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 leastbound vibrational state of a diatomic molecule with −Cn/r (n > 2) asymptotic interaction can have only 1, 2, and up to a maximum of n − 2 rotational levels. A classification scheme of diatomic molecu...