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Monolayers of carbon monoxide (CO) on Pt(111) surfaces are one of the most studied adsorption systems. However, molecular models of this system still do not take into account the reliable potential of lateral interactions between adsorbed CO molecules. Recent advances in experimental technique have brought high-resolution real-space images of CO/Pt(111) monolayers. For example, Yang et al. (J. Phys. Chem. C 117 (2013) 16429–16437) found island structures for coverages from 0.11 to 0.25 ML. In this study we have shown that these island structures can be explained with long-range oscillating lateral interactions. Parameters of the proposed potential were fitted to experimental scanning tunneling microscopy images with a series of Monte Carlo simulations.