Display omitted •DFT and TD-DFT theoretical methods.•Narrow band-gap small molecules.•Intramolecular charge transfer.•Calculated results give a direction to design novel donor small molecules for high-performance organic photovoltaic device. In search of novel high-performance materials for use in organic solar cells, we used density-functional theory and time-dependent density functional theory to design a series of organic small molecules derived from the recently synthesized BT(-2T-DCV-Hex)2 donor molecule. In this work, we replaced the BT unit by different acceptors in order to improve their electronic properties, optical absorption and performance in organic solar cell applications. We found that the hybrid functional B3PW91 with the 6-31G(d) basis set gave highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels of the BT(-2T-DCV-Hex)2 in better agreement with the experimental oxidation and reduction potentials. However, the range-separated hybrid functional WB97XD was the most appropriate functional for describing the maximum absorption wavelength. Our calculation indicate that the designed small molecules donor proposed here are expected to offer better performances compared to the BT(-2T-DCV-Hex)2, such as a lower HOMO energy, a narrower HOMO-LUMO energy gap, a larger absorption range and may lead to power conversion efficiencies reaching the (7–9)% range.