Symmetry properties of the effective hamiltonians of some nonrigid molecules

Group-theoretical methods are used to identify the nonvanishing parameters τ and establish relations between them in the effective Hamiltonians which describe rotation and motion with large amplitude. The cases considered are 1) bending vibration in molecules of the type XY₂ and XYZ and 2) inversion vibration in pyramidal molecules of the type XY₃. For the latter type of molecule, the symmetry properties of the parameters τ in the effective centrifugal Hamiltonian for quasidegenerate inversion states are investigated. The general form of this Hamiltonian and its symmetry properties are established and studied in an arbitrary order in the small parameter.