The electronic and optical properties of graphene quantum dots (GQDs) of size less than 10 nm are different from those of graphene sheets due to quantum confinement effects. For analyzing their use in optoelectronic applications, it is very crucial to optimally tune the bandgap and engineer the controlling parameters. In the present work, a systematic investigation of the band gap of hexagonal GQDs has been carried out by examining their HOMO and LUMO energies. Passivation of dangling bonds of these GQDs has been carried out with the help of electron-withdrawing substituents in order to tune the band gap and engineer their optical properties such as absorption and emission spectra by carrying out the simulation with Density Functional Theory formalism using Gaussian 09 software. Carrying out passivation with electronegative element fluorine (F) effectively decreases the band gap of these QDs resulting in a redshift in the absorption spectra. The HOMO and LUMO topographical surfaces have been used to understand the absorption spectra. These surfaces show some σ-bond characteristics along with π-bond properties on passivating GQDs with the F-atom which further results in alteration of their energies and a corresponding decrease in their band gap. Here, the absorption is found to be dependent on the size of GQDs and the type of passivating atoms (H or F). The results thus obtained are found to be in good consonance with those reported in the literature engaging different methods. The present analysis may prove to be useful in improving the working of solar cells and other optoelectronic devices.