Past exam of the chemistry A course of the University of Cambridge / 2023 / Paper 1 / A3 / a

The gross requirement is an anisotropic polarizability tensor, so that changing molecular orientation changes the induced response. A permanent electric dipole moment is not required; a homonuclear diatomic can therefore have a rotational Raman scattering spectrum.

For the inelastic lines of a linear rigid rotor, the detailed rule is $\Delta J=\pm 2$, with $J\ge 0$. The $\Delta J=0$ contribution is unshifted Rayleigh scattering, not a rotational Stokes Raman scattering line. Stokes Raman scattering has $\Delta J=+2$ because the molecule gains rotational energy.

For a transition starting at $J$ and ending at $J+2$, the molecule gainsEnergy conservation therefore gives the scattered-light wavenumbersThe first shifts below the laser are $6\tilde{B},10\tilde{B},14\tilde{B},18\tilde{B}$. Adjacent Stokes lines are separated by $4\tilde{B}$, while the first line is $6\tilde{B}$ from the Rayleigh line. The figure uses positive Raman shift ${\tilde{\nu }}_L-{\tilde{\nu }}_{\mathrm{S}}$; increasing shift means decreasing scattered-light wavenumber.