The results are reported of an ab initio study of bromine dioxide BrO2, 1, and of the T-shaped trans- and cis-dihydroxides 2 and 3 of dihydrogen bromate (HO)(2)BrO. The thermochemistry has been explored of potential synthetic routes to (HO)(2)BrO involving water addition to BrO2, hydroxyl addition to bromous acid HOBrO, 4, protonation/reduction of bromic acid HOBrO2, 5, via tautomers 6-8 of protonated bromic acid, and by reduction/protonation of bromic acid via radical anion [HOBrO2](-), 9. The potential energy surface analyses were performed at the MP2(full)/6-311G* level (or better) and with the consideration of aqueous solvation at the SMD(MP2(full)/6-311G*) level (or better), and higher-level energies were computed at levels up to QCISD(full,T)/6-311++G(2df,2pd)//MP2. The addition of RO radical to bromous acid or bromite esters and the reduction of protonated bromic acid or protonated bromate esters are promising leads for possible synthetic exploration. Spin density distributions and molecular electrostatic potentials were computed at the QCISD(full)/6-311G*//MP2(full)/6-311G* level to characterize the electronic structures of 1-3. Both radicals employ maximally occupied (pseudo) pi-systems to transfer electron density from bromine to the periphery. While the formation of the (3c-5e) pi-system suffices to avoid hypervalency in 1, the formation of the (4c-7e) pi-system in 2 or 3 still leaves the bromine formally hypervalent and (HO)(2)BrO requires delocalization of bromine density into sigma*-SMOs over the trans O-Br-O moiety. Molecular orbital theory is employed to describe the mechanisms for the avoidance of hypervalency and for spin delocalization and spin polarization. The (4c-7e) pi-system in 2 is truly remarkable in that it contains five pi-symmetric spin molecular orbitals (SMO) with unique shapes.