We investigated the optoelectronic and photovoltaic properties of three types of acceptor–donor–acceptor-based non-fullerene acceptor (NFA) molecules for organic solar cell (OSC) applications. Density functional theory and its time-dependent variant were employed to compute the quadrupole moment perpendicular to the π-system (Q₂₀), open circuit voltage (V_OC), and other relevant solar cell parameters. The role of functionalization in the acceptor unit on the overall device performance was explored by incorporating halogen and methoxy-based electron-withdrawing groups. The electronegativity differences between the halogen atoms and the methoxy group demonstrated contrasting effects on the energy levels, molecular orbitals, and absorption maximum. We observed a trade-off between short-circuit current (J_SC) and V_OC, which was further substantiated by an inverse correlation between Q₂₀ and V_OC. We found an optimum value of Q₂₀ in the range of 80 to 130 ea₀² to achieve an optimized solar cell performance. Among the designed systems, Se-derived NFAs with a small band gap, red-shifted absorption maximum, high-oscillator strength, small exciton binding energy, and optimum Q₂₀ turned out to be potential candidates for future applications. These criteria can be generalized to design and screen next-generation non-fullerene acceptors to achieve improved OSC performance.