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 -