The OH radical reaction with Br-2 and the subsequent reaction HOBr + Br are of exceptional importance to atmospheric chemistry and environmental chemistry. The entrance complex, transition state, and exit complex for both reactions have been determined using the coupled-cluster method with single, double, and perturbative triple excitations CCSD(T) with correlation consistent basis sets up to size cc-pV5Z and cc-pV5Z-PP. Coupled cluster effects with full triples (CCSDT) and full quadruples (CCSDTQ) are explicitly investigated. Scalar relativistic effects, spin-orbit coupling, and zero-point vibrational energy corrections are evaluated. The results from the all-electron basis sets are compared with those from the effective core potential (ECP) pseudopotential (PP) basis sets. The results are consistent. The OH + Br-2 reaction is predicted to be exothermic 4.1 +/- 0.5 kcal/mol, compared to experiment, 3.9 +/- 0.2 kcal/mol. The entrance complex HO...BrBr is bound by 2.2 +/- 0.2 kcal/mol. The transition state lies similarly well below the reactants OH + Br-2. The exit complex HOBr...Br is bound by 2.7 +/- 0.6 kcal/mol relative to separated HOBr + Br. The endothermicity of the reaction HOBr + Br -> HBr + BrO is 9.6 +/- 0.7 kcal/mol, compared with experiment 8.7 +/- 0.3 kcal/mol. For the more important reverse (exothermic) HBr + BrO reaction, the entrance complex BrO-HBr is bound by 1.8 +/- 0.6 kcal/mol. The barrier for the HBr + BrO reaction is 6.8 +/- 0.9 kcal/mol. The exit complex (Br...HOBr) for the HBr + BrO reaction is bound by 1.9 +/- 0.2 kcal/mol with respect to the products HOBr + Br.