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The rotational constant of a vibrationally excited state of a diatomic molecule will be slightly smaller than that of the vibrational ground state, as the excited state will have a slightly longer bond than the ground state (due to the anharmonicity of the vibration).
The gross selection rule for the observation of vibrational Raman transitions is that the polarisability of the molecule should change as the molecule vibrates. Both homonuclear and heteronuclear diatomics fulfill this requirement, so both molecules are vibrationally Raman active.
If the vibrational spectrum of a gas-phase heteronuclear diatomic molecule is obtained at high enough resolution, it is found that each line of the spectrum actually consists of a large number of closely spaced components.
The approximation of the potential energy to a parabola cannot be correct at all extensions, as it does not permit dissociation of the bond. At high vibrational excitations (i.e. in states with high values of the quantum number ν), the parabolic approximation is particularly poor.
The gross selection rule for vibrational transitions is that the electric dipole moment of the molecule must change in the course of the vibrational motion.
A typical potential energy curve for a diatomic molecule has the following form.