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American Chemical Society, Journal of Physical Chemistry B (Soft Condensed Matter and Biophysical Chemistry), 49(114), p. 16304-16317

DOI: 10.1021/jp110434s

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Symmetry Numbers for Rigid, Flexible and Fluxional Molecules: Theory and Applications

Journal article published in 2010 by Michael K. Gilson, Karl K. Irikura ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The use of molecular simulations and ab initio calculations to predict thermodynamic properties of molecules has become routine. Such methods rely upon an accurate representation of the molecular partition function or configurational integral, which in turn often includes a rotational symmetry number. However, the reason for including the symmetry number is unclear to many practitioners, and there is also a need for a general prescription for evaluating the symmetry numbers of flexible molecules; i.e., for molecules with thermally active internal degrees of freedom, such as internal rotors. Surprisingly, we have been unable to find any complete and convincing explanations of these important issues in textbooks or the journal literature. The present paper aims to explain why symmetry numbers are needed and how their values should be determined. Both classical and quantum approaches are provided.