Semiconductor coupled quantum dots provide a unique opportunity for tuning band gaps by tailoring band offsets, making them ideal for photovoltaic and other applications. Here, we have studied stability, trends in the band gap, band offsets, and optical properties for a series of coupled quantum dots comprised of II–VI semiconductors using a hybrid functional method. We have shown how the quantum confinement and interfacial strain considerably affect the band gap and band offsets for these heterostructures at the nanoscale. We show that the trend in band offsets obtained from our first-principles electronic structure calculations agrees with that obtained from the method of average electrostatic potential. It is found that a common anion rule for band offset is followed for these heterostructures at the nanoscale. Further, the calculated optical absorption spectra for these coupled quantum dots reveal that absorption peaks lie in the ultra-violet (UV) region, whereas absorption edges are in the visible region. In addition to electronic and optical properties, we have also explored transport properties for two representative coupled quantum dots, either having common cations or common anions, which revealed asymmetric nature in current–voltage characteristics. Therefore, these semiconductor coupled quantum dots may be useful for photovoltaic, light-emitting diode, and optoelectronic devices.