Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules
A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D...
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doaj-b8e6763960f849d380c491cfcd5f70fb2020-11-24T21:02:06ZengMDPI AGSymmetry2073-89942018-04-0110513710.3390/sym10050137sym10050137Symmetry Adaptation of the Rotation-Vibration Theory for Linear MoleculesKaty L. Chubb0Per Jensen1Sergei N. Yurchenko2Department of Physics and Astronomy, University College London, London WC1E 6BT, UKPhysikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, D-42097 Wuppertal, GermanyDepartment of Physics and Astronomy, University College London, London WC1E 6BT, UKA numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE).http://www.mdpi.com/2073-8994/10/5/137ro-vibrationallinear moleculepoint groupsmolecular symmetry groupsacetylene |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Katy L. Chubb Per Jensen Sergei N. Yurchenko |
spellingShingle |
Katy L. Chubb Per Jensen Sergei N. Yurchenko Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules Symmetry ro-vibrational linear molecule point groups molecular symmetry groups acetylene |
author_facet |
Katy L. Chubb Per Jensen Sergei N. Yurchenko |
author_sort |
Katy L. Chubb |
title |
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules |
title_short |
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules |
title_full |
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules |
title_fullStr |
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules |
title_full_unstemmed |
Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules |
title_sort |
symmetry adaptation of the rotation-vibration theory for linear molecules |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2018-04-01 |
description |
A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE). |
topic |
ro-vibrational linear molecule point groups molecular symmetry groups acetylene |
url |
http://www.mdpi.com/2073-8994/10/5/137 |
work_keys_str_mv |
AT katylchubb symmetryadaptationoftherotationvibrationtheoryforlinearmolecules AT perjensen symmetryadaptationoftherotationvibrationtheoryforlinearmolecules AT sergeinyurchenko symmetryadaptationoftherotationvibrationtheoryforlinearmolecules |
_version_ |
1716776568464867328 |