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.     

SurfKin: An ab initio kinetic code for modeling surface reactions

In this article, we describe a C/C++ program called SurfKin (Surface Kinetics) to construct microkinetic mechanisms for modeling gas–surface reactions. Thermodynamic properties of reaction species are estimated based on density functional theory calculations and statistical mechanics. Rate constants for elementary steps (including adsorption, desorption, and chemical reactions on surfaces) are calculated using the classical collision theory and transition state theory. Methane decomposition and water–gas shift reaction on Ni(111) surface were chosen as test cases to validate the code implementations. The good agreement with literature data suggests this is a powerful tool to facilitate the analysis of complex reactions on surfaces, and thus it helps to effectively construct detailed microkinetic mechanisms for such surface reactions. SurfKin also opens a possibility for designing nanoscale model catalysts. © 2014 Wiley Periodicals, Inc.     

Deconvolution of Molecular Weight Distributions Using Dynamic Flory‐Schulz Distributions

Summary: The deconvolution of molecular weight distributions (MWDs) may be useful for obtaining information about the polymerization kinetics and properties of catalytic systems. However, deconvolution techniques are normally based on steady‐state assumptions and very little has been reported about the use of non‐stationary approaches for the deconvolution of MWDs. In spite of this, polymerization reactions are often performed in batch or semi‐batch modes. For this reason, dynamic solutions are proposed here for simple kinetic models and are then used for deconvolution of actual MWD data. Deconvolution results obtained with dynamic models are compared to deconvolution results obtained with the standard stationary Flory‐Schulz distributions. For coordination polymerizations, results show that dynamic MWD models are able to describe experimental data with fewer catalytic sites, which indicates that the proper interpretation of the reaction dynamics may be of fundamental importance for kinetic characterization. On the other hand, reaction dynamics induced by modification of chain transfer agent concentration seem to play a minor role in the shape of the MWD in free‐radical polymerizations.

This Figure illustrates that MWDs obtained at unsteady conditions should not be deconvoluted with standard steady‐state Flory‐Schulz distributions.     

Mechanistic Insights into RNA Transphosphorylation from Kinetic Isotope Effects and Linear Free Energy Relationships of Model Reactions

Phosphoryl transfer reactions are ubiquitous in biology and the understanding of the mechanisms whereby these reactions are catalyzed by protein and RNA enzymes is central to reveal design principles for new therapeutics. Two of the most powerful experimental probes of chemical mechanism involve the analysis of linear free energy relations (LFERs) and the measurement of kinetic isotope effects (KIEs). These experimental data report directly on differences in bonding between the ground state and the rate‐controlling transition state, which is the most critical point along the reaction free energy pathway. However, interpretation of LFER and KIE data in terms of transition‐state structure and bonding optimally requires the use of theoretical models. In this work, we apply density‐functional calculations to determine KIEs for a series of phosphoryl transfer reactions of direct relevance to the 2′‐O‐transphosphorylation that leads to cleavage of the phosphodiester backbone of RNA. We first examine a well‐studied series of phosphate and phosphorothioate mono‐, di‐ and triesters that are useful as mechanistic probes and for which KIEs have been measured. Close agreement is demonstrated between the calculated and measured KIEs, establishing the reliability of our quantum model calculations. Next, we examine a series of RNA transesterification model reactions with a wide range of leaving groups in order to provide a direct connection between observed Brønsted coefficients and KIEs with the structure and bonding in the transition state. These relations can be used for prediction or to aid in the interpretation of experimental data for similar non‐enzymatic and enzymatic reactions. Finally, we apply these relations to RNA phosphoryl transfer catalyzed by ribonuclease A, and demonstrate the reaction coordinate–KIE correlation is reasonably preserved. A prediction of the secondary deuterium KIE in this reaction is also provided. These results demonstrate the utility of building up knowledge of mechanism through the systematic study of model systems to provide insight into more complex biological systems such as phosphoryl transfer enzymes and ribozymes.     

Co‐evolution of non‐linear PLS model components

The issue of outer model weight updating is important in extending partial least squares (PLS) regression to modelling data that shows significant non‐linearity. This paper presents a novel co‐evolutionary component approach to the weight updating problem. Specification of the non‐linear PLS model is achieved using an evolutionary computational (EC) method that can co‐evolve all non‐linear inner models and all input projection weights simultaneously. In this method, modular symbolic non‐linear equations are used to represent the inner models and binary sequences are used to represent the projection weights. The approach is flexible, and other representations could be employed within the same co‐evolutionary framework. The potential of these methods is illustrated using a simulated pH neutralisation process data set exhibiting significant non‐linearity. It is demonstrated that the co‐evolutionary component architecture can produce results which are competitive with non‐linear neural network‐based PLS algorithms that use iterative projection weight updating. In addition, a data sampling method for mitigating overfitting to the training data is described. Copyright © 2007 John Wiley & Sons, Ltd.     

Microkinetic model for NO–CO reaction: Model reduction

The objective of this work is to elucidate controlling mechanisms in NO_x reduction, develop reduced‐order reaction models, and analyze the reactor performance using the reduced‐order reaction model for the NO–CO reaction. We start with the microkinetic model on platinum, which describes the mechanism of catalytic reduction of NO by CO. The formation of the main product N₂O and the competitive formation of the side product N₂ are accounted for in the microkinetic model. Sensitivity and reaction path analysis have been carried out to determine the rate‐limiting steps as well as the most abundant reactive intermediates in the system. Owing to the differences between system performance at high and low temperatures, the model has been analyzed in detail in these temperature regimes. Two closed‐form expressions, corresponding to the two global reactions involved, have been derived. The characteristic features of the microkinetic model such as the sharp increase in NO conversion and the selectivity to N₂O are captured well by the reduced model. The reduced‐order model has been extended to the rhodium catalyst as well. © 2012 Wiley Periodicals, Inc. Int J Chem Kinet 44: 577–585, 2012     

Analyzing the uniqueness of the rate constants calculated from complex kinetic systems: A study of the hydrolysis of ciclohexanecarbonitriles

In this article, a novel methodology for the study of complex reaction mechanisms is explored, and applied to the kinetic analysis of the hydrolysis reactions of ciclohexanecarbonitriles. The kinetic data were first analyzed with the help of classic linear techniques. Subsequently, the determination of the rate constants by a non‐linear, least‐squares (LS) fitting method, followed by a novel eigenvalue‐eigenvector analysis of the sensitivity coefficients, permitted us to obtain the maximum possible information from the kinetic data. The non‐linear, LS‐fitting method, carried out by means of a new version of OPKINE program, allowed the calculation of all the rate constants of the mechanism; in addition, the sensitivity analysis permitted us to establish the uniqueness and reliability of calculated rate coefficients. Finally, the results of the sensitivity analysis were tested by means of a simulation procedure, and the results compared to those obtained from classic linear methods. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 611–626, 1999.     

Role of Emissive and Non‐Emissive Complex Formations in Photoinduced Electron Transfer Reaction of CdTe Quantum Dots

Bimolecular photoinduced electron transfer (PET) from excited state CdTe quantum dot (QD*) to an electron deficient molecule 2,4‐dinitrotoluene (DNT) is studied in toluene. We observed two types of QD‐DNT complex formations; (i) non‐emissive complex, in which DNT is embedded deep inside the surface polymer layer of QD and (ii) emissive complex, in which DNT molecules are attached to QDs but approach to the QD core is shielded by polymer layer. Because of its non‐emissive nature, the lifetime of QD is not affected by dark complex formation, though the steady‐state emission is greatly quenched. However, emissive complex formation causes both, lifetime and steady‐state emission quenching. In our fitting model, consideration of Poisson distribution of the attached quencher (DNT) molecules at QD surface enables a comprehensive fitting to our time resolved data. QD‐DNT complex formation was confirmed by an isothermal titration calorimetry (ITC) study. Fitting to the time resolved data using a stochastic kinetic model shows moderate increase (0.05 ns^?1 to 0.072 ns^?1) of intrinsic quenching rate with increasing the QD particle size (from ≈3.2 nm to ≈5.2 nm). Our fitting also reveals that the number of DNT molecules attached to a single QD increases from ≈0.1–0.2 to ≈1.2–1.7, as the DNT concentration is increased from ≈1 mm to 17.5 mm . Complex formation at higher quencher concentration assures that the observed PET kinetics is a thermodynamically controlled process where solvent diffusion has no role on it.     

Mathematical modeling of self-oscillations in ethane oxidation over nickel

The methodology of constructing a phenomenological model for complex heterogeneous catalytic reactions is described in detail. The proposed approach is applicable to development of mathematical models describing the onset of self-oscillations in hydrocarbon oxidation on the transition metal surface. The approach is based on construction of a microkinetic scheme taking into account the formation of main reaction products and intermediates, on estimation of the heat of reaction, activation energy, and preexponential factor for elementary steps and includes development and a subsequent analysis of the corresponding mathematical model. Catalytic reactions are considered in the ideal adsorption layer approximation without taking into account the relationship between coverages and spatial coordinates. Accordingly, the mathematical model is an independent system of ordinary differential equations. This methodology is used to develop a point (lumped) model for ethane oxidation over nickel, which is based on a 36-step microkinetic scheme taking into account the oxidation and reduction of nickel and the formation of total (CO₂ and H₂O) or partial (CO and H₂) ethane oxidation products, as well as the dehydrogenation of ethane into ethylene. The proposed model predicts the onset of self-oscillations in this reaction at atmospheric pressure in the temperature range from 850 to 1400 K. The kinetic oscillations are caused by the cyclic oxidation and reduction of nickel. The self-oscillations of the reaction rate are accompanied by oscillations of the catalyst temperature. The results of modeling are compared with experimental data.     

Classic and multivariate modeling treatment of the kinetics and mechanism of isomerization of 5‐cholesten‐3‐one catalyzed by sodium ethoxide

A classic kinetic methodology including the treatment of the steady‐state method and a multivariate modeling kinetic treatment were applied to the kinetics and mechanism of the isomerization reaction of 5‐cholesten‐3‐one to 4‐cholesten‐3‐one catalyzed by EtO⁻ in ethanol absolute. The rate constants, thermodynamic parameters of activation, equilibrium constant, and the isomerization enthalpy were determined. The multivariate modeling kinetic treatment allows us to calculate the concentrations of the species, in which the 3,5‐dienolate is included as a highly reactive intermediate species and was able to discriminate among several applicable mechanisms validating the one comprising two reversible steps. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 38: 38–47, 2006     

Time‐Varying Flexible Least Squares for Thermal Desorption of Gases

Time‐varying linear regression via flexible least squares is used to determine temperature‐dependent kinetic parameters during low‐pressure, steady‐state, temperature‐programmed desorption from catalytic surfaces. The flexible least squares approach optimizes time‐varying parameters by minimizing dynamic and measurement discrepancies between a linear theoretical model and experimental data using linear regression. The effectiveness of this approach is demonstrated by calculation of accurate temperature‐dependent activation energies, preexponential factors, and differential conversion functions for the evolution of 3‐methyl‐2‐oxetanone (β‐lactone) during the selective oxidation of isobutane over aluminum phosphomolybdates.     

Free radical terpolymerization of three non‐homopolymerizable monomers, 1 Kinetic scheme

In previous papers two models were proposed which describe the terpolymerization of non‐homopolymerizable donor and acceptor monomers. The first one is based on the terminal model considering only the propagation reactions of the free monomers. The second one is the complex model considering only the reactions of charge‐transfer complexes. This paper describes a new kinetic scheme involving the participation of both the free monomers and the charge‐transfer complexes. Quantitative treatment of the overall polymerization rate by this new kinetic scheme allows to evaluate the degree of the participation of the free monomers and the charge‐transfer complexes. For the first time therefore it is possible to determine quantitatively the influence of charge‐transfer complexes on the free radical terpolymerization of non‐homopolymerizable monomers.     

Biomass pyrolysis kinetics: A comparative critical review with relevant agricultural residue case studies

Biomass pyrolysis is a fundamental thermochemical conversion process that is of both industrial and ecological importance. From designing and operating industrial biomass conversion systems to modeling the spread of wildfires, an understanding of solid state pyrolysis kinetics is imperative. A critical review of kinetic models and mathematical approximations currently employed in solid state thermal analysis is provided. Isoconversional and model-fitting methods for estimating kinetic parameters are comparatively evaluated. The thermal decomposition of biomass proceeds via a very complex set of competitive and concurrent reactions and thus the exact mechanism for biomass pyrolysis remains a mystery. The pernicious persistence of substantial variations in kinetic rate data for solids irrespective of the kinetic model employed has exposed serious divisions within the thermal analysis community and also caused the broader scientific and industrial community to question the relevancy and applicability of all kinetic data obtained from heterogeneous reactions. Many factors can influence the kinetic parameters, including process conditions, heat and mass transfer limitations, physical and chemical heterogeneity of the sample, and systematic errors. An analysis of thermal decomposition data obtained from two agricultural residues, nutshells and sugarcane bagasse, reveals the inherent difficulty and risks involved in modeling heterogeneous reaction systems.     

Model Calculations and Experimental Studies as a Route Toward Simplification of the Kinetic Mechanism of the H2O2–NaSCN–NaOH–CuSO4 Homogeneous Oscillator

Oscillatory chemical reactions are usually characterized by complicated kinetic mechanisms in which the source of instability is combined with the parallel dissipative process. One of such systems is the H₂O₂–NaSCN–NaOH–CuSO₄ homogeneous oscillator, in which dynamic instabilities are associated with the irreversible oxidation of thiocyanate ions with hydrogen peroxide. Following our previous studies on this system, we now propose further intuitive and substantial simplification of its kinetic mechanism toward the scheme involving only five intermediates. Its compatibility with our previous, nine‐variable model is verified in terms of model calculations, compared with experimental potentiometric and spectrophotometric data. In particular, supercritical nature of a Hopf bifurcation as a route toward oscillations born out of a single steady state upon increasing catalyst (copper species) concentration was observed in the model and an analogous type of bifurcation is suggested by available experimental data. Our work is a step toward final reduction of the mechanism of the studied system to the “minimum oscillator,” the concept used earlier, e.g., for the Belousov–Zhabotinsky reaction, of however remarkably different kinetic mechanism.     

A Two‐Step Interval and Modified Rosenbrock Method for Kinetic Parameter Estimation in Copolymerization Systems: A Robust and Reliable Approach

Summary: The kinetics of solution free radical copolymerization of isobutyl methacrylate (i‐BMA) and lauryl methacrylate (LMA) in benzene, initiated with 2,2‐azoisobutyronitrile (AIBN) were studied at different monomer feed compositions at low conversion levels. In order to avoid the complications of copolymerization kinetics, the pseudo‐kinetic rate constant method was applied in constant and variable volume polymerization systems. A two‐step procedure based on interval analysis and the modified Rosenbrock method was used to estimate the kinetic parameters of copolymerization. In the first step, initiation, coupled propagation‐termination and transfer rate parameters were determined from steady state kinetic equations using interval analysis. Since the objective function is non‐linear, non‐convex and has multiple local optima, a robust computational technique, based on the Interval Newton/Generalized Bisection (IN/GB) algorithm, was developed to solve this set of non‐linear algebraic equations. This method was used with mathematical and computational guarantees of certainty to find the global optimum. In the second step, the system of mole balance, population balance and moment equations, which are highly stiff ordinary differential equations, were discritized and solved by the modified Rosenbrock method. The results of the first computational step were inserted as an active or equality constraint in the second step to calculate the individual elementary rate parameters of the reaction. Statistical analysis indicated that the copolymer composition is well described by the terminal unit model (TUM), but the implicit penultimate unit effect (IPUE) model of Fukuda and coworkers is more suitable for describing the rate data. In contrast to most previously studied systems, it was found that propagation and coupled rate parameters are greater than those predicted by the TUM.

Variation of number average molecular weight of the copolymer in polymerization system for various initial monomer feed compositions at different reaction times (solid lines are computed results).     

Alternative Representations of the Correlation Energy in Density‐Functional Theory: A Kinetic‐Energy Based Adiabatic Connection

The adiabatic‐connection framework has been widely used to explore the properties of the correlation energy in density‐functional theory. The integrand in this formula may be expressed in terms of the electron–electron interactions directly, involving intrinsically two‐particle expectation values. Alternatively, it may be expressed in terms of the kinetic energy, involving only one‐particle quantities. In this work, we explore this alternative representation for the correlation energy and highlight some of its potential for the construction of new density functional approximations. The kinetic‐energy based integrand is effective in concentrating static correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the correlation energy in density‐functional theory     

Harnessing the Combined Power of Theoretical and Experimental Data through Multiscale Informatics

Monumental, recent and rapidly continuing, improvements in the capabilities of ab initio theoretical kinetics calculations provides reason to believe that progress in the field of chemical kinetics can be accelerated through a corresponding evolution of the role of theory in kinetic modeling and its relationship with experiment. The present article reviews and provides additional demonstrations of the unique advantages that arise when theoretical and experimental data across multiple scales are considered on equal footing, including the relevant uncertainties of both, within a single mathematical framework. Namely, the multiscale informatics framework simultaneously integrates information from a wide variety of sources and scales: ab initio electronic structure calculations of molecular properties, rate constant determinations for individual reactions, and measured global observables of multireaction systems. The resulting model representation consists of a set of theoretical kinetics parameters (with constrained uncertainties) that are related through elementary kinetics models to rate constants (with propagated uncertainties) that in turn are related through physical models to global observables (with propagated uncertainties). An overview of the approach and typical implementation is provided along with a brief discussion of the major uncertainties (parametric and structural) in theoretical kinetics calculations, kinetic models for complex chemical mechanisms, and physical models for experiments. Higher levels of automation in all aspects, including closed‐loop autonomous mixed‐experimental‐and‐computational model improvement, are advocated for facilitating scalability of the approach to larger systems with reasonable human effort and computational cost. The unique advantages of combining theoretical and experimental data across multiple scales are illustrated through a series of examples. Previous results demonstrating the utility of simultaneous interpretation of theoretical and experimental data for assessing consistency in complex systems and for reliable, physics‐based extrapolation of limited data are briefly summarized. New results are presented to demonstrate the high predictive accuracy of multiscale informed models for both small (molecular properties) and large (global observables) scales. These new results provide examples where the optimization yields physically realistic parameter adjustments and where physical model uncertainties in experiments are larger than kinetic model uncertainties. New results are also presented to demonstrate the utility of the multiscale informatics approach for design of experiments and theoretical calculations, accounting for both theoretical and experimental existing knowledge as well as relevant parametric and structural uncertainties in interpreting potential new data. These new results provide examples where neglecting structural uncertainties in design of experiments results in failure to identify the most worthwhile experiment. Further progress in the chemical kinetics field (particularly at the intersection of theory, kinetic modeling, and experiment) would benefit from increased attention to understanding parametric and structural uncertainties for all three—the uncertainty magnitude and cross‐correlations among model parameters as well as limitations of the model structures themselves.     

Model‐free multivariate curve resolution combined with model‐based kinetics: algorithm and applications

Multivariate curve resolution techniques are powerful tools to extract from sequences of spectra of a chemical reaction system the number of independent chemical components, their associated spectra, and the concentration profiles in time. Usually, these solutions are not unique because of the so‐called rotational ambiguity. In the present work, we reduce the non‐uniqueness by enforcing the consistency of the computed concentration profiles with a given kinetic model. Traditionally, the kinetic modeling is realized in a separate step, which follows the multivariate curve resolution procedure. In contrast to this, we consider a hybrid approach that combines the model‐free curve resolution technique with the model‐based kinetic modeling in an overall optimization. For a two‐component model problem, the range of possible solutions is analyzed, and its reduction to a single, unique solution by means of the hybrid kinetic modeling is shown. The algorithm reduces the rotational ambiguity and improves the quality of the kinetic fitting. Numerical results are also presented for a multi‐component catalytic reaction system that obeys the Michaelis–Menten kinetics. Copyright © 2012 John Wiley & Sons, Ltd.     

Comprehensive H2/O2 kinetic model for high‐pressure combustion

An updated H₂/O₂ kinetic model based on that of Li et al. (Int J Chem Kinet 36, 2004, 566–575) is presented and tested against a wide range of combustion targets. The primary motivations of the model revision are to incorporate recent improvements in rate constant treatment and resolve discrepancies between experimental data and predictions using recently published kinetic models in dilute, high‐pressure flames. Attempts are made to identify major remaining sources of uncertainties, in both the reaction rate parameters and the assumptions of the kinetic model, affecting predictions of relevant combustion behavior. With regard to model parameters, present uncertainties in the temperature and pressure dependence of rate constants for HO₂ formation and consumption reactions are demonstrated to substantially affect predictive capabilities at high‐pressure, low‐temperature conditions. With regard to model assumptions, calculations are performed to investigate several reactions/processes that have not received much attention previously. Results from ab initio calculations and modeling studies imply that inclusion of H + HO₂ = H₂O + O in the kinetic model might be warranted, though further studies are necessary to ascertain its role in combustion modeling. In addition, it appears that characterization of nonlinear bath‐gas mixture rule behavior for H + O₂(+ M) = HO₂(+ M) in multicomponent bath gases might be necessary to predict high‐pressure flame speeds within ～15%. The updated model is tested against all of the previous validation targets considered by Li et al. as well as new targets from a number of recent studies. Special attention is devoted to establishing a context for evaluating model performance against experimental data by careful consideration of uncertainties in measurements, initial conditions, and physical model assumptions. For example, ignition delay times in shock tubes are shown to be sensitive to potential impurity effects, which have been suggested to accelerate early radical pool growth in shock tube speciation studies. In addition, speciation predictions in burner‐stabilized flames are found to be more sensitive to uncertainties in experimental boundary conditions than to uncertainties in kinetics and transport. Predictions using the present model adequately reproduce previous validation targets and show substantially improved agreement against recent high‐pressure flame speed and shock tube speciation measurements. Comparisons of predictions of several other kinetic models with the experimental data for nearly the entire validation set used here are also provided in the Supporting Information. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 44: 444–474, 2012