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Spin state is found to determine the mechanism and active site of catalytic hydrogenation on metal cation catalysts.
Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for “bottom-up” multiscale fibril growth rate predictions. These were compared to “top-down” results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description.
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. 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. Here, 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.
An iterative approach utilizing density functional theory (DFT, PW91-GGA)-informed mean-field microkinetic models and reaction kinetics experiments is used to determine the reaction mechanism and the active site for formic acid (HCOOH, FA) decomposition over a Pd/C catalyst. Models parametrized using DFT energetics on clean Pd(100) and Pd(111) required large corrections to the DFT energetics for capturing our experimental data. Further, both Pd(111) and Pd(100) models predicted a high coverage of adsorbed CO (CO*), inconsistent with the assumption of a clean surface at which the rate parameters for these models were calculated. To better represent the active site under reaction conditions and explicitly account for the presence of CO*, subsequent microkinetic models were formulated using DFT energetics that were calculated on partially (5/9 ML) CO*-covered Pd (111) and (100) facets. Upon parameter adjustment, the resultant 5/9 ML CO*-covered Pd(100) model, although consistent in terms of CO* coverage, was unable to capture the dehydration path measured in the experiments and was, therefore, deemed not to offer an accurate representation of the active site for FA decomposition over Pd/C. In contrast, a partially CO*-covered Pd(111) model was better at representing the catalytic active site, as in addition to being consistent in terms of CO* coverages, it required small adjustments of the DFT parameters to accurately capture the experimental data set (both dehydrogenation and dehydration). Our results suggest that the reaction occurs via the spectroscopically elusive carboxyl (COOH*) intermediate and that spectator CO*-assisted decomposition pathways play an important role under typical experimental conditions. In addition, our study highlights the importance of striving for coverage self-consistent microkinetic models and for including spectator-assisted mechanisms in order to develop an improved picture of the active site under reaction conditions.
Cu-rich Pt–Cu bimetallic catalysts are among the most promising candidates for actively catalyzing the hydrodechlorination of 1,2-dichloroethane (1,2-DCA) toward ethylene production. Combining reaction kinetics experiments with density functional theory (DFT) calculations and mean-field microkinetic modeling, we present a systematic mechanistic study for 1,2-DCA hydrodechlorination on Cu-rich Pt–Cu alloy catalysts. Our DFT (PBE+(TS+SCS)) results suggest that increasing Cu content in the Pt–Cu alloy destabilizes C 2 -species adsorption while stabilizing the binding of atomic chlorine. The reaction energetics of all the elementary steps in the 1,2-DCA reaction network were calculated on a Pt 1 Cu 3 (111) model surface. The DFT results were then used to construct a microkinetic model, and the model-predicted reaction rates were compared with our reaction kinetics experimental results on a Cu-rich SiO 2 -supported Pt–Cu alloy catalyst through a parameter estimation procedure. Both the reaction kinetics experiments and the microkinetic model after parameter adjustments yielded 100% selectivity to ethylene. The microkinetic model pointed to a reaction pathway involving two sequential chlorine-removal steps on the Pt–Cu alloy catalyst, a mechanism distinct from the one previously identified on pure Pt/SiO 2 catalysts, which involved an initial hydrogen-removal step. Adjustments to the DFT-derived parameters indicate the possible formation of chlorine-induced Cu-enriched surface sites during 1,2-DCA hydrodechlorination conditions, sites that are more active than those encountered in the bulk Pt 1 Cu 3 (111) alloy surface. Furthermore, our study offers valuable initial insights on the 1,2-DCA hydrodechlorination reaction mechanism and the nature of the active sites on PtCu bimetallic catalysts.
Mean-field microkinetic models (MKMs) are appealing for their relatively facile construction, computational tractability, and high-throughput catalyst screening capabilities. As such, they will continue to be a valuable tool for materials design in heterogeneous catalysis even as the field aims to describe more complex systems. Numerous prior reports have provided the groundwork for constructing first-principles-based MKMs, including the analysis of strategies for incorporating lateral interactions into thermodynamic parameters (e.g., adsorption energies). Yet, there remains a need for concerted dialogue on methods for calculating and incorporating coverage-dependent kinetic parameters into MKMs. In this Perspective, we assess strategies for doing so, including the corresponding key physical implications and computational challenges. Here, we emphasize that decoupling thermodynamic and kinetic parameters within MKMs can violate thermodynamic consistency and risk unphysical solutions. For some reactions and catalyst materials, scaling relationships can predict coverage-dependent activation energies, but there are several exceptions evident in the literature, indicating that this approach is not universally applicable and that the field could benefit from research aimed at elucidating the limitations. Conducting high-coverage transition state searches is a rigorous but computationally costly strategy, and the effects of various methods for mitigating this cost on resulting energetics have yet to be broadly explored and validated. The goal of this Perspective is to generate discussion on and inspire focused research into the physical relevance of approaches for describing coverage-dependent reaction barriers in MKMs, including the development of computationally tractable methodologies, to advance the applicability of MKMs across diverse reaction chemistries and conditions.
The transient operation of methanation reactors can become desirable when coupled with fluctuating renewable energies in Power-to-Gas scenarios, which requires suitable kinetic approaches that can describe the transient catalytic phenomena. A combined experimental and theoretical investigation of the transient CO 2 methanation is conducted using concentration forcing to derive a suitable microkinetic model. Methanation experiments are performed with a Ni/SiO 2 catalyst in a Berty-type reactor at industrially relevant conditions. The microkinetics are based on previous work and were automatically constructed for the Ni(111) facet using the Reaction Mechanism Generator. A feasible set of energetic parameters of the microkinetic models was identified in a theory-constrained optimization procedure within the DFT uncertainty space that can accurately reproduce the experimental results on a first-principles basis. The microkinetic model unravels that the formation of H 2 O* and CH 3 * control the activity and selectivity of Ni(111) under the investigated conditions.
Accurate modeling of catalytic reactions on undercoordinated sites requires accounting for the structural and ensemble-specific nature of the active sites. This study examines how common microkinetic modeling (MKM) assumptions affect predicted kinetics and mechanisms on the stepped Pt(211) facet for the ethane dehydrogenation (EDH) and the ethane hydrogenolysis (EH). Six (211) MKMs were developed, differing in (i) the number of active sites represented, (ii) adsorbate site occupancy treatment, and (iii) inclusion of cross-facet interactions. These models are benchmarked against a particle-based microkinetic model (PB-MKM), which best represents step-edge behavior. MKM assumptions caused deviations in turnover frequencies exceeding ten orders of magnitude and led to contrasting mechanistic and selectivity predictions. Multi-site MKMs overestimate activity by inflating free site availability, single-site models underestimate activity, and uniform occupancy models overpredict coverage of multi-dentate intermediates, leading to reaction-specific artifacts. Overall, the Combined Site Edge Model (CSEM), a single-site MKM accounting for site occupancy and cross-facet interactions, most closely approximates PB-MKM predictions. All models predict similar kinetics when surfaces are clean or primarily occupied by monodentate species. This work provides practical guidance for selecting MKM frameworks for undercoordinated catalytic surfaces and highlights the critical role of modeling assumptions in catalytic predictions.
Degrees of rate control (DRC), apparent activation energies, and apparent reaction orders are established local sensitivity diagnostics for interpreting microkinetic models, but applying them routinely to large mechanisms often requires substantial reaction-specific bookkeeping, perturbation design, and postprocessing. Here, in this study, we present a unified derivative-based workflow that evaluates these quantities from a single compiled reaction-network model and target-rate definition. For any user-provided microkinetic model, the workflow compiles the mechanism into stoichiometrically consistent mass-action rate equations, solves the surface dynamics, and uses automatic differentiation to compute sensitivities with respect to rate constants, temperature, and gas partial pressures. By combining their calculations in the same framework, the workflow clearly demonstrates the relationships between different DRCs and the apparent activation energy. Using existing examples of propylene partial oxidation and methane oxidation on Pd(100), we verify expected transient redistribution of rate control, distinguish net Campbell DRCs from one-sided directional sensitivities, and show how apparent activation energy can be reconstructed either from one-sided DRCs or from state-based DRCs while critical mechanistic insights are obtained consistently. In the methane oxidation case, a pathway-subset test further illustrates how a simplified mechanism preserves key kinetic signatures of a full model, showing the potential of our user-friendly tool for model construction beyond kinetic analysis.
Catalytic hydrodechlorination is a promising strategy for treating industrial 1,2-dichloroethane wastes, for which Pt and Pt-based alloy catalysts are widely used. Here, we performed a detailed mechanistic study for 1,2-dichloroethane hydrodechlorination on Pt using a synergistic approach combining density functional theory (DFT) calculations, reaction kinetics experiments, and microkinetic modeling. Using planewave DFT calculations, we evaluated the reaction energy and activation energy barrier of each elementary step involved in the reaction network on Pt(111). The calculated energetics were then incorporated into a comprehensive mean-field microkinetic model accounting for a total of 65 elementary steps. The model-predicted reaction rates were compared with the results from our reaction kinetics experiments on SiO2-supported Pt catalysts. Our results indicated that the hydrodechlorination of 1,2-dichloroethane on Pt(111) starts with a H-removal step; then, it proceeds through a sequence of alternating dechlorination and dehydrogenation steps until vinylidene (CH 2 C*) is formed; finally, CH 2 C* is hydrogenated to the final product, ethane, sequentially via vinyl (CH 2 CH*), ethylene, and ethyl (CH 3 CH 2 *) intermediates. After model parameter adjustments, we achieved good agreement between our theoretical model and experimental results; the adjustments to the calculated parameters are consistent with the typically anticipated coverage effects. Furthermore, our study offers valuable mechanistic insights, which are useful for improving catalysts for this chemistry.
Although perovskite oxyhydrides (POHs) have shown promise as a support for selective hydrogenation, it is unknown if they themselves can catalyze alkyne semi-hydrogenation. Here, we use first-principles density functional theory, coupled with microkinetic modeling, to investigate acetylene semi-hydrogenation on a prototypical POH, cubic BaTiO 2.5 H 0.5 (BTOH). Two different mechanisms are examined on a representative surface of BTOH under the reaction conditions: both are based on the Horiuti–Polanyi mechanism, but the way of H 2 dissociation is different. In mechanism 1, a lattice hydride H atom and then a surface adsorbed H atom sequentially hydrogenate the adsorbed acetylene. In mechanism 2, two lattice hydride H atoms from the BTOH sequentially hydrogenate the adsorbed acetylene. In both mechanisms, the H atoms are replenished from gas phase H 2 dissociation. Using density functional theory (DFT), we have calculated pathways for these two mechanisms in hydrogenation of acetylene to ethylene, as well as further to ethane. Microkinetic modeling based on the DFT energetics indicates that at 523 K, hydrogenation to ethylene and ethane via mechanism 1 occurs at a rate up to two orders of magnitude faster than via mechanism 2. A selectivity analysis for the temperature range of 373–673 K shows that the product observed is essentially only ethylene within the more active mechanism 1. This is because at the steady state, there is a significant amount of surface anion vacancies that facilitate heterolytic H 2 dissociation and help stabilize a vinyl intermediate. In conclusion, the present findings suggest that POHs are capable of selective hydrogenation, thanks to their rich hydrogen surface-redox chemistry.
Popular computational catalyst design strategies rely on the identification of reactivity descriptors, which can be used along with Brønsted–Evans–Polanyi (BEP) and scaling relations as input to a microkinetic model (MKM) to make predictions for activity or selectivity trends. The main benefit of this approach is related to the inherent dimensionality reduction of the large material space to just a few catalyst descriptors. Conversely, it is well documented that a small set of descriptors is insufficient to capture the intricacies and complexities of a real catalytic system. The inclusion of coverage effects through lateral adsorbate-adsorbate interactions can narrow the gap between simplified descriptor predictions and real systems, but mean-field MKMs cannot properly account for local coverage effects. This shortcoming of the mean-field approximation can be rectified by switching to a lattice-based kinetic Monte Carlo (kMC) method using cluster expansion representation of adsorbate–adsorbate lateral interactions. Using the prototypical CO oxidation reaction as an example, we critically evaluate the benefits of kMC over MKM in terms of trend predictions and computational cost when using only a small set of input parameters. After confirming that in the absence of lateral interactions the kMC and MKM approaches yield identical trends and mechanistic information, we observed substantial differences between the two kinetic models when lateral interactions were introduced. Here, the mean-field implementation applies coverage corrections directly to the descriptors, causing an artificial overprediction of the activity of strongly binding metals. In contrast, the cluster expansion in kMC implementation can differentiate among the highly active metals but it is very sensitive to the set of included interaction parameters. Considering that computational screening relies on a minimal set of descriptors, for which MKM makes reasonable trend predictions at a ca. three orders of magnitude lower computational cost than kMC, the MKM approach does provide a better entry point for computational catalyst design.
In this work, we investigated redox mechanisms for the high temperature (HT) water–gas shift reaction (WGSR) on the Fe 3 O 4 (1 1 1) surface using density functional theory (DFT) calculations and mean-field microkinetic modeling (MKM). The redox pathways branched into three Langmuir-Hinshelwood processes (LH1, LH2 and LH3) and one Mars-van-Krevelen (MVK) process (in the presence of oxygen vacancy) from multidentate binding of CO and CO 2 over four available reactive sites (Fe oct2 , Fe tet1 , Fe bridge, and O1). We found that the LH1 and LH2 processes have CO adsorption at a single iron site (Fe oct2 or Fe tet1 ), while the LH3 and MVK processes have stronger chemisorption of CO or CO 2 by both the Fe oct2 site and the O 1 site. From the mechanistic study of these reaction path, we recognized that availability of O 1 sites was key to proceed to either CO oxidation by the single site (LH1, LH2) or by the dual site (LH3, MVK). We observed that the reaction energetics were significantly different in the CO oxidation steps, where the single or dual site results in markedly different apparent activation energy (73–281 kJ/mol) and reaction rates (10 -3 –10 -10 mol∙m -2 ∙s -1 ) among the four reaction mechanisms. The utilization of mean field MKM with DFT reaction energetics helps explain the experimental debates for the catalytic reaction details as well as providing a possible direction to engineer the catalyst with higher activity.
A Python-TensorFlow tool that learns chemical kinetics (LearnCK) for systematic and automatic reduction of microkinetic models using artificial neural networks (NNs).
Single-atom transition metals embedded in nitrogen-doped graphene have emerged as promising electrocatalysts due to their high activity and low material cost. These materials have been shown to catalyze a variety of electrochemical reactions, but their active sites under reaction conditions remain poorly understood. Using first-principles density functional theory calculations, we develop a pH-dependent microkinetic model to evaluate the relative performance of transition metal catalysts embedded in fourfold N-substituted double carbon vacancies in graphene for the oxygen evolution reaction. We find that reaction pathways involving intermediates co-adsorbed on the metal site are preferred on all transition metals. These pathways lead to enhancements in catalytic activity and broaden the activity peak when compared with purely thermodynamics-based predictions. Furthermore, these findings demonstrate the importance of investigating reaction pathways on graphene-based catalysts and other two-dimensional (2D) materials that involve metal active centers decorated by spectator intermediate species.
Hydrogen bonding interactions alter the nanoscale reaction mechanisms of many chemistries. Yet, it remains unclear how they affect heterogeneously catalyzed decomposition of formic acid (FA), a reaction of intense interest since FA is a promising hydrogen carrier. In this work, we elucidate how hydrogen bonding affects the reaction mechanisms for FA decomposition on Cu(111) by combining first-principles density functional theory calculations to calculate reaction energetics, Latin-hypercube sampling to elucidate stable high-coverage adsorbate configurations, and coverage self-consistent mean-field microkinetic models to predict reaction kinetics. We demonstrate that hydrogen-bonded complexes of FA with formate (bimolecular FA–HCOO complexes) can play a dominant role in FA decomposition. Specifically, our first-principles calculations show that hydrogen bonding of FA with HCOO may stabilize the crucial monodentate HCOO intermediate and the transition states for HCOO decomposition, especially at low coverages. We predict that, depending on the reaction conditions, 40–80% of the reaction flux goes through pathways involving the bimolecular FA–HCOO complexes. Additionally, the active site for FA decomposition on Cu(111) involves a high coverage (~0.4 monolayers (ML)) of these complexes, which unexpectedly stabilize intermediates and transition states via van der Waals interactions. Our work provides molecular insights consistent with previous experimental observations on supported Cu/Al 2 O 3 catalysts. This paves the way toward the development of novel catalysts for FA decomposition as well as for other industrially important chemistries with intermediates capable of hydrogen bonding, such as ammonia electrooxidation and CO 2 hydrogenation.
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