The results of an investigation of the electric-field-gradient-induced birefringence of the noble gases He, Ne, Ar and of the octahedral system SF6 are presented. For all these systems the induced anisotropy of the refractive index is related to the sole temperature-independent contribution b(omega), a combination of quadratic response functions. These hyperpolarizabilities, as well as their dispersion coefficients to seventh order, are calculated at the optical experimental frequency by the CCSD response approach. The dispersion coefficients are used to determine the curve of b(omega) in the normal dispersion region. We show that for atoms the dipole-dipole-quadrupole and the dipole-dipole-magnetic dipole contributions to the dispersion coefficients of b(omega) have intimate relations to the Cauchy moments and to the dispersion coefficients for the Verdet and the Cotton-Mouton constants.