Uncertainty Quantification Framework Applied to the Water-Gas Shift Reaction over Pt-Based Catalysts

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 + H2O reversible arrow CO2 + H-2). Specifically, this WGS study models a Pt/TiO2 catalyst as a Pt-8 cluster supported on a rutile TiO2 (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.