and then decreases due to the influence of gas phase dynamics. Graphene growth rates are analyzed across ordinary reactor configurations and four configurations with inner tubes at 20 Torr pressure and 1500 SCCM flow rate. Comprehensive evaluation suggests that the ordinary reactor configuration performs best under these conditions. This research offers insights into the macroscopic growth mechanism of large-scale graphene and provides guidance for designing growth conditions in large-area graphene production.

Spiers Memorial Lecture: New directions in molecular scattering.

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Machine Learning Interatomic Potentials for Reactive Hydrogen Dynamics at Metal Surfaces Based on Iterative Refinement of Reaction Probabilities.

The reactive chemistry of molecular hydrogen at surfaces, notably dissociative sticking and hydrogen evolution, plays a crucial role in energy storage and fuel cells. Theoretical studies can help to decipher underlying mechanisms and reaction design, but studying dynamics at surfaces is computationally challenging due to the complex electronic structure at interfaces and the high sensitivity of dynamics to reaction barriers. In addition, ab initio molecular dynamics, based on density functional theory, is too computationally demanding to accurately predict reactive sticking or desorption probabilities, as it requires averaging over tens of thousands of initial conditions. High-dimensional machine learning-based interatomic potentials are starting to be more commonly used in gas-surface dynamics, yet robust approaches to generate reliable training data and assess how model uncertainty affects the prediction of dynamic observables are not well established. Here, we employ ensemble learning to adaptively generate training data while assessing model performance with full uncertainty quantification (UQ) for reaction probabilities of hydrogen scattering on different copper facets. We use this approach to investigate the performance of two message-passing neural networks, SchNet and PaiNN. Ensemble-based UQ and iterative refinement allow us to expose the shortcomings of the invariant pairwise-distance-based feature representation in the SchNet model for gas-surface dynamics.

Multiscale gas transport behavior in heterogeneous shale matrix consisting of organic and inorganic nanopores

The complicated nanoporous structure and significant heterogeneity of shale matrix make it challenging to fully understand the gas transport behavior in shale. Towards this end, herein a multiscale approach was presented via coupling molecular dynamics (MD) simulations, analytical model and pore network model (PNM). Using MD simulations, we showed that gas transport in organic nanopores manifests a typical slippage feature whereas gas slippage breaks down in inorganic nanopores, which should be attributed to “rough” potential energy surface (PES) of inorganic walls. Based on the results of MD simulations, a unified gas transport model was derived to describe gas flow behaviors in organic and inorganic pores by integrating continuum flow theory and gas-surface dynamics theory. In particular, gas transport process in heterogeneous shale matrix was performed with the help of pore network model and the influence of multiple factors on the gas permeability of shale matrix were analysed and discussed.

Ring Polymer Molecular Dynamics in Gas-Surface Reactions: Inclusion of Quantum Effects Made Simple.

Accurately modeling gas-surface collision dynamics presents a great challenge for theory, especially in the low-energy (or temperature) regime where quantum effects are important. Here, a path integral-based nonequilibrium ring polymer molecular dynamics (NE-RPMD) approach is adapted to calculate dissociative initial sticking probabilities (S0) of H2 on Cu(111) and D2O on Ni(111), revealing the distinct quantum nature in the two benchmark surface reactions. NE-RPMD successfully captures quantum tunneling in H2 dissociation at very low energies, where the quasi-classical trajectory (QCT) method suddenly fails. Additionally, QCT substantially overestimates S0 of D2O because of severe zero point energy (ZPE) leakage, even at collision energies greater than the ZPE-corrected barrier. Instead, NE-RPMD predicts S0 values of D2O in much improved agreement with reference results obtained by the quantum wavepacket method with reasonable corrections of the thermal contribution. Our results suggest NE-RPMD as a promising approach to model quantum effects in gas-surface reactions.

Inelastic Scattering of N2 off W(001): Reconciling Experiment and Theory at Low Collision Energies

The inelastic scattering dynamics of N2 off W(001) has recently been the subject of theoretical investigations, which were found to be unable to describe low-collision-energy molecular beam experiments. This discrepancy was suggested to originate from the neglect of van der Waals interactions in the construction of the potential energy surface. By making use of a newly developed potential energy surface, accounting for such dispersion interactions, we show that quasi-classical dynamics simulations, including dissipation to surface electrons and phonons, lead to an adequate description of the low-collision-energy experiments and, more specifically, the trapping-desorption component of inelastic scattering. This work highlights the prominent influence of van der Waals forces on gas–surface dynamics observables in the low-collision-energy regime.

Accurate Neural Network Description of Surface Phonons in Reactive Gas-Surface Dynamics: N2 + Ru(0001).

Ab initio molecular dynamics (AIMD) simulations enable the accurate description of reactive molecule–surface scattering especially if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the molecule–surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N2 + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of molecular and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10–5 to be computed, showing good agreement with experimental results.

Note: Velocity map imaging the scattering plane of gas surface collisions.

The ability of gas-surface dynamics studies to resolve the velocity distribution of the scattered species in the 2D scattering plane has been limited by technical capabilities and only a few different approaches have been explored in recent years. In comparison, gas-phase scattering studies have been transformed by the near ubiquitous use of velocity map imaging. We describe an innovative means of introducing a dielectric surface within the electric field of a typical velocity map imaging experiment. The retention of optimum velocity mapping conditions was validated by measurements of iodomethane-d3 photodissociation and SIMION calculations. To demonstrate the system's capabilities, the velocity distributions of ammonia molecules scattered from a polytetrafluoroethylene surface have been measured for multiple product rotational states.

Energy loss in gas-surface dynamics: Electron–hole pair and phonon excitation upon adsorbate relaxation

We study the effect of electron and phonon degrees of freedom on the relaxation dynamics of adsorption processes in gas-surface systems by using ab initio molecular dynamics that incorporates an electronic friction force (AIMDEF). As representative cases we have chosen three systems with different adsorption energies and adsorbate-to-surface atom mass ratios: H on Pd(100), N on Ag(111), and N2 on Fe(110). We show, through inspection of the total energies and trajectories of the hot adsorbates on the surface, that electron–hole (e–h) pair excitations dominate relaxation of the light gas species, while the phonon channel is dominant for the heavy species. In the latter case e–h pairs become more important at the final thermalization stages.

Methane dissociation on Pt(111): Searching for a specific reaction parameter density functional.

The theoretical description of methane dissociating on metal surfaces is a current frontier in the field of gas-surface dynamics. Dynamical models that aim at achieving a highly accurate description of this reaction rely on potential energy surfaces based on density functional theory calculations at the generalized gradient approximation. We focus here on the effect that the exchange-correlation functional has on the reactivity of methane on a metal surface, using CHD3 + Pt(111) as a test case. We present new ab initio molecular dynamics calculations performed with various density functionals, looking also at functionals that account for the van der Waals (vdW) interaction. While searching for a semi-empirical specific reaction parameter density functional for this system, we find that the use of a weighted average of the PBE and the RPBE exchange functionals together with a vdW-corrected correlation functional leads to an improved agreement with quantum state-resolved experimental data for the sticking probability, compared to previous PBE calculations. With this semi-empirical density functional, we have also investigated the surface temperature dependence of the methane dissociation reaction and the influence of the rotational alignment on the reactivity, and compared our results with experiments.

Cutting a chemical bond with demon's scissors: Mode- and bond-selective reactivity of methane on metal surfaces

In this paper we discuss several aspects of methane reactive sticking on Pt(111) in the light of supersonic molecular beam experiments (including state-resolved measurements) and quasi-classical trajectory calculations based on an accurate reaction specific reactive force field constructed from Density Functional Theory (DFT) data. With the aim of understanding the origin of the full bond selectivity recently achieved experimentally and to predict how selectivity depends on the collision conditions, we discuss in detail, the role of initial translational and (mode-specific) vibrational energy of CH4 and all its deuterated isotopomers, as well as surface temperature effects. Last but not least, the systematic and detailed theoretical analysis presented here serves as an illustration of the possibilities and usefulness of accurate reaction specific reactive force fields built from DFT data. This approach allows investigating dynamical aspects of the interaction of polyatomic molecules on surfaces through quasi-classical trajectory calculations accounting for the full dimensionality of the system (including both molecular and surface degrees of freedom): something that a few years ago was just a dream for the gas–surface dynamics community.

Using Hessian update formulae to construct modified Shepard interpolated potential energy surfaces: Application to vibrating surface atoms

Modified Shepard interpolation based on second order Taylor series expansions has proven to be a flexible tool for constructing potential energy surfaces in a range of situations. Extending this to gas-surface dynamics where surface atoms are allowed to move represents a substantial increase in the dimensionality of the problem, reflected in a dramatic increase in the computational cost of the required Hessian (matrix of second derivatives) evaluations. This work demonstrates that using approximate Hessians derived from well known Hessian update formulae and a single accurate Hessian can provide an effective way to avoid this expensive accurate Hessian determination.

Ready, Set and no Action: A Static Perspective on Potential Energy Surfaces commonly used in Gas-Surface Dynamics

Ready, Set and no Action: A Static Perspective on Potential Energy Surfaces commonly used in Gas-Surface Dynamics

Ready, Set and no Action: A Static Perspective on Potential Energy Surfaces commonly used in Gas-Surface Dynamics

In honoring the seminal contribution of Henry Eyring and Michael Polanyi who first introduced the concept of potential energy surfaces (PESs) to describe chemical reactions in gas-phase [Z. Phys. Chem. 12, 279-311, (1931)], this work comes to review and assess state-of-the-art approaches towards first-principle based modeling in the field of gas-surface dynamics. Within the Born-Oppenheimer and frozen surface approximations, the O2-Ag(100) interaction energetics are used as a showcase system to accentuate the complex landscape exhibited by the PESs employed to describe the impingement of diatomics on metal substrates and draw attention to the far-from-trivial task of continuously representing them within all six molecular degrees of freedom. To this end, the same set of ab initio reference data obtained within Density Functional Theory (DFT) are continuously represented by two different state-of-the-art high-dimensional approaches, namely the Corrugation-Reducing Procedure and Neural Networks. Exploiting the numerically undemanding nature of the resulting representations, a detailed static evaluation is performed on both PESs based on an extensive global minima search. The latter proved particularly illuminating in revealing representation deficiencies which affect the dynamical picture yet go otherwise unnoticed within the so-called "divide-and-conquer" approach.

Employing a cylindrical single crystal in gas-surface dynamics

We describe the use of a polished, hollow cylindrical nickel single crystal to study effects of step edges on adsorption and desorption of gas phase molecules. The crystal is held in an ultra-high vacuum apparatus by a crystal holder that provides axial rotation about a [100] direction, and a crystal temperature range of 89 to 1100 K. A microchannel plate-based low energy electron diffraction/retarding field Auger electron spectrometer (AES) apparatus identifies surface structures present on the outer surface of the cylinder, while a separate double pass cylindrical mirror analyzer AES verifies surface cleanliness. A supersonic molecular beam, skimmed by a rectangular slot, impinges molecules on a narrow longitudinal strip of the surface. Here, we use the King and Wells technique to demonstrate how surface structure influences the dissociation probability of deuterium at various kinetic energies. Finally, we introduce spatially-resolved temperature programmed desorption from areas exposed to the supersonic molecular beam to show how surface structures influence desorption features.

Communication: Angle-resolved thermal dissociative sticking of CH4 on Pt(111): Further indication that rotation is a spectator to the gas-surface reaction dynamics

Effusive molecular beam measurements of angle-resolved thermal dissociative sticking coefficients for CH(4) impinging on a Pt(111) surface, at a temperature of 700 K, are reported and compared to theoretical predictions. The reactivity falls off steeply as the molecular angle of incidence increases away from the surface normal. Successful modeling of the thermal dissociative sticking behavior, consistent with existent CH(4) supersonic molecular beam experiments involving rotationally cold molecules, required that rotation be treated as a spectator degree of freedom.

Non-adiabatic effects during the dissociative adsorption of O2 at Ag(111)? A first-principles divide and conquer study

We study the gas-surface dynamics of O2 at Ag(111) with the particular objective to unravel whether electronic non-adiabatic effects are contributing to the experimentally established inertness of the surface with respect to oxygen uptake. We employ a first-principles divide and conquer approach based on an extensive density-functional theory mapping of the adiabatic potential energy surface (PES) along the six O2 molecular degrees of freedom. Neural networks are subsequently used to interpolate these grid data to a continuous representation. The low computational cost with which forces are available from this PES representation allows then for a sufficiently large number of molecular dynamics trajectories to quantitatively determine the very low initial dissociative sticking coefficient at this surface. Already these adiabatic calculations yield dissociation probabilities close to the scattered experimental data. Our analysis shows that this low reactivity is governed by large energy barriers in excess of 1.1 eV very close to the surface. Unfortunately, these adiabatic PES characteristics render the dissociative sticking a rather insensitive quantity with respect to a potential spin or charge non-adiabaticity in the O2–Ag(111) interaction. We correspondingly attribute the remaining deviations between the computed and measured dissociation probabilities primarily to unresolved experimental issues with respect to surface imperfections.

Coverage effects in the adsorption of H2 on Pd(100) studied by ab initio molecular dynamics simulations

The interaction of hydrogen with palladium surfaces represents one of the model systems for the study of the adsorption and absorption at metal surfaces. Theoretical gas-surface dynamics studies have usually concentrated on the adsorption dynamics on clean surfaces. Only recently it has become possible, based on advances in the electronic structure codes and improvements in the computer power, to address the much more complex problem of the adsorption dynamics on precovered surfaces. Here, I present ab initio molecular dynamics (AIMD) simulations based on periodic density functional theory (DFT) calculations of the adsorption of H(2) on hydrogen-precovered Pd(100) for a broad variety of different hydrogen coverage structures. The stability of the adsorbate structures and the adsorption dynamics are analyzed in detail. Calculated sticking probabilities are larger than expected for pure site-blocking consistent with experimental results. It turns out that the adsorption dynamics on the strongly corrugated surfaces depends sensitively on the dynamic response of the substrate atoms upon the impact of the impinging H(2) molecules. In addition, for some structures the adsorption probability was evaluated as a function of the kinetic energy. Adsorbate structures corresponding to the same coverage but with different arrangements of the adsorbed atoms can lead to a qualitatively different dependence of the adsorption probability on the kinetic energy changing also the order of the preferred structures, as far as the adsorption is concerned, as a function of the kinetic energy. This indicates that dynamical effects such as steering and dynamical trapping play an important role in the adsorption on these precovered substrates.

Ab Initio Molecular Dynamics Simulations of the Adsorption of H2 on Palladium Surfaces

The interaction of hydrogen with palladium surfaces represents a model system for the study of the adsorption and absorption at metal surfaces. Theoretical gas-surface dynamics studies have usually concentrated on the adsorption dynamics on clean surfaces. Only recently has it become possible, based on advances in electronic structure codes and improvements in computer power, to address the much more complex problem of the adsorption dynamics on precovered surfaces. Herein, recent ab initio molecular dynamics studies are discussed that address the adsorption dynamics of hydrogen molecules on hydrogen- and sulfur-precovered Pd surfaces. In addition, the relaxation dynamics of the hydrogen atoms after the dissociation on clean Pd(100) are presented.