  We present a numerical approach to magnetic optical rotation based on
real-time time-dependent electronic-structure theory. Not relying on
perturbation expansions in the magnetic-field strength, the formulation allows
us to test the range of validity of the linear relation between the rotation
angle per unit path length and the magnetic-field strength that was established
empirically by Verdet 160 years ago. Results obtained from time-dependent
coupled-cluster and time-dependent current density-functional theory are
presented for the closed-shell molecules H2, HF, and CO in magnetic fields up
to 55 kT at standard temperature and pressure conditions. We find that Verdet's
linearity remains valid up to roughly 10-20 kT, above which significant
deviations from linearity are observed. Among the three current
density-functional approximations tested in this work, the current-dependent
Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in
comparison with time-dependent coupled-cluster singles and doubles results for
the magnetic optical rotation.
