Analysis of reaction schemes using maximum rates of constituent steps

Concepts Relevant for the Kinetic Analysis of Reversible Reaction Systems

The net rate of a reversible chemical reaction is the difference between unidirectional rates of traversal along forward and reverse reaction paths. In a multistep reaction sequence, the forward and reverse trajectories, in general, are not the microscopic reverse of one another; rather, each unidirectional route is comprised of distinct rate-controlling steps, intermediates, and transition states. Consequently, traditional descriptors of rate (e.g., reaction orders) do not reflect intrinsic kinetic information but instead conflate unidirectional contributions determined by (i) the microscopic occurrence of forward/reverse reactions (i.e., unidirectional kinetics) and (ii) the reversibility of reaction (i.e., nonequilibrium thermodynamics). This review aims to provide a comprehensive resource of analytical and conceptual tools which deconvolute the contributions of reaction kinetics and thermodynamics to disambiguate unidirectional reaction trajectories and precisely identify rate- and reversibility-controlling molecular species and steps in reversible reaction systems. The extrication of mechanistic and kinetic information from bidirectional reactions is accomplished through equation-based formalisms (e.g., De Donder relations) grounded in principles of thermodynamics and interpreted in the context of theories of chemical kinetics developed in the past 25 years. The aggregate of mathematical formalisms detailed herein is general to thermochemical and electrochemical reactions and encapsulates a diverse body of scientific literature encompassing chemical physics, thermodynamics, chemical kinetics, catalysis, and kinetic modeling.

Accurate descriptions of molecule-surface interactions in electrocatalytic CO2 reduction on the copper surfaces

Copper-based catalysts play a pivotal role in many industrial processes and hold a great promise for electrocatalytic CO₂ reduction reaction into valuable chemicals and fuels. Towards the rational design of catalysts, the growing demand on theoretical study is seriously at odds with the low accuracy of the most widely used functionals of generalized gradient approximation. Here, we present results using a hybrid scheme that combines the doubly hybrid XYG3 functional and the periodic generalized gradient approximation, whose accuracy is validated against an experimental set on copper surfaces. A near chemical accuracy is established for this set, which, in turn, leads to a substantial improvement for the calculated equilibrium and onset potentials as against the experimental values for CO₂ reduction to CO on Cu(111) and Cu(100) electrodes. We anticipate that the easy use of the hybrid scheme will boost the predictive power for accurate descriptions of molecule-surface interactions in heterogeneous catalysis.

Sensitivity Analysis in the Microkinetic Description of Electrocatalytic Reactions

A methodology to determine how the variation in a kinetic parameter affects the global kinetic response of an electrochemical reaction is proposed. The so-called sensitivity analysis is applied to quantify the contribution of single reaction steps of an electrocatalytic system under an oscillatory regime using microkinetic analysis.

Micro-kinetic Description of Electrocatalytic Reactions: The Role of Self-organized Phenomena

In this perspective we proposed a workflow for the construction of micro-kinetic models that consists of at least four stages, starting with information gathering that allows proposing possible reaction mechanisms....

Dynamic Microkinetic Modeling for Heterogeneously Catalyzed Hydrogenation Reactions: a Coverage-Oriented View

In most studies, the microkinetics for multistep reactions are numerically solved due to their complexity; the obtained numerical results are only valid under given reaction conditions at a static point. In this work, the microkinetics of heterogeneously catalyzed hydrogenation reactions are analytically solved as a function of three coupled physical parameters, which are energy, reaction rate, and coverage. The results correlate the surface reactions and the gaseous-phased reactant/product by energy and thus provide a dynamic view over the whole reaction process rather than at a static point. The analytical expressions are given for a simple hydrogenation reaction and three more complicated hypothetical hydrogenation reactions with side products, side reaction paths, or even multiple active sites. Compared with the numerical solution, the analytical solution is valid under all reaction conditions in practice and can provide more guidance to optimize the overall outcome or catalyst development.

Mechanistic Insight into the Origin of Stereoselectivity in the Ribose-Mediated Strecker Synthesis of Alanine

Enantioenriched amino acids are produced in a hydrolytic kinetic resolution of racemic aminonitriles mediated by chiral pentose sugars. Experimental kinetic and spectroscopic results combined with DFT computational studies and microkinetic modeling help to identify the nature of the intermediate species and provide insight into the stereoselectivity of their hydrolysis in the prebiotically relevant ribose-alanine system. These studies support a synergistic role for sugars and amino acids in the emergence of homochirality in biological molecules.

Microkinetic Modeling: A Tool for Rational Catalyst Design

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

Requiem for the Rate-Determining Step in Complex Heterogeneous Catalytic Reactions?

The concept of the rate determining step, i.e., the step having the strongest influence on the reaction rate or even being the only one present in the rate equation, is often used in heterogeneous catalytic reactions. The utilization of this concept mainly stems from a need to reduce complexity in deriving explicit rate equations or searching for a better catalyst based on the theoretical insight. When the aim is to derive a rate equation with eventual kinetic modelling for single-route mechanisms with linear sequences, the analytical rate expressions can be obtained based on the theory of complex reactions. For such mechanisms, a single rate limiting step might not be present at all and the common practice of introducing such steps is due mainly to the convenience of using simpler expressions. For mechanisms with a combination of linear and nonlinear steps or those just comprising non-linear steps, the reaction rates are influenced by several steps depending on reaction conditions, thus a reduction in complexity to a single rate limiting step can lead to misinterpretations. More widespread utilization of a microkinetic approach when the reaction rate constants can be computed with reasonable accuracy based on the theoretical insight, and availability of software for kinetic modelling, when a system of differential equations for reactants and products will be solved together with differential equations for catalytic species and the algebraic conservation equation for the latter, will eventually make the concept of the rate limiting step obsolete.

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.