NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
Point Groups and Molecular Symmetry
K.Sridharan
Dean
School of Chemical & Biotechnology
SASTRA University
Thanjavur – 613 401
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
Table of Contents
1 Point groups and molecular symmetry ........................................................................................ 3
1.1
Point group ...................................................................................................................... 3
1.2
What is the need of point group? ................................................................................... 3
1.3
How to assign the point group to a molecule? ........................................................... 4
2. Flow chart for deriving the point group of a molecule ............................................................... 5
3. Derivation of point group of molecules ...................................................................................... 7
4. References ................................................................................................................................... 8
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
1 Point groups and molecular symmetry
1.1 Point group
Symmetry operations generated by the symmetry elements present in a molecule form a
symmetry group or a point group.
1.2 What is the need of point group?
It is a simple way of labeling a molecule and a short hand description of the
molecule. It is very much useful in probing the properties of a molecule.
Example 1:
The point group of [FeCl 4 ]- is T d . It means that the complex ion is having
tetrahedral shape as shown in Figure 1.2.1. We can predict the spectral transition
of this ion from its shape.
Cl
Fe
Cl
Cl
Cl
Fig 1.2.1 [FeCl 4 ]- ion, T d
Example 2:
The point group of [PtCl 4 ]2- is D 4h . It means that this complex ion has square
planar geometry.as shown in Figure 1.2.2
Cl
Cl
Pt
Cl
Cl
Fig 1.2.2 PtCl 4 ion, D 4h
Example 3:
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
This molecule has the point group C 2v . This molecule has a butterfly structure as
shown in Figure 1.2.3
Cl
Cl
Te
Cl
Cl
Fig 1.2.3 TeCl 4 , C 2v
1.3 How to assign the point group to a molecule?
Step 1: Get the shape of the molecule
Step 2: Find out all the symmetry elements
Step 3: Follow the flow chart to get the point group
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
2. Flow chart for deriving the point group of a molecule
Start
Is C ∞ present?
Yes
No
Is i present?
Is C n present?
yes
No
D ∞h
No
I
Cs, Ci, C1
Yes
No
Is 6C 5 present?
Yes
C ∞v
i?
Yes
O
No
Ih
No
i?
Yes
Is 3C 4 present?
Yes
Oh
Td
Yes 6σ?
No
N
No
i?
Yes
Is 4C 3 present?
Y
T
Th
B
No
No
nC 2 ┴ C n ?
Yes
A
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
A
D nh
yes
B
Is σ h present?
Is S 2n present?
No
D nd
Y
Y
S 2n
No
Is nσ v present?
Is σ h present?
No
Y C nh
Dn
No
Cn
No
Is nσ v present?
Y C nv
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
3. Derivation of point group of molecules
Example 1: PF 5
Outermost electronic configuration of P is 3s23p3
Number of valence electrons
=5
Number of electrons from five F = 5
Total number of electrons
= 10
Number of bond pairs
= 10/2 = 5
Hence, the shape of PF 5 is trigonal bipyramid
C3
C2
F
F
F
P
F
C2'
σh
F
C2"
1.
2.
3.
4.
C 3 axis is present
Three C 2 axes ┴ the principal axis, C 3
σ h plane is present
Hence, the point group is D 3h
Example 2: H 2 O
Outermost electronic configuration of oxygen = 2s22p4
Number of valence electrons of oxygen
=6
Number of electrons from two hydrogens = 2
Total number of electrons
=8
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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
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Total number of electron pairs
= 8/2 = 4
Number of bond pairs
= 2
Number of bond pairs
= 4-2 = 2
Structure is tetrahedral and two lone pairs occupy two corners of the tetrahedron
and the shape is V
C2
σv
O
H
H
σv'
1. C 2 axis is present
2. Two σ v planes
3. Hence, the point group is C 2v
4. References
1. “Inorganic Chemistry: Principles of Structure and Reactivity”, James
E.Huheey, Ellen A.Keiter, Richard L.Keiter, Okhil K.Medhi, Pearson
Education, Delhi, 2006
2. ‘Chemical Applications of Group Theory”, 2/e, F.Albert Cotton, Wiley
Eastern, New Delhi, 1986
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