The molecular polarizability and optical activity tensors

The occurrence of Raman scattering is connected to the change in polarizability during the transition of the molecule from one vibrational state to the other. Circular polarization ROA arises from interference of the electric dipole electric dipole polarizability tensor with the electric dipole - magnetic dipole and the electric dipole electric quadrupole optical activity tensors. Due to limited space, no rigorous derivation of the theory will be given here, but only the most important results shall be shown. 

The following common conventions are used complex entities have been noted by a tilde and can be decomposed into a real and an imaginary part, e.g. in the case of the polarizability tensor  

In the discussion of Raman and ROA theory an important concept is that of the invariants. The values of invariants, the simplest example of which is the mean polarizability a, do not alter if the principal axes of the molecule are rotated. 

Ordinary Raman scattering intensity (far from resonance) can be expressed in terms of two invariants the isotropic transition polarizability a, and the anisotropic transition polarizability 

In Raman optical activity one encounters three additional invariants the isotropic part of the magnetic dipole optical activity tensor aG, and its anisotropic part, and 

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Optical activity in light scattering thus arises from interference between the molecular polarizability and optical activity tensors. 

In 1969, Atkins and Barron discovered the fundamental scattering mechanism responsible for ROA in which interference between the light waves scattered via the molecular polarizability and optical activity tensors of a molecule yields a dependence of the scattered intensity on the degree of circular polarization of the incident light and to a circular component in the scattered light [1], A more definitive version of the theory was presented 2 years later by Barron and Buckingham [12] which introduced as an appropriate experimental observable the dimensionless circular intensity difference (CID), defined as... 

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