The Lie algebraic approach is extended to two-dimensional problems (rotations and vibrations in a plane). Bending vibrations of linear polyatomic molecules are discussed. The algebraic approach is particularly well suited to treat coupled bending modes. The formalism needed to treat coupled benders is introduced and a sample case, acetylene, is analyzed in terms of two coupled local benders.

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 .

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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.