The geometries and electronic structures of a thiol-terminated molecular diode interacting with group-11 metal clusters (Cu, Ag, Au) have been investigated using density functional theory with a hybrid exchange-correlation energy functional. The charge transfer and bonding nature at the metal-molecule interface are illustrated from natural bond orbital analysis. The metal-sulfur bonds are found to be directional, and the charge transfer is localized along the bond. The extent of charge transfer to the terminal sulfur is higher for bonding with Cu and Ag (similar to0.40) than with Au (similar to0.17). The electronic conduction across the molecular diode has been analyzed from the change in the electronic structure and the shape of the molecular orbitals of the free molecule and metal-molecule complexes. The results suggest that while the inclusion of Au scarcely affects the unoccupied molecular orbitals, the effect is more pronounced in the cases of Cu and Ag. The threshold energy for conduction estimated for these metal-molecule complexes indicates a higher required bias voltage for Au than for Cu and Ag.