Upload
a-zaman-sagor
View
441
Download
1
Tags:
Embed Size (px)
DESCRIPTION
4th lecture of Monirul Islam Sir
Citation preview
Molecular symmetry and group theory
Dr. Md. Monirul Islam Department of Chemistry
University of Rajshahi
Groups and their basic properties
Point groupThe collection of symmetry operations upon a molecule that satisfy all the characteristics of a group is defined as point group for that molecule.
For example,The symmetry operations on PF5 molecule are
Point group of PF5
The symmetry operations on NH3 molecule are
Point group of NH3
𝐸 ,𝐶31 ,𝐶3
2 ,𝜎𝑣 (1 ) ,𝜎𝑣 (2 ) ,𝜎𝑣 (3)
Classification of molecules into point groups
C
H F
Cl Br
Symmetry elements: E
Point group: C1
C
Br F
O
Symmetry elements: E,
Point group: Cs
O𝜎
C C
Br Cl
BrClH
H
i
C
H
H
Br
Br
Cl
Cl
Symmetry elements: E, i
Point group: Ci
O O
1H H2
C2
Classification of molecules into point groups
C2
O
H H
C2
𝜎 𝑣𝜎 𝑣′
C2v
N
H(1)(2)H
(3)H
C3
v(1)
v(2)
v(3) C3v
Cnv Cn
P
C3
C3
Cnh
Classification of molecules into point groups
NN
H
H
C2
𝜎 h
C2h
Trans-N2H2
H
C3
𝜎 h
C3h
B(OH)3
BO
H
OH
O
Classification of molecules into point groups group
P
Cl
ClN P
Cl
Cl
NP
Cl
Cl
N
N
P
Cl
Cl
i.e.,(+)P
P
P(+)
(-)P(-)N
(+)N
N(-)
N(+)
(-)
• is coincident with axis
• A molecule belonging to the point group :
Classification of molecules into point groups
Dihedral point group belonging to axes
C
HHH
H
H H
𝐶2
𝐶2 𝐶2
C C
H
H
H
H
HH
𝐶3
Gauche : a molecule belonging to the point group
• and axes point group
Classification of molecules into point groups
Dihedral point group belonging to axes
• , and point group
C C C
H
H
H
H
𝐶2
𝐶2
𝐶2
𝜎 𝑑
𝜎 𝑑
Allene : a molecule belonging to the point group
C C
H H
HHH
H
C
H
H
H
H
H
H
Classification of molecules into point groups
Dihedral point group belonging to axes
• , and point group
𝜎 𝑑𝜎 𝑑
𝜎 𝑑
𝐶3𝐶2
𝐶2
𝐶2
Staggered : belonging to the point group
Classification of molecules into point groups
Dihedral point group belonging to axes
• , and point group
CC
H
H
H
H
𝜎 h
𝐶2
𝐶2
Ethene:
C
O
O
O𝜎 h
𝐶2 𝐶2
𝐶2
:
More examples
: Benzene :
Cubic Point Groups: Td
Point groups of higher symmetry: Cn more than one
Symmetry operations
Cubic Point Groups: Td
Symmetry operations
Infinite point group
C NH C∞
C OO C∞
∞𝜎 𝑣
∞𝜎 𝑣
∞𝐶2
𝜎 h
HCN molecule (linear) CO2 molecule (linear)
Symmetry elements: Symmetry elements
Point group : Point group :
Molecules
Linear?
? 𝐷∞h𝐶∞ h
YNTwo or more
with n>2
YN
Y
?N
?
N𝑇
Y?
𝑇 𝑑
𝜎 𝑑
𝜎 h 𝑇 h
Y
Point group flow chart
?Y𝐼 h
?Y𝑂h
𝑂N N
N?
?𝐶 𝑠Y
N
?𝐶𝑖Y
𝐶1
N
?N
Y
N
?𝐶 h𝑛Y
N
?𝐶𝑛𝑣Y
N
?𝑆2𝑛Y
? N ? N 𝐷𝑛
Y
𝐷 h𝑛
Y
𝐷𝑛𝑑
Y
𝐶𝑛N
Assignments of Points Groups
Example H2O
1. It is a Non-linear molecule2. It has only one Cn(C2) axis3. It does not belong Cn ┴ C2 4. It has v
5. Point group C2V
Example NH3
1. It is a Non-linear molecule2. It has only one Cn(C3) axis3. It does not belong Cn ┴ C2 4. It has v
5. Point group C3V
Example Allene
C C C
H
H
H
H
C2, S4
C2’
C2’