Efficient donor-acceptor (D-A) molecular scaffolds should be developed for the advancement of organic solar cells (OSCs). Density functional theory (DFT) and time-dependent density functional theory (TDDFT) studies provide an effective methodology to perform initial studies to design and investigate D-A molecular systems. Two fluorine-substituted bis-benzothiadiazoles (FBBTs) are designed and optimized using the DFT method. The results show better planarity for FBBT2, which is attributed to π-extension between the FBBT units. A series of D-A small molecules CB1-4 are designed utilizing FBBT2 to study the effect of systematically substituting carbazole donor and cyano-based acceptor groups on the optoelectronic properties of FBBT. DFT calculations are performed using the B3LYP functional. The designed D-A scaffolds exhibit systematic tuning of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), HOMO-LUMO gap (from 2.333 eV to 1.825 eV). The observed HOMO-LUMO gap follows the trend CB1 > CB2 > CB4 > CB3. The Voc (open-circuit voltage) and power conversion efficiency (PCE) for CB1-4 are presented with the PC71BM acceptor. The overall trend observed for the Voc follows the order CB1 < CB4 < CB2 < CB3. The PCE trend observed using the Scharber model follows the trend CB3 > CB4 > CB2 > CB1. The results show that end cap modeling of π-extended FBBT with cyano-based acceptor groups significantly improves the observed PCE and Voc.