Application of Group Theory to Molecular Systems

Wai-Kee Li, Gong-Du Zhou and Thomas Chung Wai Mak

in Advanced Structural Inorganic Chemistry

Published in print March 2008 | ISBN: 9780199216949
Published online May 2008 | e-ISBN: 9780191711992 | DOI:

Series: International Union of Crystallography Texts on Crystallography

 Application of Group Theory to Molecular Systems

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This chapter applies the group theoretic technique introduced in Chapter 6 to a number of chemically interesting problems. These problems include molecular orbital treatment of AH n (n = 2-6) molecules and cyclic conjugated polyenes (with and without d-orbital participation), construction of hybrid orbitals, relationship between molecular orbital and hybridization theories, molecular vibrations, etc. A large number of worked examples have been selected to illustrate that group theory can be used to simplify the physical problem and yield solutions of chemical significance. The advantage of this method becomes more obvious when the symmetry of the chemical system increases. Indeed, for highly symmetric molecules, very complex problems can have simple and elegant solutions. Even for less symmetric systems, symmetry arguments can still lead to meaningful results and conclusions that cannot be easily obtained otherwise.

Keywords: carbonyl stretching modes; cyclic conjugated polyenes; hybridization schemes; infrared activity; molecular orbital theory; molecular vibrations; normal modes; Raman activity; rule of mutual exclusion; vibrational spectra

Chapter.  21434 words.  Illustrated.

Subjects: Crystallography

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