We have studied the oxidation of SO₂ to SO₃ by four peroxyradicals and two carbonyl oxides (Criegee intermediates) using both density functional theory, B3LYP, and explicitly correlated coupled cluster theory, CCSD(T)-F12. All the studied peroxyradicals react very slowly with SO₂ due to energy barriers (activation energies) of around 10 kcal/mol or more. We find that water molecules are not able to catalyze these reactions. The reaction of stabilized Criegee intermediates with SO₂ is predicted to be fast, as the transition states for these oxidation reactions are below the free reactants in energy. The atmospheric relevance of these reactions depends on the lifetimes of the Criegee intermediates, which, at present, is highly uncertain.