Identification of the most stable silver cluster ions produced under plasma solution conditions

For several decades, silver nanoparticles have been grown from a solution of silver salts under electrode-free plasma conditions. Yet, details of the atom-by-atom growth from ¹Ag⁺ to ⁱAg_mⁿ⁺ (cluster of m atoms with n charge) is not known. Here, we report with theoretical calculations the thermodynamically driven growth of silver clusters up to m = 5 and n = 4 in water. These pathways are elucidated from high quality DFT energies of reaction and formation with a continuum solvation model, and all possible isomers for each cluster size are considered. We find that (i) all steps are favourable, and (ii) the most stable pathway involves neither neutral clusters nor those with high positive charges, but rather those with relatively low charged states. The most stable pathway can be understood based on the extra stability associated with clusters that are sigma-aromatic, however, clusters with higher charges violate this rule. The results for the most favoured species, (¹Ag₂⁰ and ¹Ag₄²⁺) are in agreement with experimental findings, and we postulate that ¹Ag₃⁺ and ²Ag₅²⁺ should also be present in appreciable quantities for future spectroscopic confirmation. We use time-dependent density functional theory to predict optical spectra of the most important clusters as a guide to future experiments.