By the method of the electron density functional in the variant DFT/B3L-YP5 the structures of small silver clusters (Agn, n = 1-3, 13) and their molecular complexes with antibacterial medication dioxidine (Dx) were calculated. The features in the geometric structure and energy of the interaction “metal cluster - dioxidine ligand” depending on the size (nuclearity) of the metal cluster are considered. For small clusters (n = 1-3), the tendency of metal coordination to only one of the oxygen atoms of the ligand molecule was revealed. The most stable are the complexes of silver trimers Dx-Ag3 and the icosahedral cluster of silver Dx-Ag13. These complexes are coordinated by two oxygen atoms of the hydroxyl groups of the dioxydine molecule at once. The difference between the obtained optimized structures of the silver-dioxidine complexes and the previously studied silver complexes with hydroxide ligands, for which the hydrogen atom of the hydroxyl group of the ligand is displaced during interaction, is shown.