Model ofncoupled anharmonic oscillators and applications to octahedral molecules

Abstract

We propose an algebraic model of n coupled one-dimensional anharmonic oscillators and apply it to the study of the stretching modes of XYe octahedral molecules. We derive a new result on the theory of discrete groups and use it within the framework of the algebraic model to provide a four-parameter fit to the published vibrational energies of SF 6 , WF 6 , and UF 6 accurate within 0.9 cm -1 .

Boson-realization model for the vibrational spectra of tetrahedral molecules

“…Recently, an alternative technique [5] for the automatic computation of symmetrized local mode basis functions was used to provide a four parameter potential model for the stretching modes of octahedron XY 6 that gave an excellent fit to the published experimental vibrational eigenvalues of SF 6 , W F 6 and UF 6 . An improved algebraic method [6], where the one-dimensional Morse oscillator was described by the Lie algebra u(2), was proposed to provide another better fit to those experimental data with four parameters plus one fixed parameter N that describes the anharmonic property of the Morse potential.…”

“…An improved algebraic method [6], where the one-dimensional Morse oscillator was described by the Lie algebra u(2), was proposed to provide another better fit to those experimental data with four parameters plus one fixed parameter N that describes the anharmonic property of the Morse potential. This algebraic approach was extended to study the vibrational spectra, both stretching and bending, of tetrahedral molecules [4], where the interactions between stretching and bending vibrations were neglected and seven adjustable parameters plus two fixed parameters N i were used to fit the experimental data.…”

A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy

“…However, for a good description of the vibrational energies of Be 4 it is necessary to include interactions which are related to the vibrational angular momenta associated with the degenerate modes E and F 2 . These kind of terms is absent in the former versions of the model [12,14]. We now proceed to show how they can be obtained in the present formalism.…”

“…(12,13). In order to find the algebraic expression forl A2 we first introduce a scale transformation…”

“…This difficulty could be surmounted by treating the vibrational degrees of freedom separately from the rotations. In 1984 Van Roosmalen et al proposed a U (2) based model to describe the stretching vibrational modes in ABA molecules [11] which was later extended to describe the stretching vibrations of polyatomic molecules such as octahedral and benzene like molecules [12]. Recently the bending modes have also been included in the framework, which was subsequently applied to describe C 2v -triatomic molecules [13] and the lower excitations of tetrahedral molecules [14], using a scheme which combines Lie-algebraic and point group methods.…”