Investigation of fermi resonances in CHX3 molecules with an internal-coordinate hamiltonian

Abstract

A Hamiltonian for CHX₃ molecules in terms of symmetrized curvilinear internal coordinates and their conjugate momenta has been derived and used to study the Fermi resonances between the CH stretching and HCX bending vibrations. The kinetic energy operator is obtained by expanding the G matrix in displacement coordinates and retaining the terms mos important for the Fermi resonance problem. This Hamiltonian is used to interpret the observed CH stretching and bending vibrational spectrum of flouromform, CHF₃. Eigenvalues are calculated variationally using a separable basis set consisting of functions which are products of a Morse oscillator eigenfunction for the stretch and a two-dimensional harmonic oscillator wavefunction for the bend. Potential-energy parameters are optimized using the least-squares method. The energy levels up to N=v₁+1/2v₄= 6 (for A₁ states) and 11/2 (for E states) can be fitted well (the standard deviation of the fit is 4.7 cm^–1) and relative intensities show the correct behaviour as compared to experiment. Expressions for the tridiagonal parameters x_sb and Φ_sbb are obtained in a closed form and evaluated for fluoroform. The results for CHF₃ and CHD₃ are also compared to results from ab initio calculations.