  The interaction between vortex beam (VB) and molecule has drawn much
attention in recent years, but the lack of theoretical method somehow limits
its further analysis, especially when the molecular rotational degree of
freedom is involved and coupled with the molecular electronic states. To
incorporate the molecular rotation into the theoretical study, in this paper,
we describe the diatomic molecular states in Hund's coupling basis and express
interaction Hamiltonian in form of spherical harmonics expansion, and then
investigate the rotational transition of molecular states driven by VB. The
theory clearly illustrates that each photon of VB may carry a total angular
momentum of 0, $\hbar$, or 2$\hbar$, and therefore could drive O, P, Q, R and S
branches of diatomic molecular rotational transitions with some specific
selection rules. These results indicate that VB could provide new methods for
preparing and measuring the diatomic molecular states.
