Steady-State CO Oxidation on Pd(111): First-Principles Kinetic Monte Carlo Simulations and Microkinetic Analysis

Dynamics of Elementary Steps on Metal Surfaces at High Coverages: The Prevalence and Kinetic Competence of Contiguous Bare-Atom Ensembles

The rate of elementary steps on densely-covered surfaces depends sensitively on repulsive interactions within dense adlayers, situations ubiquitous in practice and with kinetic consequences seldom captured by Langmuirian treatments of surface catalysis. This study develops an ensemble-based method that assesses how such repulsion influences the prevalence and kinetic competence of bare-atom ensembles of different size. Chemisorbed CO (CO*) is used as an example because it forms dense adlayers on metal nanoparticles during CO2 hydrogenation (CO2-H2) and other reactions, leading to significant repulsion that weakens the binding of CO* and kinetically-relevant transition states (TS). This approach is enabled by density functional theory and probability formalisms and describes the prevalence of ensembles of contiguous bare atoms from their formation energy (via CO* desorption); it then determines their competence in stabilizing the TS and mediating the reaction rates. The specific conclusions reflect the extent to which a given TS and CO* desorbed to form bare ensembles "sense" repulsion and the contribution of each ensemble size to each reaction channel mediated by distinct TS structures. These formalisms are illustrated by assessing the relative contributions, kinetic relevance, and ensemble size requirements for two CO2-H2 routes (direct and H-assisted CO2 activation to CO and H2O) on Ru nanoparticles, but they are not restricted to specific bound species or reaction channels. This method is essential to assess the kinetic relevance of elementary steps in a given catalytic sequence and to determine the contributions from parallel reaction channels at the crowded surfaces that prevail in the practice of surface 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.

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'.

First-principles modeling of the highly dynamical surface structure of a MoS2 catalyst with S-vacancies

Vacancy sites, e.g., S-vacancies, are essential for the performance of MoS₂ catalysts. As earlier studies have revealed that the size and shape of the S-vacancies may affect the catalytic activity, we have studied the behavior and mobility of such vacancies on MoS₂ using DFT calculations and kinetic Monte-Carlo (kMC) simulations. The diffusion barriers for the S-vacancies are highly dependent on the immediate environment: isolated single S-vacancies are found to be immobile. In contrast, small nS-vacancies formed from n = 2 to 5 neighboring S-vacancies are often highly dynamic systems that can move within a confined area. Large extended nS-vacancies are generally unstable and transform quickly into alternating patterns of S-atoms and vacancy sites. These results illustrate the importance of recognizing MoS₂ (but also other catalysts) as dynamic structures when trying to tune their catalytic performances by introducing specific defect structures.

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.

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.

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.

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.

Micro-Kinetic Modelling of CO-TPD from Fe(100)—Incorporating Lateral Interactions

The experimentally determined temperature programmed desorption profile of CO from Fe(100) is characterized by four maxima, i.e., α1-CO, α2-CO, α3-CO, and β-CO (see e.g., Moon et al., Surf. Sci. 1985, 163, 215). The CO-TPD profile is modeled using mean-field techniques and kinetic Monte Carlo to show the importance of lateral interactions in the appearance of the CO-TPD-profile. The inclusion of lateral interactions results in the appearance of a new maximum in the simulated CO-TPD profile if modeled using the mean-field, quasi-chemical approach or kinetic Monte Carlo. It is argued that α2-CO may thus originate from lateral interactions rather than a differently bound CO on Fe(100). A detailed sensitivity analysis of the effect of the strength of the lateral interactions between the species involved (CO, C, and O), and the choice of the transition state, which affects the activation energy for CO dissociation, and the energy barrier for diffusion on the CO-TPD profile is presented.

Understanding CO oxidation on the Pt(111) surface based on a reaction route network

Kinetic analysis by the rate constant matrix contraction on the reaction route network of CO oxidation on the Pt(111) surface obtained by the artificial force induced reaction reveals the impact of entropic contributions arising from a variety of local minima and transition states.

Dense CO Adlayers as Enablers of CO Hydrogenation Turnovers on Ru Surfaces

High CO* coverages lead to rates much higher than Langmuirian treatments predict because co-adsorbate interactions destabilize relevant transition states less than their bound precursors. This is shown here by kinetic and spectroscopic data-interpreted by rate equations modified for thermodynamically nonideal surfaces-and by DFT treatments of CO-covered Ru clusters and lattice models that mimic adlayer densification. At conditions (0.01-1 kPa CO; 500-600 K) which create low CO* coverages (0.3-0.8 ML from in situ infrared spectra), turnover rates are accurately described by Langmuirian models. Infrared bands indicate that adlayers nearly saturate and then gradually densify as pressure increases above 1 kPa CO, and rates become increasingly larger than those predicted from Langmuir treatments (15-fold at 25 kPa and 70-fold at 1 MPa CO). These strong rate enhancements are described here by adapting formalisms for reactions in nonideal and nearly incompressible media (liquids, ultrahigh-pressure gases) to handle the strong co-adsorbate interactions within the nearly incompressible CO* adlayer. These approaches show that rates are enhanced by densifying CO* adlayers because CO hydrogenation has a negative activation area (calculated by DFT), analogous to how increasing pressure enhances rates for liquid-phase reactions with negative activation volumes. Without these co-adsorbate effects and the negative activation area of CO activation, Fischer-Tropsch synthesis would not occur at practical rates. These findings and conceptual frameworks accurately treat dense surface adlayers and are relevant in the general treatment of surface catalysis as it is typically practiced at conditions leading to saturation coverages of reactants or products.