Rotational and vibrational spectroscopy are observe in the microwave and infrared regions of the electromagnetic spectrum. While both of these spectroscopies depend on a change in the molecular dipole moment, they are quite different in their assumptions. Rotational spectroscopy is based on a rigid rotator approximation, which means that to a first approximation we assume that the molecule has fixed nuclei relative to the center of mass. Without this assumption we cannot separate the nuclear wave function into rotational and vibrational parts that can be solved separately. Since the real motion involves simultaneous rotational and vibrational motion we will introduce that fact as a centripedal corretion to account for the fact that rotational lines are not exactly evenly spaced. The assumptions of the expansion of the dipole moment that lead to observed rotational spectra (due to a rotating dipole) and vibrational spectra (due to a dipole derivative) are discussed in the following presentation.
