We have carried out detailed ab-initio based density functional theory calculations on pristine graphene and pristine graphene nanosheets containing 8, 18, and 32 carbon atoms by constructing supercells, both with and without functionalizing the supercells with different functionalizing groups. After optimizing all the supercells, we calculated the variations in the transverse displacement of carbon atoms, changes in C-C and C-O bond length, and bond angles both in terms of supercell size and functionalizing groups, in order to infer the structural stability. Further, we computed the band structure, total density of states to understand the changes in the hybridization between states and deviations in the Dirac point near the Fermi energy as a result of functionalizing the supercells with different functionalizing groups. Finally, we calculated the excessive surface charge density, Σ and quantum capacitance, C_q of all graphene nanosheets from the density of state using the two – dimensional free – electron model, to find the suitability of these graphene nanosheets as potential cathode materials in battery applications.