Including lateral interactions into microkinetic models of catalytic reactions

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.

Capturing the Coverage Dependence of Aromatics' Adsorption through Mean-Field Models

To capture the dominant interactions (surface-mediated and through-space) in catalytic hydrodeoxygenation systems, coverage-dependent mean-field models of aromatic adsorption are developed on Pt(111) and Ru(0001). We derive three key insights from this work: (1) we can universally apply mean-field models to capture the coverage-dependent behavior of oxygenated aromatics on transition-metal surfaces, (2) we can deconvolute surface-mediated and through-space interactions from the mean-field model, and (3) we can develop relatively accurate models that predict the adsorption energy of aromatics on transition-metal surfaces for the full coverage range using the work function at the lowest modeled coverage. Our approach enables the rapid prediction of the coverage-dependent behavior of oxygenated aromatics on transition-metal surfaces, reducing the computational cost associated with these studies by an order of magnitude.

Catalytic resonance of ammonia synthesis by simulated dynamic ruthenium crystal strain

Ammonia affords dense storage for renewable energy as a fungible liquid fuel, provided it can be efficiently synthesized from hydrogen and nitrogen. In this work, the catalysis of ammonia synthesis was computationally explored beyond the Sabatier limit by dynamically straining a ruthenium crystal (±4%) at the resonant frequencies (10² to 10⁵⁺ Hz) of N₂ surface dissociation and hydrogenation. Density functional theory calculations at different strain conditions indicated that the energies of NH_x surface intermediates and transition states scale linearly, allowing the description of ammonia synthesis at a continuum of strain conditions. A microkinetic model including multiple sites and surface diffusion between step and Ru(0001) terrace sites of varying ratios for nanoparticles of differing size revealed that dynamic strain yields catalytic ammonia synthesis conversion and turnover frequency comparable to industrial reactors (400°C, 200 atm) but at lower temperature (320°C) and an order of magnitude lower pressure (20 atm).

Microkinetic Modeling: A Tool for Rational Catalyst Design

The design of heterogeneous catalysts relies on understanding the fundamental surface kinetics that controls catalyst performance, and microkinetic modeling is a tool that can help the researcher in streamlining the process of catalyst design. Microkinetic modeling is used to identify critical reaction intermediates and rate-determining elementary reactions, thereby providing vital information for designing an improved catalyst. In this review, we summarize general procedures for developing microkinetic models using reaction kinetics parameters obtained from experimental data, theoretical correlations, and quantum chemical calculations. We examine the methods required to ensure the thermodynamic consistency of the microkinetic model. We describe procedures required for parameter adjustments to account for the heterogeneity of the catalyst and the inherent errors in parameter estimation. We discuss the analysis of microkinetic models to determine the rate-determining reactions using the degree of rate control and reversibility of each elementary reaction. We introduce incorporation of Brønsted-Evans-Polanyi relations and scaling relations in microkinetic models and the effects of these relations on catalytic performance and formation of volcano curves are discussed. We review the analysis of reaction schemes in terms of the maximum rate of elementary reactions, and we outline a procedure to identify kinetically significant transition states and adsorbed intermediates. We explore the application of generalized rate expressions for the prediction of optimal binding energies of important surface intermediates and to estimate the extent of potential rate improvement. We also explore the application of microkinetic modeling in homogeneous catalysis, electro-catalysis, and transient reaction kinetics. We conclude by highlighting the challenges and opportunities in the application of microkinetic modeling for catalyst design.

Comparison of Coverage-Dependent Binding Energy Models for Mean-Field Microkinetic Rate Predictions

The binding energies of adsorbates at catalytic surfaces are in general functions of adsorbate coverage, with corresponding consequences for equilibrium surface coverages and reaction rates under relevant conditions. This coverage dependence is commonly incorporated into mean-field microkinetic models by writing adsorption energies as an algebraic function of coverage and parametrizing against density functional theory models. In this work, we compare the performance of three different analytical coverage-dependent forms, including linear and piecewise models and a logarithmic form inspired by Wilson's activity model, against accurate results obtained from a lattice-based cluster expansion (CE) representation of adsorbate interactions combined with a Monte Carlo evaluation of reaction rates. We take as a model system O₂ dissociation-limited NO oxidation to NO₂ over Pt(111), parametrize all models against the same set of previously reported coverage-dependent NO and O binding energies, and solve kinetic models under the same set of assumptions. Steady-state coverages from the analytical models are similar to each other and the ensemble-averaged CE result, other than the discontinuities in O and NO coverages that appear in the piecewise model. Predicted steady-state rates differ more substantially, reflecting the sensitivity of the O₂ dissociation activation energy to coverage-dependent binding energies. The activity model predicts reaction rates reliably at low temperatures and systematically deviates from CE rates at high temperatures, where minority surface sites, having low local coverage around vacant pairs, dominate overall reaction rates. The results highlight the challenges of developing coverage-dependent microkinetic models that are reliable across a range of conditions.

Efficient Implementation of Cluster Expansion Models in Surface Kinetic Monte Carlo Simulations with Lateral Interactions: Subtraction Schemes, Supersites, and the Supercluster Contraction

While lateral interaction models for reactions at surfaces have steadily gained popularity and grown in terms of complexity, their use in chemical kinetics has been impeded by the low performance of current kinetic Monte Carlo (KMC) algorithms. The origins of the additional computational cost in KMC simulations with lateral interactions are traced back to the more elaborate cluster expansion Hamiltonian, the more extensive rate updating, and to the impracticality of rate-catalog-based algorithms for interacting adsorbate systems. Favoring instead site-based algorithms, we propose three ways to reduce the cost of KMC simulations: (1) representing the lattice energy by a smaller Supercluster Hamiltonian without loss of accuracy, (2) employing the subtraction schemes for updating key quantities in the simulation that undergo only small, local changes during a reaction event, and (3) applying efficient search algorithms from a set of established methods (supersite approach). The cost of the resulting algorithm is fixed with respect to the number of lattice sites for practical lattice sizes and scales with the square of the range of lateral interactions. The overall added cost of including a complex lateral interaction model amounts to less than a factor 3. Practical issues in implementation due to finite numerical accuracy are discussed in detail, and further suggestions for treating long-range lateral interactions are made. We conclude that, while KMC simulations with complex lateral interaction models are challenging, these challenges can be overcome by modifying the established variable step-size method by employing the supercluster, subtraction, and supersite algorithms (SSS-VSSM). © 2019 Wiley Periodicals, Inc.

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.

Catalysis-tunable Heusler alloys in selective hydrogenation of alkynes: A new potential for old materials

Heusler alloys (X 2 YZ) are well-established intermetallic compound materials in various fields because their function can be precisely adjusted by elemental substitution (e.g., X 2 YZ 1-x Z' x ). Although intermetallic compound catalysts started attracting attention recently, catalysis researchers are not familiar with Heusler alloys. We report their potential as novel catalysts focusing on the selective hydrogenation of alkynes. We found that Co2MnGe and Co2FeGe alloys have great alkene selectivity. Mutual substitution of Mn and Fe (Co2Mn x Fe1-x Ge) enhanced the reaction rate without changing selectivity. The substitution of Ga for Ge decreased the selectivity but increased the reaction rate monotonically with Ga composition. Elucidation of these mechanisms revealed that the fine tuning of catalytic properties is possible in Heusler alloys by separately using ligand and ensemble effects of elemental substitution.

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.

Kinetic modelling of heterogeneous catalytic systems

The importance of heterogeneous catalysis in modern life is evidenced by the fact that numerous products and technologies routinely used nowadays involve catalysts in their synthesis or function. The discovery of catalytic materials is, however, a non-trivial procedure, requiring tedious trial-and-error experimentation. First-principles-based kinetic modelling methods have recently emerged as a promising way to understand catalytic function and aid in materials discovery. In particular, kinetic Monte Carlo (KMC) simulation is increasingly becoming more popular, as it can integrate several sources of complexity encountered in catalytic systems, and has already been used to successfully unravel the underlying physics of several systems of interest. After a short discussion of the different scales involved in catalysis, we summarize the theory behind KMC simulation, and present the latest KMC computational implementations in the field. Early achievements that transformed the way we think about catalysts are subsequently reviewed in connection to latest studies of realistic systems, in an attempt to highlight how the field has evolved over the last few decades. Present challenges and future directions and opportunities in computational catalysis are finally discussed.

Kinetic Monte Carlo simulations of heterogeneously catalyzed oxidation reactions

In this perspective, we focus on the catalyzed oxidation of CO and HCl over the model catalyst RuO₂(110) and how the kinetics of these reactions can only properly be modeled by kinetic Monte Carlo (kMC) simulations when lateral interactions of the surface species are taken into account.

Additional constraints in adsorption-desorption kinetics

In this work, the adsorption-desorption kinetic in the framework of the lattice gas model is analyzed. The transition probabilities are written as an expansion of the occupation configurations. Due to that, the detail balance principle determine half of the adsorption A{i} and desorption D{i} coefficients, consequently, different functional relations between them are proposed. Introducing additional constrains, it is demonstrated that when those coefficients are linearly related through a parameter gamma , there are values of lateral interaction V , that lead to anomalous behavior in the adsorption isotherms, the sticking coefficient and the thermal programmed desorption spectra. Diagrams for the allowed values of V and gamma are also shown. Alternatively, a more reliable formulation for the adsorption desorption kinetic based on the transition state theory is introduced. In such way the equilibrium and non equilibrium observables do not present anomalous or inconsistent behavior.