Interaction of small neutral coinage metal clusters (M-19 = Ag-19/Au-19) with thiol/alkoxy radical (E = -SCH3, -OCH3, and -OCH2CH3) has been investigated to understand the bonding mechanism in the coinage metal-molecule junctions, which would allow to design biocompatible materials. In this study, structure, reactivity, and energy decomposition analysis (EDA) of M-19-E complexes have been unravelled using density functional theory (DFT) based Perdew, Burke and Ernzerhof (PBE) method. In addition, the theory of "atoms in molecules" (AIM) has also been used characterize the nature of interaction. The calculated reactivity descriptors predict that the vertex atoms (Ag/Au) are the most reactive site for nucleophilic attack. The atoms lying at the center of each face are favourable for an electrophilic attack in both the cases. Geometrical parameters illustrate that the structure of the molecules change significantly before and after interactions. The signatures of del(2)rho(r) and H-c for the anchoring bonds are respectively positive and negative, revealing that these bonds are partially electrostatic and covalent in nature. EDA calculation indicates that the largest contribution to the M-X (X=O/S) bond arise from Delta E-orb and Delta E-elstat contributions. Specifically, contribution from the orbital interaction is higher than the electrostatic contribution, which further confirms the covalent nature of the interaction.