Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules

• Main Authors: Katy L. Chubb, Per Jensen, Sergei N. Yurchenko
• Format: Article
• Language: English
• Published: MDPI AG 2018-04-01
• Series: Symmetry
• Subjects: ro-vibrational; linear molecule; point groups; molecular symmetry groups; acetylene
• Online Access: http://www.mdpi.com/2073-8994/10/5/137
• ISSN: 2073-8994

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).