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

Leveraging Machine Learning Potentials for In-Situ Searching of Active sites in Heterogeneous Catalysis

This Perspective explores the integration of machine learning potentials (MLPs) in the research of heterogeneous catalysis, focusing on their role in identifying in situ active sites and enhancing the understanding of catalytic processes. MLPs utilize extensive databases from high-throughput density functional theory (DFT) calculations to train models that predict atomic configurations, energies, and forces with near-DFT accuracy. These capabilities allow MLPs to handle significantly larger systems and extend simulation times beyond the limitations of traditional ab initio methods. Coupled with global optimization algorithms, MLPs enable systematic investigations across vast structural spaces, making substantial contributions to the modeling of catalyst surface structures under reactive conditions. The review aims to provide a broad introduction to recent advancements and practical guidance on employing MLPs and also showcases several exemplary cases of MLP-driven discoveries related to surface structure changes under reactive conditions and the nature of active sites in heterogeneous catalysis. The prevailing challenges faced by this approach are also discussed.

Active learning-based automated construction of Hamiltonian for structural phase transitions: a case study on BaTiO3

The effective Hamiltonians have been widely applied to simulate the phase transitions in polarizable materials, with coefficients obtained by fitting to accurate first-principles calculations. However, it is tedious to generate distorted structures with symmetry constraints, in particular when high-ordered terms are considered. In this work, we implement and apply a Bayesian optimization-based approach to sample potential energy surfaces, automating the effective Hamiltonian construction by selecting distorted structures via active learning. Taking BaTiO3(BTO) as an example, we demonstrate that the effective Hamiltonian can be obtained using fewer than 30 distorted structures. Follow-up Monte Carlo simulations can reproduce the structural phase transition temperatures of BTO, comparable to experimental values with an error<10%. Our approach can be straightforwardly applied on other polarizable materials and paves the way for quantitative atomistic modelling of diffusionless phase transitions.

Machine Learning of Reactive Potentials

In the past two decades, machine learning potentials (MLPs) have driven significant developments in chemical, biological, and material sciences. The construction and training of MLPs enable fast and accurate simulations and analysis of thermodynamic and kinetic properties. This review focuses on the application of MLPs to reaction systems with consideration of bond breaking and formation. We review the development of MLP models, primarily with neural network and kernel-based algorithms, and recent applications of reactive MLPs (RMLPs) to systems at different scales. We show how RMLPs are constructed, how they speed up the calculation of reactive dynamics, and how they facilitate the study of reaction trajectories, reaction rates, free energy calculations, and many other calculations. Different data sampling strategies applied in building RMLPs are also discussed with a focus on how to collect structures for rare events and how to further improve their performance with active learning.

Structure Sensitivity of Metal Catalysts Revealed by Interpretable Machine Learning and First-Principles Calculations

The nature of the active sites and their structure sensitivity are the keys to rational design of efficient catalysts but have been debated for almost one century in heterogeneous catalysis. Though the Brønsted-Evans-Polanyi (BEP) relationship along with linear scaling relation has long been used to study the reactivity, explicit geometry, and composition properties are absent in this relationship, a fact that prevents its exploration in structure sensitivity of supported catalysts. In this work, based on interpretable multitask symbolic regression and a comprehensive first-principles data set, we discovered a structure descriptor, the topological under-coordinated number mediated by number of valence electrons and the lattice constant, to successfully address the structure sensitivity of metal catalysts. The database used for training, testing, and transferability investigation includes bond-breaking barriers of 20 distinct chemical bonds over 10 transition metals, two metal crystallographic phases, and 17 different facets. The resulting 2D descriptor composing the structure term and the reaction energy term shows great accuracy to predict the reaction barriers and generalizability over the data set with diverse chemical bonds in symmetry, bond order, and steric hindrance. The theory is physical and concise, providing a constructive strategy not only to understand the structure sensitivity but also to decipher the entangled geometric and electronic effects of metal catalysts. The insights revealed are valuable for the rational design of the site-specific metal catalysts.

Indirect Measurement of Variables in a Heterogeneous Reaction for Biodiesel Production

This research focuses on the development of a state observer for performing indirect measurements of the main variables involved in the soybean oil transesterification reaction with a guishe biochar-based heterogeneous catalyst; the studied reaction takes place in a batch reactor. The mathematical model required for the observer design includes the triglycerides' conversion rate, and the reaction temperature. Since these variables are represented by nonlinear differential equations, the model is linearized around an operation point; after that, the pole placement and linear quadratic regulator (LQR) methods are considered for calculating the observer gain vector L(x). Then, the estimation of the conversion rate and the reaction temperature provided by the observer are used to indirectly measure other variables such as esters, alcohol, and byproducts. The observer performance is evaluated with three error indexes considering initial condition variations up to 30%. With both methods, a fast convergence (less than 3 h in the worst case) of the observer is remarked.

Using a single complex to predict the reaction energy profile: a case study of Pd/Ni-catalyzed ethylene polymerization

Mechanism-driven catalyst screening could be greatly accelerated by quantitative prediction models of the reaction energy profile. Here, we propose a novel method for molecular representation, taking palladium- and nickel-catalyzed ethylene polymerization as model reactions. The geometric parameters (GPfra) and electron occupancies (EOfra) from the non-ligand fragment of the η3-complex were extracted as the molecular descriptors, followed by constructing the reaction energy profile prediction models on the basis of various regression algorithms. The models showed great accuracy with respect to both theoretical and experimental data. More importantly, the models are convenient for training and utilization. On one hand, all the features were easily captured from the single η3-complex. On the other hand, further investigation also demonstrated that the models could be constructed with a small training sample size. We believe that our featurization method could possibly be generalized to more organometallic reactions and paves the way to efficient catalyst design.

Designing main-group catalysts for low-temperature methane combustion by ozone

The catalytic combustion of methane at a low temperature is becoming increasingly key to controlling unburned CH₄ emissions from natural gas vehicles and power plants, although the low activity of benchmark platinum-group-metal catalysts hinders its broad application. Based on automated reaction route mapping, we explore main-group elements catalysts containing Si and Al for low-temperature CH₄ combustion with ozone. Computational screening of the active site predicts that strong Brønsted acid sites are promising for methane combustion. We experimentally demonstrate that catalysts containing strong Bronsted acid sites exhibit improved CH₄ conversion at 250 °C, correlating with the theoretical predictions. The main-group catalyst (proton-type beta zeolite) delivered a reaction rate that is 442 times higher than that of a benchmark catalyst (5 wt% Pd-loaded Al₂O₃) at 190 °C and exhibits higher tolerance to steam and SO₂. Our strategy demonstrates the rational design of earth-abundant catalysts based on automated reaction route mapping.

Comprehensive Study of Oxygen Vacancies on the Catalytic Performance of ZnO for CO/H2 Activation Using Machine Learning-Accelerated First-Principles Simulations

Oxygen vacancies (OVs) play important roles on any oxide catalysts. In this work, using an investigation of the OV effects on ZnO(101̅0) for CO and H₂ activation as an example, we demonstrate, via machine learning potentials (MLPs), genetic algorithm (GA)-based global optimization, and density functional theory (DFT) validations, that the ZnO(101̅0) surface with 0.33 ML OVs is the most likely surface configuration under experimental conditions (673 K and 2.5 MPa syngas (H₂:CO = 1.5)). It is found that a surface reconstruction from the wurtzite structure to a body-centered-tetragonal one would occur in the presence of OVs. We show that the OVs create a Zn₃ cluster site, allowing H₂ homolysis and C-O bond cleavage to occur. Furthermore, the activity of intrinsic sites (Zn_3c and O_3c sites) is almost invariable, while the activity of the generated OV sites is strongly dependent on the concentration of the OVs. It is also found that OV distributions on the surface can considerably affect the reactions; the barrier of C-O bond dissociation is significantly reduced when the OVs are aligned along the [12̅10] direction. These findings may be general in the systems with metal oxides in heterogeneous catalysis and may have significant impacts on the field of catalyst design by regulating the concentration and distribution of the OVs.

An automated reaction route mapping for the reaction of NO and active species on Ag4 clusters in zeolites

A computational investigation of the catalytic reaction on multinuclear sites is very challenging. Here, using an automated reaction route mapping method, the single-component artificial force induced reaction (SC-AFIR) algorithm, the catalytic reaction of NO and OH/OOH species over the Ag₄²⁺ cluster in a zeolite is investigated. The results of the reaction route mapping for H₂ + O₂ reveal that OH and OOH species are formed over the Ag₄²⁺ cluster via an activation barrier lower than that of OH formation from H₂O dissociation. Then, reaction route mapping is performed to examine the reactivity of the OH and OOH species with NO molecules over the Ag₄²⁺ cluster, resulting in the facile reaction path of HONO formation. With the aid of the automated reaction route mapping, the promotion effect of H₂ addition on the SCR reaction was computationally proposed (boosting the formation of OH and OOH species). In addition, the present study emphasizes that automated reaction route mapping is a powerful tool to elucidate the complicated reaction pathway on multi-nuclear clusters.

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.

Machine Learning Models Predict Calculation Outcomes with the Transferability Necessary for Computational Catalysis

Virtual high-throughput screening (VHTS) and machine learning (ML) have greatly accelerated the design of single-site transition-metal catalysts. VHTS of catalysts, however, is often accompanied with a high calculation failure rate and wasted computational resources due to the difficulty of simultaneously converging all mechanistically relevant reactive intermediates to expected geometries and electronic states. We demonstrate a dynamic classifier approach, i.e., a convolutional neural network that monitors geometry optimizations on the fly, and exploit its good performance and transferability in identifying geometry optimization failures for catalyst design. We show that the dynamic classifier performs well on all reactive intermediates in the representative catalytic cycle of the radical rebound mechanism for the conversion of methane to methanol despite being trained on only one reactive intermediate. The dynamic classifier also generalizes to chemically distinct intermediates and metal centers absent from the training data without loss of accuracy or model confidence. We rationalize this superior model transferability as arising from the use of electronic structure and geometric information generated on-the-fly from density functional theory calculations and the convolutional layer in the dynamic classifier. When used in combination with uncertainty quantification, the dynamic classifier saves more than half of the computational resources that would have been wasted on unsuccessful calculations for all reactive intermediates being considered.

Achieving Theory-Experiment Parity for Activity and Selectivity in Heterogeneous Catalysis Using Microkinetic Modeling

Microkinetic modeling based on density functional theory (DFT) energies plays an essential role in heterogeneous catalysis because it reveals the fundamental chemistry for catalytic reactions and bridges the microscopic understanding from theoretical calculations and experimental observations. Microkinetic modeling requires building a set of ordinary differential equations (ODEs) based on the calculation results of thermodynamic properties of adsorbates and kinetic parameters for the reaction elementary steps. Solving a microkinetic model can extract information on catalytic chemistry, including critical reaction intermediates, reaction pathways, the surface species distribution, activity, and selectivity, thus providing vital guidelines for altering catalysts.

However, the quantitative reliability of traditional microkinetic models is often insufficient to conclusively extrapolate the mechanistic details of complex reaction systems. This can be attributed to several factors, the most important of which is the limitation of obtaining an accurate estimation of the energy inputs via traditional calculation methods. These limitations include the difficulty of using static DFT methods to calculate reaction energies of adsorption/desorption processes, often rate-controlling or selectivity-determining steps, and the inadequate consideration of surface coverage effects. In addition, the robust microkinetic software is rare, which also complicates the resolution of complex catalytic systems.

In this Account, we review our recent works toward refining the predictions of microkinetic modeling in heterogeneous catalysis and achieving theory–experiment parity for activity and selectivity. First, we introduce CATKINAS, a microkinetic software developed in our group, and show how it disentangles the problem that traditional microkinetic software has and how it can now be applied to obtain kinetic results for more sophisticated reaction systems. Second, we describe a molecular dynamics method developed recently to obtain the free-energy changes for the adsorption/desorption process to fill in the missing energy inputs. Third, we show that a rigorous consideration of surface coverage effects is pivotal for building more realistic models and obtaining accurate kinetic results. Following a series of studies on acetylene hydrogenation reactions on Pd catalysts, we demonstrate how this new approach can provide an improved quantitative understanding of the mechanism, active site, and intrinsic structural sensitivity. Finally, we conclude with a brief outlook and the remaining challenges in this field.

Kinetic Monte Carlo simulations for heterogeneous catalysis: Fundamentals, current status, and challenges

Kinetic Monte Carlo (KMC) simulations in combination with first-principles (1p)-based calculations are rapidly becoming the gold-standard computational framework for bridging the gap between the wide range of length scales and time scales over which heterogeneous catalysis unfolds. 1p-KMC simulations provide accurate insights into reactions over surfaces, a vital step toward the rational design of novel catalysts. In this Perspective, we briefly outline basic principles, computational challenges, successful applications, as well as future directions and opportunities of this promising and ever more popular kinetic modeling approach.

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.

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SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s11244-021-01543-9.

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.

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.

Structure-Based Relative Energy Prediction Model: A Case Study of Pd(II)-Catalyzed Ethylene Polymerization and the Electronic Effect of Ancillary Ligands

Rapidly mapping a reaction energy profile to understand the reaction mechanism is of great importance and highly desired for the discovery of new chemical reactions. Herein, a combination of density functional theory (DFT) calculations and regression analysis has been applied to construct quantitative structures-based energy prediction models, considering Pd(II)-catalyzed ethylene polymerization as an example, for rapid construction of the reaction energy profile. It is inspiring that only geometrical parameters of the reaction center of one species are capable of predicting the whole energy profile with high accuracy. The reaction energies of ethylene insertion and β-H elimination, which directly correlate with polymerization activity and the possibility of branch formation, were studied to elucidate the electronic effects of ancillary ligands. Further analyses of these models from the statistical and chemical points of view afforded useful information on the design of the catalyst ligand. The current work is expected to methodologically shed new light on rapidly mapping the energy profile of chemical reactions and further provide useful information for the development of the reactions.