This study presents a computational investigation into the design of triphenylamine-based donor chromophores incorporating 2-(1,1-dicyanomethylene)rhodanine as the acceptor unit. Three molecular architectures (System-1 to System-3) were developed by introducing distinct thiophene-derived $\pi$-bridges to modulate their electronic and optical characteristics for potential application in bulk heterojunction organic solar cells (OSCs). Geometrical optimizations were performed at the B3LYP/6-31+G(d,p) level, while excited-state and absorption properties were evaluated using TD-DFT with the CAM-B3LYP functional. Frontier orbital analysis revealed efficient charge transfer from donor to acceptor moieties, with System-3 showing the narrowest HOMO–LUMO gap (1.96 eV) and the lowest excitation energy (2.968 eV). Charge transport properties, estimated from reorganization energies, indicated that System-2 exhibited the most favorable balance for ambipolar transport, featuring the lowest electron reorganization energy (0.317 eV) and competitive hole mobility. Photovoltaic parameters calculated with PC₆₁BM as acceptor predicted superior $V_{oc}$, $J_{sc}$, and fill factor values for System-2, resulting in the highest theoretical power conversion efficiency (10.95%). These findings suggest that $\pi$-bridge engineering in triphenylamine-based systems can significantly enhance optoelectronic performance, offering promising donor materials for next-generation OSC devices.