The band gap is one of the most important factors for controlling the physical properties. The search for polymers having narrow band gaps is a current topic. Tuning of the band gap by structural modification is possible. There are some approaches used for designing narrow band gap polymers. One of the approaches used for designing low band gap polymers is the donor acceptor concept where it is thought that regularly alternating conjugated donor and acceptor like moieties in a conjugated chain will induce a small band gap and at the same time will lead to widening of the valence and conduction bands. Forcing the polymers to adopt unfavorable structures and decreasing the bond length alternation along the conjugated backbone are other two methods used for synthesizing narrow band gap polymers. Yamashita et al. synthesized copolymers composed of benzobis(1,2,5- thiadiazole) and [1,2,5] thiadiazolo[3,4-b]thieno[3,4-e] pyrazine units as acceptor and thiophene and pyrrole units as donors. These synthesized copolymers have very narrow band gaps. The success with designing these systems were attributed to the donor-acceptor concept. We intended to understand the reasons for narrow band gaps and to determine whether donor acceptor concept is valid. Density functional theory (DFT) calculations were performed for homo and co-oligomers (having 1:1 and 1:2 acceptor to donor ratios) of thiophene (Th), pyrrole (Py), benzo[1,2-c;3,4- c']bis[1,2,5]-thidiazole (BBT) and [1,2,5] thiadiazolo[3,4-b]thieno[3,4-e] pyrazine (TTP) We estimated the band gaps of polymers by extrapolating the HOMO-LUMO gaps of the oligomers, using second degree polynomial fit, at the B3P86-30% /CEP-31g* level of theory. Theoretical analysis showed that the main reason for the band gap reduction is not the donor-acceptor concept and the prediction of the band width widening is not valid. Influence of the quinoid structures and reduce in the bond length alternation are the resons for the band gap reduction.