The interaction of a large amplitude internal motion with other vibrations in molecules. The effective Hamiltonian for the large amplitude motion

Abstract

A theory for the interaction of a large amplitude internal motion (LAM) with the small amplitude vibrations in molecules is formulated. Valence internal coordinates are used for the development of the kinetic and potential energies in terms of the usual G⁻¹, G, and F matrices with all three being functions of the internal coordinates. A coordinate transformation is defined that separates the large amplitude internal motion from the other vibrations in zeroth order in the kinetic energy but at the same time modifies the force constants for the 3N‐7 vibrations. The higher order momentum coupling between the large and small amplitude vibrations is developed. Expressions are obtained for the small amplitude coordinate dependence of the kinetic energy coefficient for the large amplitude motion. A Van Vleck transformation is used to obtain the effective Hamiltonian of the large amplitude motion for the vth vibrational state of the other vibrations. The effective Hamiltonian is suitable as a parametric equation for analysis of experimental data or as the starting point for quantitative theoretical calculations. No attempt has been made to formulate the interaction of the large amplitude internal motions and other vibrations with the overall rotational motion, which is taken as the zero angular momentum state.