Model of<i>n</i>coupled 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 ${\mathit{XY}}_{6}$ 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 ${\mathrm{SF}}_{6}$, ${\mathrm{WF}}_{6}$, and ${\mathrm{UF}}_{6}$ accurate within 0.9 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.