Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

A Molecular View of Methane Activation on Ni(111) through Enhanced Sampling and Machine Learning

A combination of machine learned interatomic potentials (MLIPs) and enhanced sampling simulations is used to investigate the activation of methane on a Ni(111) surface. The work entails the development and iterative refinement of MLIPs, initially trained on a data set constructed via ab initio molecular dynamics simulations, supplemented by adaptive biasing forces, to enrich the sampling of catalytically relevant configurations. Our results reveal that upon incorporation of collective variables that capture the behavior of the reactant molecule, as well as additional frames that describe the dynamic response of the catalytic surface, it is possible to enhance considerably the accuracy of predicted energies and forces. By employing enhanced sampling schemes in the refinement of the MLIP, we systematically explore the potential energy surface, leading to a refined MLIP capable of predicting density functional theory-level energies and forces and replicating key geometric characteristics of the catalytic system. The resulting free energy landscapes at several temperatures provide a detailed view of the thermodynamics and dynamics of methane activation. Specifically, as methane approaches and dissociates on the catalytic surface, the process involves the dynamic interplay of CH4 and the Ni catalyst that includes both enthalpic and entropic contributions. The progression toward the transition state involves a CH4 moiety that is increasingly restrained in its ability to rotate or translate, while the stage following the transition state is characterized by a notable rise of the Ni atom that interacts with the cleaved C-H bond. This leads to an increase in the mobility of the adsorbed species, a feature that becomes more pronounced at higher temperatures.

The Importance of Reaction Energy in Predicting Chemical Reaction Barriers with Machine Learning Models

Improving our fundamental understanding of complex heterocatalytic processes increasingly relies on electronic structure simulations and microkinetic models based on calculated energy differences. In particular, calculation of activation barriers, usually achieved through compute-intensive saddle point search routines, remains a serious bottleneck in understanding trends in catalytic activity for highly branched reaction networks. Although the well-known Brønsted-Evans-Polyani (BEP) scaling - a one-feature linear regression model - has been widely applied in such microkinetic models, they still rely on calculated reaction energies and may not generalize beyond a single facet on a single class of materials, e. g., a terrace sites on transition metals. For highly branched and energetically shallow reaction networks, such as electrochemical CO2 reduction or wastewater remediation, calculating even reaction energies on many surfaces can become computationally intractable due to the combinatorial explosion of states that must be considered. Here, we investigate the feasibility of activation barrier prediction without knowledge of the reaction energy using linear and nonlinear machine learning (ML) models trained on a new database of over 500 dehydrogenation activation barriers. We also find that inclusion of the reaction energy significantly improves both classes of ML models, but complex nonlinear models can achieve performance similar to the simplest BEP scaling when predicting activation barriers on new systems. Additionally, inclusion of the reaction energy significantly improves generalizability to new systems beyond the training set. Our results suggest that the reaction energy is a critical feature to consider when building models to predict activation barriers, indicating that efforts to reliably predict reaction energies through, e. g., the Open Catalyst Project and others, will be an important route to effective model development for more complex systems.

STM Visualization of N2 Dissociative Chemisorption on Ru(0001) at High Impinging Kinetic Energies

This paper examines the reactive surface dynamics of energy- and angle-selected N₂ dissociation on a clean Ru(0001) surface. Presented herein are the first STM images of highly energetic N₂ dissociation on terrace sites utilizing a novel UHV instrument that combines a supersonic molecular beam with an in situ STM that is in-line with the molecular beam. Atomically resolved visualization of individual N₂ dissociation events elucidates the fundamental reactive dynamics of the N₂/Ru(0001) system by providing a detailed understanding of the on-surface dissociation dynamics: the distance and angle between nitrogen atoms from the same dissociated N₂ molecule, site specificity and coordination of binding on terrace sites, and the local evolution of surrounding nanoscopic areas. These properties are precisely measured over a range of impinging N₂ kinetic energies and angles, revealing previously unattainable information about the energy dissipation channels that govern the reactivity of the system. The experimental results presented in this paper provide insight into the fundamental N₂ dissociation mechanism that, in conjunction with ongoing theoretical modeling, will help determine the role of dynamical processes such as energy transfer to surface phonons and nonadiabatic excitation of electron-hole pairs (ehps). These results will not only help uncover the underlying chemistry and physics that give rise to the unique behavior of this activated dissociative chemisorption system but also represent an exciting approach to studying reaction dynamics by pairing the angstrom-level spatiotemporal resolution of an in situ STM with nonequilibrium fluxes of reactive gases generated in a supersonic molecular beam to access highly activated chemical dynamics and observe the results of individual reaction events.

Free-Energy Landscape and Isomerization Rates of Au4 Clusters at Finite Temperatures

In metallic nanoparticles, the geometry of atomic positions controls the particle's electronic band structure, polarizability, and catalytic properties. Analyzing the structural properties is a complex problem; the structure of an assembled cluster changes from moment to moment due to thermal fluctuations. Conventional structural analyses based on spectroscopy or diffraction cannot determine the instantaneous structure exactly and can merely provide an averaged structure. Molecular simulations offer an opportunity to examine the assembly and evolution of metallic clusters, as the preferred assemblies and conformations can easily be visualized and explored. Here, we utilize the adaptive biasing force algorithm applied to first-principles molecular dynamics to demonstrate the exploration of a relatively simple system, which permits a comprehensive study of the small metal cluster Au₄ in both neutral and charged configurations. Our simulation work offers a quantitative understanding of these clusters' dynamic structure, which is significant for single-site catalytic reactions on metal clusters and provides a starting point for a detailed quantitative understanding of more complex pure metal and alloy clusters' dynamic properties.

Structural dynamics of Ru clusters during nitrogen dissociation in ammonia synthesis

The dynamic evolution of catalyst structures greatly influences the reactivity, especially sub-nanometer clusters, exhibiting complex configurational fluctuation. In the present work, we study the structural dynamics of a Ru₁₉ cluster during the dissociation of N₂ and calculate the reaction free energies using ab initio molecular dynamics (AIMD). Our AIMD calculation predicts a peak-shaped reaction entropy curve due to the adsorption-induced phase transition of the Ru₁₉ cluster. The low melting points of sub-nanometer clusters make it possible to activate N₂ at low temperatures. This work demonstrates that the dynamic changes of cluster structures have a non-negligible effect on reaction free energy and offer an opportunity for achieving ammonia synthesis under mild conditions.

Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis

Enhanced sampling ab initio simulations enable to study chemical phenomena in catalytic systems including thermal effects & anharmonicity, & collective dynamics describing enthalpic & entropic contributions, which can significantly impact on reaction free energy landscapes.

Stability and molecular pathways to the formation of spin defects in silicon carbide

Spin defects in wide-bandgap semiconductors provide a promising platform to create qubits for quantum technologies. Their synthesis, however, presents considerable challenges, and the mechanisms responsible for their generation or annihilation are poorly understood. Here, we elucidate spin defect formation processes in a binary crystal for a key qubit candidate-the divacancy complex (VV) in silicon carbide (SiC). Using atomistic models, enhanced sampling simulations, and density functional theory calculations, we find that VV formation is a thermally activated process that competes with the conversion of silicon (VSi) to carbon monovacancies (VC), and that VV reorientation can occur without dissociation. We also find that increasing the concentration of VSi relative to VC favors the formation of divacancies. Moreover, we identify pathways to create spin defects consisting of antisite-double vacancy complexes and determine their electronic properties. The detailed view of the mechanisms that underpin the formation and dynamics of spin defects presented here may facilitate the realization of qubits in an industrially relevant material.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Artificial Neural Networks

Nonadiabatic (NA) molecular dynamics (MD) allows one to study far-from-equilibrium processes involving excited electronic states coupled to atomic motions. While NAMD involves expensive calculations of excitation energies and NA couplings (NACs), ground-state properties require much less effort and can be obtained with machine learning (ML) at a fraction of the ab initio cost. Application of ML to excited states and NACs is more challenging, due to costly reference methods, many states, and complex geometry dependence. We developed a NAMD methodology that avoids time extrapolation of excitation energies and NACs. Instead, under the classical path approximation that employs a precomputed ground-state trajectory, we use a small fraction (2%) of the geometries to train neural networks and obtain excited-state energies and NACs for the remaining 98% of the geometries by interpolation. Demonstrated with metal halide perovskites that exhibit complex MD, the method provides nearly two orders of computational savings while generating accurate NAMD results.