Stochastic surface walking reaction sampling for resolving heterogeneous catalytic reaction network: A revisit to the mechanism of water-gas shift reaction on Cu

Δ2 machine learning for reaction property prediction

The emergence of Δ-learning models, whereby machine learning (ML) is used to predict a correction to a low-level energy calculation, provides a versatile route to accelerate high-level energy evaluations at a given geometry. However, Δ-learning models are inapplicable to reaction properties like heats of reaction and activation energies that require both a high-level geometry and energy evaluation. Here, a Δ2-learning model is introduced that can predict high-level activation energies based on low-level critical-point geometries. The Δ2 model uses an atom-wise featurization typical of contemporary ML interatomic potentials (MLIPs) and is trained on a dataset of ∼167 000 reactions, using the GFN2-xTB energy and critical-point geometry as a low-level input and the B3LYP-D3/TZVP energy calculated at the B3LYP-D3/TZVP critical point as a high-level target. The excellent performance of the Δ2 model on unseen reactions demonstrates the surprising ease with which the model implicitly learns the geometric deviations between the low-level and high-level geometries that condition the activation energy prediction. The transferability of the Δ2 model is validated on several external testing sets where it shows near chemical accuracy, illustrating the benefits of combining ML models with readily available physical-based information from semi-empirical quantum chemistry calculations. Fine-tuning of the Δ2 model on a small number of Gaussian-4 calculations produced a 35% accuracy improvement over DFT activation energy predictions while retaining xTB-level cost. The Δ2 model approach proves to be an efficient strategy for accelerating chemical reaction characterization with minimal sacrifice in prediction accuracy.

Deep reaction network exploration at a heterogeneous catalytic interface

Characterizing the reaction energies and barriers of reaction networks is central to catalyst development. However, heterogeneous catalytic surfaces pose several unique challenges to automatic reaction network characterization, including large sizes and open-ended reactant sets, that make ad hoc network construction the current state-of-the-art. Here, we show how automated network exploration algorithms can be adapted to the constraints of heterogeneous systems using ethylene oligomerization on silica-supported single-site Ga³⁺ as a model system. Using only graph-based rules for exploring the network and elementary constraints based on activation energy and size for identifying network terminations, a comprehensive reaction network is generated and validated against standard methods. The algorithm (re)discovers the Ga-alkyl-centered Cossee-Arlman mechanism that is hypothesized to drive major product formation while also predicting several new pathways for producing alkanes and coke precursors. These results demonstrate that automated reaction exploration algorithms are rapidly maturing towards general purpose capability for exploratory catalytic applications.

Elucidation of Cu-Zn Surface Alloying on Cu(997) by Machine-Learning Molecular Dynamics

The Cu-Zn surface alloy has been extensively involved in the investigation of the true active site of Cu/ZnO/Al₂O₃, the industrial catalyst for methanol synthesis which remains under controversy. The challenge lies in capturing the interplay between the surface and reaction under operating conditions, which can be overcome given that the explicit dynamics of the system is known. To provide a better understanding of the dynamic of Cu-Zn surface at the atomic level, the structure and the formation process of the Cu-Zn surface alloy on Cu(997) were investigated by machine-learning molecular dynamics (MD). Gaussian process regression aided with on-the-fly learning was employed to build the force field used in the MD. The simulation reveals atomistic details of the alloying process, that is, the incorporation of deposited Zn adatoms to the Cu substrate. The surface alloying is found to start at upper and lower terraces near the step edge, which emphasize the role of steps and kinks in the alloying. The incorporation of Zn at the middle terrace was found at the later stage of the simulation. The rationalization of alloying behavior was performed based on statistics and barriers of various elementary events that occur during the simulation. It was observed that the alloying scheme at the upper terrace is dominated by the confinement of Zn step adatoms by other adatoms, highlighting the importance of step fluctuations in the alloying process. On the other hand, the alloying scheme at the lower terrace is dominated by direct exchange between the Zn step adatom and the Cu atom underneath. The alloying at the middle terrace is dominated by the wave deposition mechanism and deep confinement of Zn adatoms. The short propagation of alloyed Zn in the middle terrace was observed to proceed by means of indirect exchange instead of local exchange as proposed in the previous scanning tunneling microscopy (STM) observation. The comparison of migration rate and activation energies to the result of STM observation is also made. We have found that at a certain distance from the surface, the STM tip significantly affects the elementary events such as vacancy formation and direct exchange.

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

Autonomous computations that rely on automated reaction network elucidation algorithms may pave the way to make computational catalysis on a par with experimental research in the field. Several advantages of this approach are key to catalysis: (i) automation allows one to consider orders of magnitude more structures in a systematic and open-ended fashion than what would be accessible by manual inspection. Eventually, full resolution in terms of structural varieties and conformations as well as with respect to the type and number of potentially important elementary reaction steps (including decomposition reactions that determine turnover numbers) may be achieved. (ii) Fast electronic structure methods with uncertainty quantification warrant high efficiency and reliability in order to not only deliver results quickly, but also to allow for predictive work. (iii) A high degree of autonomy reduces the amount of manual human work, processing errors, and human bias. Although being inherently unbiased, it is still steerable with respect to specific regions of an emerging network and with respect to the addition of new reactant species. This allows for a high fidelity of the formalization of some catalytic process and for surprising in silico discoveries. In this work, we first review the state of the art in computational catalysis to embed autonomous explorations into the general field from which it draws its ingredients. We then elaborate on the specific conceptual issues that arise in the context of autonomous computational procedures, some of which we discuss at an example catalytic system.

Dynamics of Heterogeneous Catalytic Processes at Operando Conditions

The rational design of high-performance catalysts is hindered by the lack of knowledge of the structures of active sites and the reaction pathways under reaction conditions, which can be ideally addressed by an in situ/operando characterization. Besides the experimental insights, a theoretical investigation that simulates reaction conditions-so-called operando modeling-is necessary for a plausible understanding of a working catalyst system at the atomic scale. However, there is still a huge gap between the current widely used computational model and the concept of operando modeling, which should be achieved through multiscale computational modeling. This Perspective describes various modeling approaches and machine learning techniques that step toward operando modeling, followed by selected experimental examples that present an operando understanding in the thermo- and electrocatalytic processes. At last, the remaining challenges in this area are outlined.

A reaction route network for methanol decomposition on a Pt(111) surface

A reaction route network for the decomposition reaction of methanol on a Pt(111) surface was constructed by using the artificial force-induced reaction (AFIR) method, which can search for reaction paths automatically and systematically. Then, the network was kinetically analyzed by applying the rate constant matrix contraction (RCMC) method. Specifically, the time hierarchy of the network, the time evolution of the population initially given to CH₃ OH to the other species on the network, and the most favorable route from CH₃ OH to major and minor products were investigated by the RCMC method. Consistently to previous studies, the major product on the network was CO+4H, and the most favorable route proceeded through the following steps: CH₃ OH → CH₂ OH+H → HCOH+2H → HCO+3H → CO+4H. Furthermore, paths to byproducts found on the network and their kinetic importance were discussed. The present procedure combining AFIR and RCMC was thus successful in explaining the title reaction without using any information on its product or the reaction mechanism.

In Situ Active Site for CO Activation in Fe-Catalyzed Fischer-Tropsch Synthesis from Machine Learning

In situ-formed iron carbides (FeC_x) are the key components responsible for Fischer-Tropsch synthesis (FTS, CO + H₂ → long-chain hydrocarbons) on Fe-based catalysts in industry. The true active site is, however, highly controversial despite more than a century of study, which is largely due to the combined complexity in both FeC_x structures and mechanism of CO hydrogenation. Herein powered by machine learning simulation, millions of structure candidates for FeC_x bulk and surfaces are explored under FTS conditions, which leads to resolving the active site for CO activation. This is achieved without a priori input from experiment by first constructing the thermodynamics convex hull of bulk phases, followed by identifying the low surface energy surfaces and evaluating the adsorption ability of CO and H, and finally determining the lowest energy reaction pathway of CO activation. Rich information on FeC_x structures and CO hydrogenation pathways is gleaned: (i) Fe₅C₂, Fe₇C₃, and Fe₂C are the three stable bulk phases under FTS in producing olefins, where Fe₇C₃ and Fe₂C have multiple energetically nearly degenerate bulk crystal phases; (ii) only three low surface energy surfaces of these bulk phases, namely, χ-Fe₅C₂(510), χ-Fe₅C₂(111), and η-Fe₂C(111), expose the Fe sites that can adsorb H atoms exothermically, where the surface Fe:C ratio is 2, 1.75, and 2, respectively; (iii) CO activation via direct dissociation can occur at the surface C vacancies (e.g., with a barrier of 1.1 eV) that are created dynamically via hydrogenation. These atomic-level understandings facilitate the building of the structure-activity correlation and designing better FT catalysts.

Perspective on computational reaction prediction using machine learning methods in heterogeneous catalysis

Heterogeneous catalysis plays a significant role in the modern chemical industry. Towards the rational design of novel catalysts, understanding reactions over surfaces is the most essential aspect. Typical industrial catalytic processes such as syngas conversion and methane utilisation can generate a large reaction network comprising thousands of intermediates and reaction pairs. This complexity not only arises from the permutation of transformations between species but also from the extra reaction channels offered by distinct surface sites. Despite the success in investigating surface reactions at the atomic scale, the huge computational expense of ab initio methods hinders the exploration of such complicated reaction networks. With the proliferation of catalysis studies, machine learning as an emerging tool can take advantage of the accumulated reaction data to emulate the output of ab initio methods towards swift reaction prediction. Here, we briefly summarise the conventional workflow of reaction prediction, including reaction network generation, ab initio thermodynamics and microkinetic modelling. An overview of the frequently used regression models in machine learning is presented. As a promising alternative to full ab initio calculations, machine learning interatomic potentials are highlighted. Furthermore, we survey applications assisted by these methods for accelerating reaction prediction, exploring reaction networks, and computational catalyst design. Finally, we envisage future directions in computationally investigating reactions and implementing machine learning algorithms in heterogeneous catalysis.

Reaction prediction via atomistic simulation: from quantum mechanics to machine learning

It is an ultimate goal in chemistry to predict reaction without recourse to experiment. Reaction prediction is not just the reaction rate determination of known reactions but, more broadly, the reaction exploration to identify new reaction routes. This review briefly overviews the theory on chemical reaction and the current methods for computing/estimating reaction rate and exploring reaction space. We particularly focus on the atomistic simulation methods for reaction exploration, which are benefited significantly by recently emerged machine learning potentials. We elaborate the stochastic surface walking global pathway sampling based on the global neural network (SSW-NN) potential, developed in our group since 2013, which can explore complex reactions systems unbiasedly and automatedly. Two examples, molecular reaction and heterogeneous catalytic reactions, are presented to illustrate the current status for reaction prediction using SSW-NN.

Understanding supported noble metal catalysts using first-principles calculations

Heterogeneous catalysis on supported and nonsupported nanoparticles is of fundamental importance in the energy and chemical conversion industries. Rather than laboratory analysis, first-principles calculations give us an atomic-level understanding of the structure and reactivity of nanoparticles and supports, greatly reducing the efforts of screening and design. However, unlike catalysis on low index single crystalline surfaces, nanoparticle catalysis relies on the tandem properties of a support material as well as the metal cluster itself, often with charge transfer processes being of key importance. In this perspective, we examine current state-of-the-art quantum-chemical research for the modeling of reactions that utilize small transition metal clusters on metal oxide supports. This should provide readers with useful insights when dealing with chemical reactions on such systems, before discussing the possibilities and challenges in the field.

Understanding CO oxidation on the Pt(111) surface based on a reaction route network

Kinetic analysis by the rate constant matrix contraction on the reaction route network of CO oxidation on the Pt(111) surface obtained by the artificial force induced reaction reveals the impact of entropic contributions arising from a variety of local minima and transition states.

Towards operando computational modeling in heterogeneous catalysis

An increased synergy between experimental and theoretical investigations in heterogeneous catalysis has become apparent during the last decade. Experimental work has extended from ultra-high vacuum and low temperature towards operando conditions. These developments have motivated the computational community to move from standard descriptive computational models, based on inspection of the potential energy surface at 0 K and low reactant concentrations (0 K/UHV model), to more realistic conditions. The transition from 0 K/UHV to operando models has been backed by significant developments in computer hardware and software over the past few decades. New methodological developments, designed to overcome part of the gap between 0 K/UHV and operando conditions, include (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased molecular dynamics, (iv) microkinetic models of reaction networks and (v) machine learning approaches. The importance of the transition is highlighted by discussing how the molecular level picture of catalytic sites and the associated reaction mechanisms changes when the chemical environment, pressure and temperature effects are correctly accounted for in molecular simulations. It is the purpose of this review to discuss each method on an equal footing, and to draw connections between methods, particularly where they may be applied in combination.