Rate-Based Construction of Kinetic Models for Complex Systems

Predicting Long-Time-Scale Kinetics under Variable Experimental Conditions with Kinetica.jl

Predicting the degradation processes of molecules over long time scales is a key aspect of industrial materials design. However, it is made computationally challenging by the need to construct large networks of chemical reactions that are relevant to the experimental conditions that kinetic models must mirror, with every reaction requiring accurate kinetic data. Here, we showcase Kinetica.jl, a new software package for constructing large-scale chemical reaction networks in a fully automated fashion by exploring chemical reaction space with a kinetics-driven algorithm; coupled to efficient machine-learning models of activation energies for sampled elementary reactions, we show how this approach readily enables generation and kinetic characterization of networks containing ∼103 chemical species and ≃104-105 reactions. Symbolic-numeric modeling of the generated reaction networks is used to allow for flexible, efficient computation of kinetic profiles under experimentally realizable conditions such as continuously variable temperature regimes, enabling direct connection between bottom-up reaction networks and experimental observations. Highly efficient propagation of long-time-scale kinetic profiles is required for automated reaction network refinement and is enabled here by a new discrete kinetic approximation. The resulting Kinetica.jl simulation package therefore enables automated generation, characterization, and long-time-scale modeling of complex chemical reaction systems. We demonstrate this for hydrocarbon pyrolysis simulated over time scales of seconds, using transient temperature profiles representing those of tubular flow reactor experiments.

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.

Efficient Acceleration of Reaction Discovery in the Ab Initio Nanoreactor: Phenyl Radical Oxidation Chemistry

Over the years, many computational strategies have been employed to elucidate reaction networks. One of these methods is accelerated molecular dynamics, which can circumvent the expense required in dynamics to find all reactants and products (local minima) and transition states (first-order saddle points) on a potential energy surface (PES) by using fictitious forces that promote reaction events. The ab initio nanoreactor uses these accelerating forces to study large chemical reaction networks from first-principles quantum mechanics. In the initial nanoreactor studies, this acceleration was done through a piston periodic compression potential, which pushes molecules together to induce entropically unfavorable bimolecular reactions. However, the piston is not effective for discovering intramolecular and dissociative reactions, such as those integral to the decomposition channels of phenyl radical oxidation. In fact, the choice of accelerating forces dictates not only the rate of reaction discovery but also the types of reactions discovered; thus, it is critical to understand the biases and efficacies of these forces. In this study, we examine forces using metadynamics, attractive potentials, and local thermostats for accelerating reaction discovery. For each force, we construct a separate phenyl radical combustion reaction network using solely that force in discovery trajectories. We elucidate the enthalpic and entropic trends of each accelerating force and highlight their efficiency in reaction discovery. Comparing the nanoreactor-constructed reaction networks with literature renditions of the phenyl radical combustion PES shows that a combination of accelerating forces is best suited for reaction discovery.

Automated Generation of Microkinetics for Heterogeneously Catalyzed Reactions Considering Correlated Uncertainties

The study presents an ab-initio based framework for the automated construction of microkinetic mechanisms considering correlated uncertainties in all energetic parameters and estimation routines. 2000 unique microkinetic models were generated within the uncertainty space of the BEEF-vdW functional for the oxidation reactions of representative exhaust gas emissions from stoichiometric combustion engines over Pt(111) and compared to experiments through multiscale modeling. The ensemble of simulations stresses the importance of considering uncertainties. Within this set of first-principles-based models, it is possible to identify a microkinetic mechanism that agrees with experimental data. This mechanism can be traced back to a single exchange-correlation functional, and it suggests that Pt(111) could be the active site for the oxidation of light hydrocarbons. The study provides a universal framework for the automated construction of reaction mechanisms with correlated uncertainty quantification, enabling a DFT-constrained microkinetic model optimization for other heterogeneously catalyzed systems.

Graph-Driven Reaction Discovery: Progress, Challenges, and Future Opportunities

Graph-based descriptors, such as bond-order matrices and adjacency matrices, offer a simple and compact way of categorizing molecular structures; furthermore, such descriptors can be readily used to catalog chemical reactions (i.e., bond-making and -breaking). As such, a number of graph-based methodologies have been developed with the goal of automating the process of generating chemical reaction network models describing the possible mechanistic chemistry in a given set of reactant species. Here, we outline the evolution of these graph-based reaction discovery schemes, with particular emphasis on more recent methods incorporating graph-based methods with semiempirical and ab initio electronic structure calculations, minimum-energy path refinements, and transition state searches. Using representative examples from homogeneous catalysis and interstellar chemistry, we highlight how these schemes increasingly act as "virtual reaction vessels" for interrogating mechanistic questions. Finally, we highlight where challenges remain, including issues of chemical accuracy and calculation speeds, as well as the inherent challenge of dealing with the vast size of accessible chemical reaction space.

Quantifying the Impact of Parametric Uncertainty on Automatic Mechanism Generation for CO2 Hydrogenation on Ni(111)

Automatic mechanism generation is used to determine mechanisms for the CO2 hydrogenation on Ni(111) in a two-stage process while considering the correlated uncertainty in DFT-based energetic parameters systematically. In a coarse stage, all the possible chemistry is explored with gas-phase products down to the ppb level, while a refined stage discovers the core methanation submechanism. Five thousand unique mechanisms were generated, which contain minor perturbations in all parameters. Global uncertainty assessment, global sensitivity analysis, and degree of rate control analysis are performed to study the effect of this parametric uncertainty on the microkinetic model predictions. Comparison of the model predictions with experimental data on a Ni/SiO2 catalyst find a feasible set of microkinetic mechanisms within the correlated uncertainty space that are in quantitative agreement with the measured data, without relying on explicit parameter optimization. Global uncertainty and sensitivity analyses provide tools to determine the pathways and key factors that control the methanation activity within the parameter space. Together, these methods reveal that the degree of rate control approach can be misleading if parametric uncertainty is not considered. The procedure of considering uncertainties in the automated mechanism generation is not unique to CO2 methanation and can be easily extended to other challenging heterogeneously catalyzed reactions.

Theoretical and Experimental Study of 3-Pentanol Autoignition: Ab Initio Calculation, Shock Tube Experiments, and Kinetic Modeling

3-Pentanol is a potential alternative fuel or a green fuel additive for modern engines. The H-abstraction reactions from 3-pentanol by H, CH₃, HO₂, and OH radicals are significant in the 3-pentanol oxidation process. However, corresponding rate constants are forced to rely on either analogy from sec-butanol or estimation from alkanes due to a lack of direct experimental and theoretical study. In this work, stationary points on the potential energy surfaces (PESs) were calculated with the high-level DLPNO-CCSD(T)/CBS(T-Q)//M06-2X/cc-pVTZ method, which is further used to benchmark against the CBS-QB3 method. Then, the high-pressure limit rate constants for target reactions, over a broad range of temperature (400-2000 K), were calculated with the phase-space theory and conventional transition state theory. A comparison was made between the calculated rate constants and the values available in Carbonnier et al. [ Proc. Combust. Inst. 2019, 37(1), 477-484]. The rate constants for the above H-abstraction reactions in the Carbonnier model were updated with the calculated results, followed by a modification based on the computed results of 3-pentanol + HO₂ to obtain the revised model. Validation against the shock tube (ST) and the jet-stirred reactor (JSR) measurements from the literature proved the revised model an optimal one. Furthermore, using an ST, ignition delay times (IDTs) for the 3-pentanol/air mixtures were measured spanning a temperature range of 920-1450 K, pressures of 6, 10, and 20 bar, and equivalence ratios of 0.5, 1.0, and 1.5. Generally, IDTs decrease with increasing temperature and reflected shock pressure. Improved predictions to present experimental data were obtained by using the revised model as compared with the Carbonnier model. Finally, sensitivity analysis was conducted using the revised model to gain an in-depth comprehension of the 3-pentanol autoignition.

Reaction Mechanism Generator v3.0: Advances in Automatic Mechanism Generation

In chemical kinetics research, kinetic models containing hundreds of species and tens of thousands of elementary reactions are commonly used to understand and predict the behavior of reactive chemical systems. Reaction Mechanism Generator (RMG) is a software suite developed to automatically generate such models by incorporating and extrapolating from a database of known thermochemical and kinetic parameters. Here, we present the recent version 3 release of RMG and highlight improvements since the previously published description of RMG v1.0. Most notably, RMG can now generate heterogeneous catalysis models in addition to the previously available gas- and liquid-phase capabilities. For model analysis, new methods for local and global uncertainty analysis have been implemented to supplement first-order sensitivity analysis. The RMG database of thermochemical and kinetic parameters has been significantly expanded to cover more types of chemistry. The present release includes parallelization for faster model generation and a new molecule isomorphism approach to improve computational performance. RMG has also been updated to use Python 3, ensuring compatibility with the latest cheminformatics and machine learning packages. Overall, RMG v3.0 includes many changes which improve the accuracy of the generated chemical mechanisms and allow for exploration of a wider range of chemical systems.

The Exploration of Chemical Reaction Networks

Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various algorithmic advances have shown that such structural screenings must and can be automated and routinely carried out. This will replace the standard approach of manually studying a selected and restricted number of molecular structures for a chemical mechanism. The complexity of the task has led to many different approaches. However, all of them address the same general target, namely to produce a complete atomistic picture of the kinetics of a chemical process. It is the purpose of this overview to categorize the problems that should be targeted and to identify the principal components and challenges of automated exploration machines so that the various existing approaches and future developments can be compared based on well-defined conceptual principles.

Development and Assessment of a Criterion for the Application of Brønsted-Evans-Polanyi Relations for Dissociation Catalytic Reactions at Surfaces

We propose and assess a criterion for the application of Brønsted–Evans–Polanyi (BEP) relations for dissociation reactions at surfaces. A theory-to-theory comparison with density functional theory calculations is presented on different reactions, metal catalysts, and surface terminations. In particular, the activation energies of CH, CO, and trans-COOH dissociation reactions on (100), (110), (111), and (211) surfaces of Ni, Cu, Rh, Pd, Ag, and Pt are considered. We show that both the activation energy and the reaction energy can be decomposed into two contributions that reflect the influence of reactant and products in determining either the activation energy or the reaction energy. We show that the applicability of the BEP relation implies that the reaction energy and activation energy correlate to these two contributions in the range of conditions to be described by the BEP relation. A lack of correlation between these components for the activation energy is related to a change in the character of the transition state (TS) and this turns out to be incompatible with a BEP relation because it results in a change of the slope of the BEP relation. Our analysis reveals that these two contributions follow the same trends for the activation energy and for the reaction energy when the path is not characterized either by the formation of stable intermediates or by the change of the binding mechanism of the reactant. As such, one can assess whether a BEP relation can be applied or not for a set of conditions only by means of thermochemical calculations and without requiring the identification of the TS along the reaction pathway. We provide evidence that this criterion can be successfully applied for the preliminary discrimination of the applicability of the BEP relations. For instance, on the one hand, our analysis provides evidence that the two contributions are fully anticorrelated for the trans-COOH dissociation reactions on different metals and surfaces, thus revealing that the reaction is characterized by a change in the TS character. In this situation, no BEP relation can be used to describe the activation energy trend among the different metals and surfaces in full agreement with our DFT calculations. On the other hand, our criterion reveals that the TS character is not expected to change for CH dissociation reactions both for the same facet, different metals and for same metal, different facets, in good agreement with the DFT calculations of the activation energy. The formation of multiple stable intermediates along the reaction pathways and the change of the binding mechanism of one of the reactants are demonstrated to affect the validity of the criterion. As a whole, our findings make possible an assessment of the applicability of the BEP relation and paves the way toward its use for the exploration of complex reaction networks for different metals and surfaces.

Detailed kinetic model for hexyl sulfide pyrolysis and its desulfurization by supercritical water

The automated reaction mechanism generator is used to model the decomposition of hexyl sulfide with and without supercritical water.

On-the-fly kinetics of hydrogen abstraction from polycyclic aromatic hydrocarbons by methyl/ethyl radicals

This work provides a rigorous procedure, within the framework of the Reaction Class Transition State Theory (RC-TST) and the Structure-Activity Relationship (SAR), for predicting reliable thermal rate constants on-the-fly for hydrogen abstraction reactions by methyl/ethyl radicals from Polycyclic Aromatic Hydrocarbons (PAHs) in a temperature range of 300-3000 K. All necessary RC-TST parameters were derived from ab initio calculations for a representative set of 36 reactions on which different error analyses and comparisons with available literature data were carried out. In addition to the good agreement between the RC-TST rate constants and the literature data, the detailed error analyses show that RC-TST/SAR, utilizing either the Linear Energy Relationship (LER) where only the reaction energy is needed or Barrier Height Grouping (BHG) where no additional data is needed, can predict the thermal rate constants for any reaction in the title reaction class with an average systematic error of less than 50% when compared to the explicit rate calculations. Therefore, the constructed RC-TST procedure can be confidently used to obtain reliable rate constants on the fly in an attempt to effectively construct detailed kinetic mechanisms for PAH-related fuels.

Microkinetic Analysis and Scaling Relations for Catalyst Design

Microkinetic analysis plays an important role in catalyst design because it provides insight into the fundamental surface chemistry that controls catalyst performance. In this review, we summarize the development of microkinetic models and the inclusion of scaling relationships in these models. We discuss the importance of achieving stoichiometric and thermodynamic consistency in developing microkinetic models. We also outline how analysis of the maximum rates of elementary steps can be used to determine which transition states and adsorbed intermediates are kinetically significant, allowing the derivation of general reaction kinetics rate expressions in terms of changes in binding energies of the relevant transition states and intermediates. Through these analyses, we present how to predict optimal surface coverages and binding energies of adsorbed species, as well as the extent of potential rate improvement for a catalytic system. For systems in which the extent of potential rate improvement is small because of limitations imposed by scaling relations, different approaches, including the addition of promoters and formation of catalysts containing multiple functionalities, can be used to break the scaling relations and obtain further rate enhancement.

Potential Energy Surface for Large Barrierless Reaction Systems: Application to the Kinetic Calculations of the Dissociation of Alkanes and the Reverse Recombination Reactions

The isodesmic reaction method is applied to calculate the potential energy surface (PES) along the reaction coordinates and the rate constants of the barrierless reactions for unimolecular dissociation reactions of alkanes to form two alkyl radicals and their reverse recombination reactions. The reaction class is divided into 10 subclasses depending upon the type of carbon atoms in the reaction centers. A correction scheme based on isodesmic reaction theory is proposed to correct the PESs at UB3LYP/6-31+G(d,p) level. To validate the accuracy of this scheme, a comparison of the PESs at B3LYP level and the corrected PESs with the PESs at CASPT2/aug-cc-pVTZ level is performed for 13 representative reactions, and it is found that the deviations of the PESs at B3LYP level are up to 35.18 kcal/mol and are reduced to within 2 kcal/mol after correction, indicating that the PESs for barrierless reactions in a subclass can be calculated meaningfully accurately at a low level of ab initio method using our correction scheme. High-pressure limit rate constants and pressure dependent rate constants of these reactions are calculated based on their corrected PESs and the results show the pressure dependence of the rate constants cannot be ignored, especially at high temperatures. Furthermore, the impact of molecular size on the pressure-dependent rate constants of decomposition reactions of alkanes and their reverse reactions has been studied. The present work provides an effective method to generate meaningfully accurate PESs for large molecular system.

Modeling study of the anti-knock tendency of substituted phenols as additives: an application of the reaction mechanism generator (RMG)

This work presents kinetic modeling efforts to evaluate the anti-knock tendency of several substituted phenols if used as gasoline additives. They are p-cresol, m-cresol, o-cresol, 2,4-xylenol, 2-ethylphenol, and guaiacol. A detailed kinetic model was constructed to predict the ignition of blends of the phenols in n-butane with the help of reaction mechanism generator (RMG), an open-source software package. The resulting model, which has 1465 species and 27 428 reactions, was validated against literature n-butane ignition data in the low-to-intermediate temperature range. To rank the anti-knock tendency of the additives, engine-like simulations were performed in a closed adiabatic homogenous batch reactor with a volume history derived from the pressure profile of a real research octane number (RON) engine test. The ignition timings of the additive blends were compared to that of primary reference fuels (PRFs) to quantitatively predict the anti-knock ability. The model predictions agree well with experimental determinations of the changes in RON induced by the additives. This study explains the chemical mechanism by which methyl-substituted phenols increase RON, and demonstrates how fundamental chemical kinetics can be used to evaluate practical fuel additive performance.

Modeling Ignition of a Heptane Isomer: Improved Thermodynamics, Reaction Pathways, Kinetics, and Rate Rule Optimizations for 2-Methylhexane

Accurate chemical kinetic combustion models of lightly branched alkanes (e.g., 2-methylalkanes) are important to investigate the combustion behavior of real fuels. Improving the fidelity of existing kinetic models is a necessity, as new experiments and advanced theories show inaccuracies in certain portions of the models. This study focuses on updating thermodynamic data and the kinetic reaction mechanism for a gasoline surrogate component, 2-methylhexane, based on recently published thermodynamic group values and rate rules derived from quantum calculations and experiments. Alternative pathways for the isomerization of peroxy-alkylhydroperoxide (OOQOOH) radicals are also investigated. The effects of these updates are compared against new high-pressure shock tube and rapid compression machine ignition delay measurements. It is shown that rate constant modifications are required to improve agreement between kinetic modeling simulations and experimental data. We further demonstrate the ability to optimize the kinetic model using both manual and automated techniques for rate parameter tunings to improve agreement with the measured ignition delay time data. Finally, additional low temperature chain branching reaction pathways are shown to improve the model's performance. The present approach to model development provides better performance across extended operating conditions while also strengthening the fundamental basis of the model.

Performance of First-Principles-Based Reaction Class Transition State Theory

Performance of the Reaction Class Transition State Theory (RC-TST) for prediction of rates constants of elementary reactions is examined using data from its previous applications to a number of different reaction classes. The RC-TST theory is taking advantage of the common structure denominator of all reactions in a given family combined with structure activity relationships to provide a rigorous theoretical framework to obtain rate expression of any reaction within a reaction class in a simple and cost-effective manner. This opens the possibility for integrating this methodology with an automated mechanism generator for "on-the-fly" generation of accurate kinetic models of complex reacting systems.

A Signature of Roaming Dynamics in the Thermal Decomposition of Ethyl Nitrite: Chirped-Pulse Rotational Spectroscopy and Kinetic Modeling

Chirped-pulse (CP) Fourier transform rotational spectroscopy is uniquely suited for near-universal quantitative detection and structural characterization of mixtures that contain multiple molecular and radical species. In this work, we employ CP spectroscopy to measure product branching and extract information about the reaction mechanism, guided by kinetic modeling. Pyrolysis of ethyl nitrite, CH3CH2ONO, is studied in a Chen type flash pyrolysis reactor at temperatures of 1000-1800 K. The branching between HNO, CH2O, and CH3CHO products is measured and compared to the kinetic models generated by the Reaction Mechanism Generator software. We find that roaming CH3CH2ONO → CH3CHO + HNO plays an important role in the thermal decomposition of ethyl nitrite, with its rate, at 1000 K, comparable to that of the radical elimination channel CH3CH2ONO → CH3CH2O + NO. HNO is a signature of roaming in this system.