This paper reports designing a series of new D-π-A topology-based metal-free organic dye molecules using ullazine and perylene by DFT methods. This work emphasizes the combination of ullazine analogs as donors and perylene dicarboxylic anhydride as an acceptor along with acetylene linker as π-bridge for DSSC applications. The structural and optoelectronic properties of dyes before and after adsorption on to TiO2 semiconductor have been investigated. The screening of the designed dyes is carried out based on the energy gap (Eg), maximum absorption wavelength (λmax), light-harvesting efficiency (LHE), excited-state lifetime (τ), the free energy of electron injection (ΔGinj) and regeneration (ΔGreg). DFT results reveal that the presence of ullazine analogs as a donor reduces the energy gap (Eg) and leads to red-shift in absorption maximum. Further, two different binding modes of dye molecules with (TiO2)38 cluster have been investigated to unravel the binding associated changes in the electronic structure. The results show that the completely dissociated bidentate bridging (CBB2) mode is more favorable, which contains two carboxylic groups. Findings emphasize the remarkable charge transfer characteristics which favors the fast electron injection from excited dye to the conduction band of TiO2. For the first time, this study provides comprehensive structural and electronic information combined with the Dye-TiO2 interactions for the development of perylene based dyes for DSSC applications. This article demonstrates the rational design of novel N-doped Polyaromatic Hydrocarbons as Donors for the Perylene based Dye-Sensitized Solar Cells using state of the art computational methods. This study results in the relatively efficient new dye molecules for DSSC applications. Complete electronic and structural aspects of anatase-TiO2 interaction with designed dye molecules have been elucidated in detail.