The chemical interaction of the gaseous species H-2, Br-2, and HBr with boron surfaces has been theoretically investigated, using the density functional theory (DFT). The cluster model used was the B-12 icosahedron, arranged to correspond to the alpha-B (001) surface. It could be concluded that all three diatomic species adsorb dissociatively when approaching the boron surface from an atop site position. Three different adsorption sites were investigated for monatomic hydrogen and bromine. The order of adsorption energy was the same for both species; hollow < bridge < atop site, with the numerical value of adsorption energy for an atop site being 290 vs 397 kJ/mol for hydrogen and bromine, respectively. The barrier of migration between two atop sites was found to be 191 kJ/mol for hydrogen and 127 kJ/mol for bromine. With the lower adsorption energy in combination with the lower migration barrier, bromine probably exhibits a higher surface mobility compared to hydrogen. The abstraction of adsorbed hydrogen and bromine (from atop site) with gaseous H atoms was found to be slightly exothermic (by 40 kJ/mol), whereas the abstraction of adsorbed hydrogen with gaseous bromine was slightly endothermic (by 45 kJ/mol). The abstractions of adsorbed species following a Langmuir-Hinshelwood mechanism were highly endothermic.