Ab initio calculation of the vibrational magnetic dipole moment

To theoretically explain the vibrational magnetic dipole moment of a molecule with degenerate vibrational levels, it is necessary to go beyond the Born-Oppenheimer approximation. To obtain a nonzero electronic contribution to the vibrational g factor, electronic excited states must be included. Moreover, the usual perturbation expression for the vibrational magnetic moment becomes zero for degenerate vibrational states, unless higher order perturbation terms are included. For ab initio computation of these magnetic moments two simplified models have been tested by calculating the molecular g factors for the C2H2, HCN, OCS, and NH3 molecules and comparing them to experimental values.