Symmetry and Group Theory (CHMS3102)
BSc, Chemistry - CHMS
Semester: Resit
Level: 300
Year: 2016
UNIVERSITY OF BAMENDA FACULTY OF SCIENCE
RE-SIT SEMESTER EXAMINATIONS 2016
Department: chemistry Course instructors: Paul CHONGWAIN
Month: September, 2016 Course code & Number: CHMS3102
Course title: Symmetry and Group theory in Chemistry
Time allowed: 3 hours Credit value: 4
Instructions: Attempt all Questions.
QI.Define the following terms: Symmetry element, Symmetry operation, Representation
and Point group as used in this course.
Identify the symmetry elements and their operations in the molecule trans-butadiene.
Deduce the point group for this molecule.
Q2. Write down the secular determinant for cis-butadiene molecule, defining all the
symbols used. Obtain the solutions to the energy values for this system and arrange the
energy value in increasing order. Determine the total energy of the occupied pie
molecular orbitals
Q3.How many representations maybe generated from a molecule? Using a molecule of
your choice give at least three basis for a representation. Given the point group C
4V
,
find the direct products in terms of the irreducible representations: See attached table
(i)
A
1
x A
2
(ii)
A
1
x B
1
(iii)
B
2
x B
1
(iv) ExE
(v)
∑
Q4. Determine the distribution of the irreducible representations in the following
reducible representations using the C
2V
character table
C
2
v
E
C2
v
(xy)
v
(yx)
r
1
10
0
6
0
r
2
6
0
2
0
r
3
4
0
4
0
r
3
30
0
0
6
(b) Show that the matrices representing the following symmetry operations: E, C2, i and
Oh form a group under the C
2h
point group
Q5. The hydrogen sulphide molecule belongs to the point group C
2V
(character table
provided). Using vectors or a suitable basis for representation, determine the
vibrational modes associated with this molecule. Identify the Infra-red and Raman
active modes of vibration.
www.schoolfaqs.net
