We study a dependence of the optical excitation energies of low-coordinated sites in nano-clusters of MgO on the oxygen coordination. The calculations were performed using the ab initio Hartree-Fock method for a quantum cluster of up to 12 ions embedded in an (MgO) 1 0 8 cubic nano-cluster. The optical absorption energies were calculated using the configuration interaction technique for single (CIS) and double electronic excitations (CISD). The low-coordinated sites included the oxygen corner, cluster edge and cluster grain. The results show a consistent reduction of the exciton excitation energies as the oxygen coordination decreases. The hole component of the unrelaxed excited state at the oxygen corner is localised on the corner oxygen ion, whereas the excited electron is delocalised around the hole outside the cluster. The hole and electron components of excited states for other coordinations are delocalised around at least several oxygen ions. We also demonstrate the possibility of energy transfer from the sites with higher coordination to those with lower coordination and finally to the localisation centres.