Model ofncoupled anharmonic oscillators and applications to octahedral molecules

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 ${\mathrm{cm}}^{\mathrm{-}1}$.