Rotational structure of weakly bound molecular ions

Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A 80 (2009) 052705], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We also provide analytic estimates of the rotational constants of any such levels up to threshold for dissociation and obtain a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the longrange part of the molecular potential.