We have developed a new genetic algorithm approach to search for the global lowest-energy structures of ligand-protected metal clusters. In combination with density functional theory, our genetic algorithm simulations show that the ground state of [Ag-7(DMSA)(4)](-) has eight instead of four Ag-S bonds and has a much lower energy than the structure based on the [Ag-7(SR)(4)](-) cluster with a quasi-two-dimensional Ag, core. The simulated X-ray diffraction pattern of the [Ag-7(DMSA)(4)](-) cluster is in good agreement with the experimental result. Our calculations for the [Ag-7(SR)(4)](-) and [Ag-7(DMSA)(4)](-) clusters reveal for the first time that -RS-Ag-RS-can be a stable motif in thiolate-protected Ag clusters. In addition, the lowest-energy structures of [Ag7S4](-), [Ag6S4](-), and [Ag5S4](-) are predicted.