We have investigated the electronic structure and thermodynamic properties of supercell of the -Al2O3 by first-principles calculation in framework of density functional theory (DFT) and full potential linearized augmented plane wave (FP-LAPW) with generalized gradient
approximation (GGA) and by quasi-harmonic Debye model. Our calculated value for direct
band gap of α-Al2O3 is 7.2 eV which is very close to its experimental measurement. Through the quasi-harmonic Debye model, in which the phononic effects are considered, we have obtained successfully the thermodynamic parameters including the relative volume and heat capacity over a pressure range 0-70 Gpa and a wide temperature range of 0-2000 K.