Role of Oxygen during Methane Oxidation on Pd$_1$/PdO$_1$@CeO$_2$ Surface: A Combined Density Functional Theory, Microkinetic, and Machine Learning Approach

This work explores the role of oxygen in industrial methane oxidation. Oxygen, a well-known oxidizing agent, drives CH$_4$ conversion to CO$_2$ and H$_2$O. We report how oxygen influences oxidation on single Pd and PdO clusters supported on CeO$_2$(111). Oxygen is introduced by (1) lattice O in PdO and (2) O$_2$ adsorption on an isolated Pd atom, forming PdO$_x$ clusters. Density-functional theory (DFT) mapped multiple reaction pathways on the Pd$_1$/PdO$_1$@CeO$_2$(111) surface; both Pd and PdO clusters were found to thermodynamically favour methane activation. The computed barrier for CH$_4$ activation is 0.63 eV on PdO$_1$@CeO$_2$(111). A single Pd atom markedly accelerates O$_2$ dissociation to PdO$_2$, and the presence of lattice oxygen lowers this barrier by 0.36 eV relative to an oxygen-deficient surface, enhancing catalytic efficiency. Reaction selectivity, coverage-dependent production rates, degree of rate control (DRC), and intrinsic turnover frequency (TOF) were quantified through steady-state microkinetic modelling. The simulations predict full conversion of CH$_4$ to CO$_2$ and H$_2$O above 600 K, whereas partial-oxidation intermediates dominate at lower temperature and high O coverage. Rate constants for all elementary steps were derived via the Sure Independence Screening and Sparsifying Operator (SISSO) symbolic-regression method, yielding a concise predictive expression based on charge, coordination number, and key Pd-O/C-H distances. These combined DFT-microkinetic-SISSO results clarify oxygen's mechanistic participation and provide practical guidelines for designing Pd/CeO$_2$ catalysts with improved activity toward methane oxidation, a reaction of pressing environmental and industrial importance.