In this paper, we present the first systematic study of correlations between energy levels of (Tl+)2, (In+)2, and (Ga+)2 dimer centers and the crystalline environment by using dielectric theory of chemical bonding for complex crystals. Our model has successfully built links between the EA′, EB′, and EC′ of these centers and the environmental factor h. The h has linear relationships with EA′, EB′, and EC′. The calculated results are in good agreement with the experimental values. This model can serve as a prediction tool and can be applied to assign the absorption band energies of (Tl+)2, (In+)2, and (Ga+)2 centers.