Overtone Spectra and Intensities of Tetrahedral Molecules in Boson-Realization Models

Abstract

The stretching and bending vibrational spectrum and the intensities of infrared transitions in a tetrahedral molecule are studied in two boson-realization models, where the interactions between stretching and bending vibrations are described by a quadratic cross term and by Fermi resonance terms, called harmonically coupled and Fermi resonance boson-realization model, respectively. The later is a development of our recent model. As an example, the two models are applied to the overtone spectrum and the intensities of silicon tetrafluorde. Those models provide fits to the published experimental vibrational eigenvalues with standard deviations 1.956 cm &1 and 0.908 cm &1 , respectively. The intensities of infrared transitions of its complete vibrations are calculated in the two models, and results show a good agreement with the observed data.1998 Academic Press

Anharmonic force field and vibrational frequencies of tetrafluoromethane (CF4) and tetrafluorosilane (SiF4)

“…McDowell and co-workers reported a partial set of anharmonicity constants as well. In recent theoretical work, the low lying vibrational spectrum of SiF 4 has been modeled 36,37 using an algebraic approach. 38 Patterson and Pine 39 determined B 0 ϭ0.136 76(3) cm Ϫ1 , whence r 0 ϭ1.559 82 (17) Å.…”

Vibrational Excitations of Methane in the Framework of a Local-Mode Anharmonic Model

“…where g ϭ g͑r͉͒ rϭre [24] and F r corresponds to the second derivatives of the potential energy. We shall first analyze the harmonic Hamiltonian [23].…”

“…Algebraic models have also been proposed to model the vibrational excitations of methane (19 -23) and other tetrahedral molecules (24). These models are established in a localmode scheme either using a harmonic oscillator basis (20,24) or a U(2) anharmonic algebra (19,(21)(22)(23).…”

“…These models are established in a localmode scheme either using a harmonic oscillator basis (20,24) or a U(2) anharmonic algebra (19,(21)(22)(23). In a local-mode description spurious degrees of freedom arise naturally and a procedure to eliminate them must be implemented.…”

Algebraic Description of Anharmonic Stretching Vibrations

“…These approaches suffer from the neglect of the Fermi resonance interactions between stretching and bending modes. Due to their importance as a mechanism for intramolecular energy transfer and for descriptions of excited stretching and bending vibrations, Fermi resonances have been taken into account in simple Fermi resonance-local mode models for bent triatomic [8] and pyramidal XH 3 [9] systems and in boson-realization models for bent triatomic [10] and XY 4 [11] molecules. In this paper we will introduce a Fermi resonance-algebraic model, where a U(2) algebra is used for describing the vibration of each bond.…”