Magnetic dipole optical activity tensor

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... 

In the general non-resonant case there are three contributions to the observed ROA spectra aG, the isotropic ROA invariant stemming from the electric dipole-magnetic dipole optical activity tensor, which is also responsible for the anisotropic invariant y, and the anisotropic invariant due to the quadru-pole transition tensor. The anisotropic invariants are also often written as = P(G ) and = P(A). ... 

Ordinary Raman scattering is determined by derivatives of the electric dipole-electric dipole tensor ae, and ROA by derivatives of cross-products of this tensor with the imaginary part G,e of the electric dipole-magnetic dipole tensor (the optical activity tensor) and the tensor Ae which results from the double contraction of the third rank electric dipole-electric quadrupole tensor Ae with the third rank antisymmetric unit tensor s of Levi-Civita. The electronic property tensors have the form ... 

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. 

Some of those have long been known a is the electric dipole polarizability (a symmetric polar tensor of dimension P) in length formalism, k (an asymmetric axial tensor of dimension P t) is related to the optical activity, A is the mixed dipole-quadrupole polarizability, x is the magnetic susceptibility (or magnetizability), written as a sum of diamagnetic and paramagnetic components. 

Symmetry arguments show that parity-odd, time-even molecular properties which have a non-vanishing isotropic part underlie chirality specific experiments in liquids. In linear optics it is the isotropic part of the optical rotation tensor, G, that gives rise to optical rotation and vibrational optical activity. Pseudoscalars can also arise in nonlinear optics. Similar to tlie optical rotation tensor, the odd-order susceptibilities require magnetic-dipole (electric-quadrupole) transitions to be chirally sensitive. 

More details of this development, including the extension to the higher-order tensors containing magnetic dipole and electric quadrupole transition moments that are resonsible for optical activity phenomena, can be found elsewhere [l2.l. 

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