Three separate, but related, investigations were made of defects by using various complementary theoretical techniques. It was noted that pair-potential methods were well-suited to the calculation of the energies of formation, aggregation and migration of defects when no charge redistribution occurred. The CNDO or INDO semi-empirical methods had to be used to treat very large clusters or unit cells that contained hundreds of atoms, while first-principles methods (Hartree-Fock, density-functional theory) were suitable for treating small unit cells which contained up to 32 atoms. The use of these methods was considered for the treatment of isolated defects and clusters in MgO and corundum, and of O atom interstitials in MgO. It was recalled that the irradiation of MgO produced F centers and therefore O atoms. Little had been known about the fate of these O atoms until recent investigations had revealed that an interstitial O atom in MgO combined with a lattice O2- ion so as to form a symmetrical O--O- dumb-bell that was centered on a lattice site. However, one investigation had predicted that the stable position for the dumb-bell was directed along <111> while the other predicted that the most stable configuration was directed along <110>. The former investigation had involved the use of the full-potential linear muffin-tin orbital method, whereas the latter investigation had used a periodic Hartree-Fock self-consistent field large unit cell method. A significant difference between the 2 investigations was that, in the former case, the large unit cell or super-cell had contained 8 primitive unit cells whereas, in the latter case, 16 primitive unit cells in a super-cell were used. A CNDO method had been used to check that neither the charge distribution nor the defect levels in the band gap changed significantly as the size of the super-cell was increased from 16 to 128 primitive unit cells. In order to resolve the persistent discrepancy, and whether it arose from a fundamental difference between the linear muffin-tin orbital and Hartree-Fock methods (or was an artefact that was due to differences in super-cell size), the Hartree-Fock calculations were repeated using super-cells with 8 primitive cells. Great attention was paid to lattice relaxation. It was concluded that both methods predicted that the dumb-bell was the stable configuration because the same energy minimum had been located. Thus, any differences were attributed to the effect of the methods which were used.

P.W.M.Jacobs, E.A.Kotomin, N.E.Christensen, T.Brudevoll: Materials Science Forum, 1997, 239-241, 391-4