The incorporation of a nitrate ion into silver-water aqueous clusters has been examined using PBEO density functional theory with the solvent model density (SMD) solvation model. The Gibbs free energy of solvation and other thermodynamic variables are calculated using the harmonic/rigid rotor/ideal gas model at 298.15 K for aqueous solutes including the effects of solute relaxation in water and with London dispersive forces at the D3 level. Free energies of solvation for Ag+ and NO3- were found to agree well with experimental values of -118.2 and -60.1 kcal/mol, respectively, calculated using cluster-continuum models with six to eight water molecules and including solute relaxation and London D3 dispersive interactions. An analysis of data of varying cluster size upon calculated free energy is presented. A direct procedure is applied to aqueous clusters such as Ag-n(z)(NO3-)(H2O)(5), Ag-n(z)(H2O)(5), and (NO3-)(H2O)(6) n = 1-4; z = 0, +1 in the SMD solvent representation to calculate equilibrium constants for nitrate association with silver clusters in solution that includes fully relaxed solutes. The equilibrium structures of the nitrate-containing clusters involve one or more bonds from nitrate oxygen to positive silver clusters. Water molecules interact with nitrate through H atoms, and overall, the structure represents a silver nitrate cluster with water ligands having similarity to a close ion pair in many aspects. The neutral silver atom is attached to nitrate through H-bonded water molecules. The ratio of nitrate-containing silver clusters to nitrate-free clusters using a calculated equilibrium constant of 0.51 L/mol for Ag+ is small in the range of many experiments. Similar values are found for positive silver clusters up to four atoms in size. The resulting procedures were applied to aqueous clusters of Ag-n(NO3)(m)(+(n-m)) that have been previously experimentally studied for silver reduction in aqueous solution. A chain-like structure with collinear and bidentate oxygen bonds to silver was found, and the equilibrium constants for clustering were determined. A simplified model calculation for the reduction of Ag(H2O)(6) (+) clusters in the presence of silver clusters in aqueous media was studied to understand catalytic effects observed in these systems. The reduction potentials vary with silver cluster size indicating a more favorable reduction caused by the presence of larger silver clusters.