Improved screening of doped ZrO${}_2$ catalysts for CO${}_2$ hydrogenation from graph-based machine learning

Dopants can tune the activity of zirconia-based CO${}_2$ hydrogenation catalysts through changes in adsorbate and transition-state (TS) energetics. Computing these quantities with density functional theory (DFT) becomes expensive when several dopants, reaction intermediates, and TSs must be screened. Here, we further develop the graph-based machine learning method Wasserstein Weisfeiler-Lehman Gaussian Process Regression (WWL-GPR): we introduce additional electronic-structure and local-environment features relevant for oxide surfaces and use the resulting model to predict adsorption and TS energies on ZrO${}_2$(101) surfaces doped with Al${}^{3+}$, Cd${}^{2+}$, Ga${}^{3+}$, In${}^{3+}$, and Zn${}^{2+}$. Adsorbate-surface structures are represented as attributed graphs that combine bonds connectivity and features. We benchmark WWL-GPR against thermodynamic scaling relations (TSR) for reaction intermediates and Bronsted-Evans-Polanyi relations (BEP) for TSs, and then propagate the predicted energies to microkinetic CH${}_3$OH-yield estimates. WWL-GPR consistently improves the prediction of reaction intermediate energetics relative to linear scaling approaches and provides TS estimates that are competitive with BEP-based models. These improvements become especially relevant when the predicted energetics are propagated through the reaction network. Microkinetic calculations show that WWL-GPR-derived energies give CH${}_3$OH yields closer to DFT-derived yields than the linear-relation workflow. Degree-of-rate-control analysis links the activity errors to dopant-dependent rate-controlling steps, including HCOO* formation, H${}_2$COOH* dissociation, and H${}_3$CO* formation. These results support WWL-GPR as a data-efficient surrogate for connecting atomistic energetics with catalyst-screening observables on doped oxide surfaces.