Parallel kinetic Monte Carlo simulation framework incorporating accurate models of adsorbate lateral interactions

On the Capabilities of Transition Metal Carbides for Carbon Capture and Utilization Technologies

The search for cheap and active materials for the capture and activation of CO2 has led to many efforts aimed at developing new catalysts. In this context, earth-abundant transition metal carbides (TMCs) have emerged as promising candidates, garnering increased attention in recent decades due to their exceptional refractory properties and resistance to sintering, coking, and sulfur poisoning. In this work, we assess the use of Group 5 TMCs (VC, NbC, and TaC) as potential materials for carbon capture and sequestration/utilization technologies by combining experimental characterization techniques, first-principles-based multiscale modeling, vibrational analysis, and catalytic experiments. Our findings reveal that the stoichiometric phase of VC exhibits weak interactions with CO2, displaying an inability to adsorb or dissociate it. However, VC often exhibits the presence of surface carbon vacancies, leading to significant activation of CO2 at room temperature and facilitating its catalytic hydrogenation. In contrast, stoichiometric NbC and TaC phases exhibit stronger interactions with CO2, capable of adsorbing and even breaking of CO2 at low temperatures, particularly notable in the case of TaC. Nevertheless, NbC and TaC demonstrate poor catalytic performance for CO2 hydrogenation. This work suggests Group 5 TMCs as potential materials for CO2 abatement, emphasizes the importance of surface vacancies in enhancing catalytic activity and adsorption capability, and provides a reference for using the infrared spectra as a unique identifier to detect oxy-carbide phases or surface C vacancies within Group 5 TMCs.

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.

Multiscale Investigation of the Mechanism and Selectivity of CO2 Hydrogenation over Rh(111)

CO2 hydrogenation over Rh catalysts comprises multiple reaction pathways, presenting a wide range of possible intermediates and end products, with selectivity toward either CO or methane being of particular interest. We investigate in detail the reaction mechanism of CO2 hydrogenation to the single-carbon (C1) products on the Rh(111) facet by performing periodic density functional theory (DFT) calculations and kinetic Monte Carlo (kMC) simulations, which account for the adsorbate interactions through a cluster expansion approach. We observe that Rh readily facilitates the dissociation of hydrogen, thus contributing to the subsequent hydrogenation processes. The reverse water-gas shift (RWGS) reaction occurs via three different reaction pathways, with CO hydrogenation to the COH intermediate being a key step for CO2 methanation. The effects of temperature, pressure, and the composition ratio of the gas reactant feed are considered. Temperature plays a pivotal role in determining the surface coverage and adsorbate composition, with competitive adsorption between CO and H species influencing the product distribution. The observed adlayer configurations indicate that the adsorbed CO species are separated by adsorbed H atoms, with a high ratio of H to CO coverage on the Rh(111) surface being essential to promote CO2 methanation.

Transition Metal Carbides as Supports for Catalytic Metal Particles: Recent Progress and Opportunities

Transition metal carbides (TMCs) constitute excellent alternatives to traditional oxide-based supports for small metal particles, leading to strong metal-support interactions, which drastically modify the catalytic properties of the supported metal atoms. Moreover, they possess extremely high melting points and good resistance to carbon deposition and sulfur poisoning, and the catalytic activities of some TMCs per se have been shown to be similar to those of Pt-group metals for a considerable number of reactions. Therefore, the use of TMCs as supports can give rise to bifunctional catalysts with multiple active sites. However, at present, only TiC and MoxC have been tested experimentally as supports for metal particles, and it is largely unclear which combinations may best catalyze which chemical reactions. In this Perspective, we review the most significant works on the use of TMCs as supports for catalytic applications, assess the current status of the field, and identify key advances being made and challenges, with an eye to the future.

Comprehensive Density Functional and Kinetic Monte Carlo Study of CO2 Hydrogenation on a Well-Defined Ni/CeO2 Model Catalyst: Role of Eley-Rideal Reactions

A detailed multiscale study of the mechanism of CO2 hydrogenation on a well-defined Ni/CeO2 model catalyst is reported that couples periodic density functional theory (DFT) calculations with kinetic Monte Carlo (kMC) simulations. The study includes an analysis of the role of Eley-Rideal elementary steps for the water formation step, which are usually neglected on the overall picture of the mechanism, catalytic activity, and selectivity. The DFT calculations for the chosen model consisting of a Ni4 cluster supported on CeO2 (111) show large enough adsorption energies along with low energy barriers that suggest this catalyst to be a good option for high selective CO2 methanation. The kMC simulations results show a synergic effect between the two 3-fold hollow sites of the supported Ni4 cluster with some elementary reactions dominant in one site, while other reactions prefer the another, nearly equivalent site. This effect is even more evident for the simulations explicitly including Eley-Rideal steps. The kMC simulations reveal that CO is formed via the dissociative pathway of the reverse water-gas shift reaction, while methane is formed via a CO2 → CO → HCO → CH → CH2 → CH3 → CH4 mechanism. Overall, our results show the importance of including the Eley-Rideal reactions and point to small Ni clusters supported on the CeO2 (111) surface as potential good catalysts for high selective CO2 methanation under mild conditions, while very active and selective toward CO formation at higher temperatures.

Speeding up the Detection of Adsorbate Lateral Interactions in Graph-Theoretical Kinetic Monte Carlo Simulations

Kinetic Monte Carlo (KMC) has become an indispensable tool in heterogeneous catalyst discovery, but realistic simulations remain computationally demanding on account of the need to capture complex and long-range lateral interactions between adsorbates. The Zacros software package (https://zacros.org) adopts a graph-theoretical cluster expansion (CE) framework that allows such interactions to be computed with a high degree of generality and fidelity. This involves solving a series of subgraph isomorphism problems in order to identify relevant interaction patterns in the lattice. In an effort to reduce the computational burden, we have adapted two well-known subgraph isomorphism algorithms, namely, VF2 and RI, for use in KMC simulations and implemented them in Zacros. To benchmark their performance, we simulate a previously established model of catalytic NO oxidation, treating the O* lateral interactions with a series of progressively larger CEs. For CEs with long-range interactions, VF2 and RI are found to provide impressive speedups relative to simpler algorithms. RI performs best, giving speedups reaching more than 150× when combined with OpenMP parallelization. We also simulate a recently developed methane cracking model, showing that RI offers significant improvements in performance at high surface coverages.

Exact distributed kinetic Monte Carlo simulations for on-lattice chemical kinetics: lessons learnt from medium- and large-scale benchmarks

Kinetic Monte Carlo (KMC) simulations have been instrumental in multiscale catalysis studies, enabling the elucidation of the complex dynamics of heterogeneous catalysts and the prediction of macroscopic performance metrics, such as activity and selectivity. However, the accessible length- and time-scales have been a limiting factor in such simulations. For instance, handling lattices containing millions of sites with 'traditional' sequential KMC implementations is prohibitive owing to large memory requirements and long simulation times. We have recently established an approach for exact, distributed, lattice-based simulations of catalytic kinetics which couples the Time-Warp algorithm with the Graph-Theoretical KMC framework, enabling the handling of complex adsorbate lateral interactions and reaction events within large lattices. In this work, we develop a lattice-based variant of the Brusselator system, a prototype chemical oscillator pioneered by Prigogine and Lefever in the late 60s, to benchmark and demonstrate our approach. This system can form spiral wave patterns, which would be computationally intractable with sequential KMC, while our distributed KMC approach can simulate such patterns 15 and 36 times faster with 625 and 1600 processors, respectively. The medium- and large-scale benchmarks thus conducted, demonstrate the robustness of the approach, and reveal computational bottlenecks that could be targeted in further development efforts. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Assessing the Impact of Adlayer Description Fidelity on Theoretical Predictions of Coking on Ni(111) at Steam Reforming Conditions

Methane steam reforming is an important industrial process for hydrogen production, employing Ni as a low-cost, highly active catalyst, which, however, suffers from coking due to methane cracking. Coking is the accumulation of a stable poison over time, occurring at high temperatures; thus, to a first approximation, it can be treated as a thermodynamic problem. In this work, we developed an Ab initio kinetic Monte Carlo (KMC) model for methane cracking on Ni(111) at steam reforming conditions. The model captures C-H activation kinetics in detail, while graphene sheet formation is described at the level of thermodynamics, to obtain insights into the "terminal (poisoned) state" of graphene/coke within reasonable computational times. We used cluster expansions (CEs) of progressively higher fidelity to systematically assess the influence of effective cluster interactions between adsorbed or covalently bonded C and CH species on the "terminal state" morphology. Moreover, we compared the predictions of KMC models incorporating these CEs into mean-field microkinetic models in a consistent manner. The models show that the "terminal state" changes significantly with the level of fidelity of the CEs. Furthermore, high-fidelity simulations predict C-CH island/rings that are largely disconnected at low temperatures but completely encapsulate the Ni(111) surface at high temperatures.

Formation of active sites on transition metals through reaction-driven migration of surface atoms

Adopting low-index single-crystal surfaces as models for metal nanoparticle catalysts has been questioned by the experimental findings of adsorbate-induced formation of subnanometer clusters on several single-crystal surfaces. We used density functional theory calculations to elucidate the conditions that lead to cluster formation and show how adatom formation energies enable efficient screening of the conditions required for adsorbate-induced cluster formation. We studied a combination of eight face-centered cubic transition metals and 18 common surface intermediates and identified systems relevant to catalytic reactions, such as carbon monoxide (CO) oxidation and ammonia (NH₃) oxidation. We used kinetic Monte Carlo simulations to elucidate the CO-induced cluster formation process on a copper surface. Scanning tunneling microscopy of CO on a nickel (111) surface that contains steps and dislocations points to the structure sensitivity of this phenomenon. Metal-metal bond breaking that leads to the evolution of catalyst structures under realistic reaction conditions occurs much more broadly than previously thought.

Ethane Dehydrogenation over the Core-Shell Pt-Based Alloy Catalysts: Driven by Engineering the Shell Composition and Thickness

Pt-based catalysts as the commercial catalysts in ethane dehydrogenation (EDH) face one of the main challenges of realizing the balance between coke formation and catalytic activity. In this work, a strategy to drive the catalytic performance of EDH on Pt-Sn alloy catalysts is proposed by rationally engineering the shell surface structure and thickness of core-shell Pt@Pt₃Sn and Pt₃Sn@Pt catalysts from a theoretical perspective. Eight types of Pt@Pt₃Sn and Pt₃Sn@Pt catalysts with different Pt and Pt₃Sn shell thicknesses are considered and compared with the industrially used Pt and Pt₃Sn catalysts. Density functional theory (DFT) calculations completely describe the reaction network of EDH, including the side reactions of deep dehydrogenation and C-C bond cracking. Kinetic Monte Carlo (kMC) simulations reveal the influences of the catalyst surface structure, experimentally related temperatures, and reactant partial pressures. The results show that CHCH* is the main precursor for coke formation, and Pt@Pt₃Sn catalysts generally have higher C₂H₄(g) activity and lower selectivity compared to those of Pt₃Sn@Pt catalysts, which is attributed to the unique surface geometrical and electronic properties. 1Pt₃Sn@4Pt and 1Pt@4Pt₃Sn are screened out as catalysts exhibiting excellent performance; especially, the 1Pt₃Sn@4Pt catalyst has much higher C₂H₄(g) activity and 100% C₂H₄(g) selectivity compared to those of 1Pt@4Pt₃Sn and the widely used Pt and Pt₃Sn catalysts. The two descriptors C₂H₅* adsorption energy and reaction energy of its dehydrogenation to C₂H₄* are proposed to qualitatively evaluate the C₂H₄(g) selectivity and activity, respectively. This work facilitates a valuable exploration for optimizing the catalytic performance of core-shell Pt-based catalysts in EDH and reveals the great importance of the fine control of the catalyst shell surface structure and thickness.

Large-scale benchmarks of the time-warp/graph-theoretical kinetic Monte Carlo approach for distributed on-lattice simulations of catalytic kinetics

Motivated by the need to perform large-scale kinetic Monte Carlo (KMC) simulations, in the context of unravelling complex phenomena such as catalyst reconstruction and pattern formation, we extend the work of Ravipati et al. [S. Ravipati, G. D. Savva, I.-A. Christidi, R. Guichard, J. Nielsen, R. Réocreux and M. Stamatakis, Comput. Phys. Commun., 2022, 270, 108148] in benchmarking the performance of a distributed-computing, on-lattice KMC approach. The latter, implemented in our software package Zacros, combines the graph-theoretical KMC framework with the Time-Warp algorithm for parallel discrete event simulations, and entails dividing the lattice into subdomains, each assigned to a processor. The cornerstone of the Time-Warp algorithm is the state queue, to which snapshots of the simulation state are saved regularly, enabling historical KMC information to be corrected when conflicts occur at subdomain boundaries. Focusing on three model systems, we highlight the key Time-Warp parameters that can be tuned to optimise performance. The frequency of state saving, controlled by the state saving interval, δ_snap, is shown to have the largest effect on performance, which favours balancing the overhead of re-simulating KMC history with that of writing state snapshots to memory. Also important is the global virtual time (GVT) computation interval, Δτ_GVT, which has little direct effect on the progress of the simulation but controls how often the state queue memory can be freed up. We also find that pre-allocating memory for the state queue data structure favours performance. These findings will guide users in maximising the efficiency of Zacros or other distributed KMC software, which is a vital step towards realising accurate, meso-scale simulations of heterogeneous catalysis.

Quantum Tunnelling Driven H2 Formation on Graphene

It is commonly believed that it is unfavorable for adsorbed H atoms on carbonaceous surfaces to form H₂ without the help of incident H atoms. Using ring-polymer instanton theory to describe multidimensional tunnelling effects, combined with ab initio electronic structure calculations, we find that these quantum-mechanical simulations reveal a qualitatively different picture. Recombination of adsorbed H atoms, which was believed to be irrelevant at low temperature due to high barriers, is enabled by deep tunnelling, with reaction rates enhanced by tens of orders of magnitude. Furthermore, we identify a new path for H recombination that proceeds via multidimensional tunnelling but would have been predicted to be unfeasible by a simple one-dimensional description of the reaction. The results suggest that hydrogen molecule formation at low temperatures are rather fast processes that should not be ignored in experimental settings and natural environments with graphene, graphite, and other planar carbon segments.

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.

Stability and Bandgap Engineering of In1-xGaxSe Monolayer

Bandgap engineering of semiconductor materials represents a crucial step for their employment in optoelectronics and photonics. It offers the opportunity to tailor their electronic and optical properties, increasing the degree of freedom in designing new devices and widening the range of their possible applications. Here, we report the bandgap engineering of a layered InSe monolayer, a superior electronic and optical material, by substituting In atoms with Ga atoms. We developed a theoretical understanding of In1−xGaxSe stability and electronic properties in its whole compositional range (x=0−1) through first-principles density functional theory calculations, the cluster expansion method, and kinetic Monte Carlo simulations. Our findings highlight the possibility of modulating the InGaSe bandgap by ≈0.41 eV and reveal that this compound is an excellent candidate to be employed in many optoelectronic and photonic devices.

Effects of surface diffusion in electrocatalytic CO2 reduction on Cu revealed by kinetic Monte Carlo simulations

Kinetic Monte Carlo (KMC) methods are frequently used for mechanistic studies of thermally driven heterogeneous catalysis systems but are underused for electrocatalysis. Here, we develop a lattice KMC approach for electrocatalytic CO₂ reduction. The work is motivated by a prior experimental report that performed electroreduction of a mixed feed of ¹²CO₂ and ¹³CO on Cu; differences in the ¹³C content of C2 products ethylene and ethanol (Δ¹³C) were interpreted as evidence of site selectivity. The lattice KMC model considers the effect of surface diffusion on this system. In the limit of infinitely fast diffusion (mean-field approximation), the key intermediates ¹²CO* and ¹³CO* would be well mixed on the surface and no evidence of site selectivity could have been observed. Using a simple two-site model and adapting a previously reported microkinetic model, we assess the effects of diffusion on the relative isotope fractions in the products using the estimated surface diffusion rate of CO* from literature reports. We find that the size of the active sites and the total surface adsorbate coverage can have a large influence on the values of Δ¹³C that can be observed. Δ¹³C is less sensitive to the CO* diffusion rate as long as it is within the estimated range. We further offer possible methods to estimate surface distribution of intermediates and to predict intrinsic selectivity of active sites based on experimental observations. This work illustrates the importance of considering surface diffusion in the study of electrochemical CO₂ reduction to multi-carbon products. Our approach is entirely based on a freely available open-source code, so will be readily adaptable to other electrocatalytic systems.

Effect of Surface Oxidation on Oxidative Propane Dehydrogenation over Chromia: An Ab Initio Multiscale Kinetic Study

An increasingly utilized way for the production of propene is propane dehydrogenation. The reaction presents an alternative to conventional processes based on petroleum resources. In this work, we investigate theoretically how Cr₂O₃ catalyzes this reaction in oxidative and reducing environments. Although previous studies showed that the reduced catalyst is selective for the non-oxidative dehydrogenation of propane, real operating conditions are oxidative. Herein, we use multiscale modeling to investigate the difference between the oxidized and reduced catalyst and their performance. The complete reaction pathway for propane dehydrogenation, including C-C cracking, formation of side products (propyne, ethane, ethylene, acetylene, and methane), and catalyst coking on oxidized and reduced surfaces of α-Cr₂O₃(0001), is calculated using density functional theory with the Hubbard correction. Parameters describing adsorption, desorption, and surface reactions are used in a kinetic Monte Carlo simulation, which employed industrially relevant conditions (700-900 K, pressures up to 2 bar, and varying oxidants: N₂O, O₂, and none). We observe that over the reduced surface, propene and hydrogen form with high selectivity. When oxidants are used, the surface is oxidized, which changes the reaction mechanism and kinetics. During a much faster reaction, H₂O forms as a coproduct in a Mars-van Krevelen cycle. Additionally, CO₂ is also formed, which represents waste and adversely affects the selectivity. It is shown that the oxidized surface is much more active but prone to the formation of CO₂, while the reduced surface is less active but highly selective toward propene. Moreover, the effect of the oxidant used is investigated, showing that N₂O is preferred to O₂ due to higher selectivity and less catalyst coking. We show that there exists an optimum degree of surface oxidation, where the yield of propene is maximized. The coke, which forms during the reaction, can be burnt away as CO₂ with oxygen.

Mechanistic insights into carbon-carbon coupling on NiAu and PdAu single-atom alloys

Carbon-carbon coupling is an important step in many catalytic reactions, and performing sp³-sp³ carbon-carbon coupling heterogeneously is particularly challenging. It has been reported that PdAu single-atom alloy (SAA) model catalytic surfaces are able to selectively couple methyl groups, producing ethane from methyl iodide. Herein, we extend this study to NiAu SAAs and find that Ni atoms in Au are active for C-I cleavage and selective sp³-sp³ carbon-carbon coupling to produce ethane. Furthermore, we perform ab initio kinetic Monte Carlo simulations that include the effect of the iodine atom, which was previously considered a bystander species. We find that model NiAu surfaces exhibit a similar chemistry to PdAu, but the reason for the similarity is due to the role the iodine atoms play in terms of blocking the Ni atom active sites. Specifically, on NiAu SAAs, the iodine atoms outcompete the methyl groups for occupancy of the Ni sites leaving the Me groups on Au, while on PdAu SAAs, the binding strengths of methyl groups and iodine atoms at the Pd atom active site are more similar. These simulations shed light on the mechanism of this important sp³-sp³ carbon-carbon coupling chemistry on SAAs. Furthermore, we discuss the effect of the iodine atoms on the reaction energetics and make an analogy between the effect of iodine as an active site blocker on this model heterogeneous catalyst and homogeneous catalysts in which ligands must detach in order for the active site to be accessed by the reactants.

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

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

A multiscale modelling approach to elucidate the mechanism of the oxygen evolution reaction at the hematite-water interface

Photoelectrochemical (PEC) splitting of water to make hydrogen is a promising clean-energy technology. The oxygen evolution reaction (OER) largely determines the energy efficiency in PEC water-splitting. Hematite, which is a cheap and sustainable semiconductor material with excellent chemical properties, a favourable band gap (2.1 eV) and composed of earth abundant elements is a suitable model photoanode material for studying OER. To understand the design of energy efficient anodes, it is highly desirable to have mechanistic insight into OER at an atomistic level which can be directly connected to experimentally measured quantities. We present a multiscale computational model of OER which connects the thermodynamics and kinetics of elementary charge transfer reactions in OER to kinetics of OER at laboratory length and time scales. We couple density functional theory (DFT) and DFT based molecular dynamics (DFT-MD) simulations with solvent effects at an atomistic level with kinetic Monte Carlo (kMC) simulations at a coarse-grained level in our multiscale model. The time and applied bias potential dependent surface coverage, which are experimentally not known, and the O₂ evolution rate during OER at the hematite-water interface are calculated by the multiscale model. Furthermore, the multiscale model demonstrates the effect of explicitly modelling the interaction of water with the electrode surface via direct adsorption.

Concluding remarks: Reaction mechanisms in catalysis: perspectives and prospects

We consider the current status of our understanding of reaction mechanisms in catalysis in the light of the papers presented in this Discussion. We identify some of the challenges in both theoretical and experimental studies, which we illustrate by considering three key reactions.

The role of oxygenated species in the catalytic self-coupling of MeOH on O pre-covered Au(111)

The oxidation of alcohols plays a central role in the valorisation of biomass, in particular when performed with a non-toxic oxidant such as O₂. Aerobic oxidation of methanol on gold has attracted attention lately and the main steps of its mechanism have been described experimentally. However, the exact role of O and OH on each elementary step and the effect of the interactions between adsorbates are still not completely understood. Here we investigate the mechanism of methanol oxidation to HCOOCH₃ and CO₂. We use Density Functional Theory (DFT) to assess the energetics of the underlying pathways, and subsequently build lattice kinetic Monte Carlo (kMC) models of increasing complexity, to elucidate the role of different oxygenates. Detailed comparisons of our simulation results with experimental temperature programmed desorption (TPD) spectra enable us to validate the mechanism and identify rate determining steps. Crucially, taking into account dispersion (van der Waals forces) and adsorbate-adsorbate lateral interactions are both important for reproducing the experimental data.

Directing reaction pathways via in situ control of active site geometries in PdAu single-atom alloy catalysts

The atomic scale structure of the active sites in heterogeneous catalysts is central to their reactivity and selectivity. Therefore, understanding active site stability and evolution under different reaction conditions is key to the design of efficient and robust catalysts. Herein we describe theoretical calculations which predict that carbon monoxide can be used to stabilize different active site geometries in bimetallic alloys and then demonstrate experimentally that the same PdAu bimetallic catalyst can be transitioned between a single-atom alloy and a Pd cluster phase. Each state of the catalyst exhibits distinct selectivity for the dehydrogenation of ethanol reaction with the single-atom alloy phase exhibiting high selectivity to acetaldehyde and hydrogen versus a range of products from Pd clusters. First-principles based Monte Carlo calculations explain the origin of this active site ensemble size tuning effect, and this work serves as a demonstration of what should be a general phenomenon that enables in situ control over catalyst selectivity.

Single-Atom Alloys for the Electrochemical Oxygen Reduction Reaction

Single-atom alloys (SAAs) consisting of isolated transition-metal atoms doped in the surface of coinage metal hosts exhibit unique catalytic properties, harnessing the high activity of the dopant metals with the selectivity of the coinage metal hosts. Here we use density functional theory (DFT) to study SAAs comprised of Ni, Pd, Pt, Co and Rh doped into Ag and Au hosts, as candidate electrocatalysts for the oxygen reduction reaction (ORR) in proton-exchange membrane (PEM) fuel-cells. Our calculations reveal that the PdAu SAA exhibits a slightly lower theoretical overpotential, enhanced selectivity for 4-e- ORR, and tolerance to CO-poisoning compared to Pt(111). While the number of active sites of PdAu SAA is lower than that of Pt(111), the aforementioned desirable properties could bring the overall catalytic performance thereof close to that of Pt/C, indicating that the PdAu SAA could be a viable material for electrocatalytic ORR in PEM fuel-cells.

Multi-scale Simulation of Equilibrium Step Fluctuations on Cu(111) Surfaces

Understanding the nature of active sites is a non-trivial task, especially when the catalyst is sensitively affected by chemical reactions and environmental conditions. The challenge lies on capturing explicitly the dynamics of catalyst evolution during reactions. Despite the complexity of catalyst reconstruction, we can untangle them into several elementary processes, of which surface diffusion is of prime importance. By applying density functional theory-kinetic Monte Carlo (DFT-KMC) simulation employed with cluster expansion (CE), we investigated the microscopic mechanism of surface diffusion of Cu with defects such as steps and kinks. Based on the result, the energetics obtained from CE have shown good agreement with DFT calculations. Various diffusion events during the step fluctuations are discussed as well. Aside from the adatom attachment, the diffusion along the step edge is found to be the dominant mass transport mechanism, indicated by the lowest activation energy. We also calculated time correlation functions at 300, 400, and 500 K. However, the time exponent in the correlation function does not strictly follow the power law behavior due to the limited step length, which inhibits variation in the kink density.

Computational Methods in Heterogeneous Catalysis

The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. We finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.

First-Principles-Based Multiscale Modelling of Nonoxidative Butane Dehydrogenation on Cr2O3(0001)

Propane (C3H8) and butane (C4H10) are short straight-chain alkane molecules that are difficult to convert catalytically. Analogous to propane, butane can be dehydrogenated to butenes (also known as butylenes) or butadiene, which are used industrially as raw materials when synthesizing various chemicals (plastics, rubbers, etc.). In this study, we present results of detailed first-principles-based multiscale modelling of butane dehydrogenation, consisting of three size- and time-scales. The reaction is modelled over Cr2O3(0001) chromium oxide, which is commonly used in the industrial setting. A complete 108-step reaction pathway of butane (C4H10) dehydrogenation was studied, yielding 1-butene (CH2CHCH2CH3) and 2-butene (CH3CHCHCH3), 1-butyne (CHCCH2CH3) and 2-butyne (CH3CCCH3), butadiene (CH2CHCHCH2), butenyne (CH2CHCCH), and ultimately butadiyne (CHCCCH). We include cracking and coking reactions (yielding C1, C2, and C3 hydrocarbons) in the model to provide a thorough description of catalyst deactivation as a function of the temperature and time. Density functional theory calculations with the Hubbard U model were used to study the reaction on the atomistic scale, resulting in the complete energetics and first-principles kinetic parameters for the dehydrogenation reaction. They were cast in a kinetic model using mean-field microkinetics and kinetic Monte Carlo simulations. The former was used to obtain gas equilibrium conditions in the steady-state regime, which were fed in the latter to provide accurate surface kinetics. A full reactor simulation was used to account for the macroscopic properties of the catalytic particles: their loading, specific surface area, and density and reactor parameters: size, design, and feed gas flow. With this approach, we obtained first-principles estimates of the catalytic conversion, selectivity to products, and time dependence of the catalyst activity, which can be paralleled to experimental data. We show that 2-butene is the most abundant product of dehydrogenation, with selectivity above 90% and turn-over frequency above 10-3 s-1 at T = 900 K. Butane conversion is below 5% at such low temperature, but rises above 40% at T > 1100 K. Activity starts to drop after ∼6 h because of surface poisoning with carbon. We conclude that the dehydrogenation of butane is a viable alternative to conventional olefin production processes.

Controlling Hydrocarbon (De)Hydrogenation Pathways with Bifunctional PtCu Single-Atom Alloys

The conversions of surface-bound alkyl groups to alkanes and alkenes are important steps in many heterogeneously catalyzed reactions. On the one hand, while Pt is ubiquitous in industry because of its high activity toward C-H activation, many Pt-based catalysts tend to overbind reactive intermediates, which leads to deactivation by carbon deposition and coke formation. On the other hand, Cu binds intermediates more weakly than Pt, but activation barriers tend to be higher on Cu. We examine the reactivity of ethyl, the simplest alkyl group that can undergo hydrogenation and dehydrogenation via β-elimination, and show that isolated Pt atoms in Cu enable low-temperature hydrogenation of ethyl, unseen on Cu, while avoiding the decomposition pathways on pure Pt that lead to coking. Furthermore, we confirm the predictions of our theoretical model and experimentally demonstrate that the selectivity of ethyl (de)hydrogenation can be controlled by changing the surface coverage of hydrogen.

Comparison of Queueing Data-Structures for Kinetic Monte Carlo Simulations of Heterogeneous Catalysts

On-lattice kinetic Monte Carlo (KMC) is a computational method used to simulate (among others) physicochemical processes on catalytic surfaces. The KMC algorithm propagates the system through discrete configurations by selecting (with the use of random numbers) the next elementary process to be simulated, e.g., adsorption, desorption, diffusion, or reaction. An implementation of such a selection procedure is the first-reaction method in which all realizable elementary processes are identified and assigned a random occurrence time based on their rate constant. The next event to be executed will then be the one with the minimum interarrival time. Thus, a fast and efficient algorithm for selecting the most imminent process and performing all of the necessary updates on the list of realizable processes post execution is of great importance. In the current work, we implement five data-structures to handle the elementary process queue during a KMC run: an unsorted list, a binary heap, a pairing heap, a one-way skip list, and finally, a novel two-way skip list with a mapping array specialized for KMC simulations. We also investigate the effect of compiler optimizations on the performance of these data-structures on three benchmark models, capturing CO oxidation, a simplified water gas shift mechanism, and a temperature-programmed desorption run. Excluding the least efficient and impractical for large-problems unsorted list, we observe a 3× speedup of the binary or pairing heaps (most efficient) compared to the one-way skip list (least efficient). Compiler optimizations deliver a speedup of up to 1.8×. These benchmarks provide valuable insight into the importance of, often-overlooked, implementation-related aspects of KMC simulations, such as the queueing data-structures. Our results could be particularly useful in guiding the choice of data-structures and algorithms that would minimize the computational cost of large-scale simulations.

A Caching Scheme To Accelerate Kinetic Monte Carlo Simulations of Catalytic Reactions

Kinetic Monte Carlo (KMC) simulations have been instrumental in advancing our fundamental understanding of heterogeneously catalyzed reactions, with particular emphasis on structure sensitivity, ensemble effects, and the interplay between adlayer structure and adsorbate-adsorbate lateral interactions in shaping the observed kinetics. Yet, the computational cost of KMC remains high, thereby motivating the development of acceleration schemes that would improve the simulation efficiency. We present an exact such scheme, which implements a caching algorithm along with shared-memory parallelization to improve the computational performance of simulations incorporating long-range adsorbate-adsorbate lateral interactions. This scheme is based on caching information about the energetic interaction patterns associated with the products of each possible lattice process (adsorption, desorption, reaction etc.). Thus, every time a reaction occurs ("ongoing reaction"), it enables fast updates of the rate constants of "affected reactions", i.e., possible reactions in the region of influence of the "ongoing reaction". Benchmarks on KMC simulations of NO_x oxidation/reduction, yielded acceleration factors of up to 20, when comparing single-thread runs without caching to runs on 16 threads with caching, for simulations with a cluster expansion Hamiltonian that incorporates up to 8th-nearest-neighbor interactions.

A fast species redistribution approach to accelerate the kinetic Monte Carlo simulation for heterogeneous catalysis

The first-principles kinetic Monte Carlo (kMC) simulation has been demonstrated as a reliable multiscale modeling approach in silico to disclose the interplay among all the elementary steps in a complex reaction network for heterogeneous catalysis. Heterogeneous catalytic systems frequently contain fast surface diffusion processes of some adsorbates while the elementary steps in it would be much slower than those in fast diffusion. Consequently, the kMC simulation for these systems is easily trapped in the sub-basins of a super basin on a potential energy surface due to the continuous and repeated sampling of these fast processes, which would significantly increase the total accessible simulation time and even make it impossible to get the reasonable simulation results using the kMC simulation. In this work, we present an improved fast species redistribution (FSR) method for the kMC simulation to overcome the stiffness problem resulting from the low-barrier surface diffusion to accelerate the heterogeneous catalytic kMC simulation. Taking CO oxidations on Pt(111) and Pt(100) as examples, we demonstrate that the FSR approach can properly reproduce the results of an equivalent first-principles microkinetic model simulation with more reasonable reaction rates. The improved kMC simulation based on the FSR method can accurately incorporate the effect of the fast diffusion of species on the surface and provide several orders of magnitude of acceleration compared to the standard kMC simulation.

How Size Matters: Electronic, Cooperative, and Geometric Effect in Perovskite-Supported Copper Catalysts for CO2 Reduction

In heterogeneous catalysis, bifunctional catalysts often outperform one-component catalysts. The activity is also strongly influenced by the morphology, size, and distribution of catalytic particles. For CO2 hydrogenation, the size of the active copper area on top of the SrTiO3 perovskite catalyst support can affect the activity, selectivity, and stability. Here, a detailed theoretical study of the effect of bifunctionality on an important chemical CO2 transformation reaction, the reverse water gas shift (RWGS) reaction, is presented. Using density functional theory computation results for the RWGS pathway on three surfaces, namely, Cu(111), SrTiO3, and the Cu/SrTiO3 interface between both solid phases, we construct the energy landscape of the reaction. The adsorbate-adsorbate lateral interactions are taken into account for catalytic surfaces, which show a sufficient intermediate coverage. The mechanism, combining all three surfaces, is used in mesoscale kinetic Monte Carlo simulations to study the turnover and yield for CO production as a function of particle size. It is shown that the reaction proceeds faster at the interface. However, including copper and the support sites in addition to the interface accelerates the conversion even further, showing that the bifunctionality of the catalyst manifests in a more complex interplay between the phases than just the interface effect, such as the hydrogen spillover. We identify three distinct effects, the electronic, cooperative, and geometric effects, and show that the surrounded smaller Cu features on the set of supporting SrTiO3 show a higher CO formation rate, resulting in a decreasing RWGS model trend with the increasing Cu island size. The findings are in parallel with experiments, showing that they explain the previously observed phenomena and confirming the size sensitivity for the catalytic RWGS reaction.

A DFT and KMC based study on the mechanism of the water gas shift reaction on the Pd(100) surface

We present a combined density functional theory (DFT) and Kinetic Monte Carlo (KMC) study of the water gas shift (WGS) reaction on the Pd(100) surface. We propose a mechanism comprising both the redox and the associative pathways for the WGS within a single framework, which consists of seven core elementary steps, which in turn involve splitting of a water molecule followed by the production of an H-atom and an OH-species on the Pd(100) surface. In the following steps, these intermediates then recombine with each other and with CO leading to the evolution of CO₂, and H₂. Seven other elementary steps, involving the diffusion and adsorption of the surface intermediate species are also considered for a complete description of the mechanism. The geometrical and electronic properties of each of the reactants, products, and the transition states of the core elementary steps are presented. We also discuss the analysis of Bader charges and spin densities for the reactants, transition states and the products of these elementary steps. Our study indicates that the WGS reaction progresses simultaneously via the direct oxidation and the carboxyl paths on the Pd(100) surface.

Controlled Pore Generation in Single-Layer Graphene Oxide for Membrane Desalination

Nanoporous graphene was proposed as an efficient material for reverse osmosis water desalination membranes because it allows water molecules to pass at high flux while rejecting hydrated salt ions. Nevertheless, from an experimental point of view it is still difficult to control the pore size. A scalable method to generate pores is urgently required for the diffusion of this technology. We propose, by theoretical calculations, an innovative and scalable strategy to better control the dimension of the pores in graphene-based membranes by reduction of single-layer graphene oxide (GO). The latter is first annealed at a controlled mild temperature to induce the aggregation of its randomly distributed oxygen-containing functional groups into small nanometric clusters. The layer then undergoes a high-temperature reducing treatment that causes the desorption of the functional groups along with carbon removal only in the oxidized areas, producing subnanometric pores while leaving unchanged the remaining pristine graphene areas.