Four-component Hartree–Fock calculations of magnetic-field induced circular birefringence—Faraday effect—in noble gases and dihalogens

The effects of relativity on the magnetic-field induced circular birefringence, or Faraday effect, in He, Ne, Ar, Xe, Rn, $F2$⁠, $Cl2$⁠, $Br2$⁠, and $I2$ have been determined at the four-component Hartree–Fock level of theory. A measure of the birefringence is given by the Verdet constant, which is a third-order molecular property and thus relates to quadratic response functions. A fully analytical nonlinear polarization propagator approach is employed. The results are gauge invariant as a consequence of the spatial symmetries in the molecular systems. The calculations include electronic as well as vibrational contributions to the property. Comparison with experiment is made for He, Ne, Ar, Xe, and $Cl2$⁠, and, apart from neon, the theoretical values of the Verdet constant are within 10% of the experimental ones. The inclusion of nonrelativistically spin-forbidden excitations in the propagator parametrization has significant effects on the dispersion in general, but such effects are in the general case largely explained by the use of a resonant-divergent propagator theory. In the present work we do, however, observe noticeable relativistic corrections to the Verdet constant in the off-resonant regions for systems with light elements (⁠$F2$ and $Cl2$⁠), and nonrelativistic results for the Verdet constant of $Br2$ are in error by 25% in the low-frequency region.