F-S(H)(+) centers (oxygen vacancies with a trapped electron and a nearby hydroxyl group) at the (001) surface of MgO have been characterized in terms of electronic structure, magnetic properties, and chemical reactivity toward adsorption Of O-2 and N-2 molecules by means of cluster model density functional calculations. Two different arrangements of the OH group on the surface have been considered: the computed properties are in excellent agreement with observed EPR and IR data and show the existence of important analogies between the two arrangements (e.g., a similar polarization of the spin density), but also of some significant differences (e.g., for one kind of F-S(H)(+), a special interaction between the OH group and the trapped electron has been detected). At short distances from the surface, a transfer of the trapped electron from the surface to the admolecules occurs, with formation of charge-transfer complexes F-S(H)(2+)/N-2(-) or F-S(H)(2+)/O-2(-) While F-S(H)(2+)/O-2(-) is stable even at room temperature with respect to dissociation into F-S(H)(+) + O-2 fragments, and F-S(H)(2+)/N-2(-) is a metastable surface complex.