Operando Cluster Catalysis via Coupled Surface–Subsurface Dynamics

Catalytic surfaces and subsurfaces undergo continuous restructuring under reaction conditions, yet how coupled surface–subsurface dynamics governs the emergence and performance of active sites remains unresolved. Here, we introduce a machine-learning-accelerated multiscale framework that integrates grand-canonical Monte Carlo sampling, neural-network molecular dynamics, and first-principles microkinetics to resolve operando catalyst restructuring at the atomic scale. Using Pd-catalyzed acetylene hydrogenation as a prototypical system, we show that adsorbed hydrocarbons weaken Pd–Pd bonds, whereas subsurface carbon anchors low-coordination atoms, together promoting the operando formation of Pd 1 single atoms and Pd 2, Pd 3, Pd 6, and Pd 10 clusters. A population-weighted activity analysis identifies Pd 10 as the dominant active ensemble, achieving an ∼36,000-fold rate enhancement and >99% ethylene selectivity over clean and hydrocarbon-covered Pd surfaces. A structure–activity landscape based on cluster height further quantifies this relationship. Extending this approach to Ag, Cu, Au, Ni, Rh, and Pt reveals that operando cluster formation requires moderate hydrocarbon coadsorption and subsurface carbon. This transferable approach reveals how coupled surface–subsurface dynamics govern the emergence and performance of active sites, offering broad applicability to other reactions in complex environments.