Symmetry and its shapes (I.R and raman activaty)

#Symmetry is common phenomenon in the world
around us
#It is difficult to overestimate the importance of
symmetry in many aspects of science, not only in
chemistry

Mirror image relationship indicate the
facial symmetry
Mirror image

By using symmetry we can compare two different things
for example in chemistry we can compare two molecules
.
(a) Is more symmetrical than (b)

Water molecule
revolving anticlock
wise
Symmetry operation – A rearrangement of a body after
which it appears unchanged
A symmetry operation moves molecule about an axis , a
point ,or a plane to a position indistinguishable

Symmetry elements
1) Axis of rotation
2) Mirror planes
3)Center of symmetry
4)Improper rotation
5)Identity

Proper axis of rotation Cn
 A rotation about this axis by an angle Q=360/n leaves the molecule in an
INDISTINGUISHIBLE confrigation such axis is called n fold proper axis of
rotation
 Example water C2 axis

Some Gumatricle images
C6
C4 C3 C2

Plane of symmetry σ
 A molecule posses a plane of symmetry if reflection through
through the plane leaves molecule un changed
σh if plane of symmetry is PERIPENDICULAR to principal axis
σv if plane of symmetry is PARLLEL to principal axis
σd if vertical plane bisect the angle between two C2 axis
 Example in water there is two σv and no σh
Red is molecular
plane

Plane of symmetry in BF3 molicule
 One σh i.e molecular plane
 Three σd

Impoper axis of rotation
 A molecule is said to posses an improper axis of rotation of order n
if rotation about the axis by 360/n followed by REFLECTION in a
plane PEPANICULAR to axis leaves molecule INDISTINGUISHIBLE
position
 If molecule has plane of symmetry σh perpendicular to proper axis
of rotation C2,C4 and C6 the axis naturally become S2,S4,S6
respectively
 An s2 axis is equivalent to i
 Example staggered ethane

Inversion iIf a point exist in center of molecule such that
IDENTICAL atoms are found on either side at equal
distance from it the central point is called center of
inversion
In H2O and BF3 molecule there is no i
In C2H4 molecule there is i
ethene

i in some geometrical
image
i
present
i absent

Identity E
If sequence of operation brings molecule back to its
original configuration ,the net operation is called
identity operation E
Example two C2 rotation in H2O molecule equivalent
to E
1 2
C2 .

Identity E
to E
1
2 12
C2 C2

Identity E
to E
1
2 112 2
C2 C2

Total symmetry of some molecule
 The symmetry of molecule can be determined by listing all
the element present on it
 H2O E,C2, v (yz), v(xz)

Ethene
 E, 3C2, h, v, v ,i
C CC
H H
H
H

Exercise
 NH3 choose write option 1.E,C2,3 v, h
 Di chloroethylene trans cis



2.E,C2,3 v
3.E,C3,3 v
4.E,C4,3 h
1.E,C2, d, v 1.E,C2, h, v
2.E,C2, h,i
3.E,C3, d, 
d
4.E,C2, v, ,i 
v
2.E,C2, v,

 
 
v
3.E,C1, v, i
4.E,C1, d, i
Cl
Cl
Cl
Cl

Symmetry Points group
 The group of symmetry operation of molecule is called point group
 several molecule may have the same set of operation
 For example following molecule have same set of operation i.e
E,C2, , hence belong to same point group
Cl Cl

Point group very high symmetry
 Linear molecule

i absent i present
vC hD
 Special groups

dT hI


d
No symmetry
element except
E i
C1 Cs Ci
Point group very low symmetry
If there is Sn collinear with Cn and there is no other element
present except i the point group is S2n

point group based on principle axis
n﬩C2 ﬩
h h
v
nvCndD nD nC
d nhC

Finding normal mode of vibration
 Determine the point group of the molecule.
 Obtain the reducible representations for all the symmetry operations of
the point group.
 Split the rep into the irreps using the standard reduction formula.
 The irreps thus obtained correspond to the translational,
,rotational and vibrational degrees of freedom .
 By subtracting translational and rotational degrees of freedom from
we obtained irrap for vibrational motion.
N3
N3

For Water molecule
 The reducible representation are
311-9
CEC vv22v


   3131111111191
4
1
1 An
   1)1(31)1(11111191
4
1
2 An
   2)1(31111)1(11191
4
1
1 Bn

   313111)1()1(11191
4
1
2 Bn
21213 323A BBAN 
)RRRTT( zyxzy3  xNvib T
A
B
Using A and B we get
)()323A( 2121212121 ABBABBBBAvib 
212A Bvib 

Raman and I.R active Vibration
 The molecule vibration is I.R active if there is change in dipole moment with vibration.
 The molecule vibration is Raman active if there is change in polarizability with
vibration.
Rule of Mutual Exclusion
 If a molecule has center of symmetry then Raman active vibrations are infra –red inactive
and vice versa . If there is no center of symmetry then all normal mode of vibration is both
Raman and I.R active.
 Example centrosymmetric CO2 molecule one mode is Raman active and two mode is I.R
active and in non centrosymmetric like H2O and NH3 all modes are both Raman and I.R
active.

I.R and Raman active vibration in
centrosymmetric molecule
 Vibration belong to basis x,y,z are I.R active.
 In other hand vibration belong to basis are Raman
active .
zxyz,xy,,z,y,x 222

Linear molecule
Diatomic
Triatomic
Homonuclear Hitronuclear
O O H Cl
No change in
dipolemument
with vibration
Change in
dipolemument
with vibration
Change in
polarizability
with vibration
Change in
polarizability
with vibration
I.R active
Raman
active

AB2 type molecule
Liner Bent
H H
O
O C O

Linear A-B-A
Centrosymmetric
Normal Mode of vibration
I.Ractive Ramanactive
>

Linear A-B-A,A-B-C
NoN Centrosymmetric
>
All are I.R and Ramanactive

Bent AB2
Non Centrosymmetric
>
C
vC2
212 BA 

Bent ABB,ABC
Non Centrosymmetric
C
sC

A3

AB3 type molecule
Planer Pyramidal
H H H
N
hD3 vC3

PIaner AB3
Non Centrosymmetric
>
CV
CV
EAA  221
EA 2
EA 1
hD3

Pyramidal AB3
Non Centrosymmetric
C
>
vC3
EA 22 1 

4/10/2018
Lowering in symmetry
Elongation or contraction of A-B bond also lowers the molecular
symmetry e.g. pyramidal AB3 molecule is lowered in symmetry from
C3v to Cs .

AB4 type molecule
Tetrahedral Square planer
F F
XeB
H
H HH
F F
dT hD4

Tetrahedral AB4
Non Centrosymmetric
>
CV
CV
CV
dT
21 2FEA 
22F 21 2FEA 

Square planer AB4
Centrosymmetric
CV
CV
>
C
V
C
V
C
VC
V
C
V
C
V >
hD4
uuuggg EBABBA 222211 
uu EA 22  ggg BBA 211 
uB2

4/10/2018
AB4 type molecules also poses some other geometry
Lowering of symmetry
1. If one of the B atom is replaced by another atom say C ,the point group of molecule
CAB3 is lowered to C3v in case of tetrahedral and C2v in squreplaner.
2. If two of the B atoms of AB4 molecule are replaced by C, then point group symmetry
of C2AB2 will be distorted to C2v.
3. In case of ABCD the symmetry is again lowered to Cs or C1.

AB5 type molecule
Trigonal bipyramidal Square pyramidral
F F
IF P
vC4hD3
F
F
F
F F
F
F

T.B.P AB5
Non Centrosymmetric
>
CV
CV
CV
hD3
EEAA  222 21
EA  22 2 EEA  22 1

S.P AB4
Non Centrosymmetric
CV
CV
CV
>
C
V
>
C
V
vC4
EBBA 323 211 
EBA 33 21  EBA 323 11 

4/10/2018
Lowering of symmetry
In these type of molecules if one of the axial atom is replaced by
atom C then the point group symmetry of molecule AB4C is lowered
from D3h to C3v.
 If both of the axial atoms are replaced, the molecule AB3C2 will have
same point group D3h
Replacement of one or two equatorial atoms lowers the symmetry of
AB4C or AB3C2 to point group C2v

AB6 type molecule
Octahedral
F F
S
F F
F
F

O.H. AB6
Centrosymmetric
CV
CV
CV
Forbidden
hO
ugugg FFFEA 2211 2 
uF12 ggg FEA 21  uF2

4/10/2018
Lowering of symmetry
Substitution in the axial atoms forming AB5C or AB4C2 tetragon
ally distort the geometry & reduce the point group to C4v or D4h .
When axial groups are removed the AB6 molecule degenerates to
the square planar AB4.

Symmetry and its shapes (I.R and raman activaty)

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