Symmetry in Chemical Bonding

In earlier chapters we classified the symmetry of atomic orbitals (AOs) in a number of example molecules. It is now time to develop the ideas of molecular orbital (MO) theory and use it to describe chemical bonding. Symmetry classifications help in the MO description of chemical bonding because symmetry controls how the AOs on neighbouring atoms mix together. MOs are the wavefunctions for electrons in the complex field of the many nuclei and other eleetrons that make up a molecule. The complexity of MOs can be dealt with by constructing them from the AOs of the isolated atoms. The MOs are formed by mixing the AOs based on the idea of interference described by the superposition of waves when waves come together in the same phase they reinforce one another, whereas waves of opposite phase will tend to cancel each other out. 

In this chapter we will find that only AOs of the same symmetry can mix by superposition to give MOs. To construct MOs, the symmetry of the AOs for the interacting atoms are first established and then each matching set is used to produce SALCs which predict the shapes of the MOs. This is simply an application of symmetry analysis to a basis of AOs, and so we will always be able to construct the same number of MOs as there are AOs in the basis. 

Molecular Symmetry David J. Willock 2009 John Wiley Sons, Ltd. ISBN 978-0-470-85347-4 

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The reader will find simple applications of group theory in Chapters 10 and 15. A non-mathematical introduction to the subject is given in Symmetry and Structure by S. F. A. Kettle, Wiley, Chichester and New York, 1995. Also relevant, useful and/or relatively non-mathematical are Symmetry in Coordination Chemistry by J. P. Fackler Jr., Academic Press, New York, 1965 Symmetry in Chemistry by H. H. Jaffe and M. Orchin, Wiley, New York, 1965 Molecular Symmetry and Group Theory by A. Vincent, Wiley, London, 1977 Symmetry in Chemical Bonding and Structure by W. E. Hatfield and W. E. Parker, Merrill, Columbus, Ohio, 1974 and Group Theory for Chemists by G. Davidson, Macmillan, London, 1991. More mathematical is Chemical Applications of Group Theory by F. A. Cotton, Wiley, New York, 1990. 

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