Conjugated polymers are promising candidates in the design of polymer solar cell materials with suitable electronic properties. Recent studies show that the use of different functional groups as side chain in thiophene-based polymers changes the electronic and conformation structures. Here we design new thiophene-based molecules by replacing the hydrogen attached to the backbone of P3MT with electron-donating and electron-withdrawing groups. We then calculate the HOMO, LUMO, and HOMO-LUMO energy gap to quantify the theoretical merit of the new polymers as solar absorbers and their inter-ring torsional potential to understand their suitability to link together in high conductivity, extended conjugated systems. Calculations are done with first-principles density functional theory (DFT), implemented using B3LYP with dispersion function and 6-31G(d,p) as basis set. Our results show that the HOMO-LUMO gap is sensibly lowered by donating groups and we found that the substitution of the hydrogen with -NH2, and -F gives an energy gap lower than the energy gap of P3MT. The lowest energy gap was found when substituting with -NH2. Electron-withdrawing groups lower the HOMO, with the overall lowest found when -NO2 is used. -COCl, -CONH2, and -Cl give a steric hindrance greater than that of PTB7, which is set as reference. Our calculations show a possible approach to the rational design of donor materials when substituents are inserted systematically in a generic oligomer.