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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 \u00d7 2 \u00d7 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 \u00d7 4 \u00d7 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 \u00d7 20 \u00d7 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\u2013CO repulsion, with finite-size periodicity and surface coverage modulating the strength of entropic confinement in the PMF profile. Comparison between rigid and relaxed 2 \u00d7 2 \u00d7 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\u2013surface dynamics.<\/jats:p>","DOI":"10.1021\/jacsau.6c00303","type":"journal-article","created":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T11:03:55Z","timestamp":1784631835000},"page":"4417-4427","source":"Crossref","is-referenced-by-count":2,"title":["Coverage-Dependent\nFree-Energy Bottlenecks in CO Adsorption\nand Desorption on Ru(0001)"],"prefix":"10.1021","volume":"6","author":[{"given":"Jin-En","family":"He","sequence":"first","affiliation":[{"name":"Chinese Academy of Sciences , , ,","place":["Fuzhou, China, 350002"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0928-8541","authenticated-orcid":true,"given":"Mingjun","family":"Yang","sequence":"additional","affiliation":[{"name":"Shenzhen Jingtai Technology Co., Ltd. (XtalPi) , Fubao Community , ,","place":["Shenzhen, China, 518045"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3821-5843","authenticated-orcid":true,"given":"Zhe-Ning","family":"Chen","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences , , ,","place":["Fuzhou, China, 350002"]},{"name":"Fujian Key Laboratory of Theoretical and Computational Chemistry , ,","place":["Xiamen, China, 361005"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7472-3736","authenticated-orcid":true,"given":"Tong","family":"Zhu","sequence":"additional","affiliation":[{"name":"East China Normal University , , ,","place":["Shanghai, China, 200062"]},{"name":"Shanghai Innovation Institute , ,","place":["Shanghai, China, 200003"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8021-7458","authenticated-orcid":true,"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences , , ,","place":["Fuzhou, China, 350002"]},{"name":"Fujian Key Laboratory of Theoretical and Computational Chemistry , ,","place":["Xiamen, China, 361005"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,7,21]]},"reference":[{"key":"2026083023164464800_cit1","doi-asserted-by":"publisher","first-page":"8307","DOI":"10.1039\/C8CS00398J","article-title":"Towards operando computational modeling\nin heterogeneous catalysis","volume":"47","author":"Grajciar","year":"2018","journal-title":"Chem. 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Chem."},{"key":"2026083023164464800_cit45","unstructured":"Chen, J.\n          \n          Desorption\nUmbrella\nSampling using CO\/Ru(0001) 6D or 42D PES. https:\/\/github.com\/njuchenjun\/co_ru_us, 2024."},{"key":"2026083023164464800_cit46","doi-asserted-by":"crossref","unstructured":"He, J.-E.; Yang, M.; Chen, Z.-N.; Zhu, T.; Chen, J.\n          Source code and datasets for: Coverage-Dependent\nFree-Energy Bottlenecks in CO Adsorption and Desorption on Ru(0001). https:\/\/github.com\/njuchenjun\/co_ru_2026, 2026.","DOI":"10.1021\/jacsau.6c00303"},{"key":"2026083023164464800_cit47","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-4541-9","volume-title":"An Introduction to\nthe Bootstrap; Monographs on Statistics and Applied Probability","author":"Efron","year":"1993"},{"key":"2026083023164464800_cit48","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/0039-6028(91)90580-L","article-title":"In-situ FT-IRAS study\nof the CO oxidation reaction over Ru(001): I. 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