Applications of Symmetry and Group Theory for the Investigation of Molecular Vibrations |
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Authors: | Jaan Laane Esther J Ocola |
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Institution: | (1) Department of Chemistry, Texas A&M University, College Station, TX 77843-3255, USA |
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Abstract: | The application of symmetry and mathematical group theory is a powerful tool for investigating the vibrations of molecules.
In this paper, we present an overview of the methods utilized. First we briefly discuss the quantum mechanical nature of vibrations
and the experimental methods used. We then present the principal concepts for applying group theory to molecules. The symmetry
operations which are used to comprise groups are described and then used to determine the point groups of molecules. The properties
of character tables are presented and the method for obtaining a reducible representation for all the motions of a molecule
is detailed. This can then be broken down to obtain the irreducible representation which contains the symmetry species of
the individual vibrations. The determination of symmetry adapted linear combinations is outlined and the basis for spectroscopic
selection rules is presented. The paper concludes by examining how matrix algebra along with symmetry concepts simplifies
calculations with molecular force constants. |
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