Fermi resonances and local modes in water, hydrogen sulfide, and hydrogen selenide

A simple vibrational curvilinear internal coordinate Hamiltonian for bent H2X molecules is constracted by expanding the g matrix elements and the potential energy function in terms of the Morse variable y=1−exp(−ar) and retaining important local mode and Fermi resonance terms. The eigenvalues of this Hamiltonian are calculated variationally using Morse oscillator basis functions for the stretches and harmonic oscillator basis functions for the bend. The nonlinear least-squares method is used to optimize the potential energy parameters. The model is applied to water, hydrogen sulfide, and hydrogen selenide. Experimental vibrational levels up to 18 500 cm−1 for five symmetrical isotopic species of water are reproduced with a standard deviation of about 4 cm−1. For both hydrogen sulfide and hydrogen selenide two symmetrical isotopic species were included in the optimization procedure and standard deviations of 1.0 and 0.66 cm−1 were obtained. The potential energy parameters obtained agree well with previous anharmonic force field calculations.