Why Does Raman Activity Require Anisotropic Polarizability?

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The discussion centers on the relationship between molecular polarizability and Raman activity, emphasizing that a change in polarizability is essential for a molecule to be Raman active. The explanation references Atkins' Physical Chemistry textbook, which details how isotropic polarizability leads to a single frequency in the induced dipole formula, while anisotropic polarizability introduces additional frequencies corresponding to Stokes and anti-Stokes lines due to rotational motion. The conversation seeks a more intuitive understanding of this relationship, noting that the Raman effect can be viewed as a two-photon process, which necessitates the use of a rank-2 tensor, known as the polarizability tensor, to represent the electromagnetic field. This approach aims to clarify the connection between anisotropic polarizability and Raman activity beyond the mathematical framework.
Dario56
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It's mentioned that the normal mode of molecule needs to involve the change in molecular polarizability to be Raman active.

Explanation is provided in Physical Chemistry textbook by Atkins on the example of the rotational Raman spectra. Only the frequency of the electric field ##(f_i)## occurs in the induced dipole formula if the polarizability is isotropic. If it's anisotropic, two additional frequenices occur ##(f_i + 2f_R)## and ##(f_i - 2f_R)## corresponding to Raman shift (Stokes and anti-Stokes lines), where ##f_R## is rotational frequency of the molecule. This explanation is clear, but it's quite math based without much intution.

Can you give more intuitive explanation of the relation between anisotropic polarizability and Raman activity?
 
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I had typed out a long explanation but then realized it was far more math-based than your OP! The most intuitive explanation is probably that the Raman effect is a two-photon process. Since the EM field is represented by a vector, two-photon processes must be represented by a rank-2 tensor. We call that tensor the polarizability tensor. I don't know if that helps at all.
 
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