A simple curvilinear internal coordinate model for vibrational energy levels

Abstract

A simple curvilinear internal coordinate Hamiltonian model for vibrational term values of well bent XY2 molecules is developed. The stretching vibrations are described in the zero-order picture by Morse oscillators and the bend by a harmonic oscillator. Coupling terms are approximated by harmonic oscillator formulas. Van Vleck perturbation theory is used to transform the Hamiltonian matrix to a block diagonal form. Analytical expressions for the matrix elements are derived. Fermi resonances between the stretches and the bend and local modes are taken into account by diagonalizing the block diagonal Hamiltonian matrix. Rotational parameters (α constants) are calculated with perturbation theory expressions. Potential energy parameters are optimized with the nonlinear least-squares method using vibrational term values and α constants as data. The model is applied to five isotopic species of hydrogen sulfide and to two isotopic species of sulfur dioxide. The potential energy parameters obtained agree well with parameters determined by other methods.