By Sidney F. A. Kettle
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Extra resources for Symmetry and Structure: Readable Group Theory for Chemists 3rd edition by Kettle, Sidney F. A. (2007) Paperback
We can now see them for what they are. Essentially, they are pictures of the four irreducible representations of the C2v point group. Put another way, the application of group theory to chemical problems is a way of exploiting the differing nodal patterns associated with different phenomena (if this sounds a bit obtuse, there will be plenty of examples in the following chapters). 21 – and, indeed, we will do this as far as possible. However, the road may not always be easy. Consider a molecule as simple as methane.
4 are called character tables. As has already been indicated, character tables are of prime importance for the topics discussed in this book. 2 become the unexpected properties of character tables. It is these ‘unexpected properties’ (which are actually fundamental and far from accidental) which are at the heart of their value in chemistry. In the next chapter, when the bonding in the water molecule is discussed, the existence, and to some extent the origin, of these properties will become clear.
In this figure the four points in space (hydrogen atoms) have been labelled with the suffixes a, b, c or d – so that in order to study the effects of the symmetry operations all that has to be done is to see how these labels are rearranged. 28, a figure that should be studied carefully until the reader is fully conversant with it, feels comfortable with it. It will be noted that each symmetry operation gives rise to a different final arrangement of labels, a feature which would not have been found with the simple H2 O molecule and the reason for the present choice of example.