A general treatment of vibration‐rotation coordinates for triatomic molecules

Abstract

Abstract An exact, within the Born–Oppenheimer approximation, body‐fixed Hamiltonian for the nuclear motions of a triatomic system is presented. This Hamiltonian is expressed in terms of two arbitrarily defined internal distances and the angle between them. The body‐fixed axis system is related to these coordinates in a general fashion. Problems with singularities and the domain of the Hamiltonian are discussed using specific examples of axis embedding. A number of commonly used coordinate systems including Jacobi, bond‐length‐bond‐angle, and Radau coordinates are special cases of this Hamiltonian. Sample calculations on the H 2 S molecule are presented using all these and other coordinate systems. The possibility of using this Hamiltonian for reactive scattering calculations is also discussed.