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

1
Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
2
Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, A-6020 Innsbruck, Tirol, Austria
3
Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(7), 862; https://doi.org/10.3390/sym11070862
Received: 9 June 2019 / Revised: 26 June 2019 / Accepted: 27 June 2019 / Published: 2 July 2019
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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 CH 3 where the internal rotation (torsion) of one CH 3 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 G 36 , but the construction of symmetrised basis functions is most conveniently done in terms of the 72-element extended molecular symmetry group G 36 (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 G 36 (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 G 36 (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 G 36 (M) (G 36 (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. View Full-Text
Keywords: ro-vibrational; point groups; molecular symmetry groups; ethane ro-vibrational; point groups; molecular symmetry groups; ethane
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Mellor, T.M.; Yurchenko, S.N.; Mant, B.P.; Jensen, P. Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3. Symmetry 2019, 11, 862.

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