Reduce: A program for reducing reducible representations
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 Dh and Cv 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.
Physics, Astronomy, and Materials Science
O'Brien, James F., and Bruno F. Schmidt. "REDUCE: A program for reducing reducible representations." Journal of Chemical Education 75, no. 10 (1998): 1338.
Journal of Chemical Education