  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.
