To theoretically explain the vibrational magnetic dipole moment of a m
olecule with degenerate vibrational levels, it is necessary to go beyo
nd the Born-Oppenheimer approximation. To obtain a nonzero electronic
contribution to the vibrational g factor, electronic excited states mu
st be included. Moreover, the usual perturbation expression for the vi
brational magnetic moment becomes zero for degenerate vibrational stat
es, 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.