Results of laboratory measurements are presented for the capture of ground-state atomic silicon ions by benzene and naphthalene molecules in the gas phase and for the kinetics of the reactions of the resulting adduct ions Si+.benzene and Si+.naphthalene with the molecules D2, CO, N2, O2, H2O, NH3, C2H2, and C4H2 at 296 +/- 2 K. The addition of these aromatic molecules to Si+ is seen to modify significantly the reactions of the atomic silicon ion. A wide range in reactivity is observed with both aromatic adduct ions and, while some common features are apparent in this chemistry, significant differences in reactivity also are seen, particularly for the reactions with C2H2 and C4H2. The reactions occurring in the presence of benzene appear to involve a pi-complex in which the atomic silicon ion is poised above the aromatic ring ready for reaction with an incoming molecule. In contrast, the reactions occurring in the presence of naphthalene seem to proceed with a neutral silicon atom perched above the (charged) aromatic surface. The intermediates for both types of reaction appear to undergo multistep transformations before separation into products. A case is made for the importance of reactions of adducts of Si+ with benzene, naphthalene, and larger PAH molecules and analogous adducts with other atomic ions in the synthesis of molecules in interstellar and circumstellar environments, both when benzene and the PAH molecules exist as free molecules and when they are embedded in surfaces of hydrogenated amorphous carbon (HAC) or exist dehydrogenated in larger hexagonal lattices such as graphite or fullerene molecules.