Strategies for modeling π-conjugated donor molecules for photovoltaic performance in the community of organic solar cells are well renowned in the literature. The recent study is based on the modeling of five highly conjugated bicarbazole-based donor molecules (XJ1–XJ5) by the alteration of acetylene-linked 9,9′-bicarbazole triphenylamine (XJ) molecule due to the attachment of five different acceptors through thiophene bridging. DFT simulations were conducted to investigate the geometrical, optoelectronic, and photovoltaic properties by using the CAM-B3LYP/6-31G (d, p) level of theory. FMOs and DOS analysis revealed a reduction of band gap and high charge transfer in the newly designed conjugated systems. TD-DFT method was used to investigate the absorption spectra which revealed that freshly modeled molecules owned higher absorption in the visible region than the reference XJ. The designed molecules showed remarkable photovoltaic characteristics due to the lower transition energies (ΔE), reduced band gap (EG), higher absorption maximum (λm), small binding energies (EB) and high dipole moment. The small values of reorganization energy (RE) for hole and electron possessed high charge mobility. The simulated open-circuit voltage (VOC) with PC61BM acceptor and fill factor (FF) for all the designed systems, in the range 1.78–1.91 V and 0.9253–0.9294 respectively, were found to be greater than reference XJ thereby increasing power conversion efficiency (PCE) of the solar cells. Therefore, all the designed molecules (XJ1–XJ5) are highly recommended for experimentation to fabricate efficient organic solar cells with remarkable photovoltaic applications. The current work is one of the few in-depth investigations in the direction of eco-friendly organic photovoltaics development that will pave the way for researchers to design highly efficient materials for future OSCs by structural engineering.