Photochemistry during the polar spring leads to atmospheric mercury depletion events (AMDEs): Hg(0), which typically lives for months in the atmosphere, and can experience losses of more than 90% in less than a day. These dramatic losses are known to be initiated largely by Br + Hg + M -> BrHg center dot + M, but the fate of BrHg center dot is a matter of guesswork. It is believed that BrHg center dot largely reacts with halogen oxides XO (X = Cl, Br, and I) to form BrHgOX compounds, but these species have never been studied experimentally. Here, we use quantum chemistry to characterize the structures, vibrational frequencies, and thermodynamics of these BrHgOX species and their BrHgXO isomers. The BrHgXO isomers have never previously been studied in experiments or computations. We find the BrHgOX species are 24-28 kcal/mol more stable than their BrHgXO isomers. When formed during polar AMDEs, BrHgBrO and BrHgIO appear sufficiently stable in that they will not dissociate before undergoing deposition, but BrHgClO is probably not that stable.