The structural and electronic properties of Au and Au2 adsorbed on five coordinated oxygen and magnesium regular terrace sites, on the neutral Fs color center (oxygen vacancy containing two electrons), and on the charged Fs+ color center (oxygen vacancy containing one electron) of the MgO(100) surface have been investigated using a density functional theory cluster embedding approach. Two types of calculations have been performed. In one, we optimized and calculated the energetics of the systems using a generalized gradient approximation, and in the second, we used a combined approach, optimizing the geometries using a local density approximation and then performing a single point energy calculation using a generalized gradient approximation. Our studies also examine the effect of relaxation of the substrate. This was accomplished through two studies: first, both the MgO surface and the Au atoms were optimized, and second, the MgO surface atoms were kept fixed while the Au atoms were allowed to relax. We report the geometry, adsorption, and dimerization energies of the lowest energy and low energy isomers at each adsorption site, charge transfers from the MgO surface to the Au atoms in the lowest energy isomers, and compare our findings with previous theoretical studies. This comparison allowed us to establish in most of the cases limits for the adsorption energies, binding energies, and geometrical parameters at each adsorption site. For the case of Au2, for each adsorption site, our studies confirm the lowest energy isomer and most of the low energy isomers, previously reported, when both the surface and the Au2 are optimized. For most cases, the studies with frozen MgO surface atoms produced similar results as the studies when the MgO surface atoms were optimized. However, for the Mg site we found that the restrictions introduced by keeping the surface frozen favored the coexistence of an additional low energy isomer, and for the Fs+ site, the restrictions favored the dissociation of the adsorbed Au2 dimer into two surface adsorbed Au atoms. In general, both fully generalized gradient and combined calculations produced similar results, though, in the case of the Fs site the combined calculations found another low lying isomer, and in the case of the Fs+ site it predicted the dissociation of the adsorbed Au2 dimer, and inverted the energetic order of the lowest energy and low energy isomers. An increase in the charge transfer from the MgO surface to the Au atoms at the different adsorption sites according with the number of localized electrons at the adsorption sites was found. Finally, we found that the site with the largest adsorption and dimerization energies, and where an Au atom is most stable and can grow, is the neutral Fs center.