Details

Autor(en) / Beteiligte

• Mellor, Thomas M.
• Yurchenko, Sergei N.
• Mant, Barry P.
• Jensen, Per

Titel

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

Ist Teil von

• Symmetry (Basel), 2019-07, Vol.11 (7), p.862

Ort / Verlag

Basel: MDPI AG

Erscheinungsjahr

2019

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• 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.