For Raman spectra the molecules undergo transitions in which an incident photon is absorbed and another scattered photon is emitted. The general selection rule for such a transition to be allowed is that the molecular polarizability must be anisotropic, which means that it is not the same in all directions. Polarizability is a 3-dimensional tensor that can be represented as an ellipsoid. The polarizability ellipsoid of spherical top molecules is in fact spherical so those molecules show no rotational Raman spectrum. For all other molecules both Stokes and anti-Stokes lines can be observed and they have similar intensities due to the fact that many rotational states are thermally populated. The selection rule for linear molecules is ΔJ = 0, ±2. The reason for the values ±2 is that the polarizability returns to the same value twice during a rotation. The value ΔJ = 0 does not correspond to a molecular transition but rather to Rayleigh scattering in which the incident photon merely changes direction.
The selection rule for symmetric top molecules is
: ΔK = 0
: If K = 0, then ΔJ = ±2
: If K ≠ 0, then ΔJ = 0, ±1, ±2
Transitions with ΔJ = +1 are said to belong to the R series, whereas transitions with  belong to an S series. Since Raman transitions involve two photons, it is possible for the molecular angular momentum to change by two units.