Use of group theory for the analysis of vibrational spectra

Abstract

To facilitate the use of group theory in the analysis of vibrational spectra, a set of Maple procedures is provided generating the normal coordinates and determining the spectral activities of polyatomic molecules. Our program, called Bethe, is based on the frequently applied point groups and provides an interactive access to the group data as needed in physical chemistry and elsewhere. Owing to the demand of the users the normal coordinates of the molecules are provided either in terms of Cartesian or internal coordinates. Program summary Title of program: Bethe Catalogue number: ADUH Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADUH Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed: All computers with a license of the computer algebra package Maple 1 1 Maple is a registered trademark of Waterloo Maple Inc. Installations:University of Kassel (Germany) Operating systems under which the program has been tested: Linux 8.1+ and Windows 2000 Program language used: Maple 7 and 8 Memory required to execute with typical data: 10–30 MB No. of lines in distributed program including test data, etc.:11 859 No. of bytes in distributed program including test data, etc.:312 229 Distribution format:tar.gz Nature of the physical problem: Interaction of the infrared light with the molecule can lead to the excitation of the molecular vibrations [1]. Analysis of such vibrations is performed by the point group theory and helps to interpret the molecular spectra. Method of solution: 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. Restrictions onto the complexity of the problem: 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 C i , C s , C n , C n h , C n v , the dihedral groups D n , D n h , D n d , the improper cyclic groups S 2 n ( n ⩽ 10 ) , the cubic groups O, T, O h , T h , T d and the icosahedral groups I, I h . Unusual features of the program: 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 [2]. 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. Typical running time: Although the program replies ‘promptly’ on most requests, the running time depends strongly on the particular task.