The interactions of pure (Au-k, Ag-k, and Cu-k; k = 1-3) and binary alloy (AunAgm and AunCum; m + n = k <= 3) metal clusters with hydrogen sulfide (H2S) have been investigated by using density functional theory (BP86, B3LYP, and CAM-B3LYP) and ab initio methods (MP2 and CCSD(T)), with a focus on the nature of metal-sulfur bonds. Binding energy calculations indicate that for pure metal clusters, the tendency of metal to interact with H2S has the order of Au > Cu > Ag. In binary alloy clusters, alloying Au-k with copper and silver decreases the attraction of Au toward H2S, while alloying Ag-k and Cu-k by gold increases the attraction of Ag and Cu toward H2S, significantly. Dissociation energy values for isolated metal clusters specify the more favorable formation of binary alloy clusters (AunAgm and AunCum) over pure ones. The nature of M-S bonds (M = Au, Ag, and Cu) is also interpreted by means of the quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO), and energy decomposition analysis (EDA). According to these theories, the M-S bonds are found to be partially electrostatic and partially covalent. EDA results identify that these bonds have less than 35% covalent character and more than 65% electrostatic, and the covalent character increases in different metals in the order Au > Cu > Ag.