Contact transformations leading to effective rotational Hamiltonians for degenerate vibrational states of symmetric top molecules

Abstract Contact transformations are described in this paper for symmetric top molecules which remove the “2, +2” and “2, −1” l -type operators as well as the operators of the Δ k = ±3 interactions from the first-order terms of the expansion of the vibrational-rotational Hamiltonian in terms of the smallness parameter λ. The results are presented in a form which makes it possible to obtain effective rotational Hamiltonians for a general vibrational state Π s | v s 〉 Π t | v t l t 〉, where v s and v t are the vibrational quantum numbers pertaining to the nondegenerate and degenerate vibrational modes, respectively. A detailed discussion is given of the effective rotational Hamiltonian for the vibrational states | v t l t = 2 ±2 , 2 0 〉 of molecules of C 3 v or D 3 symmetry.