Rotational structures of long-range diatomic molecules

We present a systematic understanding of the rotational structure of a long-range (vibrationally highly-excited) diatomic molecule. For example, we show that depending on a quantum defect, the least-bound vibrational state of a diatomic molecule with $-C_n/r^n$ ($n>2$) asymptotic interaction can have only 1, 2, and up to a maximum of $n-2$ rotational states. A classification scheme of diatomic molecules is proposed, in which each class has a distinctive rotational structure and corresponds to different atom-atom scattering properties above the dissociation limit.