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Symmetry 2010, 2(1), 213-229; doi:10.3390/sym2010213
Article

On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy

*  and
Received: 27 November 2009; in revised form: 11 February 2010 / Accepted: 24 February 2010 / Published: 25 February 2010
(This article belongs to the Special Issue Feature Papers: Symmetry Concepts and Applications)
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Abstract: Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy should be extended for completeness by considering the time reversal operator, as far as the Hamiltonian is invariant with respect to the inversion of the direction of motion. This can explain the degeneracy of pairs of vibrational and rotational states spanning the so-called separably degenerate irreducible representations, in symmetric tops of low symmetry, and Kramers degeneracy in odd electron molecules in the absence of magnetic fields. An extension with account of time reversal is also useful to determine relative phase conventions on vibration-rotation wavefunctions, which render all vibration-rotation matrix elements real. An extension of a molecular symmetry group may be required for molecules which can attain different geometries by large amplitude periodical motions, if such motions are hindered and are not completely free. Special cases involving the internal rotation are discussed in detail. It is observed that the symmetry classification of vibrational modes involving displacements normal to the internal rotation axis is not univocal, but can be done in several ways, which actually correspond to different conventions on the separation of vibration and internal rotation in the adopted basis functions. The symmetry species of the separate vibrational and torsional factors of these functions depend on the adopted convention.
Keywords: molecular symmetry; groups and representations; time reversal; Kramers degeneracy; internal rotation molecular symmetry; groups and representations; time reversal; Kramers degeneracy; internal rotation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Lattanzi, F.; Di Lauro, C. On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy. Symmetry 2010, 2, 213-229.

AMA Style

Lattanzi F, Di Lauro C. On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy. Symmetry. 2010; 2(1):213-229.

Chicago/Turabian Style

Lattanzi, Franca; Di Lauro, Carlo. 2010. "On the Physical Reasons for the Extension of Symmetry Groups in Molecular Spectroscopy." Symmetry 2, no. 1: 213-229.


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