Induced magnetic moment optical activity

For the optical activity of achiral chromophores with a dissymmetric environment, two types of theoretical treatments have been proposed coupled oscillator treatment and one-electron treatment. The charge distribution of the magnetic dipole transition correlates Coulombically with an electric dipole induced in the substituents, and the colinear component of the induced dipole provides, with the zero-th order magnetic moment, a non-vanishing rotational strength. 

Optical activity arises from the coupling of given electric-allowed transitions with a chiral orientation (coupled oscillator mechanism or two-electron mechanism) or from the electric or magnetic moments of a transition being pertubed by a chiral static field (asymmetrically perturbed field mechanism or one-electron mechanism) in the given one molecule. A similar mechanism of the optical activity can be expected for molecular assemblies which are composed of chiral and achiral ones. This type of optical activity is called induced optical activity and depends on types of inter-molecular interaction modes. 

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. 

Indeed, around 1980, first experimental results on atomic parity violation have been reported, in particular measurements of the optical activity of bismuth, thallium and lead vapours as well as measurements of an induced electric dipole (El) amplitude to a highly forbidden magnetic dipole transition (Ml) in caesium. These experiments have nowadays reached very high resolution so that even effects from the nuclear anapole moment, which results from weak interactions within the nucleus, have been observed in caesium. The electronic structure calculations for caesium are progressing to a sub-percent accuracy for atomic parity violating effects and the reader is referred to chapter 9 of the first part of this book [12]. 

Figure 2 Cartoon illustrating the photon-induced transitions in a molecule. (A) Electronic absorption from ground to excited state is expressed as shown, where is the electric dipole moment operator (B) magnetic absorption and the mathematical expression, where is the magnetic dipole moment operator and (C) interaction of electronic and magnetic absorption, yielding optical activity.

---