Molecular Symmetry and Group Theory |
Using the images in the table below, click on the F atom in the product which should be coloured red after successive clockwise rotations through 90° performed about the C_{4} axis in XeF_{4}. (All the F atoms are identical - one has been coloured red merely for convenience!)
NB. The C_{4} operation performed two/three/four times is represented as C_{4}^{2}/C_{4}^{3}/C_{4}^{4} respectively.
Rotation | Clickable Image | Corresponding Answer |
---|---|---|
C_{4} | ||
C_{4}^{2} | ||
C_{4}^{3} | ||
C_{4}^{4} |
As all the F atoms are identical, the result of C_{4}^{2} is also indistinguishable from the starting position. C_{4}^{2} is therefore a second operation associated with the C_{4} element. Are C_{4}^{3} and C_{4}^{4} other operations?
After performing C_{4}^{4} the molecule has now returned to its starting position. What symmetry operation is this equivalent to? Can you think of an operation equivalent to C_{4}^{2} ?
The total number of independent symmetry operations that can be performed on a molecule is of fundamental importance. So as long as we consider all the symmetry elements (including E), we do not need to count operations (such as C_{4}^{2} and C_{4}^{4}) that have equivalents. The C_{4} symmetry element therefore generates only two operations: C_{4} and C_{4}^{3}.
All planar molecules have a mirror plane σ. The operation performed twice (σ^{2}) is equivalent to the operation E (no change), so the element σ generates a single operation. | |||
The H_{2}O molecule has two σ planes and a C_{2} axis. This molecule therefore has four symmetry elements: E, C_{2}, σ and σ′. | |||
Each of these elements generates a single operation, and these operations are known by the same symbols: E, C_{2}, σ and σ′. |
We shall see later that the correct determination of the symmetry operations that can be performed on a molecule is essential for the application of group theory.
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