Mercury, a highly toxic metal, is emitted to the atmosphere mostly as gaseous Hg(0). Atmospheric Hg(0) enters ecosystems largely through via uptake by vegetation, while Hg(II) largely enters ecosystems in oceans and via rainfall. Consequently, the redox chemistry of atmospheric mercury strongly influences its fate and its global biogeochemical cycling. Here we report on the oxidation and reduction of Hg(I) (BrHg and HOHg radicals) in reactions with ozone, and how the electronic structure of these Hg(I) species affects the kinetics of these reactions. The oxidation reactions lead to XHgO• + O2 (X=Br and OH), while the reduction reaction produces Hg(0), HOX, and O2. According to our calculations with CCSD(T), NEVPT2, and CAM-B3LYP-D3BJ, the kinetics of both oxidation reactions are very similar. These two oxidation reactions are much faster than their reduction counterparts, and this effect is remarkably stronger for the oxidation of HOHg(I) by ozone. Modeling of field data supports the idea that OH and/or O3 (rather than Br) dominates Hg(II) production in the continental boundary layer. Almost all models invoking OH- and ozone-initiated oxidation of Hg(0) assume that these reactions directly produces Hg(II), despite the lack of plausible mechanism for these oxidation reactions. The present work helps reconcile modeling results with mechanistic insights.