Carbon doped alumina (Al2O3:C) finds widespread use being a highly sensitive Optically Stimulated Dosimeter(OSL) phosphor. The enhanced sensitivity of this material is correlated with the number of anion vacancies produced during its synthesis. There have been a few studies which attempt to unravel the mechanism of this enhancement by looking at the effects of Al/O vacancy/substitution by C atoms. In this work, we find that there is a preferred inter-defect separation when producing two Al/O vacancies. The defect formation energies and density of states are also computed.