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Manuscript Title: Use of group theory for the analysis of vibrational spectra.
Authors: K. Ryklinskaya, S. Fritzsche
Program title: BETHE.
Catalogue identifier: ADUH
Journal reference: Comput. Phys. Commun. 162(2004)124
Programming language: Maple 7 and 8.
Computer: All computers with a license for the computer algebra package Maple [1].
Operating system: Linux 8.1+ and Windows2000.
RAM: 10-30 MB.
Keywords: fundamental transition, infrared absorption, irreducible representation, normal coordinates, point group, Raman scattering, vibrational modes, vibrational spectroscopy.
PACS: 02.20.-a., 33.20.Tp., 33.20.Ea., 33.20.Fb..
Classification: 16.3, 14.

Nature of problem:
Interaction of the infrared light with the molecule can lead to the excitation of the molecular vibrations [2]. Analysis of such vibrations is performed by the point group theory and helps to interpret the molecular spectra.

Solution method:
Point group theory is applied to determine the normal coordinates of symmetric molecules and to carry out a spectroscopic analysis of their vibrational modes. The direct product of the irreducible representations is utilized to obtain the selection rules for infrared and Raman spectroscopy.

The computation of the normal coordinates is supported for rather a large number of symmetries; in the present version the group data are provided for the cyclic and related groups Ci, Cs, Cn, Cnh, Cnv, the dihedral groups Dn, Dnh, Dnd, the improper cyclic groups S2n (n <= 10), the cubic groups O, T, Oh, Th, Td and the icosahedral groups I, Ih.

Unusual features:
All commands of the BETHE program are available for interactive work. Apart from the analysis of the vibrational motion of molecules, we also provide the group theoretical data of all the presently implemented point and double groups. The notation of the symmetry operations and the irreducible representations follows the compilation by Altmann and Herzig [3]. For reference to the program, a brief description of all the available commands is given in the user manual Bethe-commands.ps and is distributed together with the code.

Running time:
Although the program replies 'promptly' on most requests, the running time depends strongly on the particular task.

[1] Maple is a registered trademark of Waterloo Maple Inc.
[2] E. B. Wilson, J. C. Decius, P. C. Cross, Molecular vibrations (McGraw--Hill Book Company, New York, 1955).
[3] S. Altmann and P. Herzig, Point--Group Theory Tables (Clarendon Press, Oxford, 1994).