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REDUCE: A Program for Reducing Reducible Representations

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James F. O'Brien

Department of Chemistry, Southwest Missouri State University, Springfield, MO 65804

Bruno F. Schmidt

Department of Computer Science, Southwest Missouri State University, Springfield, MO 65804

J. Chem. Educ., 1998, 75 (10), p 1338

DOI: 10.1021/ed075p1338

Publication Date (Web): October 1, 1998

Section:

History, Education, and Documentation

Abstract

The treatment of symmetry continues to grow in the undergraduate curriculum. Textbooks in physical and inorganic chemistry now treat the subject in considerable detail. Application of symmetry principles to vibrational analysis and to the determination of hybrid orbitals requires the use of the "reduction formula". The tedious arithmetic involved in applying the reduction formula to reducible representations is best done by a computer. While a spreadsheet may be used with effectiveness, the program described in this paper is much more convenient.

REDUCE has 27 character tables in its data base. In addition it will do vibrational analysis on the linear point groups D_h and C_v following the approach of McGinn. It will reduce any reducible representation into the irreducible representations which comprise it. Three options that arise most commonly are presented to the user: All Vibrations, Specific Vibrations, and Hybrid Orbitals.

Keywords (Audience):

Upper-Division Undergraduate

Keywords (Domain):

Inorganic Chemistry

Keywords (Pedagogy):

Computer-Based Learning

Keywords (Subject):

Group Theory / Symmetry

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This article has been cited by 1 ACS Journal articles (1 most recent appear below).

Towards "Inverse" Character Tables? A One-Step Method for Decomposing Reducible Representations
J.-Y. Piquemal , R. Losno and B. Ancian
Journal of Chemical Education2009 86 (2), 251
- Towards "Inverse" Character Tables? A One-Step Method for Decomposing Reducible Representations
  J.-Y. Piquemal , R. Losno and B. Ancian
  Journal of Chemical Education2009 86 (2), 251
  In the framework of group theory, a new procedure is described for a one-step automated reduction of reducible representations. The matrix inversion tool, provided by standard spreadsheet software, is applied to the central part of the character table ...
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