The oxygen vacancy in bulk MgO and at its (001) surface have been studied by means of the EMBED program which adopts an embedded-cluster approach in the frame of the Hartree-Fock (HF) approximation [Comp. Phys. Comm. 82, 139 (1994); 96, 152 (1996)]: A spin restricted (RHF) or unrestricted (UHF) method has been used according to whether the vacancy contains an even number if and (F2+ centers) or an odd number (F+ center) of electrons. The semi-infinite crystal has been simulated with a three-layer slab. Particular attention has been given to the optimization of the basis functions which serve to describe the trapped electron(s) in the vacancy. The correlation energy was estimated using second order holler-Plesset theory. The three electronic configurations have been studied by allowing for relaxation of all neighboring ions. For the paramagnetic center, spin density data are provided and discussed with reference to results from EPR experiments and molecular cluster calculations. (C) 1997 American Institute of Physics.