Hi there! I'm studying that if r is the quantum number associated with the total angular momentum of a diatomic homonuclear molecule, then only odd or even values are allowed for r. Now, the selection rules for r requires a change of one unity, but if my molecule has only odd values for r, then every transition will require at least r --> r+2, and this is not allowed. So, how can I have a rotational spectrum? Maybe I have to consider transitions of higher order of approximation than the electric dipole ones? Or should I consider Raman scattering? But I'm reading that Raman scattering allows r --> r+2 if and only if there is an intermediate allowed state for which r-->r+1.
The state of the molecule is specified not only by the value of r but also of the electronic and vibrational quantum numbers and also of the nuclear spin eigenstates (ortho and para hydrogen). While it is true that for state with fixed values of these other quantum numbers r can either only be even or odd, whether one or the other alternative applies depends on the value of the other quantum number. E.g. in H2 if r is even in the electronic ground state, it will be odd in the first excited state with the same total nuclear spin. So a transition to the electronically excited state with |Delta r|=1 is possible.