Magnetic dipole transition moment, determination

Here i//0 is the ground vibrational wave function and ij/ is the wavefunction corresponding to the first excited vibrational state of the th normal mode /< is the electric dipole moment operator Qj is the normal coordinate for the /th vibrational mode the subscript 0 at derivative indicates that the term is evaluated at the equilibrium geometry. The related rotational strength or VCD intensity is determined by the dot product between the electric dipole and magnetic dipole transition moment vectors, as given in (2) ... 

In the ligand polarization mechanism for optical activity, the potential of the electric hexadecapole component, Hxy(x>-y>), produces a determinate correlation of the induced electric dipole moment in each ligand group which does not lie in an octahedral symmetry plane of the [Co Ng] chromophore (Fig. 8). The resultant first-order electric dipole transition moment has a non-vanishing component collinear with the zero-order magnetic moment of the dxy dxj yj transition in chiral complexes, and the scalar product of these two moments affords the z-component of the rotational strength, RJg, of the Aj -> Ti octahedral excitation. 

We shall encounter many examples of magnetic dipole spectra elsewhere in this book but note briefly here a few examples which again illustrate the importance of the Wigner-Eckart theorem in determining the selection rules. Rotational transitions in the metastable 1 Ag state of O2 provide an important example for an open shell system which does not possess an electric dipole moment [75]. The 1 Ag state arises from the presence of the two highest energy electrons in degenerate n-molecular orbitals if these orbitals are denoted 7r+1 and n j the wave functions for the 1 Ag state may be written... 

---