Last Update 14/ 05/ 2000
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The benzene molecule is initially presented with activated button A=B=C=D=E=F showing the six carbon atoms in black balls and the six hydrogen atoms in blue. Clicking on button A=X one hydrogen will be substituted by another atom or group of atoms (in green), for example chlorobenzene. The three next buttons A=X, BOX through A=X, D=X show ortho-, meta- and para- twice substituted benzene. The last three buttons on the same column show three substituted atoms in different positions. The green ball can represent atoms as bromine, iodine, and groups as methyl, hydroxyl and so on. Turning the molecule around the axis passing through the centre of the molecule and perpendicular to its plane it is possible to recognize if some particular symmetry axis is acting. If the same image is observed at every 60 o or 2p/6 radians of rotation the rotation axis is a six fold axis, it has a symbol 6 using Herman Margin international notation or C6 using Schoenflies notation. If the same image is repeated at rotation angles of 120 o or 2p/3 radians the axis is named three fold axis, with symbol 3 or C3 and if the repetition of the same image is at every 180o or p radians it is a two fold rotation axis with symbol 2 or C2.When the image is repeated only after a complete turn of 360o or 2p radians the symmetry axis is the trivial identity symmetry element, present in any object or molecule. The figure can be turned sequentially by a push and drag mouse action on the yellow square. Exact angles can be selected clicking on the buttons in the horizontal line.
The interested person is invited to discover the presence or absence of any symmetry axis on each of the eight kinds of molecules available in this figure.
Other symmetry axis or symmetry elements in different orientations are not studied in this page.
Symmetry operations are used in crystallography.
Bibliography
[1] Experiments in Physical Chemistry, D.P. Shoemaker, C.W. Garland and J.W. Nibler, McGraw-Hill, Inc, (1989).
[2] Inorganic Chemistry, J.E. Huheey, E.A. Keiter and R.L. Keiter, Harper Collins College Pub. (1993).
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