In present study, a progression of low bandgap carbazole molecules was developed and rendered to increase their performance for organic solar cells. Thus, a design of D-A monomers from 2,7-carbazole donors (D) and a few acceptors (A) based D-A monomers was attempted. The calculation of the electronic and optical properties of the D-A monomers considered was based on the techniques of DFT and TD-DFT at the level of B3LYP with a basis set of 6-31G (d) in the gas and chlorobenzene. The HOMO and LUMO orbital energies, the bandgap energy (Eg), and the open-circuit voltage (VOC) were calculated in the gas and solvent phase. The impacts of the acceptor groups on the calculations and optoelectronic properties of these D-A monomers are discussed in the study of the link between the electronic structure and the optoelectronic properties. Some of these D-A monomers suggested that the after-effects of this work are a good possibility for formation of organic solar cells.