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  Home > JCE Print > Journal of Chemical Education > Issues > 2005  > January  >
Research: Science and Education
A Simple Reduction Process for the Normal Vibrational Modes Occurring in Linear Molecules
William McInerny
Department of Chemistry, City College of San Francisco, San Francisco, CA 94112
Cover
January 2005
Vol. 82 No. 1
p. 140
Abstract
The students in molecular spectroscopy courses are often required to determine the permitted normal vibrations for linear molecules that belong to the groups C∞ν and D∞h. The reducible group representations generated by the use of Cartesian coordinates can be reduced by the use of a simple algebraic process applied to the group representations. The method relies on the linear independence of the cosines of integral multiples of the rotation angle j. The systems of linear equations that arise can be solved readily by hand calculations, even in the most general cases. When compared with the results of standard textbook presentations, this approach is easy, efficient, and certain. This kind of process would appear to be extendible to other continuous groups.
More Information
*  Citation
 McInerny, William. J. Chem. Educ. 2005 82 140.
*  Keywords
 Computational Chemistry; Graduate Education / Research; Group Theory; Group Theory / Symmetry; Mathematics / Symbolic Mathematics; Physical Chemistry; Problem Solving / Decision Making; Quantum Chemistry; Theoretical Chemistry; Upper-Division Undergraduate
*  History
 Created:
Last Updated:		 November 29, 2004
December 10, 2004
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