A general and robust approach for defining and solving microkinetic catalytic systems

Abstract

Recent approaches for the rational design of heterogeneous catalysts have relied on first-principles-based microkinetic modeling to efficiently screen large phase spaces of catalytic materials for optimal activity and selectivity. Microkinetic modeling allows the calculation of catalytic rate and selectivity under a given set of conditions without a priori assumptions of rate or selectivity controlling steps by simultaneously solving nonlinear algebraic equations comprising species mass balances bound by the pseudo steady-state approximation. We introduce a general approach to define and solve microkinetic systems that relies solely on its stoichiometric matrix and kinetic parameters of considered reaction steps. Our approach relies on linearization of the microkinetic system, enabling analytical calculation of system derivatives for use in quasi-Newton solution schemes that exhibit excellent robustness and efficiency with minimal dependence on initial conditions.To develop a general approach for solving complex microkinetic systems, we start by defining all species in the system as S j 's rather than p j 's and h j 's. The rate equations Scheme 1. Three-step catalytic mechanism. Scheme 2. Reactions rate equations.

CatMAP: A Software Package for Descriptor-Based Microkinetic Mapping of Catalytic Trends

“…As new numerical methods for solving for kinetic steady states (e.g. homotopy continuation [56], advanced root-finding [57], numerical integration [58], or utilization of independent solvers [59]) are implemented it may become possible to circumvent these heuristics. The CatMAP package is designed to accommodate the implementation of advances via the ''Mapper'' and ''Solver'' classes, but even the simple strategies currently implemented in Cat-MAP are sufficiently fast and robust to enable the solution of relatively complex kinetic systems [53].…”

On the Rational Design of Zeolite Clusters for Converging Reaction Barriers: Quantum Study of Aldol Kinetics Confined in HZSM-5

“…Microkinetic calculations are useful for generating testable predictions from complex, multistep reaction models. − For each reaction pathway, we seek to determine the apparent activation energy consistent with the temperature-dependent Gibbs free energies computed for reactants, products, intermediates, and transition states. As in our previous work, we invoke the pseudo-steady-state approximation, , assuming that the concentrations of stable adsorbates are constant in time to yield a well-defined kinetic system that does not require information from the adsorption isotherms of reactants/products. Each aldol pathway consists of three or four elementary steps, assuming concerted or stepwise dehydration, respectively (see eqs and ).…”

Autonomous Reaction Network Exploration in Homogeneous and Heterogeneous Catalysis

“…Given a vast reaction network that includes an identified catalyst, the question remains, how the catalytic mechanism can be understood and quantified from this network. Micro-kinetic modeling of the network, e.g., by solving a Markovian master equation based on state and transition probabilities [218][219][220][221][222][223][224][225][226][227], preferably accounting for first-principles-derived uncertainties in these probabilities [142,228,229], is desirable. However, this is computationally demanding for vast reaction networks, especially if several reaction networks should be compared with one another.…”