Preprint Article Version 1 This version is not peer-reviewed

# The Symmetry of Linear Molecules

Version 1 : Received: 10 April 2018 / Approved: 11 April 2018 / Online: 11 April 2018 (08:07:38 CEST)

A peer-reviewed article of this Preprint also exists.

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

Journal reference: Symmetry 2018, 10, 137
DOI: 10.3390/sym10050137

## Abstract

A numerical application of linear-molecule symmetry properties, described by the D∞h point group, is formulated in terms of lower-order symmetry groups Dnh with finite n. Character tables and irreducible representation transformation matrices are presented for Dnh groups with arbitrary n-values. These groups are subsequently used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules as part of the variational nuclear motion program TROVE. The TROVE symmetrisation procedure is based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians. The solutions of these eigenvalue problems have now been extended to include the classification of basis-set functions using , the eigenvalue (in units of ℏ) of the vibrational angular momentum operator ${\stackrel{^}{L}}_{z}$ . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of Dnh. 12C2H2 is used as an example of a linear molecule of D∞h point group symmetry to illustrate the symmetrisation procedure.

## Subject Areas

symmetry; linear molecules; group theory; finite symmetry; point groups