The interaction of chalcogen dihydrides (H2E; E = 0, S, and Se) with small coinage metal clusters (M-n; M = CU, Ag, and Au, n = 3 and 4) is studied based on density functional theory, with a focus on the nature of chalcogen-metal bonds. A newly developed pseudopotential-based correlation-consistent basis Set is used for metal Clusters together with the 6-311 ++G** basis set for the remaining atoms. Geometrical data identified that no significant deviation has been observed for molecules before and after complexation. For these three metals, binding energy calculations indicate that gold has the highest and silver has the lowest affinities for interaction with HE. In comparison with gold and copper, complexation between silver and chalcogen dihydrides is significantly weaker. It is found that interaction of HE molecules with the coinage metals have the order of H2Se > H2S > H2O. Therefore, in agreement with experimental works, our calculations confirm that the gold-selenium bond is the most stable. The nature of M-E bonds is also interpreted by means of the quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses. According to the QTAIM results, the bonds are found to be partially ionic and partially covalent. Natural resonance theory (NRT) is used to calculate natural bond order and bond polarity. The NRT result indicates that the percentage of polarity of M-E bonds is affected by coinage metals.