Mean-field Microkinetic Model Research Articles

Implementing the Blowers-Masel Approximation to Scale Activation Energy Based on Reaction Enthalpy in Mean-Field Microkinetic Modeling for Catalytic Methane Partial Oxidation.

Mean-field microkinetic modeling is a powerful tool for catalyst design and the simulation of catalytic processes. The reaction enthalpies in a microkinetic model often need to be adjusted when changing species' binding energies to model different catalysts, when performing thermodynamic sensitivity analyses, and when fitting experimental data. When altering reaction enthalpies, the activation energies should also be reasonably altered to ensure realistic reaction rates. The Blowers-Masel approximation (BMA) relates the reaction barrier to the reaction enthalpy. Unlike the Brønsted-Evans-Polani relationship, the BMA requires less data because only one parameter, the intrinsic activation energy, needs to be determined. We validate this application of BMA relations to model surface reactions by comparing against density functional theory data taken from the literature. By incorporating the BMA rate description into the open-source Cantera software, we enable a new workflow, demonstrated herein, allowing rapid screening of catalysts using linear scaling relationships and BMA kinetics within the process simulation software. For demonstration purposes, a catalyst screening for catalytic methane partial oxidation on 81 hypothetical metals is conducted. We compared the results with and without BMA-corrected rates. The heat maps of various descriptors (e.g., CH4 conversion, syngas yield) show that using BMA rates instead of Arrhenius rates (with constant activation energies) changes which metals are most active. Heat maps of sensitivity analyses can help identify which reactions or species are the most influential in shaping the descriptor map patterns. Our findings indicate that while using BMA-adjusted rates did not markedly affect the most sensitive reactions, it did change the most influential species.

Coverage- and Facet-Dependent Multiscale Modeling of O* and H* Adsorption on Pt Catalytic Nanoparticles.

Within computational heterogeneous catalysis, two critical factors exist-coverage and multifaceted effects-which are challenging to incorporate and contribute to differences between the results obtained from computational and experimental studies. Such disparities exist when significant adsorbate-adsorbate interactions are present, particularly when coupled with computationally limited facet sampling. Here, we designed a study to demonstrate the significance of coverage and facet effects on the predicted coverages for O* and H* on Pt nanoparticles. This is accomplished by employing multiscale modeling techniques using a three-pronged approach consisting of density functional theory (DFT), ab initio phase diagrams, and mean-field microkinetic models. Overall, adsorbate-adsorbate interactions are repulsive and far stronger for O*/Pt than for H*/Pt. For O* on Pt(111), repulsive interactions are both two- and three-body, but on Pt(100) and Pt(110), they are predominantly three-body. Through benchmarks to existing experimental literature, we demonstrate that experimentally observed coverages and desorption temperatures can be accurately estimated by computational models when the adsorbate-adsorbate interactions are included. Finally, by combining microkinetic models at the equilibrium limit with kubic harmonic interpolation, we model the impacts of the treatment of adsorbate-adsorbate interactions on the predicted O* and H* coverages over multifaceted Pt nanoparticles. Omitting adsorbate-adsorbate interactions over Pt nanoparticles leads to an overestimation of equilibrium coverages of the adsorbates (maximum of 0.29 and 0.11 ML for O* and H*, respectively) across a wide range of temperatures and pressures relevant to heterogeneous catalysis. Altogether, our work demonstrates that the inclusion of coverage and facet effects increases the accuracy of computational models for heterogeneous catalysts.

Number of sites-based solver for determining coverages from steady-state mean-field micro-kinetic models.

Kinetic models parameterized by ab-initio calculations have led to significant improvements in understanding chemical reactions in heterogeneous catalysis. These studies have been facilitated by implementations which determine steady-state coverages and rates of mean-field micro-kinetic models. As implemented in the open-source kinetic modeling program, CatMAP, the conventional solution strategy is to use a root-finding algorithm to determine the coverage of all intermediates through the steady-state expressions, constraining all coverages to be non-negative and to properly sum to unity. Though intuitive, this root-finding strategy causes issues with convergence to solution due to these imposed constraints. In this work, we avoid explicitly imposing these constraints, solving the mean-field steady-state micro-kinetic model in the space of number of sites instead of solving it in the space of coverages. We transform the constrained root-finding problem to an unconstrained least-squares minimization problem, leading to significantly improved convergence in solving micro-kinetic models and thus enabling the efficient study of more complex catalytic reactions.

Mechanistic study of CO2 hydrogenation to C1 products on molybdenum step site

The catalytic conversion of CO2 into fuel is an ideal solution to the energy and environment crisis in the context of carbon neutrality, while the design of high-performance catalysts is the key. Unfortunately, the complicated reaction mechanism makes the rational catalyst design with simulations challenging. Herein, we employed density functional theory (DFT) calculations to systematically analyze the complex reaction mechanism of CO2 hydrogenation to C1 products on the stepped metal active sites using molybdenum as the model catalyst, while the established mean-field microkinetic model (MKM) identified the more favorable production of carbon monoxide (CO) than formic acid (HCOOH), methanol (CH3OH) and methane (CH4). Our results not only provide the energetics of all elementary steps during CO2 hydrogenation to C1 products on metallic Mo but also propose the directions to steering the activity and selectivity of Mo in CO2 conversion.

Understanding the influence of solvents on the Pt-catalyzed hydrodeoxygenation of guaiacol

Bio-oil derived from fast pyrolysis of lignocellulosic biomass needs to be deoxygenated to become a substitute for petroleum fuels. Here, we study the hydrodeoxygenation mechanism of guaiacol, a bio-oil model compound derived from the lignin fraction of biomass, on Pt(111) terrace sites in the presence of water, diethyl ether, 1-butanol, and n-hexane as solvent. Using first-principles periodic density functional theory (DFT) calculations and mean-field microkinetic reactor modeling, a detailed reaction mechanism is investigated targeting various products such as catechol, phenol, anisole, benzene, cyclohexanone, and cyclohexanol. Solvent phase DFT outcomes are mostly similar to that of the vapor phase; however, microkinetic modeling results suggest that rate controlling species and transition states differ somewhat in the various reaction environments. Catechol was found to be the major aromatic product across all reaction environments. Over Pt(111), unsaturated monooxygenate production from catechol is unlikely.

Multiple redox mechanisms for water-gas shift reaction on Fe3O4 (1 1 1) surface: A density functional theory and mean-field microkinetic modeling study

We investigated redox mechanisms for the high temperature (HT) water–gas shift reaction (WGSR) on the Fe3O4 (111) 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 CO2 over four available reactive sites (Feoct2, Fetet1, Fe bridge, and O1). We found that the LH1 and LH2 processes have CO adsorption at a single iron site (Feoct2 or Fetet1), while the LH3 and MVK processes have stronger chemisorption of CO or CO2 by both the Feoct2 site and the O1 site. From the mechanistic study of these reaction path, we recognized that availability of O1 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.

Understanding the Source of Error in First-Principles-Based Micro-Kinetic Modeling: Density Functional Theory Calculations Versus the Mean-Field Approximation

First-principles-based micro-kinetic modeling has become an essential tool in the rational design of heterogeneous catalysts. Currently, most theoretical understandings and predictions are provided by this model, which combines results from density functional theory (DFT) calculations at the generalized gradient approximation level with the simulations using the mean-field micro-kinetic modeling (MF-MKM). In spite of its popularity and success in the catalyst design and screening, sometimes this combination yields undesired predictions that significantly deviate from experimental observations. It is, therefore, important to understand its success and failure and to locate the bottleneck of applying/improving the conventional MF-MKM. To this end, we have compared the errors that come from different DFT functionals with those introduced by the MF approximations against the kinetic Monte Carlo (KMC) results for the Pt-catalyzed water gas shift reaction system. It was found that the shape of the volcano map is less sensitive to the differences in the DFT functionals, even though their predictions of the key energetic parameters are distinctly different. On the other hand, the top of the volcano map, the detailed mechanism, as well as some key kinetic properties are markedly affected by the change of the energetic data. In comparison, the traditional MF-MKM that neglects the adsorbate–adsorbate interactions totally fails to describe the reaction kinetics. The inclusion of the adsorbate–adsorbate interaction effect can significantly improve the performance of the MF-MKM, which results in largely similar predictions to the reference data provided by KMC simulations. Nevertheless, the missing spatial correlation in the MF treatment can lead to an improper description in the high coverage region. Our analyses demonstrate that the accuracy of the MKM might not always be improved by only modifying the DFT-calculated energetic parameters, and close attention should be paid to the kinetic simulation method employed, particularly when quantitative kinetic properties are to be expected.

How Topological Differences between Two Oxide Surfaces Determine Selectivity—The Case of the Dehydra-Decyclization of Tetrahydrofuran

Production of butadiene from biomass-based tetrahydrofuran (THF) is explored as an alternative to the existing petroleum-based processes. Metal oxide catalysts have been shown to exhibit varying product selectivities when reacted with THF. Among those oxides, ZrO2 showed the highest selectivity for butadiene. In contrast, Al2O3 showed the highest selectivity for the competing retro-Prins products, C3H6 and HCHO. The reasons behind the varying selectivity across oxides are unclear. In this work, we employ periodic density functional theory and mean-field microkinetic modeling to investigate the mechanism of the reaction of THF to butadiene and retro-Prins products on t-ZrO2 (101) (dry and hydrous) and on γ-Al2O3 (110). Our simulations reproduce the experimental selectivity trends. High selectivity for butadiene is promoted by the presence of neighboring Lewis acid metal sites that facilitate E1cB hydroxyl elimination from a 3-butenoxide intermediate; on hydrous Al2O3; where such neighboring Lewis acid centers are not available, the butenoxide undergoes E2 elimination and retro-Prins products ensue. The THF ring opening is rate-determining on ZrO2, whereas the γ-proton elimination that yields the 3-butenoxide intermediate is rate controlling on hydroxylated Al2O3. We conclude that the local topology around the active site greatly influences the mechanism and selectivity.

A Coverage Self-Consistent Microkinetic Model for Vapor-Phase Formic Acid Decomposition over Pd/C Catalysts

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. Further, 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.

First-principles-based microkinetic rate equation theory for oxygen carrier reduction in chemical looping

The reduction kinetics of oxygen carriers with reacting gases are typically modeled using shrinking-core-based models, in which, the elemental surface reaction mechanisms are simplified as only one global reaction, and the kinetic parameters are obtained by fitting with experimental data. In this study, a theoretical scheme is proposed to couple the elemental surface reaction mechanisms with the bulk diffusion of lattice oxygen, and a first-principle-based microkinetic rate equation theory is developed to model the reduction kinetics of oxygen carrier in chemical looping. The elemental surface reaction mechanisms are computed using quantum chemistry and are integrated into the mean-field microkinetic model, in which, oxygen bulk diffusion is also included. The elemental steps of gas adsorption, surface reaction, and surface species desorption are considered in the theory. The kinetic parameters used in the model are directly calculated by using transition state theory and density functional theory instead of fitting with experimental data. The developed theory is applied to predict the reduction kinetics of a CaMn0.775Ti0.125Mg0.1O2.9-δ perovskite oxygen carrier and validated to accurately predict the reduction kinetics by H2 and CO under a wide range of temperatures and gas concentrations. The effect of surface reaction and bulk diffusion on the overall reaction rate is analyzed and the rate-controlling step is discussed. When the bulk diffusion is considerably rapid, the interior oxygen concentration in the grain remains uniform throughout the reduction process and can be considered as a function of time only. Lumped parameter analysis is used to simplify the bulk diffusion of lattice oxygen without sacrificing accuracy. The developed microkinetic rate equation theory couples the surface reaction mechanism with the bulk diffusion, bridges the gap between atom-scale first-principles quantum chemistry calculations with particle-scale heterogeneous kinetics, and provides a theoretical framework for oxygen carrier reduction/oxidation kinetics, gas conversion mechanisms, and product selectivity in chemical looping.

Single-Particle Catalysis: Revealing Intraparticle Pacemakers in Catalytic H2 Oxidation on Rh.

Self-sustained oscillations in H2 oxidation on a Rh nanotip mimicking a single catalytic nanoparticle were studied by in situ field emission microscopy (FEM). The observed spatio-temporal oscillations result from the coupling of subsurface oxide formation/depletion with reaction front propagation. An original sophisticated method for tracking kinetic transition points allowed the identification of local pacemakers, initiating kinetic transitions and the nucleation of reaction fronts, with much higher temporal resolution than conventional processing of FEM video files provides. The pacemakers turned out to be specific surface atomic configurations at the border between strongly corrugated Rh{973} regions and adjacent relatively flat terraces. These structural ensembles are crucial for reactivity: while the corrugated region allows sufficient oxygen incorporation under the Rh surface, the flat terrace provides sufficient hydrogen supply required for the kinetic transition, highlighting the importance of interfacet communication. The experimental observations are complemented by mean-field microkinetic modeling. The insights into the initiation and propagation of kinetic transitions on a single catalytic nanoparticle demonstrate how in situ monitoring of an ongoing reaction on individual nanofacets can single out active configurations, especially when combined with atomically resolving the nanoparticle surface by field ion microscopy (FIM).

A First-Principles-Based Microkinetic Study of CO2 Reduction to CH3OH over In2O3(110)

Methanol synthesis from catalytic recycling of CO2 is one viable route to produce fuel and a stock chemical from a greenhouse gas. Herein, hydrogenation of CO2 to CH3OH is investigated with density functional theory calculations combined with mean-field microkinetic modeling. The model explores the direct route for CO2 hydrogenation (HCOOH route) and the competing reverse water-gas shift (RWGS) reaction. The predicted temperature dependence of turnover frequencies, selectivities, and reaction orders are in good agreement with previous experimental results. The formation of methanol at relevant reaction temperatures (470–670 K) is found to be kinetically controlled by H2COOH dissociation to H2CO + OH, whereas the RWGS reaction is solely controlled by CO2 hydrogenation to COOH. An analysis of the kinetic behavior reveals that the stabilization of hydrogen adsorption should be one way to improve the catalyst performance.

Exploring bimetallic alloy catalysts of Co, Pd and Cu for CO2 reduction combined with ethane dehydrogenation

First principles theoretical analysis, employing the age-old Sabatier principle and microkinetic modelling, is undertaken to rationally design bimetallic alloy catalysts of Co, Pd and Cu for CO2 assisted ethane dehydrogenation reaction. Using CO2 as a mild oxidant, the reaction aims to convert a part of natural gas and meet the increasing demand of ethylene, while also mitigating the growing levels of CO2 in the atmosphere. The in silico mean field microkinetic model (MKM) facilitates the selection of bimetallic alloy catalysts based on several criteria which include; equal or enhanced conversion of CO2 and ethane, higher yield of ethylene and reduced coke formation. Catalyst compositions are evaluated at the reaction temperature of 873 K and an inlet composition of ethane and carbon dioxide as 1:1. Six bimetallic alloy catalysts are proposed as potential candidates for CO2 assisted ethane dehydrogenation reaction – CoFe, CoPd, PdNi, CuNi, CuSn and CuPt. Out of these, three alloys (CoFe, CuNi, and CuSn) consist of cheaper metals and hold considerable potential for experimental testing and scale-up studies.

Hydrodechlorination of 1,2-Dichloroethane on Platinum Catalysts: Insights from Reaction Kinetics Experiments, Density Functional Theory, and Microkinetic Modeling

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 (CH2C*) is formed; finally, CH2C* is hydrogenated to the final product, ethane, sequentially via vinyl (CH2CH*), ethylene, and ethyl (CH3CH2*) 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. Our study offers valuable mechanistic insights, which are useful for improving catalysts for this chemistry.

Evaluating the benefits of kinetic Monte Carlo and microkinetic modeling for catalyst design studies in the presence of lateral interactions

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. 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.

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.

Microkinetic Modeling and Analysis of CO2 Methanation on Ruthenium

The catalytic reduction of CO2 to methane, called CO2 methanation or the Sabatier reaction, is a reversible and exothermic reaction. A mean field microkinetic model is developed for the Sabatier re...

Multiscale modelling of CO2 reduction to methanol over industrial Cu/ZnO/Al2O3 heterogeneous catalyst: Linking ab initio surface reaction kinetics with reactor fluid dynamics

There has been a growing trend to couple different levels of modelling, such as going from first-principle calculations to the meso (e.g. kinetic Monte Carlo - KMC) and macro scale (e.g. computational fluid dynamics - CFD). In the current investigation, we put forward a CFD study of CO2 hydrogenation to methanol for heterogeneous reacting flows in reactors with complex shape geometries, coupled with first-principle calculations (density functional theory - DFT). KMC operation simulations were also performed to obtain insight into the uppermost layer conditions during the reaction. With computational fluid dynamics, the focus was placed on the non-uniform catalytic reduction of carbon dioxide to formate, which we treated with a detailed mean-field first-principle microkinetic model, analysed, and corroborated with experiments. The results showed a good consistent agreement with experimental data. The formulated methodological approach paves the way towards full virtual multiscale system descriptions of industrial processing units, encompassing all conventional stages, from catalyst design to the optimization of mass transfer parameters. Such a bridging is outlined for carbon capture and utilization.

Theoretical Investigation of Solvent Effects on the Hydrodeoxygenation of Propionic Acid over a Ni(111) Catalyst Model

The effect of two solvents, liquid water and 1,4-dioxane, has been studied from first-principles on the hydrodeoxygenation of propionic acid over a Ni(111) catalyst surface model. A mean-field microkinetic model was developed to investigate these effects at a temperature of 473 K. Under all reaction conditions, a decarbonylation mechanism is favored significantly over a decarboxylation pathway. Although no significant solvent effects were observed on the decarbonylation rate, a substantial solvent stabilization of two key surface intermediates in the decarboxylation mechanism, CH3CCOO and CH3CHCOO, leads to a notable increase of the decarboxylation rate by 2 orders of magnitude in liquid water and by 1 order of magnitude in liquid 1,4-dioxane. Furthermore, a significant solvent stabilization of the transition state of C–H bond cleavage of the α-carbon of CH3CHCO, relative to the stabilization of the C–C bond cleavage of the α-carbon of CH3CHCO, leads to a change in dominant pathway in the liquid phase environments. Finally, a sensitivity analysis shows that the C–OH bond cleavage of propionic acid and C–C bond cleavage of the α-carbon of CH3CHCO are the most rate controlling states in the gas phase. In contrast, in solvents the dehydrogenation of CH3CHCO becomes the most influential step. This shift in rate controlling state is attributed to the solvent effect on the dehydrogenation of CH3CHCO, which is facilitated in the aqueous phase. Overall, it is likely that the investigated (111) facet of Ni is not active for the hydrodeoxygenation of propionic acid in either the gas or the liquid phase and other Ni facets or phases must be responsible for the experimentally observed kinetics.

Oxygen Reduction Reaction Mechanism Study Via the Mean-Field Microkinetic Modeling and Uncertainty Quantification of Model Parameters

We describe the quantitative framework for the reaction mechanism selection based on accuracy of fitting with mean-field microkinetic models and parameters uncertainty quantification to determine how likely certain reaction steps occur if some aspects of the system are not exactly known. The latter is performed via the data collaboration approach with Tree-Structured Parzen estimator algorithm. It provides the elucidation of the reaction mechanism which can be considered based on the available experimental data and is crucial to study the reaction mechanism of ORR and other sufficiently complex reactions. We consider the ORR models developed within the rate determining steps approximation for understanding effective multi-electron transfer steps.