Electronic interactions between vacancies and impurity atoms have been generally studied using the pseudopotential formulation based on the second-order perturbation theory. The distortions of the lattice around vacancies and impurity atoms were conventionally neglected because of their great complexity. The vacancy-vacancy, vacancy-impurity, and impurity-impurity interaction potentials have been calculated in aluminum using three kinds of exchange and correlation corrections in the dielectric function of the conduction electrons. They all show the long-range oscillatory behavior. The binding energies of a divacancy, fifteen kinds of vacancy-impurity pairs, and eighteen kinds of impurity-impurity pairs have been also calculated. The results indicate small binding energies, which are generally well consistent with recent experiments and the theoretical results previously obtained from the electrostatic model based on the screening potentials. The interaction potentials have been applied to the study of small point-defect clusters, for which the configurations and binding energies have been discussed. The random-phase approximation is also found to give less reliable results. Therefore the appropriate including of many-electron effects is essential in obtaining realistic results.