We present a method to extract accurate pseudopotentials for surface passivants, within the framework of the atomic effective pseudopotential method. We retain the imaginary part of the pseudopotential in the construction procedure. This imaginary component in reciprocal space translates into a nonspherical component in real space. This asphericity allows to model surface dipoles and their ensuing band offsets. We show that these surface effects need to be taken into account to model electronic properties of quantum dots accurately—which requires to go beyond the spherical potential approximation for the passivant/surface atoms. The good level of transferability, without additional computational costs, is demonstrated for Si, CdSe, and InP nanostructures. The results are directly compared to large-scale density functional theory calculations.