Although silver is one of the first metals finding broad applications in everyday life, specific key points of the intimate mechanism of its bacteriostatic/bactericidal activity lack explanation. It is widely accepted that the antimicrobial potential of the silver cation depends on the composition and thickness of the bacterial external envelope: the outer membrane in Gram-negative bacteria is more prone to Ag+ attack than the cell wall in Gram-positive bacteria. The major cellular components able to interact strongly with Ag+ (teichoic acids, phospholipids, and lipopolysaccharides) contain mono/diesterified phosphate moieties. By applying a reliable DFT/SMD methodology, we modeled the reactions between the aforementioned constituents in typical Gram-positive and Gram-negative bacteria and hydrated Ag+ species, thus disclosing the factors that govern the process of metal-model ligand complexation. The conducted research indicates thermodynamically possible reactions in all cases but still a greater preference of the Ag+ toward the constituents in Gram-negative bacteria in comparison with their counterparts in Gram-positive bacteria. The observed tendencies shed light on the specific interactions of the silver cation with the modeled phosphate-containing units at the atomic level.