Cluster and Bloch function-based slab calculations are carried out to extend our previous study on dissociative adsorption of a hydrogen molecule on MgO surfaces. Hydrogen is easily dissociated on the three-coordination (3c-3c) site, whereas it is not an the four- (4c-4c) and five-coordination (5c-5c) sites. For mixed coordination sites, the Mg(3c)-O(4c) site weakly binds hydrogen but the Mg(4c)-O(3c) site does so even more weakly. These differences have been explained in terms of the enhanced local covalency at the low coordination number sites. As the coordination number decreases, the HOMO levels shift to higher energy and the LUMO levels shift to lower energy, the band gap becomes narrower, and the atomic charges of the surface Mg and O atoms decrease. This change in the electronic structure makes the bond alternation process, through the charge transfer from the H-2 sigma MO to the conduction band and from the valence band to the sigma(*) MO more facile.