Although silver nanoparticles are of great fundamental and practical interest, only one structure has been determined thus far: M4Ag44(SPh)30, where M is a monocation, and SPh is an aromatic thiolate ligand. This is in part due to the fact that no other molecular silver nanoparticles have been synthesized with aromatic thiolate ligands. Here we report the synthesis of M3Ag17(4-tert-butylbenzene-thiol)12, which has good stability and an unusual optical spectrum. We also present a rational strategy for predicting the structure of this molecule. First-principles calculations support the structural model, predict a HOMO-LUMO energy gap of 1.77 eV, and predict a new "monomer mount" capping motif, Ag(SR)3, for Ag nanoparticles. The calculated optical absorption spectrum is in good correspondence with the measured spectrum. Heteroatom substitution was also used as a structural probe. First-principles calculations based on the structural model predicted a strong preference for a single Au atom substitution in agreement with experiment.