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Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3

Mellor, TM; Yurchenko, SN; Mant, BP; Jensen, P; (2019) Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3. Symmetry , 11 (7) , Article 862. 10.3390/sym11070862. Green open access

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Abstract

In the present work, we report a detailed description of the symmetry properties of the eight-atomic molecule ethane, with the aim of facilitating the variational calculations of rotation-vibration spectra of ethane and related molecules. Ethane consists of two methyl groups CH3 where the internal rotation (torsion) of one CH3 group relative to the other is of large amplitude and involves tunnelling between multiple minima of the potential energy function. The molecular symmetry group of ethane is the 36-element group G36, but the construction of symmetrised basis functions is most conveniently done in terms of the 72-element extended molecular symmetry group G36(EM). This group can subsequently be used in the construction of block-diagonal matrix representations of the ro-vibrational Hamiltonian for ethane. The derived transformation matrices associated with G36(EM) have been implemented in the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). TROVE variational calculations are used as a practical example of a G36(EM) symmetry adaptation for large systems with a non-rigid, torsional degree of freedom. We present the derivation of irreducible transformation matrices for all 36 (72) operations of G36(M) (G36(EM)) and also describe algorithms for a numerical construction of these matrices based on a set of four (five) generators. The methodology presented is illustrated on the construction of the symmetry-adapted representations both of the potential energy function of ethane and of the rotation, torsion and vibration basis set functions.

Type: Article
Title: Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3
Open access status: An open access version is available from UCL Discovery
DOI: 10.3390/sym11070862
Publisher version: https://doi.org/10.3390/sym11070862
Language: English
Additional information: © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Keywords: ro-vibrational; point groups; molecular symmetry groups; ethane
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Chemistry
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy
URI: https://discovery.ucl.ac.uk/id/eprint/10078281
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