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inorganic chemistry
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1. Molecular Symmetry (Point Group) Read Cotton Ch 3 Symmetry Operation a movement of a molecule that leaves the molecule apparently unchanged (takes the molecule into an equivalent configuration). ex) rotation, inversion Symmetry Element a point, line, or plane with respect to which symmetry operations are performed. Point-group Symmetry Operations Symmetry operations that leave at least one point of the molecule unmoved. cf. space group ( + translational symmetry operations)
Symmetry Element Symmetry Operation Symbol
Identity E
n-fold Rotation Axis Rotation by 2/n (order: n) Cn
Mirror Plane Reflection
Center of Inversion Inversion i
n-fold Axis of Improper Rotation
Rotation by 2/n followed by reflection to rot. axis Sn
Reflection,
v, vertical; h, horizontal; d, dihedral
*
Inversion, i
i
C2
Rotation, Cn
or C31 or C31
or C32
In general, for a given Cn, n symmetry operations exist: Cn, Cn2,, Cnn-1, Cnn (= E)
Improper Rotation, Sn
S2 = i
S1 =
However, no C4 , h ! S42 = C2
1
2 3
4
1
2
3
4
1
2
3
4 4
1
2
3
90
Reflection
1,3, 5, 7, tetrafluorocyclotetratraene
Sym. operations: E, C31, C32, , , or E, 2C3, 3 Sym. operations: E, C2, ,
Sym. elements: E, C3, , , Sym. elements: E, C2, ,
Point Group (1) Compile a list of symmetry elements. (2) Compare it with the list that is characteristic of each point group.
N2 CO C60 SF6 CCl4 NH3 XeF4 SiBrClFI
Sym. op: E, C31, C32, , , or E, 2C3, 3
Sym. op: E, C2, ,
1 2 3 4 5 6 7 8 9 10 11 12 13