Knowledge Bank

The equilibrium polarizability of the methane molecule is isotropic due to symmetry, so that its rotational Raman spectrum is not allowed. However, this selection rule breaks down due to centrifugal distortion, and a weak rotational Raman spectrum of methane has been predicted on this $basis.1$ The effects of such perturbations may be predicted by considering the matrix elements of the contact transformed polarizability, where the transformation is that used in the perturbation treatment of the vibration-rotation $Hamiltonian.2$ The derivation of contact transformed polarizability matrix elements for asymmetric top molecules will be presented, and the rotational Raman spectrum of $CH2D2$, predicted on this basis, will be discussed.