An embedded-cluster Hartree-Fock approximation is adopted for simulating the heterolytic dissociation of hydrogen at a "tub" divacancy of MgO corresponding to the removal of two nearest neighbor ions at the (001) surface. Two stable dissociated configurations are identified, where the hydroxyl is formed either at a surface four-coordinated oxygen (T alpha) or at the five-coordinated oxygen at the bottom of the tub (T beta). In both configurations, the other atom of the molecule forms a hydride-vacancy complex (HV) near the site of the missing oxygen. The results are discussed with reference to a previous investigation concerning the isolated anion vacancy, where the dissociated configuration (F alpha) was similar to T alpha. The dissociation process in the three cases is shown to critically depend on the electrostatic field at the defect and on steric hindrance constraints. T alpha and T beta are stable with respect to the undissociated molecule by a few kcal/mol, but only the latter can be reached with low activation energy; F alpha is thermodynamically unstable. The dissociation of the HV complex in the presence of ultraviolet radiation is next studied, resulting in the removal of a neutral H atom, while a lone electron remains trapped at the vacancy. This paramagnetic state is characterized, and its features compared with those obtained from recent experiments concerning the F-s(H) color center. On the whole, only the T beta model is in fair agreement with experimental evidence concerning that center, although definite discrepancies are left.