Towards operando computational modeling in heterogeneous catalysis

Progress in computational methods and mechanistic insights on the growth of carbon nanotubes

Carbon nanotubes (CNTs), as a promising nanomaterial with broad applications across various fields, are continuously attracting significant research attention. Despite substantial progress in understanding their growth mechanisms, synthesis methods, and post-processing techniques, two major goals remain challenging: achieving property-targeted growth and efficient mass production. Recent advancements in computational methods driven by increased computational resources, the development of platforms, and the refinement of theoretical models, have significantly deepened our understanding of the mechanisms underlying CNT growth. This review aims to comprehensively examine the latest computational techniques that shed light on various aspects of CNT synthesis. The first part of this review focuses on progress in computational methods. Beginning with atomistic simulation approaches, we introduce the fundamentals and advancements in density functional theory (DFT), molecular dynamics (MD) simulations, and kinetic Monte Carlo (kMC) simulations. We discuss the applicability and limitations of each method in studying mechanisms of CNT growth. Then, the focus shifts to multiscale modeling approaches, where we demonstrate the coupling of atomic-scale simulations with reactor-scale multiphase flow models. Given that CNT growth inherently spans multiple temporal and spatial scales, the development and application of multiscale modeling techniques are poised to become a central focus of future computational research in this field. Furthermore, this review emphasizes the growing role played by machine learning in CNT growth research. Compared with traditional physics-based simulation methods, data-driven machine learning approaches have rapidly emerged in recent years, revolutionizing research paradigms from molecular simulation to experimental design. In the second part of this review, we highlight the latest advancements in CNT growth mechanisms and synthesis methods achieved through computational techniques. These include novel findings across fundamental growth stages, i.e., from nucleation to elongation and ultimately termination. We also examine the dynamic behaviors of catalyst nanoparticles and chirality-controlled growth processes, emphasizing how these insights contribute to advancing the field. Finally, in the concluding section, we propose future directions for advancements of computational approaches toward deeper understanding of CNT growth mechanisms and better support of CNT manufacturing.

Tailored Design of Trimetallic Mesoporous Au-Ag-Cu Alloys for Maximizing Electrochemical Applications

This study reports a one-step electrodeposition of ternary mesoporous gold-silver-copper (mAuAgCu) alloy films by using diblock copolymers as pore-directing agents. Additionally, it examines the effects of alloy composition on the electrocatalytic performance of mAuAgCu thin films. Using advanced characterization techniques, such as scanning transmission electron microscopy and X-ray photoelectron spectroscopy, the interplay between alloy composition, surface structure, and catalytic performance is revealed. The optimized mAu(0.60)Ag(0.20)Cu(0.20) alloy (prepared from the precursor solution with an Au:Ag:Cu ratio of 60:20:20) demonstrates the highest catalytic activity for glucose sensing. This is because the introduction of Cu facilitates a uniform distribution of defects in this mesoporous ternary alloy through controlled reduction, leading to a higher electrochemically active surface area (ECSA) and more active sites for electrochemical reactions. This research provides valuable insights into designing trimetallic alloys, demonstrating how the surface structure and alloy composition can control the catalytic performance for electrochemical applications.

DFT-Assisted Microkinetic Study of Transfer Hydrogenation over Homogeneous and Immobilized Cp*Ir Complexes

DFT calculations were done to investigate the kinetic mechanism of benzaldehyde transfer hydrogenation using [Cp*IrCl2]2 complexes in isopropyl alcohol in the presence of potassium tert-butoxide. Predicted energy barriers provide evidence that the inner-sphere (IS) mechanism (effective barrier 53.0 kJ/mol) is favored over the outer-sphere (OS) and Meerwein-Pondorf-Verley (MPV) mechanisms. Reaction kinetics was studied using both homogeneous and immobilized Cp*Ir complexes as catalysts. A mathematical model was developed to simulate the transfer hydrogenation of benzaldehyde on these catalysts, accounting for possible mass transfer limitations for the immobilized catalyst. A microkinetic model was constructed using both our density functional theory calculations and fitting of the kinetic parameters of catalyst activation and deactivation reactions. The simulation results predict that only about a quarter of Ir immobilized complexes are involved in the reaction, and this is the main reason for the observed higher activity of the homogeneous catalyst. The activity of the immobilized catalyst was found to be related to the hydride species concentration, which is a function of the base concentration. The results suggest that the amount of base has a drastic effect on the immobilized catalyst activity.

Modeling Heterogeneous Catalysis Using Quantum Computers: An Academic and Industry Perspective

Heterogeneous catalysis plays a critical role in many industrial processes, including the production of fuels, chemicals, and pharmaceuticals, and research to improve current catalytic processes is important to make the chemical industry more sustainable. Despite its importance, the challenge of identifying optimal catalysts with the required activity and selectivity persists, demanding a detailed understanding of the complex interactions between catalysts and reactants at various length and time scales. Density functional theory (DFT) has been the workhorse in modeling heterogeneous catalysis for more than three decades. While DFT has been instrumental, this review explores the application of quantum computing algorithms in modeling heterogeneous catalysis, which could bring a paradigm shift in our approach to understanding catalytic interfaces. Bridging academic and industrial perspectives by focusing on emerging materials, such as multicomponent alloys, single-atom catalysts, and magnetic catalysts, we delve into the limitations of DFT in capturing strong correlation effects and spin-related phenomena. The review also presents important algorithms and their applications relevant to heterogeneous catalysis modeling to showcase advancements in the field. Additionally, the review explores embedding strategies where quantum computing algorithms handle strongly correlated regions, while traditional quantum chemistry algorithms address the remainder, thereby offering a promising approach for large-scale heterogeneous catalysis modeling. Looking forward, ongoing investments by academia and industry reflect a growing enthusiasm for quantum computing's potential in heterogeneous catalysis research. The review concludes by envisioning a future where quantum computing algorithms seamlessly integrate into research workflows, propelling us into a new era of computational chemistry and thereby reshaping the landscape of modeling heterogeneous catalysis.

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.

How Doping Regulates As(III) Adsorption at TiO2 Surfaces: A DFT + U Study

The efficient adsorption and removal of As(III), which is highly toxic, remains difficult. TiO2 shows promise in this field, though the process needs improvement. Herein, how doping regulates As(OH)3 adsorption over TiO2 surfaces is comprehensively investigated by means of the DFT + D3 approach. Doping creates the bidentate mononuclear (Ce doping at the Ti5c site), tridentate (N, S doping at the O2c site), and other new adsorption structures. The extent of structural perturbation correlates with the atomic radius when doping the Ti site (Ce >> Fe, Mn, V >> B), while it correlates with the likelihood of forming more bonds when doping the O site (N > S > F). Doping the O2c, O3c rather than the Ti5c site is more effective in enhancing As(OH)3 adsorption and also causes more structural perturbation and diversity. Similar to the scenario of pristine surfaces, the bidentate binuclear complexes with two Ti-OAs bonds are often the most preferred, except for B doping at the Ti5c site, S doping at the O2c site, and B doping at the O3c site of rutile (110) and Ce, B doping at the Ti5c site, N, S doping at the O2c site, and N, S, B doping at the O3c site of anatase (101). Doping significantly regulates the As(OH)3 adsorption efficacy, and the adsorption energies reach -4.17, -4.13, and -4.67 eV for Mn doping at the Ti5c site and N doping at the O2c and O3c sites of rutile (110) and -1.99, -2.29, and -2.24 eV for Ce doping at the Ti5c site and N doping at the O2c and O3c sites of anatase (101), respectively. As(OH)3 adsorption and removal are crystal-dependent and become apparently more efficient for rutile vs. anatase, whether doped at the Ti5c, O2c, or O3c site. The auto-oxidation of As(III) occurs when the As centers interact directly with the TiO2 surface, and this occurs more frequently for rutile rather than anatase. The multidentate adsorption of As(OH)3 causes electron back-donation and As(V) re-reduction to As(IV). The regulatory effects of doping during As(III) adsorption and the critical roles played by crystal control are further unraveled at the molecular level. Significant insights are provided for As(III) pollution management via the adsorption and rational design of efficient scavengers.

Efficient Removal of Greenhouse Gases: Machine Learning-Assisted Exploration of Metal-Organic Framework Space

Global warming is a crisis that humanity must face together. With greenhouse gases (GHGs) as the main factor causing global warming, the adoption of relevant processes to eliminate them is essential. With the advantages of high specific surface area, large pore volume, and tunable synthesis, metal-organic frameworks (MOFs) have attracted much attention in GHG storage, adsorption, separation, and catalysis. However, as the pool of MOFs expands rapidly with new syntheses and discoveries, finding a suitable MOF for a particular application is highly challenging. In this regard, high-throughput computational screening is considered the most effective research method for screening a large number of materials to discover high-performance target MOFs. Typically, high-throughput computational screening generates voluminous and multidimensional data, which is well suited for machine learning (ML) training to improve the screening efficiency and explore the relationships between the multidimensional data in depth. This Review summarizes the general process and common methods for using ML to screen MOFs in the field of GHG removal. It also addresses the challenges faced by ML in exploring the MOF space and potential directions for the future development of ML for MOF screening. This aims to enhance the understanding of the integration of ML and MOFs in various fields and broaden the application and development ideas of MOFs.

Dynamic Active Sites In Situ Formed in Metal Nanoparticle Reshaping under Reaction Conditions

Understanding the nonequilibrium transformation of nanocatalysts under reaction conditions is important because metastable atomic structures may be created during the process, which offers unique activities in reactions. Although reshaping of metal nanoparticles (NPs) under reaction conditions has been widely recognized, the dynamic reshaping process has been less studied at the atomic scale. Here, we develop an atomistic kinetic Monte Carlo model to simulate the complete reshaping process of Pt nanoparticles in a CO environment and reveal the in situ formation of atomic clusters on the NP surface, a new type of active site beyond conventional understanding, boosting the reactivities in the CO oxidation reaction. Interestingly, highly active peninsula and inactive island clusters both form on the (111) facets and interchange in varying states of dynamic equilibrium, which influences the catalytic activities significantly. This study provides new fundamental knowledge of nanocatalysis and new guidance for the rational design of nanocatalysts.

Computational Protocol for the Spectral Assignment of NMR Resonances in Covalent Organic Frameworks

Solid-state nuclear magnetic resonance spectroscopy is routinely used in the field of covalent organic frameworks to elucidate or confirm the structure of the synthesized samples and to understand dynamic phenomena. Typically this involves the interpretation and simulation of the spectra through the assumption of symmetry elements of the building units, hinging on the correct assignment of each line shape. To avoid misinterpretation resulting from library-based assignment without a theoretical basis incorporating the impact of the framework, this work proposes a first-principles computational protocol for the assignment of experimental spectra, which exploits the symmetry of the underlying building blocks for computational feasibility. In this way, this protocol accommodates the validation of previous experimental assignments and can serve to complement new NMR measurements.

Highly parallelizable path sampling with minimal rejections using asynchronous replica exchange and infinite swaps

Capturing rare yet pivotal events poses a significant challenge for molecular simulations. Path sampling provides a unique approach to tackle this issue without altering the potential energy landscape or dynamics, enabling recovery of both thermodynamic and kinetic information. However, despite its exponential acceleration compared to standard molecular dynamics, generating numerous trajectories can still require a long time. By harnessing our recent algorithmic innovations-particularly subtrajectory moves with high acceptance, coupled with asynchronous replica exchange featuring infinite swaps-we establish a highly parallelizable and rapidly converging path sampling protocol, compatible with diverse high-performance computing architectures. We demonstrate our approach on the liquid-vapor phase transition in superheated water, the unfolding of the chignolin protein, and water dissociation. The latter, performed at the ab initio level, achieves comparable statistical accuracy within days, in contrast to a previous study requiring over a year.

Hydrogen atom scattering at the Al2O3(0001) surface: a combined experimental and theoretical study

Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields - from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the α-Al2O3(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as α-Al2O3 are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface.

The role of dynamics in heterogeneous catalysis: Surface diffusivity and N2 decomposition on Fe(111)

Dynamics has long been recognized to play an important role in heterogeneous catalytic processes. However, until recently, it has been impossible to study their dynamical behavior at industry-relevant temperatures. Using a combination of machine learning potentials and advanced simulation techniques, we investigate the cleavage of the N[Formula: see text] triple bond on the Fe(111) surface. We find that at low temperatures our results agree with the well-established picture. However, if we increase the temperature to reach operando conditions, the surface undergoes a global dynamical change and the step structure of the Fe(111) surface is destabilized. The catalytic sites, traditionally associated with this surface, appear and disappear continuously. Our simulations illuminate the danger of extrapolating low-temperature results to operando conditions and indicate that the catalytic activity can only be inferred from calculations that take dynamics fully into account. More than that, they show that it is the transition to this highly fluctuating interfacial environment that drives the catalytic process.

A Combined Reaction Path Search and Hybrid Solvation Method for the Systematic Exploration of Elementary Reactions at the Solid-Liquid Interface

We present a combined simulation method of single-component artificial force induced reaction (SC-AFIR) and effective screening medium combined with the reference interaction site model (ESM-RISM), termed SC-AFIR+ESM-RISM. SC-AFIR automatically and systematically explores the chemical reaction pathway, and ESM-RISM directly simulates the precise electronic structure at the solid-liquid interface. Hence, SC-AFIR+ESM-RISM enables us to explore reliable reaction pathways at the solid-liquid interface. We applied it to explore the dissociation pathway of an H2O molecule at the Cu(111)/water interface. The reaction path networks of the whole reaction and the minimum energy paths from H2O to H2 + O depend on the interfacial environment. The qualitative difference in the energy diagrams and the resulting change in the kinematically favored dissociation pathway upon changing the solvation environments are discussed. We believe that SC-AFIR+ESM-RISM will be a powerful tool to reveal the details of chemical reactions in surface catalysis and electrochemistry.

Accelerated discovery of multi-elemental reverse water-gas shift catalysts using extrapolative machine learning approach

Designing novel catalysts is key to solving many energy and environmental challenges. Despite the promise that data science approaches, including machine learning (ML), can accelerate the development of catalysts, truly novel catalysts have rarely been discovered through ML approaches because of one of its most common limitations and criticisms-the assumed inability to extrapolate and identify extraordinary materials. Herein, we demonstrate an extrapolative ML approach to develop new multi-elemental reverse water-gas shift catalysts. Using 45 catalysts as the initial data points and performing 44 cycles of the closed loop discovery system (ML prediction + experiment), we experimentally tested a total of 300 catalysts and identified more than 100 catalysts with superior activity compared to those of the previously reported high-performance catalysts. The composition of the optimal catalyst discovered was Pt(3)/Rb(1)-Ba(1)-Mo(0.6)-Nb(0.2)/TiO2. Notably, niobium (Nb) was not included in the original dataset, and the catalyst composition identified was not predictable even by human experts.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

The need for operando modelling of 27Al NMR in zeolites: the effect of temperature, topology and water

Solid state (ss-) 27Al NMR is one of the most valuable tools for the experimental characterization of zeolites, owing to its high sensitivity and the detailed structural information which can be extracted from the spectra. Unfortunately, the interpretation of ss-NMR is complex and the determination of aluminum distributions remains generally unfeasible. As a result, computational modelling of 27Al ss-NMR spectra has grown increasingly popular as a means to support experimental characterization. However, a number of simplifying assumptions are commonly made in NMR modelling, several of which are not fully justified. In this work, we systematically evaluate the effects of various common models on the prediction of 27Al NMR chemical shifts in zeolites CHA and MOR. We demonstrate the necessity of operando modelling; in particular, taking into account the effects of water loading, temperature and the character of the charge-compensating cation. We observe that conclusions drawn from simple, high symmetry model systems such as CHA do not transfer well to more complex zeolites and can lead to qualitatively wrong interpretations of peak positions, Al assignment and even the number of signals. We use machine learning regression to develop a simple yet robust relationship between chemical shift and local structural parameters in Al-zeolites. This work highlights the need for sophisticated models and high-quality sampling in the field of NMR modelling and provides correlations which allow for the accurate prediction of chemical shifts from dynamical simulations.

Accessing complex reconstructed material structures with hybrid global optimization accelerated via on-the-fly machine learning

The complex reconstructed structure of materials can be revealed by global optimization. This paper describes a hybrid evolutionary algorithm (HEA) that combines differential evolution and genetic algorithms with a multi-tribe framework. An on-the-fly machine learning calculator is adopted to expedite the identification of low-lying structures. With a superior performance to other well-established methods, we further demonstrate its efficacy by optimizing the complex oxidized surface of Pt/Pd/Cu with different facets under (4 × 4) periodicity. The obtained structures are consistent with experimental results and are energetically lower than the previously presented model.

Iterative multiscale and multi-physics computations for operando catalyst nanostructure elucidation and kinetic modeling

Modern heterogeneous catalysis has benefitted immensely from computational predictions of catalyst structure and its evolution under reaction conditions, first-principles mechanistic investigations, and detailed kinetic modeling, which are rungs on a multiscale workflow. Establishing connections across these rungs and integration with experiments have been challenging. Here, operando catalyst structure prediction techniques using density functional theory simulations and ab initio thermodynamics calculations, molecular dynamics, and machine learning techniques are presented. Surface structure characterization by computational spectroscopic and machine learning techniques is then discussed. Hierarchical approaches in kinetic parameter estimation involving semi-empirical, data-driven, and first-principles calculations and detailed kinetic modeling via mean-field microkinetic modeling and kinetic Monte Carlo simulations are discussed along with methods and the need for uncertainty quantification. With these as the background, this article proposes a bottom-up hierarchical and closed loop modeling framework incorporating consistency checks and iterative refinements at each level and across levels.

Challenges in modelling dynamic processes in realistic nanostructured materials at operating conditions

The question is addressed in how far current modelling strategies are capable of modelling dynamic phenomena in realistic nanostructured materials at operating conditions. Nanostructured materials used in applications are far from perfect; they possess a broad range of heterogeneities in space and time extending over several orders of magnitude. Spatial heterogeneities from the subnanometre to the micrometre scale in crystal particles with a finite size and specific morphology, impact the material's dynamics. Furthermore, the material's functional behaviour is largely determined by the operating conditions. Currently, there exists a huge length-time scale gap between attainable theoretical length-time scales and experimentally relevant scales. Within this perspective, three key challenges are highlighted within the molecular modelling chain to bridge this length-time scale gap. Methods are needed that enable (i) building structural models for realistic crystal particles having mesoscale dimensions with isolated defects, correlated nanoregions, mesoporosity, internal and external surfaces; (ii) the evaluation of interatomic forces with quantum mechanical accuracy albeit at much lower computational cost than the currently used density functional theory methods and (iii) derivation of the kinetics of phenomena taking place in a multi-length-time scale window to obtain an overall view of the dynamics of the process. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

In Situ/Operando Characterization Techniques of Electrochemical CO2 Reduction

Electrocatalytic conversion of carbon dioxide to valuable chemicals and fuels driven by renewable energy plays a crucial role in achieving net-zero carbon emissions. Understanding the structure-activity relationship and the reaction mechanism is significant for tuning electrocatalyst selectivity. Therefore, characterizing catalyst dynamic evolution and reaction intermediates under reaction conditions is necessary but still challenging. We first summarize the most recent progress in mechanistic understanding of heterogeneous CO2/CO reduction using in situ/operando techniques, including surface-enhanced vibrational spectroscopies, X-ray- and electron-based techniques, and mass spectroscopy, along with discussing remaining limitations. We then offer insights and perspectives to accelerate the future development of in situ/operando techniques.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Design of Single-Atom Catalysts and Tracking Their Fate Using Operando and Advanced X-ray Spectroscopic Tools

The potential of operando X-ray techniques for following the structure, fate, and active site of single-atom catalysts (SACs) is highlighted with emphasis on a synergetic approach of both topics. X-ray absorption spectroscopy (XAS) and related X-ray techniques have become fascinating tools to characterize solids and they can be applied to almost all the transition metals deriving information about the symmetry, oxidation state, local coordination, and many more structural and electronic properties. SACs, a newly coined concept, recently gained much attention in the field of heterogeneous catalysis. In this way, one can achieve a minimum use of the metal, theoretically highest efficiency, and the design of only one active site-so-called single site catalysts. While single sites are not easy to characterize especially under operating conditions, XAS as local probe together with complementary methods (infrared spectroscopy, electron microscopy) is ideal in this research area to prove the structure of these sites and the dynamic changes during reaction. In this review, starting from their fundamentals, various techniques related to conventional XAS and X-ray photon in/out techniques applied to single sites are discussed with detailed mechanistic and in situ/operando studies. We systematically summarize the design strategies of SACs and outline their exploration with XAS supported by density functional theory (DFT) calculations and recent machine learning tools.

ReNeGate: A Reaction Network Graph-Theoretical Tool for Automated Mechanistic Studies in Computational Homogeneous Catalysis

Exploration of the chemical reaction space of chemical transformations in multicomponent mixtures is one of the main challenges in contemporary computational chemistry. To remove expert bias from mechanistic studies and to discover new chemistries, an automated graph-theoretical methodology is proposed, which puts forward a network formalism of homogeneous catalysis reactions and utilizes a network analysis tool for mechanistic studies. The method can be used for analyzing trajectories with single and multiple catalytic species and can provide unique conformers of catalysts including multinuclear catalyst clusters along with other catalytic mixture components. The presented three-step approach has the integrated ability to handle multicomponent catalytic systems of arbitrary complexity (mixtures of reactants, catalyst precursors, ligands, additives, and solvents). It is not limited to predefined chemical rules, does not require prealignment of reaction mixture components consistent with a reaction coordinate, and is not agnostic to the chemical nature of transformations. Conformer exploration, reactive event identification, and reaction network analysis are the main steps taken for identifying the pathways in catalytic systems given the starting precatalytic reaction mixture as the input. Such a methodology allows us to efficiently explore catalytic systems in realistic conditions for either previously observed or completely unknown reactive events in the context of a network representing different intermediates. Our workflow for the catalytic reaction space exploration exclusively focuses on the identification of thermodynamically feasible conversion channels, representative of the (secondary) catalyst deactivation or inhibition paths, which are usually most difficult to anticipate based solely on expert chemical knowledge. Thus, the expert bias is sought to be removed at all steps, and the chemical intuition is limited to the choice of the thermodynamic constraint imposed by the applicable experimental conditions in terms of threshold energy values for allowed transformations. The capabilities of the proposed methodology have been tested by exploring the reactivity of Mn complexes relevant for catalytic hydrogenation chemistry to verify previously postulated activation mechanisms and unravel unexpected reaction channels relevant to rare deactivation events.

Machine Learning in the Development of Adsorbents for Clean Energy Application and Greenhouse Gas Capture

Addressing climate change challenges by reducing greenhouse gas levels requires innovative adsorbent materials for clean energy applications. Recent progress in machine learning has stimulated technological breakthroughs in the discovery, design, and deployment of materials with potential for high-performance and low-cost clean energy applications. This review summarizes basic machine learning methods-data collection, featurization, model generation, and model evaluation-and reviews their use in the development of robust adsorbent materials. Key case studies are provided where these methods are used to accelerate adsorbent materials design and discovery, optimize synthesis conditions, and understand complex feature-property relationships. The review provides a concise resource for researchers wishing to use machine learning methods to rapidly develop effective adsorbent materials with a positive impact on the environment.

Ga and Zn increase the oxygen affinity of Cu-based catalysts for the CO x hydrogenation according to ab initio atomistic thermodynamics

The direct hydrogenation of CO or CO2 to methanol, a highly vivid research area in the context of sustainable development, is typically carried out with Cu-based catalysts. Specific elements (so-called promoters) improve the catalytic performance of these systems under a broad range of reaction conditions (from pure CO to pure CO2). Some of these promoters, such as Ga and Zn, can alloy with Cu and their role remains a matter of debate. In that context, we used periodic DFT calculations on slab models and ab initio thermodynamics to evaluate both metal alloying and surface formation by considering multiple surface facets, different promoter concentrations and spatial distributions as well as adsorption of several species (O*, H*, CO* and ) for different gas phase compositions. Both Ga and Zn form an fcc-alloy with Cu due to the stronger interaction of the promoters with Cu than with themselves. While the Cu-Ga-alloy is more stable than the Cu-Zn-alloy at low promoter concentrations (<25%), further increasing the promoter concentration reverses this trend, due to the unfavoured Ga-Ga-interactions. Under CO2 hydrogenation conditions, a substantial amount of O* can adsorb onto the alloy surfaces, resulting in partial dealloying and oxidation of the promoters. Therefore, the CO2 hydrogenation conditions are actually rather oxidising for both Ga and Zn despite the large amount of H2 present in the feedstock. Thus, the growth of a GaO x /ZnO x overlayer is thermodynamically preferred under reaction conditions, enhancing CO2 adsorption, and this effect is more pronounced for the Cu-Ga-system than for the Cu-Zn-system. In contrast, under CO hydrogenation conditions, fully reduced and alloyed surfaces partially covered with H* and CO* are expected, with mixed CO/CO2 hydrogenation conditions resulting in a mixture of reduced and oxidised states. This shows that the active atmosphere tunes the preferred state of the catalyst, influencing the catalytic activity and stability, indicating that the still widespread image of a static catalyst under reaction conditions is insufficient to understand the complex interplay of processes taking place on a catalyst surface under reaction conditions, and that dynamic effects must be considered.

Global optimization of extraframework ensembles in zeolites: structural analysis of extraframework aluminum species in MOR and MFI zeolites

Metal-modified zeolites are versatile catalytic materials with a wide range of industrial applications. Their catalytic behaviour is determined by the nature of externally introduced cationic species, i.e., its geometry, chemical composition, and location within the zeolite pores. Superior catalyst designs can be unlocked by understanding the confinement effect and spatial limitations of the zeolite framework and its influence on the geometry and location of such cationic active sites. In this study, we employ the genetic algorithm (GA) global optimization method to investigate extraframework aluminum species and their structural variations in different zeolite matrices. We focus on extraframework aluminum (EFAl) as a model system because it greatly influences the product selectivity and catalytic stability in several zeolite catalyzed processes. Specifically, the GA was used to investigate the configurational possibilities of EFAl within the mordenite (MOR) and ZSM-5 frameworks. The xTB semi-empirical method within the GA was employed for an automated sampling of the EFAl-zeolite space. Furthermore, geometry refinement at the density functional theory (DFT) level of theory allowed us to improve the most stable configurations obtained from the GA and elaborate on the limitations of the xTB method. A subsequent ab initio thermodynamics analysis (aiTA) was chosen to predict the most favourable EFAl structure(s) under the catalytically relevant operando conditions.

Synthesis of Heterogeneous Catalysts in Catalyst Informatics to Bridge Experiment and High-Throughput Calculation

The coupling of high-throughput calculations with catalyst informatics is proposed as an alternative way to design heterogeneous catalysts. High-throughput first-principles calculations for the oxidative coupling of methane (OCM) reaction are designed and performed where 1972 catalyst surface planes for the CH₄ to CH₃ reaction are calculated. Several catalysts for the OCM reaction are designed based on key elements that are unveiled via data visualization and network analysis. Among the designed catalysts, several active catalysts such as CoAg/TiO₂, Mg/BaO, and Ti/BaO are found to result in high C₂ yield. Results illustrate that designing catalysts using high-throughput calculations is achievable in principle if appropriate trends and patterns within the data generated via high-throughput calculations are identified. Thus, high-throughput calculations in combination with catalyst informatics offer a potential alternative method for catalyst design.

Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5

Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.

Stability of oxidized states of free-standing and ceria-supported PtOx particles

Nanostructured materials based on CeO2 and Pt play a fundamental role in catalyst design. However, their characterization is often challenging due to their structural complexity and the tendency of the materials to change under reaction conditions. In this work, we combine calculations based on the density functional theory, a machine-learning assisted global optimization method (GOFEE), and ab initio thermodynamics to characterize stable oxidation states of ceria-supported PtyOx particles in different environments. The collection of global minima structures for different stoichiometries resulting from the global optimisation effort is used to assess the effect of temperature, oxygen pressure, and support interactions on the phase diagrams, oxidation states, and geometries of the PtyOx particles. We thus identify favoured structural motifs and O:Pt ratios, revealing that oxidized states of free-standing and ceria-supported platinum particles are more stable than reduced ones under a wide range of conditions. These results indicate that studies rationalizing activity of ceria-supported Pt clusters must consider oxidized states, and that previous understanding of such materials obtained only with fully reduced Pt clusters may be incomplete.

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.

High Stability of Methanol to Aromatic Conversion over Bimetallic Ca,Ga-Modified ZSM-5

The production of valuable aromatics and the rapid catalyst deactivation due to coking are intimately related in the zeolite-catalyzed aromatization reactions. Here, we demonstrate that these two processes can be decoupled by promoting the Ga/HZSM-5 aromatization catalyst with Ca. The resulting bimetallic catalysts combine high selectivity to light aromatics with extended catalyst lifetime in the methanol-to-aromatics process. Evaluation of the catalytic performance combined with detailed catalyst characterization suggests that the added Ca interacts with the Ga-LAS, with a strong effect on the aromatization processes. A genetic algorithm approach complemented by ab initio thermodynamic analysis is used to elucidate the possible structures of bimetallic extraframework species formed under reaction conditions. The promotion effect of minute amounts of Ca is attributed to the stabilization of the intra-zeolite extraframework gallium oxide clusters with moderated dehydrogenation activity.

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.

Realistic Modelling of Dynamics at Nanostructured Interfaces Relevant to Heterogeneous Catalysis

The focus of this short review is directed towards investigations of the dynamics of nanostructured metallic heterogeneous catalysts and the evolution of interfaces during reaction—namely, the metal–gas, metal–liquid, and metal–support interfaces. Indeed, it is of considerable interest to know how a metal catalyst surface responds to gas or liquid adsorption under reaction conditions, and how its structure and catalytic properties evolve as a function of its interaction with the support. This short review aims to offer the reader a birds-eye view of state-of-the-art methods that enable more realistic simulation of dynamical phenomena at nanostructured interfaces by exploiting resource-efficient methods and/or the development of computational hardware and software.

Improving the activity and synergistic catalysis of l-aspartate β-decarboxylase by arginine introduction on the surface

Introduction of arginine on the surface relieved the pH-dependent inactivation of l-aspartate-β-decarboxylase, which promoted its application in synthetic biology and biocatalysis.

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.

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.