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First-principle calculations based on density functional theory were used to study the adsorption of atomic sulfur and carbon on the Mg(0001) surface in a wide range of coverages from 1/4 ML(monolayer) to 1 ML. It is found that the adsorption of atomic S and C on the high coordinate hollow site is more energetically favorable than that on other adsorption sites. S atom is favorable to be adsorbed at on-surface site and C atom is favorable to be adsorbed at subsurface site. The results suggest that when the coverage increases,the binding energy for S and C atoms will decrease and the interaction between adsorbed atoms tends to be stronger. It indicates that as coverage increases,S-Mg and C-Mg interaction weakens.