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Generalizing the Molecular Symmetry Group of Longuet-Higgins to Asymmetric Tunnelling Problems

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Part of the Topics in Molecular Organization and Engineering book series (MOOE, volume 12)

Abstract

This article describes the relationship of the Molecular Symmetry (MS) group of Longuet-Higgins and, ultimately, the Complete Nuclear Permutation-Inversion (CNPI) group to a molecular potential energy surface. The characterization of energy levels when“structural degeneracies”are lifted by finite tunnelling probabilities is outlined. Cosets of the MS group are used to obtain limiting numbers for the occurrence of structures of a given symmetry. It is shown how the conservation of point group symmetry elements along steepest descent pathways across the potential energy surface provides a useful framework for understanding isomerization. These ideas lead us to a generalization of the MS group to cases where a molecule samples more than one distinct structural form on the timescale of spectroscopic resolution. Tunnelling probabilities under these conditions are discussed and the circumstances under which the MS group could adequately describe“asymmetric”interconversions are explored. A number of simple examples is presented.

Keywords

Transition State Potential Energy Surface Point Group Symmetry Operation Point Group Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  1. 1.Department of ChemistryMcMaster UniversityHamiltonCanada

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