Ab Initio Thermodynamics and First-Principles Microkinetics for Surface Catalysis

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.

Unifying thermochemistry concepts in computational heterogeneous catalysis

Thermophysical properties of adsorbates and gas-phase species define the free energy landscape of heterogeneously catalyzed processes and are pivotal for an atomistic understanding of the catalyst performance. These thermophysical properties, such as the free energy or the enthalpy, are typically derived from density functional theory (DFT) calculations. Enthalpies are species-interdependent properties that are only meaningful when referenced to other species. The widespread use of DFT has led to a proliferation of new energetic data in the literature and databases. However, there is a lack of consistency in how DFT data is referenced and how the associated enthalpies or free energies are stored and reported, leading to challenges in reproducing or utilizing the results of prior work. Additionally, DFT suffers from exchange-correlation errors that often require corrections to align the data with other global thermochemical networks, which are not always clearly documented or explained. In this review, we introduce a set of consistent terminology and definitions, review existing approaches, and unify the techniques using the framework of linear algebra. This set of terminology and tools facilitates the correction and alignment of energies between different data formats and sources, promoting the sharing and reuse of ab initio data. Standardization of thermochemistry concepts in computational heterogeneous catalysis reduces computational cost and enhances fundamental understanding of catalytic processes, which will accelerate the computational design of optimally performing catalysts.

Development of a Master Equation-Based Microkinetic Model to Investigate Gas Phase Cluster Reactions Across a Wide Pressure and Temperature Range

Small gas-phase metal clusters serve as model systems for complex catalytic reactions, enabling the exploration of the impacts of the size, doping, charge state and other factors under clean conditions. Although the mechanisms of reactions involving metal clusters are known in many cases, they are not always sufficient to interpret the experimental results, as those can be strongly influenced by the chemical kinetics under specific conditions. Therefore, our objective here is to develop a model that utilizes quantum chemical computations to comprehend and predict the precise kinetics of gas-phase cluster reactions, particularly under low-pressure conditions. In this study, we demonstrate that master equation simulations, utilizing reaction paths computed through quantum chemistry, can effectively elucidate the findings of previous experiments. Furthermore, these simulations can accurately predict the kinetics spanning from low-pressure conditions (typically observed in gas-phase cluster experiments) to atmospheric or higher pressures (typical for catalytic experiments). The models are tested for simple elementary steps (Cu4+H2). We highlight the importance of the reaction mechanism simplification in Cu4 ++H2 and provide an interpretation for the previously observed product branching in Pt++CH4.

Machine-Learning-Enabled Thermochemistry Estimator

Modeling adsorbates on single-crystal metals is critical in rational catalyst design and other research that requires detailed thermochemistry. First-principles simulations via density functional theory (DFT) are among the prevalent tools to acquire such information about surface species. While they are highly dependable, DFT calculations often require intensive computational resources and runtime. These limiting factors become particularly pronounced when investigating large sets of complex molecules on heavy noble metals. Consequently, our ability to explore these species and their corresponding energetics is limited. In this work, we establish a novel framework that utilizes techniques including molecular encoding, descriptor synthesis, and machine learning to overcome the limitation of costly DFT simulations. Simultaneously, we estimate thermochemical information efficiently at the DFT accuracy level. More specifically, we translated our training molecules into text-based identifiers through a simplified molecular-input line-entry system. Following that, we parametrize our training matrices with sets of short-range descriptors based on group methods, applying first the nearest neighbors to account for linear contributions. This is coupled with the long-range descriptors characterizing second nearest neighbors to account for nonlinear corrections. Finally, we use linear regression and machine learning techniques, such as Gaussian process regressions to regress over the linear and nonlinear matrix systems, respectively. This is the first work to our knowledge that encompasses both the first and second nearest neighbors based on the group theory throughout the featurization, training, and deployment stages. We trained and validated our models with 459 surface species on Pt(111), Ru(0001), and Ir(111) surfaces. Results exhibit robust performance to reproduce the energetics of interest, such as enthalpies, entropies, and heat capacities, at various temperatures. Notably, the mean absolute errors can be reduced by 48% during training and 19% during prediction at a minimum, when compared to the classical group method. Leveraging the novel framework, our machine-learning-enabled thermochemistry estimator significantly empowers us to research the thermochemistry of complex species on metal catalysts.

AI-Driven Electrolyte Additive Selection to Boost Aqueous Zn-Ion Batteries Stability

In tackling the stability challenge of aqueous Zn-ion batteries (AZIBs) for large-scale energy storage, the adoption of electrolyte additive emerges as a practical solution. Unlike current trial-and-error methods for selecting electrolyte additives, a data-driven strategy is proposed using theoretically computed surface free energy as a stability descriptor, benchmarked against experimental results. Numerous additives are calculated from existing literature, forming a database for machine learning (ML) training. Importantly, this ML model relies solely on experimental values, effectively addressing the challenge of large solvent molecule models that are difficult to handle with quantum chemistry computation. The interpretable linear regression algorithm identifies the number of heavy atoms in the additive molecule and the liquid surface tension as key factors. Artificial intelligence (AI) clustering categorizes additive molecules, identifying regions with the most significant impact on enhancing battery stability. Experimental verification successfully confirms the exceptional performance of 1,2,3-butanetriol and acetone in the optimal region. This integrated methodology, combining theoretical models, data-driven ML, and experimental validation, provides insights into the rational design of battery electrolyte additives.

Computational Design of Catalysts with Experimental Validation: Recent Successes, Effective Strategies, and Pitfalls

Computation has long proven useful in understanding heterogeneous catalysts and rationalizing experimental findings. However, computational design with experimental validation requires somewhat different approaches and has proven more difficult. In recent years, there have been increasing successes in such computational design with experimental validation. In this Perspective, we discuss some of these recent successes and the methodologies used. We also discuss various design strategies more broadly, as well as approximations to consider and pitfalls to try to avoid when designing for experiment. Overall, computation can be a powerful and efficient tool in guiding catalyst design but must be combined with a strong fundamental understanding of catalysis science to be most effective in terms of both choosing the design methodology and choosing which materials to pursue experimentally.

Grand Canonical Ensemble Approaches in CP2K for Modeling Electrochemistry at Constant Electrode Potentials

In electrochemical experiments, the number of electrons of the electrode immersed in the electrolyte is usually variable. Additionally, the numbers of adsorbed substances on the surface of the electrode, the solvent molecules, and counter charge ions in the near-surface region can also vary. Treating electrochemical solid-liquid interfaces with the typical fixed electron number density functional theory (DFT) approach tends to be a challenge. This can be addressed by using grand canonical ensemble approaches. We present the implementation of two grand canonical ensemble approaches in the open-source computational chemistry software CP2K that go beyond the existing canonical ensemble paradigm. The first approach is based on implicit solvent models and explicit atomistic solute (electrode with/without adsorbed species) models, and includes two recent developments: (a) grand canonical self-consistent field (GC-SCF) method (J. Chem. Phys. 2017, 146, 114104) allowing the electron number of the system to fluctuate naturally and accordingly with the experimental electrode potential, (b) planar counter charge (J. Chem. Phys. 2019, 150, 041722, Phys. Rev. B 2003, 68, 245416) salt model completely screening the net charge of the electrode model. In contrast with previous studies, in our implementation, the work function (WF) (absolute electrode potential if the potential drop at the electrolyte-vacuum interface is omitted) is the constrained quantity during an SCF optimization instead of the Fermi energy. The chemical potential of electrons (negative WF) is a natural variable of the grand potential in the GC ensemble of electronic states, and this method can easily achieve stable SCF convergence and obtain an electronic structure that precisely corresponds to a user-specified WF. The second approach referred to as the GC DFT molecular dynamics (DFT-MD) simulation scheme (Phys. Rev. Lett. 2002, 88, 213002, J. Chem. Phys. 2005, 122, 234505, J. Am. Chem. Soc. 2004, 126 (12), 3928-3938) is based on fully explicit modeling the solvent molecules and the ions and is used to calculate the electron chemical potential corresponding to an equilibrium electrochemical half-reaction (M(n+m)+ + ne- ⇌ Mm+) which involves DFT-MD, by allowing the number of electrons to vary during the DFT-MD simulation process. This opens the way for forefront electrochemical calculations in CP2K for a broad range of systems.

Toward Realistic Models of the Electrocatalytic Oxygen Evolution Reaction

The electrocatalytic oxygen evolution reaction (OER) supplies the protons and electrons needed to transform renewable electricity into chemicals and fuels. However, the OER is kinetically sluggish; it operates at significant rates only when the applied potential far exceeds the reversible voltage. The origin of this overpotential is hidden in a complex mechanism involving multiple electron transfers and chemical bond making/breaking steps. Our desire to improve catalytic performance has then made mechanistic studies of the OER an area of major scientific inquiry, though the complexity of the reaction has made understanding difficult. While historically, mechanistic studies have relied solely on experiment and phenomenological models, over the past twenty years ab initio simulation has been playing an increasingly important role in developing our understanding of the electrocatalytic OER and its reaction mechanisms. In this Review we cover advances in our mechanistic understanding of the OER, organized by increasing complexity in the way through which the OER is modeled. We begin with phenomenological models built using experimental data before reviewing early efforts to incorporate ab initio methods into mechanistic studies. We go on to cover how the assumptions in these early ab initio simulations─no electric field, electrolyte, or explicit kinetics─have been relaxed. Through comparison with experimental literature, we explore the veracity of these different assumptions. We summarize by discussing the most critical open challenges in developing models to understand the mechanisms of the OER.

Role of Cu Oxide and Cu Adatoms in the Reactivity of CO2 on Cu(110)

We investigate the interaction of CO2 with metallic and oxidized Cu(110) surfaces using a combination of near-ambient pressure scanning tunneling microscopy (NAP-STM) and theoretical calculations. While the Cu(110) and full CuO films are inert, the interface between bare Cu(110) and the CuO film is observed to react instantly with CO2 at a 10 mbar pressure. The reaction is observed to proceed from the interfacial sites of CuO/Cu(110). During reaction with CO2, the CuO/Cu(110) interface releases Cu adatoms which combine with CO3 to produce a variety of added Cu-CO3 structures, whose stability depends on the gas pressure of CO2. A main implication for the reactivity of Cu(110) is that Cu adatoms and highly undercoordinated CuO segments are created on the Cu(110) surface through the interaction with CO2, which may act as reaction-induced active sites. In the case of CO2 hydrogenation to methanol, our theoretical assessment of such sites indicates that their presence may significantly promote CH3OH formation. Our study thus implies that the CuO/Cu(110) interfacial system is highly dynamic in the presence of CO2, and it suggests a possible strong importance of reaction-induced Cu and CuO sites for the surface chemistry of Cu(110) in CO2-related catalysis.

On-the-fly kinetic Monte Carlo simulations with neural network potentials for surface diffusion and reaction

We develop an adaptive scheme in the kinetic Monte Carlo simulations, where the adsorption and activation energies of all elementary steps, including the effects of other adsorbates, are evaluated "on-the-fly" by employing the neural network potentials. The configurations and energies evaluated during the simulations are stored for reuse when the same configurations are sampled in a later step. The present scheme is applied to hydrogen adsorption and diffusion on the Pd(111) and Pt(111) surfaces and the CO oxidation reaction on the Pt(111) surface. The effects of interactions between adsorbates, i.e., adsorbate-adsorbate lateral interactions, are examined in detail by comparing the simulations without considering lateral interactions. This study demonstrates the importance of lateral interactions in surface diffusion and reactions and the potential of our scheme for applications in a wide variety of heterogeneous catalytic reactions.

What Makes On-Chip Microdevices Stand Out in Electrocatalysis?

Clean and sustainable energy conversion and storage through electrochemistry shows great promise as an alternative to traditional fuel or fossil-consumption energy systems. With regards to practical and high-efficient electrochemistry application, the rational design of active sites and the accurate description of mechanism remain a challenge. Toward this end, in this Perspective, a unique on-chip micro/nano device coupling nanofabrication and low-dimensional electrochemical materials is presented, in which material structure analysis, field-effect regulation, in situ monitoring, and simulation modeling are highlighted. The critical mechanisms that influence electrochemical response are discussed, and how on-chip micro/nano device distinguishes itself is emphasized. The key challenges and opportunities of on-chip electrochemical platforms are also provided through the Perspective.

Ab Initio-Based Modeling of Thermodynamic Cyclic Voltammograms: A Benchmark Study on Ag(100) in Bromide Solutions

Experimental cyclic voltammograms (CVs) measured in the slow scan rate limit can be entirely described in terms of the thermodynamic equilibrium quantities of the electrified solid-liquid interface. They correspondingly serve as an important benchmark for the quality of first-principles calculations of interfacial thermodynamics. Here, we investigate the partially drastic approximations made presently in computationally efficient calculations for the well-defined showcase of an Ag(100) model electrode in Br-containing electrolytes, where the nontrivial part of the CV stems from the electrosorption of Br ions. We specifically study the entanglement of common approximations in the treatment of solvation and field effects, as well as in the way macroscopic averages of the two key quantities, namely, the potential-dependent adsorbate coverage and electrosorption valency, are derived from the first-principles energetics. We demonstrate that the combination of energetics obtained within an implicit solvation model and a perturbative second order account of capacitive double layer effects with a constant-potential grand-canonical Monte Carlo sampling of the adsorbate layer provides an accurate description of the experimental CV. However, our analysis also shows that error cancellation at lower levels of theory may equally lead to good descriptions even though key underlying physics such as the disorder-order transition of the Br adlayer at increasing coverages is inadequately treated.

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.

Hyperthermal velocity distributions of recombinatively-desorbing oxygen from Ag(111)

This study presents velocity-resolved desorption experiments of recombinatively-desorbing oxygen from Ag (111). We combine molecular beam techniques, ion imaging, and temperature-programmed desorption to obtain translational energy distributions of desorbing O2. Molecular beams of NO2 are used to prepare a p (4 × 4)-O adlayer on the silver crystal. The translational energy distributions of O2 are shifted towards hyperthermal energies indicating desorption from an intermediate activated molecular chemisorption state.

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.

The importance of a charge transfer descriptor for screening potential CO2 reduction electrocatalysts

It has been over twenty years since the linear scaling of reaction intermediate adsorption energies started to coin the fields of heterogeneous and electrocatalysis as a blessing and a curse at the same time. It has established the possibility to construct activity volcano plots as a function of a single or two readily accessible adsorption energies as descriptors, but also limited the maximal catalytic conversion rate. In this work, it is found that these established adsorption energy-based descriptor spaces are not applicable to electrochemistry, because they are lacking an important additional dimension, the potential of zero charge. This extra dimension arises from the interaction of the electric double layer with reaction intermediates which does not scale with adsorption energies. At the example of the electrochemical reduction of CO₂ it is shown that the addition of this descriptor breaks the scaling relations, opening up a huge chemical space that is readily accessible via potential of zero charge-based material design. The potential of zero charge also explains product selectivity trends of electrochemical CO₂ reduction in close agreement with reported experimental data highlighting its importance for electrocatalyst design.

Data-Driven Machine Learning for Understanding Surface Structures of Heterogeneous Catalysts

The design of heterogeneous catalysts is necessarily surface-focused, generally achieved via optimization of adsorption energy and microkinetic modelling. A prerequisite is to ensure the adsorption energy is physically meaningful is the stable existence of the conceived active-site structure on the surface. The development of improved understanding of the catalyst surface, however, is challenging practically because of the complex nature of dynamic surface formation and evolution under in-situ reactions. We propose therefore data-driven machine-learning (ML) approaches as a solution. In this Minireview we summarize recent progress in using machine-learning to search and predict (meta)stable structures, assist operando simulation under reaction conditions and micro-environments, and critically analyze experimental characterization data. We conclude that ML will become the new norm to lower costs associated with discovery and design of optimal heterogeneous catalysts.

Ensemble Effects in Adsorbate-Adsorbate Interactions in Microkinetic Modeling

Adsorbates on a surface experience lateral interactions that result in a distribution of adsorption energies. The adsorbate-adsorbate interactions are known to affect the kinetics of surface reactions, which motivates efforts to develop models that accurately account for the interactions. Here, we use density functional theory (DFT) calculations combined with Monte Carlo simulations to investigate how the distribution of adsorbates affects adsorption and desorption of CO from Pt(111). We find that the mean of the average adsorption energy determines the adsorption process, whereas the desorption process can be described by the low energy part of the adsorbate stability distribution. The simulated results are in very good agreement with calorimetry and temperature-programmed desorption experiments and provide a guideline of how to include adsorbate-adsorbate interactions in DFT-based mean-field kinetic models.

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.

Pt nanoparticles under oxidizing conditions - implications of particle size, adsorption sites and oxygen coverage on stability

Platinum nanoparticles are efficient catalysts for different reactions, such as oxidation of carbon and nitrogen monoxides. Adsorption and interaction of oxygen with the nanoparticle surface, taking place under reaction conditions, determine not only the catalytic efficiency but also the stability of the nanoparticles against oxidation. In this study, platinum nanoparticles in oxygen environment are investigated by systematic screening of initial nanoparticle-oxygen configurations and employing density functional theory and a thermodynamics-based approach. The structures formed at low oxygen coverages are described by adsorption of atomic oxygen on the nanoparticles whereas at high coverages oxide-like species are formed. The relative stability of adsorption configurations at different oxygen coverages, including the phase of fully oxidized nanoparticles, is investigated by constructing p-T phase diagrams for the studied systems.

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.

Heterogeneous catalyst design by generative adversarial network and first-principles based microkinetics

Microkinetic analysis based on density functional theory (DFT) was combined with a generative adversarial network (GAN) to enable the artificial proposal of heterogeneous catalysts based on the DFT-calculated dataset. The approach was applied to the NH₃ formation reaction on Rh−Ru alloy surfaces as an example. The NH₃ formation turnover frequency (TOF) was calculated by DFT-based microkinetics. Six elementary reactions, namely, N₂ dissociation, H₂ dissociation, NH_x (x = 1–3) formation, and NH₃ desorption, were explicitly considered, and their reaction energies were evaluated by DFT calculations. Based on the TOF values and atomic compositions, new alloy surfaces were generated using the GAN. This approach successfully generated the surfaces that were not included in the initial dataset but exhibited higher TOF values. The N₂ dissociation reaction was more exothermic for the generated surfaces, leading to higher TOF. The present study demonstrates that the automatic improvement of catalyst materials is possible using DFT calculations and GAN sample generation.

Ab Initio Approach for Thermodynamic Surface Phases with Full Consideration of Anharmonic Effects: The Example of Hydrogen at Si(100)

A reliable description of surfaces structures in a reactive environment is crucial to understand materials' functions. We present a first-principles theory of replica-exchange grand-canonical-ensemble molecular dynamics and apply it to evaluate phase equilibria of surfaces in a reactive gas-phase environment. We identify the different surface phases and locate phase boundaries including triple and critical points. The approach is demonstrated by addressing open questions for the Si(100) surface in contact with a hydrogen atmosphere. In the range from 300 to 1000 K, we find 25 distinct thermodynamically stable surface phases, for which we also provide microscopic descriptions. Most of the identified phases, including few order-disorder phase transitions, have not yet been observed experimentally. Furthermore, we show that the dynamic Si-Si bonds forming and breaking is the driving force behind the phase transition between 3×1 and 2×1 adsorption patterns.

Interfacial catalytic materials; challenge for inorganic synthetic chemistry

Interfacial catalysts are indispensable functional materials in the energy transformation. The traditional empirical search strategies reach their potential. Knowledge-based approaches have not been able to deliver innovative and scalable solutions. Following a short analysis of the origin of these shortcomings a fresh attempt on the material challenge of catalysis is proposed. The approach combines functional understanding of material dynamics derived from operando analysis with digital catalysis science guiding the exploration of non-linear interactions of material genes to catalytic functions. This critically requires the ingenuity of the synthetic inorganic chemist to let us understand the reactivity of well-defined materials under the specific conditions of catalytic operation. It is the understanding of how the kinetics of phase changes brings about and destroys active sites in catalytic materials that forms the basis of realistic material concepts. A rigorous prediction and engineering of these processes may not be possible due to the complexity of options involved.

Epitaxial Core-Shell Oxide Nanoparticles: First-Principles Evidence for Increased Activity and Stability of Rutile Catalysts for Acidic Oxygen Evolution

Due to their high activity and favorable stability in acidic electrolytes, Ir and Ru oxides are primary catalysts for the oxygen evolution reaction (OER) in proton-exchange membrane (PEM) electrolyzers. For a future large-scale application, core-shell nanoparticles are an appealing route to minimize the demand for these precious oxides. Here, we employ first-principles density-functional theory (DFT) and ab initio thermodynamics to assess the feasibility of encapsulating a cheap rutile-structured TiO₂ core with coherent, monolayer-thin IrO₂ or RuO₂ films. Resulting from a strong directional dependence of adhesion and strain, a wetting tendency is only obtained for some low-index facets under typical gas-phase synthesis conditions. Thermodynamic stability in particular of lattice-matched RuO₂ films is instead indicated for more oxidizing conditions. Intriguingly, the calculations also predict an enhanced activity and stability of such epitaxial RuO₂ /TiO₂ core-shell particles under OER operation.

Relativistic Effects in Platinum Nanocluster Catalysis: A Statistical Ensemble-Based Analysis

Nanoclusters are materials of paramount catalytic importance. Among various unique properties featured by nanoclusters, a pronounced relativistic effect can be a decisive parameter in governing their catalytic activity. A concise study delineating the role of relativistic effects in nanocluster catalysis is carried by investigating the oxygen reduction reaction (ORR) activity of a Pt₇ subnanometer cluster. Global optimization analysis shows the critical role of spin-orbit coupling (SOC) in regulating the relative stability between structural isomers of the cluster. An overall improved ORR adsorption energetics and differently scaled adsorption-induced structural changes are identified with SOC compared to a non-SOC scenario. Ab initio atomistic thermodynamics analysis predicted nearly identical phase diagrams with significant structural differences for high coverage oxygenated clusters under realistic conditions. Though inclusion of SOC does not bring about drastic changes in the overall catalytic activity of the cluster, it is having a crucial role in governing the rate-determining step, transition-state configuration, and energetics of elementary reaction pathways. Furthermore, a statistical ensemble-based approach illustrates the strong contribution of low-energy local minimum structural isomers to the total ORR activity, which is significantly scaled up along the activity improving direction within the SOC framework. The study provides critical insights toward the importance of relativistic effects in determining various catalytic activity relevant features of nanoclusters.

Chemical Batteries with CO2

Efforts to obtain raw materials from CO2 by catalytic reduction as a means of combating greenhouse gas emissions are pushing the boundaries of the chemical industry. The dimensions of modern energy regimes, on the one hand, and the necessary transport and trade of globally produced renewable energy, on the other, will require the use of chemical batteries in conjunction with the local production of renewable electricity. The synthesis of methanol is an important option for chemical batteries and will, for that reason, be described here in detail. It is also shown that the necessary, robust, and fundamental understanding of processes and the material science of catalysts for the hydrogenation of CO2 does not yet exist.

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.

Surface morphology evolution of cobalt nanoparticles induced by hydrogen adsorption: a theoretical study

Determining the surface structure and morphology under working conditions is essential to obtain facet-dependent catalytic performance.

Data-efficient iterative training of Gaussian approximation potentials: Application to surface structure determination of rutile IrO2 and RuO2

Machine-learning interatomic potentials, such as Gaussian Approximation Potentials (GAPs), constitute a powerful class of surrogate models to computationally involved first-principles calculations. At a similar predictive quality but significantly reduced cost, they could leverage otherwise barely tractable extensive sampling as in global surface structure determination (SSD). This efficiency is jeopardized though, if an a priori unknown structural and chemical search space as in SSD requires an excessive number of first-principles data for the GAP training. To this end, we present a general and data-efficient iterative training protocol that blends the creation of new training data with the actual surface exploration process. Demonstrating this protocol with the SSD of low-index facets of rutile IrO₂ and RuO₂, the involved simulated annealing on the basis of the refining GAP identifies a number of unknown terminations even in the restricted sub-space of (1 × 1) surface unit cells. Particularly in an O-poor environment, some of these, then metal-rich terminations, are thermodynamically most stable and are reminiscent of complexions as discussed for complex ceramic materials.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Diffusion Barriers for Carbon Monoxide on the Cu(001) Surface Using Many-Body Perturbation Theory and Various Density Functionals

First-principles calculations play a key role in understanding the interactions of molecules with transition-metal surfaces and the energy profiles for catalytic reactions. However, many of the commonly used density functionals are not able to correctly predict the surface energy as well as the adsorption site preference for a key molecule such as CO, and it is not clear to what extent this shortcoming influences the prediction of reaction or diffusion pathways. Here, we report calculations of carbon monoxide diffusion on the Cu(001) surface along the [100] and [110] pathways, as well as the surface energy of Cu(001), and CO-adsorption energy and compare the performance of the Perdew-Burke-Ernzerhof (PBE), PBE + D2, PBE + D3, RPBE, Bayesian error estimation functional with van der Waals correlation (BEEF-vdW), HSE06 density functionals, and the random phase approximation (RPA), a post-Hartree-Fock method based on many-body perturbation theory. We critically evaluate the performance of these methods and find that RPA appears to be the only method giving correct site preference, overall barrier, adsorption enthalpy, and surface energy. For all of the other methods, at least one of these properties is not correctly captured. These results imply that many density functional theory (DFT)-based methods lead to qualitative and quantitative errors in describing CO interaction with transition-metal surfaces, which significantly impacts the description of diffusion pathways. It is well conceivable that similar effects exist when surface reactions of CO-related species are considered. We expect that the methodology presented here will be used to get more detailed insights into reaction pathways for CO conversion on transition-metal surfaces in general and Cu in particular, which will allow us to better understand the catalytic and electrocatalytic reactions involving CO-related species.

Local Ordering of Molten Salts at NiO Crystal Interfaces Promotes High-Index Faceting

Given the strong influence of surface structure on the reactivity of heterogeneous catalysts, understanding the mechanisms that control crystal morphology is an important component of designing catalytic materials with targeted shape and functionality. Herein, we employ density functional theory to examine the impact of growth media on NiO crystal faceting in line with experimental findings, showing that molten-salt synthesis in alkali chlorides (KCl, LiCl, and NaCl) imposes shape selectivity on NiO particles. We find that the production of NiO octahedra is attributed to the dissociative adsorption of H2 O, whereas the formation of trapezohedral particles is associated with the control of the growth kinetics exerted by ordered salt structures on high-index facets. To our knowledge, this is the first observation that growth inhibition of metal-oxide facets occurs by a localized ordering of molten salts at the crystal-solvent interface. These findings provide new molecular-level insight on kinetics and thermodynamics of molten-salt synthesis as a predictive route to shape-engineer metal-oxide crystals.

On the Shape-Selected, Ligand-Free Preparation of Hybrid Perovskite (CH3NH3PbBr3) Microcrystals and Their Suitability as Model-System for Single-Crystal Studies of Optoelectronic Properties

Hybrid perovskite materials are one of the most promising candidates for optoelectronic applications, e.g., solar cells and LEDs, which can be produced at low cost compared to established materials. Although this field of research has seen a huge upsurge in the past decade, there is a major lack in understanding the underlying processes, such as shape-property relationships and the role of defects. Our aerosol-assisted synthesis pathway offers the possibility to obtain methylammonium lead bromide (MAPbBr₃) microcrystals from a liquid single source precursor. The differently shaped particles are aligned on several substrates, without using a directing agent or other additives. The obtained particles show good stability under dry conditions. This allows us to characterize these materials and their pure surfaces at the single-crystal level using time- and spatially resolved methods, without any influences of size-dependent effects. By optimizing the precursor for the aerosol process, we were able to eliminate any purification steps and use the materials as processed. In addition, we performed theoretical simulations to deepen the understanding of the underlying processes in the formation of the different crystal facets and their specific properties. The model system presented provides insights into the shape-related properties of MAPbBr₃ single crystals and their directed but ligand-free synthesis.

Adsorption Enthalpies for Catalysis Modeling through Machine-Learned Descriptors

Heterogeneous catalysts are rather complex materials that come in many classes (e.g., metals, oxides, carbides) and shapes. At the same time, the interaction of the catalyst surface with even a relatively simple gas-phase environment such as syngas (CO and H₂) may already produce a wide variety of reaction intermediates ranging from atoms to complex molecules. The starting point for creating predictive maps of, e.g., surface coverages or chemical activities of potential catalyst materials is the reliable prediction of adsorption enthalpies of all of these intermediates. For simple systems, direct density functional theory (DFT) calculations are currently the method of choice. However, a wider exploration of complex materials and reaction networks generally requires enthalpy predictions at lower computational cost.The use of machine learning (ML) and related techniques to make accurate and low-cost predictions of quantum-mechanical calculations has gained increasing attention lately. The employed approaches span from physically motivated models over hybrid physics-ΔML approaches to complete black-box methods such as deep neural networks. In recent works we have explored the possibilities for using a compressed sensing method (Sure Independence Screening and Sparsifying Operator, SISSO) to identify sparse (low-dimensional) descriptors for the prediction of adsorption enthalpies at various active-site motifs of metals and oxides. We start from a set of physically motivated primary features such as atomic acid/base properties, coordination numbers, or band moments and let the data and the compressed sensing method find the best algebraic combination of these features. Here we take this work as a starting point to categorize and compare recent ML-based approaches with a particular focus on model sparsity, data efficiency, and the level of physical insight that one can obtain from the model.Looking ahead, while many works to date have focused only on the mere prediction of databases of, e.g., adsorption enthalpies, there is also an emerging interest in our field to start using ML predictions to answer fundamental science questions about the functioning of heterogeneous catalysts or perhaps even to design better catalysts than we know today. This task is significantly simplified in works that make use of scaling-relation-based models (volcano curves), where the model outcome is determined by only one or two adsorption enthalpies and which consequently become the sole target for ML-based high-throughput screening or design. However, the availability of cheap ML energetics also allows going beyond scaling relations. On the basis of our own work in this direction, we will discuss the additional physical insight that can be achieved by integrating ML-based predictions with traditional catalysis modeling techniques from thermal and electrocatalysis, such as the computational hydrogen electrode and microkinetic modeling, as well as the challenges that lie ahead.

Thermodynamic cyclic voltammograms: peak positions and shapes

Based on a mean-field description of thermodynamic cyclic voltammograms (CVs), we analyze here in full generality, how CV peak positions and shapes are related to the underlying interface energetics, in particular when also including electrostatic double layer (DL) effects. We show in particular, how non-Nernstian behaviour is related to capacitive DL charging, and how this relates to common adsorbate-centered interpretations such as a changed adsorption energetics due to dipole-field interactions and the electrosorption valency - the number of exchanged electrons upon electrosorption per adsorbate. Using Ag(111) in halide-containing solutions as test case, we demonstrate that DL effects can introduce peak shifts that are already explained by rationalizing the interaction of isolated adsorbates with the interfacial fields, while alterations of the peak shape are mainly driven by the coverage-dependence of the adsorbate dipoles. In addition, we analyze in detail how changing the experimental conditions such as the ion concentrations in the solvent but also of the background electrolyte can affect the CV peaks via their impact on the potential drop in the DL and the DL capacitance, respectively. These results suggest new routes to analyze experimental CVs and use of those for a detailed assessment of the accuracy of atomistic models of electrified interfaces e.g. with and without explicitly treated interfacial solvent and/or approximate implicit solvent models.

True Nature of the Transition-Metal Carbide/Liquid Interface Determines Its Reactivity

Compound materials, such as transition-metal (TM) carbides, are anticipated to be effective electrocatalysts for the carbon dioxide reduction reaction (CO2RR) to useful chemicals. This expectation is nurtured by density functional theory (DFT) predictions of a break of key adsorption energy scaling relations that limit CO2RR at parent TMs. Here, we evaluate these prospects for hexagonal Mo2C in aqueous electrolytes in a multimethod experiment and theory approach. We find that surface oxide formation completely suppresses the CO2 activation. The oxides are stable down to potentials as low as -1.9 V versus the standard hydrogen electrode, and solely the hydrogen evolution reaction (HER) is found to be active. This generally points to the absolute imperative of recognizing the true interface establishing under operando conditions in computational screening of catalyst materials. When protected from ambient air and used in nonaqueous electrolyte, Mo2C indeed shows CO2RR activity.

Single-atom alloy catalysts designed by first-principles calculations and artificial intelligence

Single-atom-alloy catalysts (SAACs) have recently become a frontier in catalysis research. Simultaneous optimization of reactants' facile dissociation and a balanced strength of intermediates' binding make them highly efficient catalysts for several industrially important reactions. However, discovery of new SAACs is hindered by lack of fast yet reliable prediction of catalytic properties of the large number of candidates. We address this problem by applying a compressed-sensing data-analytics approach parameterized with density-functional inputs. Besides consistently predicting efficiency of the experimentally studied SAACs, we identify more than 200 yet unreported promising candidates. Some of these candidates are more stable and efficient than the reported ones. We have also introduced a novel approach to a qualitative analysis of complex symbolic regression models based on the data-mining method subgroup discovery. Our study demonstrates the importance of data analytics for avoiding bias in catalysis design, and provides a recipe for finding best SAACs for various applications.