Higher Order Rotation-Vibration Energies of Polyatomic Molecules. III

Abstract

The Hamiltonian for a polyatomic molecule has been developed to fourth order of approximation in Part I of this series of papers. This Hamiltonian, H=H0+λH1+λ2H2+λ 3H3+λ4H4+···, was transformed, in Part II, into H′=H0+λH1′+λ2H2′+λ3H3′+λ4H4′+···, by a contact transformation, THT—1, where to second order H0+λH1′ has matrix elements which are diagonal in the quantum numbers of vibration, vs, in the representation which diagonalizes H0. H′ is further transformed in this paper (Part III), to facilitate computation, by a contact transformation, TH′T−1, in such a manner that H0†+λH1†+λ2H2† will be diagonal with respect to the quantum number, vs, in the representation which diagonalizes H0, although not, in general, diagonal in the quantum numbers of angular momentum of vibration, ls, in the case of the two dimensionally isotropic oscillator, and in the quantum numbers of angular momentum of vibration, ls, and ms, in the case of the three dimensionally isotropic oscillator.