An ab-initio calculation of the charge density rho(r) of the O site in the (001) surface of pure MgO and that doped with Li, Na, and K and with a Mg1+ vacancy is reported. An embedded cluster (Mg(4)XO(5) with X = Mg, Mg+ vacancy, Li+, Na+, and K+) in : a set of point charges that simulated the rest of the crystal was employed in the calculation. The results obtained with the embedded cluster methods for the O sites were shown to be within 2% of those calculated in slabs composed by one to three layers of pure MgO with an ab-initio method for periodic structures. The Laplacian of the charge density, -del(2) rho(r), of the O valence shell obtained with both methods showed that, in pure and perfect MgO, the O2- ion has a local maximum in -del rho(r) in a direction perpendicular to the (001) surface that does not favor the Il abstraction from methane. It was also found with the embedded cluster method that doping with alkali metal ions and the Mg+ vacancy formation produced important changes in the atomic graphs of the O ion present at the surface. These changes were such that the local minima in rho(r) of the O valence shell were produced along the O-metal bond direction. These local minima provide the sites where the electron-rich C-K bond of methane is attracted and the H abstraction occurs. The more pronounced minimum corresponded to the Li doping, decreasing when passing to Na and K and when a Mg+ vacancy was created below the O site. This trend reproduces the known reaction barriers and supports the relationship between the reactivity of the MgO surfaces and the characteristics of the topology of rho(r) of the valence shell of the O- ion.