Chubb, KL; Jensen, P; Yurchenko, SN; (2018) Symmetry adaptation of the rotation-vibration theory for linear molecules. Symmetry , 10 (5) , Article 137. 10.3390/sym10050137.

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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 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 ℓ, 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).

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