Single neutral and positively charged oxygen vacancies (F and F ⁺ centers) in α-Al₂O₃ are investigated using the supercell model (SCM) at the Hartree-Fock (HF) and density functional theory (DFT) level and the cyclic cluster model (CCM) implemented in the semiempirical MSINDO method. Results of supercell and cyclic cluster calculations for the cohesive energy of the perfect Al₂O₃ crystal are compared with the experimental value for the heat of atomization. The defect formation energy of the unrelaxed F center is calculated with the SCM. The CCM is used to calculate the defect formation energy of the F and the F⁺ centers. Relaxation effects for the nearest neighbors (NN) and the next-nearest neighbors (NNN) of the F and F⁺ centers are investigated. The obtained values are compared to other theoretical literature data.