This paper presents a systematic approach to quantify uncertainties of various quantities of interest (QoIs) in catalysis determined by microkinetic models developed from first principles. One of the main sources of uncertainty in any microkinetic simulation is attributed to the exchange-correlation approximations in density functional theory (DFT) used to calculate the rate constants for all elementary reaction steps within transition state theory. These DFT approximations are at the core of significant discrepancies between computational simulations and experimental measurements. Therefore, any model calculation should be accompanied by a measure of uncertainty. This work uses probability to represent uncertainties and latent variable models to develop probabilistic models that account for errors and correlations in DFT energies. These probabilistic models are further constrained to known reaction thermodynamics, and then propagated to QoIs such as turnover frequency (TOF), apparent activation barrier, and reaction orders. The proposed uncertainty quantification (UQ) framework is applied on the water−gas shift reaction (WGS: CO + H 2 O ⇌ CO 2 + H 2 ). Specifically, this WGS study models a Pt/TiO 2 catalyst as a Pt 8 cluster supported on a rutile TiO 2 (110) surface, where DFT energies are obtained using four separate functionals PBE, RPBE, HSE, and M06L that each have their own justification for being appropriate for this study. In this way, information from three different classes of functionals, GGA (generalized-gradient approximation), meta-GGA, and hybrid functionals, are used to generate a free energy probabilistic model. Although the uncertainty in model results spans orders of magnitude, a new approach is introduced to identify the dominant catalytic cycle under uncertainty. Overall, we find that our model captures various experimental kinetic data; however, the probability densities for TOF, apparent activation barrier, and reaction orders are relatively wide due to different flavors of DFT predicting a wide variation of transition state and oxygen vacancy formation energies. Nevertheless, we can conclude with high certainty that a CO-promoted redox cycle is the dominant mechanism over the temperature range 473−600 K and that formate and carboxyl pathways are not playing any role for the investigated active site model.

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Computational catalyst screening has the potential to significantly accelerate heterogeneous catalyst discovery. Typically, this involves developing microkinetic reactor models that are based on parameters obtained from density functional theory and transition-state theory. To reduce the large computational cost involved in computing various adsorption and transition-state energies of all possible surface states on a large number of catalyst models, linear scaling relations for surface intermediates and transition states have been developed that only depend on a few, typically one or two descriptors, such as the carbon atom adsorption energy. As a result, only the descriptor values have to be computed for various active site models to generate volcano curves in activity or selectivity. Unfortunately, for more complex chemistries the predictability of linear scaling relations is unknown. Also, the selection of descriptors is essentially a trial and error process. Here, using a database of adsorption energies of the surface species involved in the decarboxylation and decarbonylation of propionic acid over eight monometalic transition-metal catalyst surfaces (Ni, Pt, Pd, Ru, Rh, Re, Cu, Ag), we tested if nonlinear machine learning (ML) models can outperform the linear scaling relations in prediction accuracy when predicting the adsorption energy for various species on a metal surface based on data from the rest of the metal surfaces. We found linear scaling relations to hold well for predictions across metals with a mean-absolute error of 0.12 eV, and ML methods being unable to outperform linear scaling relations when the training dataset contains a complete set of energies for all of the species on various metal surfaces. Only when the training dataset is incomplete, namely, contains a random subset of species’ energies for each metal, a currently unlikely scenario for catalyst screening, do kernel-based ML models significantly outperform linear scaling relations. We also found that simple coordinate-free species descriptors, such as bond counts, achieve as good results as sophisticated coordinate-based descriptors. Finally, we propose an approach for automatic discovery of appropriate metal descriptors using principal component analysis.

A comprehensive uncertainty quantification framework has been developed for integrating computational and experimental kinetic data and to identify active sites and reaction mechanisms in catalysis. Three hypotheses regarding the active site for the water-gas shift reaction on Pt/TiO2 catalysts are tested -Pt (111), an edge interface site, and a corner interface site. Uncertainties associated with DFT calculations and model errors of microkinetic models of the active sites are informed and verified using Bayesian inference and predictive validation. Significant evidence is found for the role of the oxide support in the mechanism. Positive evidence is found in support of the edge interface active site over the corner interface site. For the edge interface site, the COpromoted redox mechanism is found to be the dominant pathway and only at temperatures above 573 K does the classical redox mechanism contribute significantly to the overall rate. At all reaction conditions, water and surface O-H bond dissociation steps at the Pt/TiO2 interface are the main rate controlling steps.

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