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

Calculations of overtone frequencies of five bent XY 2 molecules, H 2 O 16 , H 2 O 18 , D 2 O 16 , H 2 S 32 , and S 32 O 2 16 , with average rms deviations of 1–5 cm −1 are reported. The calculations are performed within the framework of the vibron model and sets of algebraic force field constants are presented. The corresponding wavefunctions are used to calculate intensities in the H 2 O 16 molecule. The calculated intensities are compared with recent measurements of the ATMOS collaboration.

We report results of calculations of five linear triatomic molecules, N 2 O, C 12 O 2 , C 13 O 2 , OCS, and HCN, with average r.m.s. deviations of 1–5 cm −1 within the framework of the vibron model. The corresponding algebraic force field constants are derived. Calculations of intensities of stretching vibrations in CO 2 and HCN are also presented.

By making use of Lie algebraic methods, we construct the complete vibrational spectrum of benzene. We use this construction to study the process of intramolecular vibrational energy relaxation in the first and second overtone of the CH stretching mode.