Chubb, K.L.; Jensen, P.; Yurchenko, S.N. Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules. Symmetry2018, 10, 137.
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. Symmetry2018, 10, 137.
Chubb, K.L.; Jensen, P.; Yurchenko, S.N. Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules. Symmetry 2018, 10, 137.
Abstract
A numerical application of linear-molecule symmetry properties, described by theD∞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 ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator . 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.
Keywords
symmetry; linear molecules; group theory; finite symmetry; point groups
Subject
PHYSICAL SCIENCES, Atomic & Molecular Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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