Theoretical calculations were made of the electronic structures and chemical bonding of various types of O-vacancy ordering in the  phase. Non-linear changes in the cohesive energy were found as a function of the vacancy concentration. It was concluded that a lattice with 2 vacancies per unit cell was the most stable one, with vacancies ordered along the <111> direction. The appearance of a semiconducting gap was analyzed, and it was suggested that the gap corresponded to a structure with a uniform distribution of O atoms over all possible O crystal lattice sites.

N.I.Medvedeva, V.A.Gubanov, D.L.Novikov, B.M.Klein: International Journal of Quantum Chemistry - Quantum Chemistry Symposia, 1995, No.29, 541-7