BY
Done by
SHOBANA.N.S
Shobana.N.S
QUEEN MARY’S COLLEGE
1
2

Symmetry is present in nature and in human
culture
3
 Understand
in bonding.
what orbitals are used
 Predict
optical activity of a
molecule.
 Predict
activity
IR and Raman spectral
4

A molecule or object is said to possess a
particular operation if that operation when
applied leaves the molecule unchanged.
5
There are 5 kinds of
operations
1.
2.
3.
4.
5.
Identity
n-Fold Rotations
Reflection
Inversion
Improper n-Fold Rotation
6
IDENTITY


E (Identity Operation) = no change in the
object.
Needed for mathematical completeness.
 Every
molecule has at least this symmetry
operation.
7




It is equal to rotation of the object 360/n
degree about an axis .
The symmetry element is line.
Principle axis = axis with the largest
possible n value.
Cnn Is equal to identity (E)
8

Symmetry element is plane.

Linear object has infinite σ.

σv- plane including principle axis

σh- plane perpendicular to principle axis.

σd- plane bisecting the dihedral angle between two σv plane.
9

(x,y,z) --> (-x,-y,-z).

Symmetry element : point

Symmetry operation : inversion through a point.

i n is equal to identity (E)
10

It is also known as ROTATION-REFLECTION AXIS.

Rotation followed by reflection.

Snn = E
( n= even number)

Sn2n = E
( n= odd number)
11


A symmetry element is a point of reference
about which symmetry operations can take
place
Symmetry elements can be
1. point
2. axis and
3. plane
12

Symmetry element : point

Symmetry operation : inversion
1,3-trans-disubstituted cyclobutane
13

Symmetry element : plane

Symmetry operation : reflection
14

Symmetry element
: line

Symmetry operation : rotation
15
element
operation
symbol
symmetry plane
reflection through plane
σ
inversion center
inversion: every
point x,y,z translated
to -x,-y,-z
i
proper axis
rotation about axis by
360/n degrees
Cn
improper axis
1. rotation by
360/n degrees
2. reflection through
plane perpendicular to
rotation axis
Sn
16
17


The collection of symmetry elements present
in a molecule forms a ‘group’, typically called
a POINT GROUP.
The symmetry elements can combine only in a
limited number of ways and these
combinations are called the POINT GROUP.
WHY IS IT CALLED A “POINT GROUP”??

Because all the symmetry elements (points,
lines, and planes) will intersect at a single
point.
18
19

Ci has 2 symmetry operations :
E
i
the identity operation
point of inversion
C2H2F2Cl2
20

It has two symmetry operations
E – identity operation
σ – reflection
1- bromo, 2-chloro ethene
CH2BrCl
21

Only one symmetry operation (E)

Molecules in this group have no symmetry

This means no symmetrical operations
possible.
Bromochlorofluoromethane
CHFBrCl
22
Rotation of the molecule to 180 degree.
hydrazine
This point group contains only two
symmetry operations:
E the identity operation
C2 a twofold symmetry axis
Examples : water, chlorine
trifluoride, hydrogen peroxide,
formaldehyde
23
(2R,3R)-tartaric acid
D-mannitol
24
Rotation of the molecule to 120 degree.
This point group contains only two symmetry operations:
E the identity operation
C3 a three fold symmetry axis
Examples: ammonia, boron trifluoride,
triphenyl phosphine
25
9b H-Phenalene
3,7,11-trimethyl cyclo dodeca 1,5,9-triene
2,6,7-trimethyl-1-aza-bicyclo
[2.2.2]octane
26

This point group contains the following symmetry
operations
E
the identity operation
Cn
n-fold symmetry axis.
nσv n reflection operation
27

This point group contains the following
symmetry operations
E
the identity operation
C2
2-fold symmetry axis.
2σv
reflection operation
28

1.
2.
3.
4.
Examples:
Ozone
Thiophene
Furan
Pyridine
Sulphur dioxide
(Z)-1,2-DICHLORO
ETHENE
Formaldehyde
29
Phenanthrene
p-dichloro benzene
O-dichloro benzene
m-Xylene
30
31
Cyclohexane (boat)
Water
32

This point group contains the following
symmetry operations
E
the identity operation
C3
3-fold symmetry axis.
3σv
reflection operation
33

Examples:
Ammonia
POCl3
Trichloro methane
Tert-butyl bromide
34

This point group contains the following
symmetry operations
E
the identity operation
C4 n-fold symmetry axis.
4σv n reflection operation
35
Calix[4]arene
EXAMPLES
Sulfur chloride pentafluoride
Bromine pentafluoride
Xenon oxytetrafluoride
Fluorine pentafluoride
36

This point group contains the following
symmetry operations
E
C∞
the identity operation
∞ -fold symmetry axis.
∞ σv n reflection operation
37


Linear Hetero nuclear Diatomic Molecule
belongs to this category
These molecules don’t have centre of
inversion.
Chloro ethyne
38

This point group contains the following
symmetry operations
E
the identity operation
Cn
n-fold symmetry axis.
σh
n reflection operation
NOTE : If n is even ‘i’ is present.
39

This point group contains the following
symmetry operations
E
the identity operation
C2
2-fold symmetry axis.
σh
reflection operation
i
inversion
40
EXAMPLES
Trans-1,3-butadiene
N2F2
trans-1,2-dichloroethylene
C2H2F2
41
1,4-dibromo-2,5-dichloro-benzene
(E)-1,2-dichloro ethene
42

This point group contains the following
symmetry operations
E
the identity operation
C3
3-fold symmetry axis.
σh
reflection operation
S3
improper axis of symmetry
43
Benzene-1,3,5-triol
44
45

This point group contains the following
symmetry operations
E
the identity operation
Cn
n-fold symmetry axis.
nC2
2-fold symmetry axis.
(perpendicular to Cn)
46

This point group contains the following
symmetry operations
E
twistane
the identity operation
C2
n-fold symmetry axis.
2C2
2-fold symmetry axis.
47

This point group contains the following
symmetry operations
E
the identity operation
C3
3-fold symmetry axis.
3C2
2-fold symmetry axis.
48
Perchlorotriphenylamine
Ru(en)3
49
Tris(oxalato)iron111
Molecular knot
50

This point group contains the following
symmetry operations
E
the identity operation
Cn
n-fold symmetry axis.
nC2
2-fold symmetry axis.
nσd
dihedral plane
NOTE : ‘i’ is present when n is odd and S2n coincident to C2 axis
51

This point group contains the following
symmetry operations
E
the identity operation
C2
n-fold symmetry axis.
2C2*
2-fold symmetry axis.
2σd
dihedral plane
2S4
improper axis of symmetry
52
allene (propa-1,2-diene)
biphenyl
53
1,3,5,7-COT
54

This point group contains the following
symmetry operations
E
the identity operation
C3
n-fold symmetry axis.
2C2
2-fold symmetry axis.
3σd
dihedral plane
2S6
improper axis of symmetry
55
Cyclohexane chair form
56
Ethane staggered form
57

This point group contains the following symmetry operations
E
2C4
the identity operation
n-fold symmetry axis.
4C2*
2-fold symmetry axis.
4σd
dihedral plane
S8
improper axis of symmetry
C2
2-fold symmetry axis.
Mn2(CO)10
58

This point group contains the following symmetry
operations
E
the identity operation
4C5
n-fold symmetry axis.
5C2*
5σd
S10
i
2-fold symmetry axis.
dihedral plane
improper axis of symmetry
inversion
59
60

This point group contains the following symmetry
operations
E
the identity operation
Cn
n-fold symmetry axis.
nC2
2-fold symmetry axis.
σh
horizontal plane
nσv
vertical plane
Sn
improper axis of symmetry
61

This point group contains the following symmetry
operations
E
the identity operation
C2
n-fold symmetry axis.
2C2
2-fold symmetry axis.
σh
2σv
S2
horizontal plane
vertical plane
improper axis of symmetry
62
DIBORANE
M2F6
ETHENE
63
64
1,4-DICHLOROBENZENE
65
[2,2] PARACYCLOPHANE
66

This point group contains the following symmetry
operations
E
the identity operation
C3
3-fold symmetry axis.
3C2
2-fold symmetry axis.
σh
horizontal plane
2σv
vertical plane
2S3
improper axis of symmetry
67
68
cyclopropane
69

This point group contains the following symmetry
operations
E
the identity operation
C4
4-fold symmetry axis.
4C2
2-fold symmetry axis.
σh
horizontal plane
4σv
vertical plane
S4
improper axis of symmetry
70
Nickel tetracarbonyl
71
[AlCl₄]−
Xenon tetrafluoride
72

This point group contains the following symmetry
operations
E
the identity operation
C5
4-fold symmetry axis.
5C2
2-fold symmetry axis.
σh
horizontal plane
5σv
vertical plane
S5
improper axis of symmetry
73
74

This point group contains the following symmetry operations
E
the identity operation
C6
6-fold symmetry axis.
6C2
2-fold symmetry axis.
σh
horizontal plane
6σv
vertical plane
S6
i
improper axis of symmetry
inversion
75
76

This point group contains the following symmetry operations
E
the identity operation
C∞
4-fold symmetry axis.
∞
C2
σh
∞
σv
S∞
i
2-fold symmetry axis.
horizontal plane
vertical plane
improper axis of symmetry
inversion
77
POSSESS CENTER OF SYMMETRY
78
79

This point group contains the following
symmetry operations
E
4C3
3C2
6σd
3S4
the identity operation
3-fold symmetry axis.
2-fold symmetry axis.
dihedral plane
improper axis of symmetry
Total: 24 elements
80
METHANE
81
NEOPENTANE
82

This point group contains the following symmetry operations
E
the identity operation
3C4
4-fold symmetry axis.
3C2
2-fold symmetry axis.
3σh
3S4
dihedral plane
improper axis of symmetry
i
inversion
C3
3-fold symmetry axis
S6
TOTAL :48 elements
improper axis of symmetry
6C2
2-fold symmetry axis.
6σd
dihedral plane
83
Cr(CO)6
[PtCl6]2-
84
PF6-
CUBANE
85
SF6
86

This point group contains the following symmetry operations
E
the identity operation
20C3
15C2
3-fold symmetry axis.
2-fold symmetry axis.
15σh
horizontal plane
20S6
improper axis of symmetry
i
inversion
20C3
3-fold symmetry axis
12S10
improper axis of symmetry
12C5
5-fold symmetry axis.
12S10*
improper axis of symmetry
TOTAL : 120 elements
87
dodecahedran
fullerenes
88
89