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Due to the necessity of reducing the reliance on fossil fuels, several systems are considered to be alternative and/or additional support for the existing battery material. In this report, structural and electronic properties of aluminium oxide (Al2O3) and aluminium sulfide (Al2S3) with hexagonal symmetry (α-phase), are investigated by utilizing density functional theory technique based on r++SCAN functional. The calculated lattice parameter and insulating gap for both systems are well matched with previous experimental studies and display higher accuracy compared to the results from local density approximation (LDA) and generalized gradient approximation (GGA) studies. The calculated insulating gap values are 10.3 eV and 4.1 eV for α-Al2O3 and α-Al2S3 respectively. For α-Al2O3 system, we observed hybridized s-p-d orbital of Al-O in the conduction states, consistent with the interpretation of past X-ray Absorption Near Edge Structure (XANES) data. Finally, the bulk and young modulus for α-Al2O3 are determined to be 251 GPa and 423 GPa which is very close to the known experimental values of 280 GPa and 451 GPa.