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

Abstract

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.

Analysis of Photocatalytic Nitrogen Fixation on Rutile TiO2(110)

“…[115][116][117][118] In this work we utilize the error estimation capabilities of the BEEF-vdW functional 75 in order to estimate its accuracy and quantify the uncertainty due to the GGA approximation. Although the quantitative accuracy of BEEF-vdW error estimation in oxide materials is not well-known, 119 the BEEF-vdW ensembles provide a systematic way to assess the sensitivity of conclusions to accuracy of approximations. 120 The error bars shown in this work correspond to ±1σ of the ensemble of 2000 energies provided by the BEEF-vdW functional.…”

Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics

“…Poor functional choice for a given reaction has yielded unphysical mechanistic predictions, such as barrierless hydrogen abstraction 81 , spurious complex-substrate charge transfer [81][82] or identification of the wrong reactive spin surface 83 . Uncertainty quantification [84][85][86] from statistical analysis of an ensemble of functionals can be used as a tool to introduce confidence intervals to catalytic predictions for a single catalyst or cycle if a suitable ensemble of functionals is chosen. Complementary to this approach, a broader understanding of prediction sensitivity to the most commonly varied functional parameters is needed in computational catalysis. Unlike spin-state splitting, relationships between catalytic intermediate structure and either exchange sensitivity or semi-local DFT errors are not yet well known.…”

Development and characterization of novel combinations of Ce‐Ni‐MFI solids for water gas shift reaction

“…The iron oxide‐based catalysts are prone to coke formation, and the commercial copper‐based catalysts deactivate in the presence of condensed water . Hence, to address these drawbacks, other metals, like noble metals, were investigated to substitute the commercial catalysts . Since the noble metals are expensive and usually deactivate in contact with sulphur, researchers investigated the activity of transition metals or metal oxides to catalyze WGSR …”

“…[8,9] Hence, to address these drawbacks, other metals, like noble metals, were investigated to substitute the commercial catalysts. [3,[10][11][12][13][14][15][16][17][18] Since the noble metals are expensive and usually deactivate in contact with sulphur, researchers investigated the activity of transition metals or metal oxides to catalyze WGSR. [1,2,4,6,19,20] Further research on WGSR has revealed that cerium oxide has high oxygen storage capacity and promotes WGSR.…”

“…Numerous researchers have reported the production of very active catalysts with dispersed metal or metal oxide particles on supports with high surface area such as alumina, zeolites, or TiO 2 . [4,[14][15][16][17][18]24,26] In this study, the silicate with the ZSM-5 (Zeolite Socony Mobil-5) or MFI (Mobil Five from ZSM-5) structure was selected as a support of the catalyst. [27] The MFI framework has two types of microporous channels around 0.5 nm; one lineal and one sinusoidal.…”