The atomic and electronic structures of neutral and positively charged monovacancies in bulk material were investigated  ab initio  by using a cluster method. The calculations were performed in real space on bulk-terminated clusters which contained up to 13 shells (about 200 atoms) around the vacancy. The vacancy-induced atomic relaxations, Jahn-Teller distortions, vacancy wave-function characteristics, and relaxation and reorientation energies were calculated as a function of the cluster size and were compared with experimental data. Potential-energy surfaces, in the 2-dimensional space of the relaxation normal modes, were presented for neutral and positive charge states of the vacancy.

S.Oğüt, H.Kim, J.R.Chelikowsky: Physical Review B, 1997, 56[18], R11353-6