Coverage-Dependent Free-Energy Bottlenecks in CO Adsorption and Desorption on Ru(0001)

The adsorption and desorption of gas-phase molecules on solid surfaces are elementary steps in heterogeneous catalysis. However, capturing these dynamics under finite-temperature and coverage-dependent conditions remains challenging because static models cannot fully describe the coupled motion of adsorbates and surface atoms. In this study, we investigate the adsorption/desorption dynamics of CO on Ru(0001) by combining machine learning potential energy surfaces (ML-PESs) with umbrella sampling molecular dynamics (US-MD). A 2 × 2 × 5 Ru(0001) model containing one CO molecule (0.250 monolayer, ML) is used to analyze temperature-dependent potential of mean force (PMF) profiles, local free-energy landscapes, and molecular orientation distributions. To clarify coverage and finite-size effects, enlarged 4 × 4 × 5 Ru(0001) models containing 1, 4, and 8 CO molecules are used to cover 0.063, 0.250, and 0.500 ML, respectively, while 20 × 20 × 5 Ru(0001) models containing 100 and 200 CO molecules are further examined at 0.250 and 0.500 ML using a fine-tuned DPA-2 potential. The PMF profiles show that CO adsorption is nearly barrierless at low coverage, whereas an adsorption-side free-energy bottleneck becomes most clearly resolved under crowded high-coverage conditions. This bottleneck arises from the cooperative effect of configurational/rotational entropy loss and lateral CO-CO repulsion, with finite-size periodicity and surface coverage modulating the strength of entropic confinement in the PMF profile. Comparison between rigid and relaxed 2 × 2 × 5 surface models further shows that neglecting lattice motion qualitatively preserves the overall temperature-dependent PMF trend but suppresses the small adsorption-side bottleneck relative to the relaxed-surface model. These results highlight the coupled roles of coverage, entropy, lateral adsorbate interactions, and surface lattice degrees of freedom in CO/Ru(0001) gas-surface dynamics.