Density functional theory is used to find incremental fragmentation energy, overall dissociation energy, and average monomer fragmentation energy of cyclic gold(I) thiolate clusters and anionic chain structures of gold(I) and silver(I) thiolate dusters as a measure of the relative stability of these systems. Two different functionals, BP86 and PBE, and two different basis sets, TZP and QZ4P, are employed. Anionic chains are examined with various residue groups including hydrogen, methyl, and phenyl. Hydrogen and methyl are shown to have approximately the same binding energy, which is higher than phenyl. Gold-thiolate clusters are bound more strongly than corresponding silver clusters. Lastly, binding energies are also calculated for pure Au-25(SR)(18)(-), Ag-25(SR)(18)(-), and mixed Au-13 (Ag-2(SH)(3))(6-) and Ag-13(Au-2(SH)(3))(6-) nanoparticles.