Raman spectroscopy is very important practical tool for quickly identifying molecules and minerals

Dear Zhiyang,

As the light nteracts with the matter, the electron orbits of matter are perturbed periodically by the  incident electric field . The oscillation of the electron cloud results in a periodic separation of charge within the molecules, which is called an induced dipole moment. 

The strength of the induced dipole moment, P, is given by P=αE, where α is the polarizability and E is the strength of electric field of the incident EM wave.

The polarizability is a material property that depends on the molecular structure and nature of the bonds.

What we see in Raman scattering is due to the changes in polarizability when the atoms moves.

α =αo α+ ∂α/dQ, where ∂Q is the physical displacement of atoms ; α the changes in polarizability. αo is the polarizability of the molecular mode at equilibrium position.

This condition may be physically interpreted as the vibrational displacement of atoms corresponding to a particular vibrational mode results in a change in the polarizability.

Now back to the energy level, individual atoms are confined to specific vibrational modes, in which the vibrational energy levels are quantized in a manner similar to electronic energies. However, the new state created by the dipole is quasi instantaneous and not measurable : we called this intermediary state a virtual state : it means that this is an intermediate state has no eigenfunctions but still the energy and lifetime can be qualified ( but not measured ).

What we measure in Raman is the induced  shift in Raman wavenumber induced by the creation of this virtual state.  This shift is  related to the difference in vibrational states of molecules ( whatever the value of the virtual state)

The changes in polarizability is  mainly used for the selection rules of vibrations modes.

So as you see ; there is not a direct equation between α and the virtual state (which cannot be measured and was  only introduced in quantum mechanics as an explanation of the underlying principle).

Hope this will help.

Eric

Dear Eric,

   Thank you very much for the explanation. It helps a lot to understand Raman scattering.

Best regards,

Zhiyang