Fachbeirat 2022

Determining Rate-Limiting Steps in Heterogeneous Catalysis under Uncertainty

Not scheduled

20m

Speaker

Sina Dortaj (Fritz-Haber-Institut)

Description

The identification of the rate-limiting steps (RDSs) of a surface catalytic reaction is one of the core objectives of mechanistic analyses. Within microkinetic modeling, RDSs are traditionally obtained through Local Sensitivity Analyses (LSA), which generally involve derivatives of the turnover frequency (TOF) with respect to the rate constants of individual elementary steps in the reaction network. High derivatives then indicate a sensitive dependence of the catalytic activity on the corresponding steps, which are consequently identified as RDSs. In first-principles microkinetic modeling where the rate constants are determined by high-level, but still approximate electronic structure theory calculations, the reliability of LSA is challenged by the intrinsic high uncertainty. With the energetic barrier entering exponentially, computed rate constants may have errors of orders of magnitude, questioning derivative-based LSA. Moreover, in first-principles kinetic Monte Carlo (kMC) simulations as most accurate form of microkinetic modeling, derivative estimates come along with high sampling noise, which renders LSA notoriously time consuming.

We address both issues by reformulating the problem of RDS determination in probabilistic terms. For this, we have developed a novel Global Sensitivity Analysis (GSA) approach on basis of the Cramers-von Mises distance and Quasi-Monte Carlo (QMC) sampling of the error space. An RDS is then a step with a large sensitivity index. While it requires running a first-principles kMC simulation for every QMC point, the approach works without derivatives or specialized parameter sampling procedures like other approaches to GSA. Using first-principles kMC models for the CO oxidation on RuO₂(110) and CO₂ reduction on ZnO/Cu as prototypical examples, we further find that already a modest number of QMC points is sufficient to extract the important information. Intriguingly, the approach is also robust against noise in the simulated TOFs, thus allowing to reduce the required kMC sampling times. As a consequence, our GSA comes at similar or even lower computational costs as prevalent LSA.

For the two models at hand, the parametric uncertainty in the rate constants results indeed in an uncertainty of the simulated TOFs of several orders of magnitude. Notwithstanding, the GSA consistently yields only very few dominant sensitivity indices. In other words, while the intrinsic model uncertainty does not allow to conclude on the absolute catalytic activity, the RDSs can still reliably be obtained.