Dynamics of Elementary Steps on Metal Surfaces at High Coverages: The Prevalence and Kinetic Competence of Contiguous...

The rate of elementary steps on densely-covered surfaces depends sensitively on repulsive interactions within dense adlayers, situations ubiquitous in practice and with kinetic consequences seldom captured by Langmuirian treatments of surface catalysis. This study develops an ensemble-based method that assesses how such repulsion influences the prevalence and kinetic competence of bare-atom ensembles of different size. Chemisorbed CO (CO*) is used as an example because it forms dense adlayers on metal nanoparticles during CO₂ hydrogenation (CO₂-H₂) and other reactions, leading to significant repulsion that weakens the binding of CO* and kinetically-relevant transition states (TS). This approach is enabled by density functional theory and probability formalisms and describes the prevalence of ensembles of contiguous bare atoms from their formation energy (via CO* desorption); it then determines their competence in stabilizing the TS and mediating the reaction rates. The specific conclusions reflect the extent to which a given TS and CO* desorbed to form bare ensembles "sense" repulsion and the contribution of each ensemble size to each reaction channel mediated by distinct TS structures. These formalisms are illustrated by assessing the relative contributions, kinetic relevance, and ensemble size requirements for two CO₂-H₂ routes (direct and H-assisted CO₂ activation to CO and H₂O) on Ru nanoparticles, but they are not restricted to specific bound species or reaction channels. This method is essential to assess the kinetic relevance of elementary steps in a given catalytic sequence and to determine the contributions from parallel reaction channels at the crowded surfaces that prevail in the practice of surface catalysis.