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Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
Physikalische und Theoretische Chemie, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, D-42097 Wuppertal, Germany
Author to whom correspondence should be addressed.
Symmetry 2018, 10(5), 137;
Received: 10 April 2018 / Revised: 23 April 2018 / Accepted: 25 April 2018 / Published: 29 April 2018
PDF [798 KB, uploaded 29 April 2018]


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 , the eigenvalue (in units of ) 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). View Full-Text
Keywords: ro-vibrational; linear molecule; point groups; molecular symmetry groups; acetylene ro-vibrational; linear molecule; point groups; molecular symmetry groups; acetylene

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Chubb, K.L.; Jensen, P.; Yurchenko, S.N. Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules. Symmetry 2018, 10, 137.

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