Theoretical Heterogeneous Catalysis: Scaling Relationships and Computational Catalyst Design

Locally Varying Surface Binding Affinity on Pd-Au Nanocrystals Enhances Electrochemical Ethanol Oxidation Activity

Noble metal nanocrystals face challenges in effectively catalyzing electrochemical ethanol oxidation reaction (EOR)-represented multistep, multielectron transfer processes due to the linear scaling relationship among binding energies of intermediates, impeding independent optimization of individual elemental steps. Herein, we develop noble metal nanocrystals with a range of local surface binding affinities in close proximity to overcome this challenge. Experimentally, this is demonstrated by applying tensile strain to a Pd surface and decorating it with discrete Au atoms, forming a diversity of binding sites with varying affinities in close proximity for guest molecules, as evidenced by CO probing and density functional theory calculations. Such a surface enables reaction intermediates to migrate between different binding sites as needed for each elemental step, thereby reducing the energy barrier for the overall EOR when compared to reactions at a single site. On these tailored surfaces, we attain specific and mass activities of 32.7 mA cm-2 and 47.8 A mgPd-1 in EOR, surpassing commercial Pd/C by 10.9 and 43.8 times, respectively, and outperforming state-of-the-art Pd-based catalysts. These results highlight the promise of this approach in improving a variety of multistep, multielectron transfer reactions, which are crucial for energy conversion applications.

Advancing electrocatalytic reactions through mapping key intermediates to active sites via descriptors

Descriptors play a crucial role in electrocatalysis as they can provide valuable insights into the electrochemical performance of energy conversion and storage processes. They allow for the understanding of different catalytic activities and enable the prediction of better catalysts without relying on the time-consuming trial-and-error approaches. Hence, this comprehensive review focuses on highlighting the significant advancements in commonly used descriptors for critical electrocatalytic reactions. First, the fundamental reaction processes and key intermediates involved in several electrocatalytic reactions are summarized. Subsequently, three types of descriptors are classified and introduced based on different reactions and catalysts. These include d-band center descriptors, readily accessible intrinsic property descriptors, and spin-related descriptors, all of which contribute to a profound understanding of catalytic behavior. Furthermore, multi-type descriptors that collectively determine the catalytic performance are also summarized. Finally, we discuss the future of descriptors, envisioning their potential to integrate multiple factors, broaden application scopes, and synergize with artificial intelligence for more efficient catalyst design and discovery.

A role for conformational changes in enzyme catalysis

The role played by conformational changes in enzyme catalysis is controversial. In addition to examining specific enzymes, studying formal models can help identify the conditions under which conformational changes promote catalysis. Here, we present a model demonstrating how conformational changes can break a generic trade-off due to the conflicting requirements of successive steps in catalytic cycles, namely high specificity for the transition state to accelerate the chemical transformation and low affinity for the products to favor their release. The mechanism by which the trade-off is broken is a transition between conformations with different affinities for the substrate. The role of the effector that induces the transition is played by a substrate "handle," a part of the substrate that is not chemically transformed but whose interaction with the enzyme is nevertheless essential to rapidly complete the catalytic cycle. A key element of the model is the formalization of the constraints causing the trade-off that the presence of multiple states breaks, which we attribute to the strong chemical similarity between successive reaction states-substrates, transition states, and products. For the sake of clarity, we present our model for irreversible one-step unimolecular reactions. In this context, we demonstrate how the different forms that chemical similarities between reaction states can take impose limits on the overall catalytic turnover. We first analyze catalysts without internal degrees of freedom and then show how two-state catalysts can overcome their limitations. Our results recapitulate previous proposals concerning the role of conformational changes and substrate handles in a formalism that makes explicit the constraints that elicit these features. In addition, our approach establishes links with studies in the field of heterogeneous catalysis, where the same trade-offs are observed and where overcoming them is a well-recognized challenge.

Engineering Frustrated Lewis Pair Active Sites in Porous Organic Scaffolds for Catalytic CO2 Hydrogenation

Frustrated Lewis pairs (FLPs), featuring reactive combinations of Lewis acids and Lewis bases, have been utilized for myriad metal-free homogeneous catalytic processes. Immobilizing the active Lewis sites to a solid support, especially to porous scaffolds, has shown great potential to ameliorate FLP catalysis by circumventing some of its inherent drawbacks, such as poor product separation and catalyst recyclability. Nevertheless, designing immobilized Lewis pair active sites (LPASs) is challenging due to the requirement of placing the donor and acceptor centers in appropriate geometric arrangements while maintaining the necessary chemical environment to perform catalysis, and clear design rules have not yet been established. In this work, we formulate simple guidelines to build highly active LPASs for direct catalytic hydrogenation of CO2 through a large-scale screening of a diverse library of 25,000 immobilized FLPs. The library is built by introducing boron-containing acidic sites in the vicinity of the existing basic nitrogen sites of the organic linkers of metal-organic frameworks collected in a "top-down" fashion from the CoRE MOF 2019 database. The chemical and geometrical appropriateness of these LPASs for CO2 hydrogenation is determined by evaluating a series of simple descriptors representing the intrinsic strength (acidity and basicity) of the components and their spatial arrangement in the active sites. Analysis of the leading candidates enables the formulation of pragmatic and experimentally relevant design principles which constitute the starting point for further exploration of FLP-based catalysts for the reduction of CO2.

Machine Learning-Accelerated High-Throughput Computational Screening: Unveiling Bimetallic Nanoparticles with Peroxidase-Like Activity

Bimetallic nanoparticles (NPs) with peroxidase-like (POD-like) activity play a crucial role in biosensing, disease treatment, environmental management, and other fields. However, their development is impeded by a vast range of tunable properties in components and structures, making the establishment of structure-effect relationships and the discovery of active materials challenging. Addressing this, we established robust scaling relationships by meticulously analyzing the catalytic reaction networks of pure metal NPs, which laid the volcano-shaped correlation between the activity and O* adsorption energy. Utilizing these relationships, we introduced an innovative and versatile descriptor of the NPs, which was then integrated into a machine learning-accelerated high-throughput computational workflow, significantly boosting the predictive accuracy for the POD-like activity of bimetallic NPs. Our methodological approach enabled the successful prediction of activities for 1260 bimetallic NPs, leading to the identification of several highly effective catalysts. Furthermore, we distilled several strategies for designing efficient bimetallic NPs based on our screening results.

Optimization of Electrochemical Reduction of Biomass Derived 5-Hydroxymethylfurfural (HMF): A Volcano Plot and Bimetallic Catalysts

2,5-bis(hydroxymethyl)furan (BHMF) derived from 5-Hydroxymethylfurfural (HMF) through a hydrogenation process has extensive applications in the production of resins, polymers, and artificial fibers. However, screening out the candidate and then modulating the active site to optimize the catalyst for high yield of BHMF are currently insufficient. In this study, Gibbs free energy diagrams of the reduction of HMF on 13 metals were presented, along with the identification of the rate-determining step (RDS) with the highest reaction barrier for each metal. We attempted to construct a volcano plot for HMFRR reaction. Additionally, a strategy was proposed to adjust the reaction barriers of RDS by combining two appropriate metals. Further experiments confirmed that Pb with the lowest energy barrier exhibited the highest HMF conversion (BHMF selectivity) among single metals. The modified catalyst by doping Ag on Pb, further boosted the HMF conversion (BHMF selectivity) from 42.1 % (59.4 %) to 80.8 % (80.9 %), respectively. These results provide an approach to rationally design and construct the catalyst system for efficient conversion of HMF.

Accessing the usefulness of atomic adsorption configurations in predicting the adsorption properties of molecules with machine learning

We present a systematic study into the effect of adding atomic adsorption configurations into the training and validation dataset for a neural network's predictions of the adsorption energies of small molecules on single metal and bimetallic, single crystal surfaces. Specifically, we examine the efficacy of models trained with and without H and X atomic adsorption configurations, where X is C, N, or O, to predict XHn adsorption energies. In addition, we compare our machine learning models to traditional simple scaling relationships. We find that models trained with the atomic adsorption configurations outperform models trained with only molecular adsorption configurations, with as much as a 0.37 eV decrease in the MAE. We find that models trained with the atomic adsorption configurations slightly outperform traditional scaling relationships. In general, these results suggest it may be possible to vastly reduce the number of adsorption configurations one needs for training and validation datasets by supplementing said data with the adsorption configurations of composite atoms or smaller molecular fragments.

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.

Thermodynamic and Kinetic Activity Descriptors for the Catalytic Hydrogenation of Ketones

Activity descriptors are a powerful tool for the design of catalysts that can efficiently utilize H2 with minimal energy losses. In this study, we develop the use of hydricity and H- self-exchange rates as thermodynamic and kinetic descriptors for the hydrogenation of ketones by molecular catalysts. Two complexes with known hydricity, HRh(dmpe)2 and HCo(dmpe)2, were investigated for the catalytic hydrogenation of ketones under mild conditions (1.5 atm and 25 °C). The rhodium catalyst proved to be an efficient catalyst for a wide range of ketones, whereas the cobalt catalyst could only hydrogenate electron-deficient ketones. Using a combination of experiment and electronic structure theory, thermodynamic hydricity values were established for 46 alkoxide/ketone pairs in both acetonitrile and tetrahydrofuran solvents. Through comparison of the hydricities of the catalysts and substrates, it was determined that catalysis was observed only for catalyst/ketone pairs with an exergonic H- transfer step. Mechanistic studies revealed that H- transfer was the rate-limiting step for catalysis, allowing for the experimental and computation construction of linear free-energy relationships (LFERs) for H- transfer. Further analysis revealed that the LFERs could be reproduced using Marcus theory, in which the H- self-exchange rates for the HRh/Rh+ and ketone/alkoxide pairs were used to predict the experimentally measured catalytic barriers within 2 kcal mol-1. These studies significantly expand the scope of catalytic reactions that can be analyzed with a thermodynamic hydricity descriptor and firmly establish Marcus theory as a valid approach to develop kinetic descriptors for designing catalysts for H- transfer reactions.

Developing Cheap but Useful Machine Learning-Based Models for Investigating High-Entropy Alloy Catalysts

This work aims to address the challenge of developing interpretable ML-based models when access to large-scale computational resources is limited. Using CoMoFeNiCu high-entropy alloy catalysts as an example, we present a cost-effective workflow that synergistically combines descriptor-based approaches, machine learning-based force fields, and low-cost density functional theory (DFT) calculations to predict high-quality adsorption energies for H, N, and NHx (x = 1, 2, and 3) adsorbates. This is achieved using three specific modifications to typical DFT workflows including: (1) using a sequential optimization protocol, (2) developing a new geometry-based descriptor, and (3) repurposing the already-available low-cost DFT optimization trajectories to develop a ML-FF. Taken together, this study illustrates how cost-effective DFT calculations and appropriately designed descriptors can be used to develop cheap but useful models for predicting high-quality adsorption energies at significantly lower computational costs. We anticipate that this resource-efficient philosophy may be broadly relevant to the larger surface catalysis community.

Unravelling CO2 Reduction Reaction Intermediates on High Entropy Alloy Catalysts: An Interpretable Machine Learning Approach to Establish Scaling Relations

Establishment of a scaling relation among the reaction intermediates is highly important but very much challenging on complex surfaces, such as surfaces of high entropy alloys (HEAs). Herein, we designed an interpretable machine learning (ML) approach to establish a scaling relation among CO2 reduction reaction (CO2 RR) intermediates adsorbed at the same adsorption site. Local Interpretable Model-Agnostic Explanations (LIME), Accumulated Local Effects (ALE), and Permutation Feature Importance (PFI) are used for the global and local interpretation of the utilized black box models. These methods were successfully applied through an iterative way and validated on CuCoNiZnMg and CuCoNiZnSnbased HEAs data. Finally, we successfully predicted adsorption energies of *H2 CO (MAE: 0.24 eV) and *H3 CO (MAE: 0.23 eV) by using the *HCO training data. Similarly, adsorption energy of *O (MAE: 0.32 eV) is also predicted from *H training data. We believe that our proposed method can shift the paradigm of state-of-the-art ML in catalysis towards better interpretability.

Invariant Molecular Representations for Heterogeneous Catalysis

Catalyst screening is a critical step in the discovery and development of heterogeneous catalysts, which are vital for a wide range of chemical processes. In recent years, computational catalyst screening, primarily through density functional theory (DFT), has gained significant attention as a method for identifying promising catalysts. However, the computation of adsorption energies for all likely chemical intermediates present in complex surface chemistries is computationally intensive and costly due to the expensive nature of these calculations and the intrinsic idiosyncrasies of the methods or data sets used. This study introduces a novel machine learning (ML) method to learn adsorption energies from multiple DFT functionals by using invariant molecular representations (IMRs). To do this, we first extract molecular fingerprints for the reaction intermediates and later use a Siamese-neural-network-based training strategy to learn invariant molecular representations or the IMR across all available functionals. Our Siamese network-based representations demonstrate superior performance in predicting adsorption energies compared with other molecular representations. Notably, when considering mean absolute values of adsorption energies as 0.43 eV (PBE-D3), 0.46 eV (BEEF-vdW), 0.81 eV (RPBE), and 0.37 eV (scan+rVV10), our IMR method has achieved the lowest mean absolute errors (MAEs) of 0.18 0.10, 0.16, and 0.18 eV, respectively. These results emphasize the superior predictive capacity of our Siamese network-based representations. The empirical findings in this study illuminate the efficacy, robustness, and dependability of our proposed ML paradigm in predicting adsorption energies, specifically for propane dehydrogenation on a platinum catalyst surface.

Titanium Oxycarbide as Platinum-Free Electrocatalyst for Ethanol Oxidation

The compound material titanium oxycarbide (TiOC) is found to be an effective electrocatalyst for the electrochemical oxidation of ethanol to CO2. The complete course of this reaction is one of the main challenges in direct ethanol fuel cells (DEFCs). While TiOC has previously been investigated as catalyst support material only, in this study we show that TiOC alone is able to oxidize ethanol to acetaldehyde without the need of expensive noble metal catalysts like Pt. It is suggested that this behavior is attributed to the presence of both undercoordinated sites, which allow ethanol to adsorb, and oxygenated sites, which facilitate the activation of water. This is a milestone in DEFC research and development and opens up innovative possibilities for the design of catalyst materials for intermediate temperature fuel cells.

Origin of Stability and Activity Enhancements in Pt-based Oxygen Reduction Reaction Catalysts via Defect-Mediated Dopant Adsorption

Platinum alloys are highly efficient electrocatalysts for the oxygen reduction reaction (ORR) in acidic conditions. However, these alloys are susceptible to metal loss through leaching and degradation, leading to reduced catalyst stability and activity. Recently, it has been shown that doping with oxophilic elements can significantly alleviate these problems, with a prominent example being Mo-doped Pt alloys. Here, to achieve atomic scale understanding of the exceptional activity and stability of these alloys, we present a detailed density functional theory description of the dopants' structures and impact on electrocatalyst properties. Beginning with the Mo/Pt system, we demonstrate that Mo can be stabilized in the form of low-dimensional oxyhydroxide moieties on Pt defects. The resulting structures enhance stability and activity via distinct physical processes, with the Mo moieties both directly inhibiting Pt dissolution at defects and indirectly enhancing ORR activity by generation of strain fields on surrounding Pt terraces. We then generalize these analyses to other metal dopant elements, and we demonstrate that similar low-dimensional oxyhydroxide structures control the electrocatalytic properties through an intricate interplay of the structures' acid stability, intrinsic activity for the ORR, and ability to induce ORR-promoting strain fields on Pt.

Theoretical Insight into the Special Synergy of Bimetallic Site in Co/MoC Catalyst to Promote N2 -to-NH3 Conversion

The catalytic mechanisms of nitrogen reduction reaction (NRR) on the pristine and Co/α-MoC(001) surfaces were explored by density functional theory calculations. The results show that the preferred pathway is that a direct N≡N cleavage occurs first, followed by continuous hydrogenations. The production of second NH3 molecule is identified as the rate-limiting step on both systems with kinetic barriers of 1.5 and 2.0 eV, respectively, indicating that N2 -to-NH3 transformation on bimetallic surface is more likely to occur. The two components of the bimetallic center play different roles during NRR process, in which Co atom does not directly participate in the binding of intermediates, but primarily serves as a reservoir of H atoms. This special synergy makes Co/α-MoC(001) have superior activity for ammonia synthesis. The introduction of Co not only facilitates N2 dissociation, but also accelerates the migration of H atom due to the antibonding characteristic of Co-H bond. This study offers a facile strategy for the rational design and development of efficient catalysts for ammonia synthesis and other reactions involving the hydrogenation processes.

Elucidating the Reactivity of Oxygenates on Single-Atom Alloy Catalysts

Doping isolated transition metal atoms into the surface of coinage-metal hosts to form single-atom alloys (SAAs) can significantly improve the catalytic activity and selectivity of their monometallic counterparts. These atomically dispersed dopant metals on the SAA surface act as highly active sites for various bond coupling and activation reactions. In this study, we investigate the catalytic properties of SAAs with different bimetallic combinations [Ni-, Pd-, Pt-, and Rh-doped Cu(111), Ag(111), and Au(111)] for chemistries involving oxygenates relevant to biomass reforming. Density functional theory is employed to calculate and compare the formation energies of species such as methoxy (CH3O), methanol (CH3OH), and hydroxymethyl (CH2OH), thereby understanding the stability of these adsorbates on SAAs. Activation energies and reaction energies of C-O coupling, C-H activation, and O-H activation on these oxygenates are then computed. Analysis of the data in terms of thermochemical linear scaling and Bro̷nsted-Evans-Polanyi relationship shows that some SAAs have the potential to combine weak binding with low activation energies, thereby exhibiting enhanced catalytic behavior over their monometallic counterparts for key elementary steps of oxygenate conversion. This work contributes to the discovery and development of SAA catalysts toward greener technologies, having potential applications in the transition from fossil to renewable fuels and chemicals.

Intermetallic Nanocrystals for Fuel-Cells-Based Electrocatalysis

Electrocatalysis underpins the renewable electrochemical conversions for sustainability, which further replies on metallic nanocrystals as vital electrocatalysts. Intermetallic nanocrystals have been known to show distinct properties compared to their disordered counterparts, and been long explored for functional improvements. Tremendous progresses have been made in the past few years, with notable trend of more precise engineering down to an atomic level and the investigation transferring into more practical membrane electrode assembly (MEA), which motivates this timely review. After addressing the basic thermodynamic and kinetic fundamentals, we discuss classic and latest synthetic strategies that enable not only the formation of intermetallic phase but also the rational control of other catalysis-determinant structural parameters, such as size and morphology. We also demonstrate the emerging intermetallic nanomaterials for potentially further advancement in energy electrocatalysis. Then, we discuss the state-of-the-art characterizations and representative intermetallic electrocatalysts with emphasis on oxygen reduction reaction evaluated in a MEA setup. We summarize this review by laying out existing challenges and offering perspective on future research directions toward practicing intermetallic electrocatalysts for energy conversions.

Realistic Modeling of the Electrocatalytic Process at Complex Solid-Liquid Interface

The rational design of electrocatalysis has emerged as one of the most thriving means for mitigating energy and environmental crises. The key to this effort is the understanding of the complex electrochemical interface, wherein the electrode potential as well as various internal factors such as H-bond network, adsorbate coverage, and dynamic behavior of the interface collectively contribute to the electrocatalytic activity and selectivity. In this context, the authors have reviewed recent theoretical advances, and especially, the contributions to modeling the realistic electrocatalytic processes at complex electrochemical interfaces,  and illustrated the challenges and fundamental problems in this field. Specifically, the significance of the inclusion of explicit solvation and electrode potential as well as the strategies toward the design of highly efficient electrocatalysts are discussed. The structure-activity relationships and their dynamic responses to the environment and catalytic functionality under working conditions are illustrated to be crucial factors for understanding the complexed interface and the electrocatalytic activities. It is hoped that this review can help spark new research passion and ultimately bring a step closer to a realistic and systematic modeling method for electrocatalysis.

Machine Learning-Based Prediction of Activation Energies for Chemical Reactions on Metal Surfaces

In computational surface catalysis, the calculation of activation energies of chemical reactions is expensive, which, in many cases, limits our ability to understand complex reaction networks. Here, we present a universal, machine learning-based approach for the prediction of activation energies for reactions of C-, O-, and H-containing molecules on transition metal surfaces. We rely on generalized Bronsted-Evans-Polanyi relationships in combination with machine learning-based multiparameter regression techniques to train our model for reactions included in the University of Arizona Reaction database. In our best approach, we find a mean absolute error for activation energies within our test set of 0.14 eV if the reaction energy is known and 0.19 eV if the reaction energy is unknown. We expect that this methodology will often replace the explicit calculation of activation energies within surface catalysis when exploring large reaction networks or screening catalysts for desirable properties in the future.

Toward Quantum Chemical Free Energy Simulations of Platinum Nanoparticles on Titania Support

Platinum nanoparticles (Pt-NPs) supported on titania surfaces are costly but indispensable heterogeneous catalysts because of their highly effective and selective catalytic properties. Therefore, it is vital to understand their physicochemical processes during catalysis to optimize their use and to further develop better catalysts. However, simulating these dynamic processes is challenging due to the need for a reliable quantum chemical method to describe chemical bond breaking and bond formation during the processes but, at the same time, fast enough to sample a large number of configurations required to compute the corresponding free energy surfaces. Density functional theory (DFT) is often used to explore Pt-NPs; nonetheless, it is usually limited to some minimum-energy reaction pathways on static potential energy surfaces because of its high computational cost. We report here a combination of the density functional tight binding (DFTB) method as a fast but reliable approximation to DFT, the steered molecular dynamics (SMD) technique, and the Jarzynski equality to construct free energy surfaces of the temperature-dependent diffusion and growth of platinum particles on a titania surface. In particular, we present the parametrization for Pt-X (X = Pt, Ti, or O) interactions in the framework of the second-order DFTB method, using a previous parametrization for titania as a basis. The optimized parameter set was used to simulate the surface diffusion of a single platinum atom (Pt1) and the growth of Pt6 from Pt5 and Pt1 on the rutile (110) surface at three different temperatures (T = 400, 600, 800 K). The free energy profile was constructed by using over a hundred SMD trajectories for each process. We found that increasing the temperature has a minimal effect on the formation free energy; nevertheless, it significantly reduces the free energy barrier of Pt atom migration on the TiO2 surface and the transition state (TS) of its deposition. In a concluding remark, the methodology opens the pathway to quantum chemical free energy simulations of Pt-NPs' temperature-dependent growth and other transformation processes on the titania support.

Thermodynamic and kinetic modeling of electrocatalytic reactions using a first-principles approach

The computational modeling of electrochemical interfaces and their applications in electrocatalysis has attracted great attention in recent years. While tremendous progress has been made in this area, however, the accurate atomistic descriptions at the electrode/electrolyte interfaces remain a great challenge. The Computational Hydrogen Electrode (CHE) method and continuum modeling of the solvent and electrolyte interactions form the basis for most of these methodological developments. Several posterior corrections have been added to the CHE method to improve its accuracy and widen its applications. The most recently developed grand canonical potential approaches with the embedded diffuse layer models have shown considerable improvement in defining interfacial interactions at electrode/electrolyte interfaces over the state-of-the-art computational models for electrocatalysis. In this Review, we present an overview of these different computational models developed over the years to quantitatively probe the thermodynamics and kinetics of electrochemical reactions in the presence of an electrified catalyst surface under various electrochemical environments. We begin our discussion by giving a brief picture of the different continuum solvation approaches, implemented within the ab initio method to effectively model the solvent and electrolyte interactions. Next, we present the thermodynamic and kinetic modeling approaches to determine the activity and stability of the electrocatalysts. A few applications to these approaches are also discussed. We conclude by giving an outlook on the different machine learning models that have been integrated with the thermodynamic approaches to improve their efficiency and widen their applicability.

How Flexibility Can Enhance Catalysis

Conformational changes are observed in many enzymes, but their role in catalysis is highly controversial. Here we present a theoretical model that illustrates how rigid catalysts can be fundamentally limited and how a conformational change induced by substrate binding can overcome this limitation, ultimately enabling barrier-free catalysis. The model is deliberately minimal, but the principle it illustrates is general and consistent with unique features of proteins as well as with previous informal proposals to explain the superiority of enzymes over other classes of catalysts. Implementing the discriminative switch suggested by the model could help overcome limitations currently encountered in the design of artificial catalysts.

Exploring Metal Nanocluster Catalysts for Ammonia Synthesis Using Informatics Methods: A Concerted Effort of Bayesian Optimization, Swarm Intelligence, and First-Principles Computation

This paper details the use of computational and informatics methods to design metal nanocluster catalysts for efficient ammonia synthesis. Three main problems are tackled: defining a measure of catalytic activity, choosing the best candidate from a large number of possibilities, and identifying the thermodynamically stable cluster catalyst structure. First-principles calculations, Bayesian optimization, and particle swarm optimization are used to obtain a Ti8 nanocluster as a catalyst candidate. The N2 adsorption structure on Ti8 indicates substantial activation of the N2 molecule, while the NH3 adsorption structure suggests that NH3 is likely to undergo easy desorption. The study also reveals several cluster catalyst candidates that break the general trade-off that surfaces that strongly adsorb reactants also strongly adsorb products.

Computational Discovery of Stable Metal-Organic Frameworks for Methane-to-Methanol Catalysis

The challenge of direct partial oxidation of methane to methanol has motivated the targeted search of metal-organic frameworks (MOFs) as a promising class of materials for this transformation because of their site-isolated metals with tunable ligand environments. Thousands of MOFs have been synthesized, yet relatively few have been screened for their promise in methane conversion. We developed a high-throughput virtual screening workflow that identifies MOFs from a diverse space of experimental MOFs that have not been studied for catalysis, yet are thermally stable, synthesizable, and have promising unsaturated metal sites for C-H activation via a terminal metal-oxo species. We carried out density functional theory calculations of the radical rebound mechanism for methane-to-methanol conversion on models of the secondary building units (SBUs) from 87 selected MOFs. While we showed that oxo formation favorability decreases with increasing 3d filling, consistent with prior work, previously observed scaling relations between oxo formation and hydrogen atom transfer (HAT) are disrupted by the greater diversity in our MOF set. Accordingly, we focused on Mn MOFs, which favor oxo intermediates without disfavoring HAT or leading to high methanol release energies─a key feature for methane hydroxylation activity. We identified three Mn MOFs comprising unsaturated Mn centers bound to weak-field carboxylate ligands in planar or bent geometries with promising methane-to-methanol kinetics and thermodynamics. The energetic spans of these MOFs are indicative of promising turnover frequencies for methane to methanol that warrant further experimental catalytic studies.

Machine Learning Descriptors for Data-Driven Catalysis Study

Traditional trial-and-error experiments and theoretical simulations have difficulty optimizing catalytic processes and developing new, better-performing catalysts. Machine learning (ML) provides a promising approach for accelerating catalysis research due to its powerful learning and predictive abilities. The selection of appropriate input features (descriptors) plays a decisive role in improving the predictive accuracy of ML models and uncovering the key factors that influence catalytic activity and selectivity. This review introduces tactics for the utilization and extraction of catalytic descriptors in ML-assisted experimental and theoretical research. In addition to the effectiveness and advantages of various descriptors, their limitations are also discussed. Highlighted are both 1) newly developed spectral descriptors for catalytic performance prediction and 2) a novel research paradigm combining computational and experimental ML models through suitable intermediate descriptors. Current challenges and future perspectives on the application of descriptors and ML techniques to catalysis are also presented.

Dynamic evolution of the active center driven by hemilabile coordination in Cu/CeO2 single-atom catalyst

Hemilability is an important concept in homogeneous catalysis where both the reactant activation and the product formation can occur simultaneously through a reversible opening and closing of the metal-ligand coordination sphere. However, this effect has rarely been discussed in heterogeneous catalysis. Here, by employing a theoretical study on CO oxidation over substituted Cu₁/CeO₂ single atom catalysts, we show that dynamic evolution of metal-support coordination can significantly change the electronic structure of the active center. The evolution of the active center is shown to either strengthen or weaken the metal-adsorbate bonding as the reaction proceeds from reactants, through intermediates, to products. As a result, the activity of the catalyst can be increased. We explain our observations by extending hemilability effects to single atom heterogenous catalysts and anticipate that introducing this concept can offer a new insight into the important role active site dynamics have in catalysis toward the rational design of more sophisticated single atom catalyst materials.

The ABC of Generalized Coordination Numbers and Their Use as a Descriptor in Electrocatalysis

The quest for enhanced electrocatalysts can be boosted by descriptor-based analyses. Because adsorption energies are the most common descriptors, electrocatalyst design is largely based on brute-force routines that comb materials databases until an energetic criterion is verified. In this review, it is shown that an alternative is provided by generalized coordination numbers (denoted by CN ¯ $\overline {{\rm{CN}}} $ or GCN), an inexpensive geometric descriptor for strained and unstrained transition metals and some alloys. CN ¯ $\overline {{\rm{CN}}} $ captures trends in adsorption energies on both extended surfaces and nanoparticles and is used to elaborate structure-sensitive electrocatalytic activity plots and selectivity maps. Importantly, CN ¯ $\overline {{\rm{CN}}} $ outlines the geometric configuration of the active sites, thereby enabling an atom-by-atom design, which is not possible using energetic descriptors. Specific examples for various adsorbates (e.g., *OH, *OOH, *CO, and *H), metals (e.g., Pt and Cu), and electrocatalytic reactions (e.g., O₂  reduction, H₂  evolution, CO oxidation, and reduction) are presented, and comparisons are made against other descriptors.

Accelerating the density-functional tight-binding method using graphical processing units

Acceleration of the density-functional tight-binding (DFTB) method on single and multiple graphical processing units (GPUs) was accomplished using the MAGMA linear algebra library. Two major computational bottlenecks of DFTB ground-state calculations were addressed in our implementation: the Hamiltonian matrix diagonalization and the density matrix construction. The code was implemented and benchmarked on two different computer systems: (1) the SUMMIT IBM Power9 supercomputer at the Oak Ridge National Laboratory Leadership Computing Facility with 1-6 NVIDIA Volta V100 GPUs per computer node and (2) an in-house Intel Xeon computer with 1-2 NVIDIA Tesla P100 GPUs. The performance and parallel scalability were measured for three molecular models of 1-, 2-, and 3-dimensional chemical systems, represented by carbon nanotubes, covalent organic frameworks, and water clusters.

A new adsorption energy-barrier relation and its application to CO2 hydrogenation to methanol over In2O3-supported metal catalysts

Herein, we report a new adsorption energy-barrier relation, the adsorbate-dependent barrier scaling (ADBS) relation, with which the catalytic activity of In₂O₃-supported metal catalysts for CO₂ hydrogenation to methanol is predicted. It is shown that Cu, Ga, NiPt and NiPd alloys exhibit high catalytic activity for CO₂ hydrogenation to methanol.

Universal properties of metal-supported oxide films from linear scaling relationships: elucidation of mechanistic origins of strong metal–support interactions

General principles of Strong Metal–Support Interactions (SMSI) overlayer formation have been elucidated using predictive models derived from ultrathin (hydroxy)oxide films on transition metal substrates.

Correlation between Electronic Descriptor and Proton-Coupled Electron Transfer Thermodynamics in Doped Graphite-Conjugated Catalysts

Graphite-conjugated catalysts (GCCs) provide a powerful framework for investigating correlations between electronic structure features and chemical reactivity of single-site heterogeneous catalysts. GCC-phenazine undergoes proton-coupled electron transfer (PCET) involving protonation of phenazine at its two nitrogen atoms with the addition of two electrons. Herein, this PCET reaction is investigated in the presence of defects, such as heteroatom dopants, in the graphitic surface. The proton-coupled redox potentials, E_PCET, are computed using a constant potential periodic density functional theory (DFT) strategy. The electronic states directly involved in PCET for GCC-phenazine exhibit the same nitrogen orbital character as those for molecular phenazine. The energy ε_LUS of this phenazine-related lowest unoccupied electronic state in GCC-phenazine is identified as a descriptor for changes in PCET thermodynamics. Importantly, ε_LUS is obtained from only a single DFT calculation but can predict E_PCET, which requires many such calculations. Similar electronic features may be useful descriptors for thermodynamic properties of other single-site catalysts.

Efficient catalyst screening using graph neural networks to predict strain effects on adsorption energy

Small-molecule adsorption energies correlate with energy barriers of catalyzed intermediate reaction steps, determining the dominant microkinetic mechanism. Straining the catalyst can alter adsorption energies and break scaling relationships that inhibit reaction engineering, but identifying desirable strain patterns using density functional theory is intractable because of the high-dimensional search space. We train a graph neural network to predict the adsorption energy response of a catalyst/adsorbate system under a proposed surface strain pattern. The training data are generated by randomly straining and relaxing Cu-based binary alloy catalyst complexes taken from the Open Catalyst Project. The trained model successfully predicts the adsorption energy response for 85% of strains in unseen test data, outperforming ensemble linear baselines. Using ammonia synthesis as an example, we identify Cu-S alloy catalysts as promising candidates for strain engineering. Our approach can locate strain patterns that break adsorption energy scaling relations to improve catalyst performance.

Improved visible light photocatalytic nitrogen fixation activity using a FeII-rich MIL-101(Fe): breaking the scaling relationship by photoinduced FeII/FeIII cycling

The scaling relations between nitrogen adsorption and NH_x destabilization are key challenges to the widespread adoption of the photocatalytic synthesis of ammonia. In this work, a Fe^II-rich MIL-101(Fe) (MIL-101(Fe^II/Fe^III)) was synthesized using a one-step solvent thermal method with ethylene glycol (EG) as a reducing agent, which can break the scaling relationship by photoinduced Fe^II (high nitrogen adsorption ability) and Fe^III (high NH_z destabilization ability) cycling. XPS was used to detect the change in iron valence state in the MIL-101(Fe^II/Fe^III) material. The photocatalytic nitrogen fixation efficiency of MIL-101(Fe^II/Fe^III) under visible light without any sacrificial agent was 466.8 μmol h^-1 g^-1, five times that of MIL-101(Fe). After photocatalytic experiments, MIL-101(Fe^II/Fe^III) retained an unchanged Fe^II/Fe^III rate, indicating that this Fe^II/Fe^III cycling can be maintained. DFT modeling of the Fe^II-rich MOF material showed that a FeII1 FeIII2 system has a higher N₂ activation capacity than a FeIII3 system. The catalytic mechanism was further proved by in situ infrared spectra and N¹⁵ isotopic tracers. Therefore, the improvement of photocatalytic activity was mainly attributed to the change in the nitrogen adsorption capacity during the photoinduced Fe^II/Fe^III cycling.

Mapping Active Site Geometry to Activity in Immobilized Frustrated Lewis Pair Catalysts

The immobilization of molecular catalysts imposes spatial constraints on their active site. We reveal that in bifunctional catalysis such constraints can also be utilized as an appealing handle to boost intrinsic activity through judicious control of the active site geometry. To demonstrate this, we develop a pragmatic approach, based on nonlinear scaling relationships, to map the spatial arrangements of the acid–base components of frustrated Lewis pairs (FLPs) to their performance in the catalytic hydrogenation of CO₂. The resulting activity map shows that fixing the donor–acceptor centers at specific distances and locking them into appropriate orientations leads to an unforeseen many‐fold increase in the catalytic activity of FLPs compared to their unconstrained counterparts.

Strain Effect on Adsorption and Reactions of AHx (A = C, N, O, X £ 3) on In2O3(110), TiO2(110) and ZrO2(101) Surfaces

More and more attention has been paid to strain-based regulation of catalytic activity. To guide regulation of catalytic performance via strain engineering, adsorption and reactions of AHx (A = C, N, O, x £ 3) were investigated on uniformly strained In2O3 (110), rutile TiO2 (110) and tetragonal ZrO2 (101) from -2% to 4%. The results show that adsorption energies vary linearly with strain; expansive strain enhances adsorption of most adsorbates. Unlike the adsorbate scaling relations which are central atom dependent, the adsorbate scaling relations on strained surfaces are central atom independent. C-H/O-H bonds are elongated/shortened with expansive strain, and adsorption energies of CHx generally change more than those of OHx and NHx, which can be rationalized with effective medium theory and pertinent bond energies. Thermodynamically In2O3(110)/ZrO2(101) is most active/inactive. The estimated variation of rate constants at 300K from 0% to 2% strain based on Brønsted−Evans−Polanyi relationship demonstrates great strain regulation potential of catalytic performance on these oxide surfaces. Finally it is demonstrated that strain tends to facilitate the reactions whose sum of stoichiometric number is positive, which can be used as a rule to guide strain engineering for heterogeneous catalysis.

Performance descriptors of nanostructured metal catalysts for acetylene hydrochlorination

Controlling the precise atomic architecture of supported metals is central to optimizing their catalytic performance, as recently exemplified for nanostructured platinum and ruthenium systems in acetylene hydrochlorination, a key process for vinyl chloride production. This opens the possibility of building on historically established activity correlations. In this study, we derived quantitative activity, selectivity and stability descriptors that account for the metal-dependent speciation and host effects observed in acetylene hydrochlorination. To achieve this, we generated a platform of Au, Pt, Ru, Ir, Rh and Pd single atoms and nanoparticles supported on different types of carbon and assessed their evolution during synthesis and under the relevant reaction conditions. Combining kinetic, transient and chemisorption analyses with modelling, we identified the acetylene adsorption energy as a speciation-sensitive activity descriptor, further determining catalyst selectivity with respect to coke formation. The stability of the different nanostructures is governed by the interplay between single atom-support interactions and chlorine affinity, promoting metal redispersion or agglomeration, respectively.