Assessment of mean-field microkinetic models for CO methanation on stepped metal surfaces using accelerated kinetic Monte Carlo

Comparative simulations of methanol steam reforming on PdZn alloy using kinetic Monte Carlo and mean-field microkinetic model

Methanol steam reforming (MSR) is an attractive route for producing clean energy hydrogen. PdZn alloys are extensively studied as potential MSR catalysts for their stability and high CO2 selectivity. Here, we investigated the reaction mechanism using density functional calculations, mean-field microkinetic modeling (MF-MKM), and kinetic Monte Carlo (kMC) simulations. To overcome the over-underestimation of CO2 selectivity by log-kMC, an ads-kMC algorithm is proposed in which the adsorption/desorption rate constants were reduced under certain requirements and the diffusion process was treated by redistributing surface species each time an event occured. The simulations show that the dominant pathway to CO2 at low temperatures is CH3OH → CH3O → CH2O → H2COOH → H2COO → HCOO → CO2. The ads-kMC predicted OH coverage is 2-3 times that of MF-MKM, while they produce similar coverage for other species. Analyses indicate that surface OH promotes the dehydrogenation of CH3OH, CH3O, and H2COOH significantly and plays a key role in the MSR process. The dissociation of water/methanol is the most important rate-limiting/rate-inhibiting step. The CO2 selectivity obtained by the two methods is close to each other and consistent with the experimental trend with temperature. Generally, the ads-kMC results agree with the MF-MKM ones, supporting the previous finding that kMC and MF-MKM predict similar results if the diffusion is very fast and adsorbate interactions are neglected. The present study sheds light on the MSR process on PdZn alloys, and the proposed scheme to overcome the stiff problems in kMC simulations is worthy of being extended to other systems.

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

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

Two-Dimensional Layered Heterojunctions for Photoelectrocatalysis

Two-dimensional (2D) layered nanomaterial heterostructures, arising from the combination of 2D materials with other low-dimensional species, feature a large surface area to volume ratio, which provides a high density of active sites for catalytic applications and for (photo)electrocatalysis (PEC). Meanwhile, their electronic band structure and high electrical conductivity enable efficient charge transfer (CT) between the active material and the substrate, which is essential for catalytic activity. In recent years, researchers have demonstrated the potential of a range of 2D material interfaces, such as graphene, graphitic carbon nitride (g-C3N4), metal chalcogenides (MCs), and MXenes, for (photo)electrocatalytic applications. For instance, MCs such as MoS2 and WS2 have shown excellent catalytic activity for hydrogen evolution, while graphene and MXenes have been used for the reduction of carbon dioxide to higher value chemicals. However, despite their great potential, there are still major challenges that need to be addressed to fully realize the potential of 2D materials for PEC. For example, their stability under harsh reaction conditions, as well as their scalability for large-scale production are important factors to be considered. Generating heterojunctions (HJs) by combining 2D layered structures with other nanomaterials is a promising method to improve the photoelectrocatalytic properties of the former. In this review, we inspect thoroughly the recent literature, to demonstrate the significant potential that arises from utilizing 2D layered heterostructures in PEC processes across a broad spectrum of applications, from energy conversion and storage to environmental remediation. With the ongoing research and development, it is likely that the potential of these materials will be fully expressed in the near future.

Kinetic Trapping of Charge-Transfer Molecules at Metal Interfaces

Despite the common expectation that conjugated organic molecules on metals adsorb in a flat-lying layer, several recent studies have found coverage-dependent transitions to upright-standing phases, which exhibit notably different physical properties. In this work, we argue that from an energetic perspective, thermodynamically stable upright-standing phases may be more common than hitherto thought. However, for kinetic reasons, this phase may often not be observed experimentally. Using first-principles kinetic Monte Carlo simulations, we find that the structure with lower molecular density is (almost) always formed first, reminiscent of Ostwald's rule of stages. The phase transitions to the upright-standing phase are likely to be kinetically hindered under the conditions typically used in surface science. The simulation results are experimentally confirmed for the adsorption of tetracyanoethylene on Cu(111) using infrared and X-ray photoemission spectroscopy. Investigating both the role of the growth conditions and the energetics of the interface, we find that the time for the phase transition is determined mostly by the deposition rate and, thus, is mostly independent of the nature of the molecule.

Linear Scaling Relationships for Furan Hydrodeoxygenation over Transition Metal and Bimetallic Surfaces

Brønsted-Evans-Polanyi (BEP) and transition-state-scaling (TSS) relationships have become valuable tools for the rational design of catalysts for complex reactions like hydrodeoxygenation (HDO) of bio-oil (containing heterocyclic and homocyclic molecules). In this work, BEP and TSS relationships are developed for all the elementary steps of furan activation (C and O hydrogenation and CHx -OHy scission, for both ring and open-ring intermediates) to oxygenates, ring-saturated compounds and deoxygenated products on the most stable facets of Ni, Co, Rh, Ru, Pt, Pd, Fe and Ir surfaces using Density Functional Theory (DFT) calculations. Furan ring opening barriers were found to be facile and strongly dependent on carbon and oxygen binding strength on the investigated surfaces. Our calculations suggest linear chain oxygenates form on Ir, Pt, Pd and Rh surfaces due to their low hydrogenation and high CHx -OHy scission barriers, while deoxygenated linear products are favoured on Fe and Ni surfaces due to their low CHx -OHy scission and moderate hydrogenation barriers. Bimetallic alloy catalysts were also screened for their potential HDO activity and PtFe catalysts were found to significantly lower the ring opening and deoxygenation barriers relative to the corresponding pure metals. The developed BEPs for monometallic surfaces can be extended to estimate the barriers on bimetallic surfaces for ring opening and ring hydrogenation reactions but fails to predict the barriers for open-ring activation reactions due to the change in transition state binding sites on the bimetallic surface. The obtained BEP and TSS relationships can be used to develop microkinetic models for facilitating accelerated catalyst discovery for HDO.

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.

Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems

The net rate of a reversible chemical reaction is the difference between unidirectional rates of traversal along forward and reverse reaction paths. In a multistep reaction sequence, the forward and reverse trajectories, in general, are not the microscopic reverse of one another; rather, each unidirectional route is comprised of distinct rate-controlling steps, intermediates, and transition states. Consequently, traditional descriptors of rate (e.g., reaction orders) do not reflect intrinsic kinetic information but instead conflate unidirectional contributions determined by (i) the microscopic occurrence of forward/reverse reactions (i.e., unidirectional kinetics) and (ii) the reversibility of reaction (i.e., nonequilibrium thermodynamics). This review aims to provide a comprehensive resource of analytical and conceptual tools which deconvolute the contributions of reaction kinetics and thermodynamics to disambiguate unidirectional reaction trajectories and precisely identify rate- and reversibility-controlling molecular species and steps in reversible reaction systems. The extrication of mechanistic and kinetic information from bidirectional reactions is accomplished through equation-based formalisms (e.g., De Donder relations) grounded in principles of thermodynamics and interpreted in the context of theories of chemical kinetics developed in the past 25 years. The aggregate of mathematical formalisms detailed herein is general to thermochemical and electrochemical reactions and encapsulates a diverse body of scientific literature encompassing chemical physics, thermodynamics, chemical kinetics, catalysis, and kinetic modeling.

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.

Kinetic description of site ensembles on catalytic surfaces

We demonstrate that the Langmuir-Hinshelwood formalism is an incomplete kinetic description and, in particular, that the Hinshelwood assumption (i.e., that adsorbates are randomly distributed on the surface) is inappropriate even in catalytic reactions as simple as A + A → A₂ The Hinshelwood assumption results in miscounting of site pairs (e.g., A*-A*) and, consequently, in erroneous rates, reaction orders, and identification of rate-determining steps. The clustering and isolation of surface species unnoticed by the Langmuir-Hinshelwood model is rigorously accounted for by derivation of higher-order rate terms containing statistical factors specific to each site ensemble. Ensemble-specific statistical rate terms arise irrespective of and couple with lateral adsorbate interactions, are distinct for each elementary step including surface diffusion events (e.g., A* + * → * + A*), and provide physical insight obscured by the nonanalytical nature of the kinetic Monte Carlo (kMC) method-with which the higher-order formalism quantitatively agrees. The limitations of the Langmuir-Hinshelwood model are attributed to the incorrect assertion that the rate of an elementary step is the same with respect to each site ensemble. In actuality, each elementary step-including adsorbate diffusion-traverses through each ensemble with unique rate, reversibility, and kinetic-relevance to the overall reaction rate. Explicit kinetic description of ensemble-specific paths is key to the improvements of the higher-order formalism; enables quantification of ensemble-specific rate, reversibility, and degree of rate control of surface diffusion; and reveals that a single elementary step can, counter intuitively, be both equilibrated and rate determining.

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.

First-principles microkinetic simulations revealing the scaling relations and structure sensitivity of CO2 hydrogenation to C1 & C2 oxygenates on Pd surfaces

CO₂ hydrogenation to alcohols and other oxygenates on Pd(211) and Pd(111) surfaces was studied by microkinetic modelling. Energy scaling relations on two surfaces were established. Activity plots as a function of reaction conditions were identified.

The enhanced extended phenomenological kinetics method to deal with timescale disparity problem among different reaction pathways

Kinetic Monte Carlo method can provide valuable mechanistic insights for catalytic systems. Nonetheless, it suffers from the notorious problem of timescale disparity due to the existence of the complex catalytic network that consists of fast events and slow events. Previously, we have proposed the extended phenomenological kinetics (XPK) method that effectively deals with the timescale disparity problem between diffusion and reaction. However, it remains a great challenge to simulate systems with timescale disparity among different reaction pathways, which is important when selectivity is the major concern. In this study, we implement the enhanced XPK method to address this problem. The new algorithm works by identifying states connected through fast transitions and compressing them into a "superstate" when the chosen states satisfy a local steadystate condition. This state compression algorithm simplifies the reaction network by concealing the fast transitions. The accuracy and efficiency of the algorithm are demonstrated by two model systems: selective catalytic hydrogenation and selective catalytic decomposition. The enhanced XPK method is expected to be beneficial to the kinetic simulations of catalytic systems, especially those with complex reaction networks.

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.

Kinetic Monte Carlo Modeling for the NO-CO Reaction Mechanism on Rh(100) and Rh(111)

The NO-CO reaction on Rh(100) and Rh(111) is a prototypical catalytic system with various practical applications, including the treatment of automotive gas exhausts. With parameters derived from first-principles calculations, the Brønsted-Evans-Polanyi (BEP) relation for the reaction steps of NO-CO on Rh(100) and Rh(111) surfaces is fitted, which is more accurate and practical for the calculation of the effect of interaction between adsorbates on activation energy compared to the basic BEP relation. Further, a kinetic Monte Carlo (kMC) model for the NO-CO reaction systems on Rh(100) and Rh(111) is constructed for the exploration of the system's reaction mechanism. Besides the temperature and pressure, the coverage and activation sites are essential factors for reaction kinetic of the NO-CO reaction system. Our results are beneficial for designing more efficient, economical, and environmentally friendly next-generation catalysts.

First principles rates for surface chemistry employing exact transition state theory: application to recombinative desorption of hydrogen from Cu(111)

We present first principles calculations of the reactive flux for thermal recombinative desorption of hydrogen from Cu(111).

A Practical Guide to Surface Kinetic Monte Carlo Simulations

This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will provide worked out examples using the kmos code, where we highlight the central approximations made in implementing a KMC model as well as possible pitfalls. This includes the mapping of the problem onto a lattice and the derivation of rate constant expressions for various elementary processes. Example KMC models will be presented within the application areas surface diffusion, crystal growth and heterogeneous catalysis, covering both transient and steady-state kinetics as well as the preparation of various initial states of the system. We highlight the sensitivity of KMC models to the elementary processes included, as well as to possible errors in the rate constants. For catalysis models in particular, a recurrent challenge is the occurrence of processes at very different timescales, e.g., fast diffusion processes and slow chemical reactions. We demonstrate how to overcome this timescale disparity problem using recently developed acceleration algorithms. Finally, we will discuss how to account for lateral interactions between the species adsorbed to the lattice, which can play an important role in all application areas covered here.

H2 Thermal Desorption Spectra on Pt(111): A Density Functional Theory and Kinetic Monte Carlo Simulation Study

Theoretical investigation of the static and kinetic behaviors of H and H2 on metal surface plays a key role in the development of hydrogenation catalysts and new materials with high H2 storage capacity. Based on the density functional theory (DFT) calculation of H and H2 adsorption on Pt(111), H(a) adatom strongly interacts with surface Pt; while H2 weakly adsorbs on Pt(111). H(a) adatoms stably occupy the face-centered cubic sites on Pt(111) which agrees with the experimental LERS observations. By using kinetic Monte Carlo (kMC) simulation, the qualitative effects of the kinetic parameters on the H2 TDS spectra indicate that the H2 desorption peaks shift to the low temperature with increasing pre-exponential factor and decreasing desorption barrier. Simultaneously, the desorption peaks shift downwards and broaden to two peaks with the increase of the lateral interaction energy among H(a) adatoms. Using the kMC simulation based on DFT calculation, the predicted H2 TDS spectra are well consistent with the experimental ones. It unanimously proves that the two peaks of TDS spectra are derived from the lateral interactions among H(a). This work provides the intrinsic kinetics of H(a) and H2 on Pt(111) at an atomic level, and gives insight into the development of hydrogenation catalysts.

CO oxidation on Ru-Pt bimetallic nanoclusters supported on TiO2(101): The effect of charge polarization

Pt-based catalyst is widely used in CO oxidation, while its catalytic activity is often undermined because of the CO poisoning effect. Here, using density functional theory, we propose the use of a Ru-Pt bimetallic cluster supported on TiO₂ for CO oxidation, to achieve both high activity and low CO poisoning effect. Excellent catalytic activity is obtained in a Ru₁Pt₇/TiO₂(101) system, which is ascribed to strong electric fields induced by charge polarization between one Ru atom and its neighboring Pt atoms. Because of its lower electronegativity, the Ru atom donates electrons to neighboring Pt. This induces strong electric fields around the top-layered Ru, substantially promoting the adsorption of O₂/CO + O₂ and eliminating the CO poisoning effect. In addition, the charge polarization also drives the d-band center of the Ru₁Pt₇ cluster to up-shift to the Fermi level. For surface O₂ activation/CO oxidation, the strong electric field and d-band center close to the Fermi level can promote the adsorption of O₂ and CO as well as reduce the reaction barrier of the rate-determining step. Meanwhile, since O₂ easily dissociates on Ru₁Pt₇/TiO₂(101) resulting in unwanted oxidation of Ru and Pt, a CO-rich condition is necessary to protect the catalyst at high temperature.