TY  - JOUR
N2  - 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 nh with finite n. Character tables and irreducible representation transformation matrices are presented for D nh 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 h) 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 nh . 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).
IS  - 5
ID  - discovery10050167
UR  - http://doi.org/10.3390/sym10050137
TI  - Symmetry adaptation of the rotation-vibration theory for linear molecules
SN  - 2073-8994
Y1  - 2018/05/01/
AV  - public
KW  - ro-vibrational; linear molecule; point groups; molecular symmetry groups; acetylene
JF  - Symmetry
A1  - Chubb, KL
A1  - Jensen, P
A1  - Yurchenko, SN
N1  - Copyright © 2018 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/)
VL  - 10
ER  -