It was recalled that most methods which were used for modelling defects in insulators used empirical potentials such as that of Mott and Littleton. However, the modelling of highly relaxed defect structures by using such methods required the use of empirical potentials under conditions that were beyond their regions of known accuracy. First-principles methods did not depend upon empirical potentials, but had rarely been used in simulating defects in ionic solids; where the existence of long-range Coulombic interactions required the use of large super-cells. It was noted that many  ab initio  methods alternated between unconstrained energy minimization and the re-imposition of the orthogonality of the wave functions. Large-scale non-linearly constrained optimization methods were suggested to offer the possibility of determining the electronic structure of defects in insulators by using first-principles methods.

A.Tackett, R.Dunning, Y.Zeng, N.A.W.Holzwarth, G.E.Matthews: Materials Science Forum, 1997, 239-241, 361-4