The gross selection rule for rotational Raman spectroscopy is that the molecule must be anisotropically polarisable, which means that the distortion induced in the electron distribution in the molecule by an electric field must be dependent upon the orientation of the molecule in the field.

i.e. An atom has a spherical electron distribution, and the dipole induced by an electric field of given strength is the same regardless of the orientation of the atom in that field. It is said to be isotropically polarisable.
For a hydrogen molecule, H2, the induced dipole is greater if the molecular axis is parallel to the field direction than if it is perpendicular to it. Thus a hydrogen molecule is anisotropically polarisable.

Note that all linear molecules have anisotropic polarisabilities, so they may all be studied by rotational Raman spectroscopy. Many linear molecules are inactive in microwave rotational spectroscopy, so one great use of Raman spectroscopy is in the study of such molecules.

However, spherical rotors are inactive in both Raman and microwave spectroscopy (they are isotropically polarisable and have no permanent electric dipole), so may not be studied by either technique.

The rotational Raman selection rules are :

ΔJ = 0 transitions do not lead to a change in the frequency of the scattered photon, and contribute to the unshifted Rayleigh radiation that passes unaltered through the sample.
The origin of the ±2 selection rule is somewhat complex, but it should be easy to see, via a conservation of angular momentum argument, that since two photons are involved (an incoming photon that is absorbed and a scattered photon that is emitted), and each has photon has an angular momentum of one unit, the maximum change in the angular momentum of the molecule is two units.

We can apply the rotational selection rules to predict the form of the spectrum. When the molecule makes a transition with ΔJ = +2, then the interaction has imparted energy to the molecule. The scattered radiation must thus have lost energy, i.e. be at a wavenumber lower than that of the incident radiation. These transitions produce the lines in the lines in the spectrum that are known as Stokes lines:

where νi is the wavenumber of the incident radiation.

When the molecule makes a transition of ΔJ = -2, the incoming photon receives energy from the molecule, and thus the scattered  radiation must have a higher energy, i.e. be at a higher wavenumber than the incident radiation. These transitions give rise to the anti-Stokes lines:

Note that in both portions of the spectrum, the spacing between adjacent lines is 4B, allowing measurement of B and hence calculation of the moment of inertia and bond lengths of the molecule, just as was possible with microwave spectroscopy.

This diagram is a simplified representation of a typical rotational Raman spectrum. The Rayleigh line arises from the unscattered radiation that passes through the sample. It is often considerably broader than the other lines in the spectrum, and lies at the wavenumber of the incident radiation. Its broadness sometimes makes it difficult to identify the incident wavenumber from the spectrum, and can lead to it obscuring the nearest of the Stokes and anti-Stokes lines.