A model molecule was built of graphene consists of 50 carbon atoms, after that was modified throughout its middle and corners with CH3, COOH, NH2 and O2 forming 20 model molecules respectively. Each model was then calculated at density functional theory DFT:B3LYP/6-31G(d,p). Results indicated that, the studied physical properties suffer strong changes in TDM and ∆E for the different position of the interaction. The interaction of graphene with CH3 and NH2 becomes more reactive for the connection at the center position where it shows highest TDM and lowest ∆E. COOH shows the highest TDM when interact with graphene at position1 and the lowest ∆E when interact with graphene at position2. While the reactivity of the interaction of graphene with O2 increased at position 2. Form the MESP calculation, it is clear that, the negativity increased by interaction of graphene with O2 at the corner in position one and four.