The atmospheric oxidation of sulfur dioxide by the parent and dimethyl Criegee intermediates (CIs) may be an important source of sulfuric acid aerosol, which has a large impact on radiative forcing and therefore upon climate. A number of computational studies have considered how the CH2OOS(O)O heteroozonide (HOZ) adduct formed in the CI + SO2 reaction converts SO2 to SO3. In this work we use the CBS-QB(3) quantum chemical method along with equation-of-motion spin-flip CCSD(dT) and MCG(3) theories to reveal new details regarding the formation and decomposition of the endo and exo conformers of the HOZ. Although similar to 75% of the parent CI + SO2 reaction is initiated by formation of the exo HOZ, hyperconjugation preferentially stabilizes many of the endo intermediates and transition structures by 1-5 kcal mol(-1). Our quantum chemical calculations, in conjunction with statistical rate theory models, predict a rate coefficient for the parent CI + SO2 reaction of 3.68 x 10(-11) cm(3) molecule(-1) s(-1), in good agreement with recent experimental measurements. RRICM/master equation simulations based on our quantum chemical data predict a prompt carbonyl + SO3 yield of >95% for the reaction of both the parent and dimethyl CI with SO2. The existence of concerted cydoreversion transition structures 10-15 kcal mol(-1) higher in energy than the HOZ accounts for most of the predicted SO3 formation.