CHEMISTRY DEPARTMENT
UNIVERSITY OF GHANA, LEGON
(All Rights Reserved)
Chem 403 Symmetry and Group Theory
Tutorial sheet II 2014/2015 Academic year
1.
Distinguish between the concepts of (a) symmetry operation, (b) symmetry
element, and (c) symmetry point group.
2. Determine the symmetry elements and assign the point group of the
following molecules or ions.
a. H2O2
b. SO2Cl2
c. PCl3
d. HCl
e. N2O4
f. PF5
g. SF4
h. SF6
i. XeF4
J. CO2
k. Eclipsed Ferrocene
1. N02
3. Draw sketches to identify the following symmetry elements: (a) a C3 axis
and a σv plane in the NH3 molecule; (b) a C4 axis and a σh plane in the
square planar [PtCl4]2– ion.
4. The following is a character table for the point group C6v
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Determine the following
i. Order of the group
ii. Group name
iii. Basis functions
iv. Nondegenerate representation
v. Degenerate representation
vi. Meaning of the following representations A,B, and E
5. For trans-l ,2-dibromo-l,2-dichloroethylene, of C2h symmetry,
a. List all the symmetry operations for the molecule.
b. Write a set of transformation matrices that describe the effect of each
symmetry operation in the C2h point group on a set of coordinates x, y, z
for a point. (Your answer should consist of four 3 x 3 matrices.)
c. Using the terms along the diagonal, obtain as many irreducible
representations as possible from the transformation matrices. (You should
be able to obtain three irreducible representations in this way, but two will
be duplicates.)
d. Using the C2h character table, verify that the irreducible representations
are mutually orthogonal.
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