A library of inorganic complexes with reversible redox chemistry and/or the ability to catalyze homogeneous oxidations by peroxides, including but not limited to combinations of polyoxometalate anions and redox-active cations, was constructed. Evaluation of library members for the ability to catalyze aerobic sulfoxidation (O-2 oxidation;of the thioether, 2-chloroethyl ethyl sulfide, GEES) led to the discovery that a combination of HAuCl4 and AgNO3 forms a catalyst that is orders of magnitude faster than the previously most reactive such catalysts (Ru(II) and (IV) complexes) and one effective at ambient temperature and 1 atm air or O-2. If no O-2 but high concentrations of thioether are present, the catalyst is inactivated by an irreversible formation of colloidal Au(0). However, this inactivation is minimal in the presence of O-2; The stoichiometry is R2S + 1/2 O-2 --> R2S(O), a 100% atom efficient oxygenation, and not oxidative dehydrogenation. However, isotope labeling studies with (H2O)-O-18 indicate that H2O and not O-2 or H2O2 is the source of oxygen in the sulfoxide product; H2O is consumed and subsequently regenerated in the mechanism. The rate: law evaluated for every species present in solution; including the products, and other kinetics data, indicate that the dominant active catalyst is Au(III)Cl2NO3(thioether) (1); the rate-limiting step involves:oxidation of the substrate thioether (CEES) by Au(III); reoxidation of the resulting Au(I) to Au(LIT) by O-2 is a fast subsequent step. The rate of sulfoxidation as Cl is replaced by Br, the solvent kinetic isotope effect (k(H2O)/k(D2O) = 1.0), and multiparameter fitting of the kinetic data establish that the mechanism of the rate-limiting step involves a bimolecular attack of GEES on a Au(III)-bound halide and it does not involve H2O. The reaction is mildly inhibited by H2O and the CEESO product because these molecules compete with those needed for turnover (Cl-, NO3-) as ligands for the active Au(III). Kinetic studies using DMSO as a model for CEESO enabled inhibition by CEESO to be assessed.