The document discusses molecular symmetry and group theory. It defines key concepts like symmetry operations, elements, and point groups. Symmetry operations include inversion, rotation, and reflection. Common symmetry elements are inversion centers, rotation axes, and planes of symmetry. Molecules can be classified into point groups based on their unique symmetry elements and operations, such as C2v for H2O. Understanding molecular symmetry allows determination of molecular structure and prediction of properties.

1. MOLECULAR SYMMETRY
Dr. Julekha. A. Shaikh
Maharashtra College of Arts, Science and Commerce
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2. Symmetry Is All Around Us
In life In Art
In Chemistry
Dr. Julekha Shaikh 2

3. Symmetry is derived from the Greek word
“symmetria” which means “measured together”.
The symmetry of molecules and solids is a very powerful tool for:-
• determination and description of structures of molecules.
• giving precise description of the molecular geometry and
molecular configuration
• Developing an understanding of bonding and physical
properties
• Predicting the nature of molecular orbitals
• Predicting if electronic and vibration spectroscopic transitions
can be observed Dr. Julekha Shaikh 3

4. Symmetry Operation:
An action which moves the object into a
position indistinguishable from the original
one though not necessarily identical with it.
Symmetry Element:
A geometrical identity such as line, plane or a
point with respect to which one or more
symmetry operations may be carried out.
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5. Types of Symmetry Elements
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Sr.no. Symmetry element symbol Symmetry operation
1 Centre of symmetry/
Inversion Centre
i Inversion of all atoms through the centre
2 Proper axis of rotation Cn One or more rotations by an angle
θ = 2 / n about the axis
3 Plane of symmetry  Reflection in the plane
4 Improper axis of
rotation
Sn One or more rotations by an angle
θ = 2 / n about the axis followed by
reflection in a plane perpendicular to the
rotation axis
5 Identity E No change

6. Imaginary point in the centre of the molecule through
which the reflection of an atom in a molecule results in
coincidence with an equivalent atom.
Centre of Symmetry/Inversion Centre (i)
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7. Dr. Julekha Shaikh 7
• If the inversion operation is carried out n times it is
expressed as in.
• For even values of n, the molecule goes back to its
original configuration. in = E where E is identity
element.
• If n is odd in = i.

8. Molecules with centre of symmetry
Molecules without centre of symmetry
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9. Imaginary line passing
through the molecule along
which rotation carried out
results into an equivalent
rotation.
Order (n) = 2 / 
For H2O molecule
n = 2 x 1800 / 1800 = 2
Cn = C2
Proper Axis of Rotation (Cn)
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10. n = 2 x 1800 / 1200 = 2 Cn = C3
3-Fold Axis of Rotation
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11. • BF3 Molecule
• Principal axis C3
• Subsidiary axis C2
XeF4 Molecule
Principal axis C4
Subsidiary axis C2
Principal and Subsidiary Axis
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The axis with highest fold symmetry
The axis with lower fold of symmetry is called Subsidiary Axis.

12. Benzene
H2 Molecule
C2
Principal axis C6
Subsidiary axis C2
Principal axis C
Subsidiary axis C2
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13. •Mirror plane which divide the
molecule into 2 equal parts
•σd => mirror plane bisects
angle formed between two
adjacent C2 axes
•σh => mirror plane
perpendicular to a principal
axis of rotation
•σv => mirror plane containing
principal axis of rotation
Plane of symmetry
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14. H2O Molecule
BF3 Molecule
C6H6 Molecule
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15. Plane of Symmetry in XeF4
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16. •Imaginary axis on which molecule when rotated
and reflected on plane perpendicular to the
rotation axis attains equivalent orientation
Improper axis of rotation (Sn)
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Improper Rotation in a Tetrahedral Molecule

17. •No physical change
•Rotation by 3600
•in = E (n = even)
Identity (E)
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18.  Collection of symmetry operations that can be carried
out about a unique point in a molecue and are inter
related to one another by certain rules.
C- type point group: A molecule with only a Cn axis
belongs to Cn point group.
D- type point group: A molecule having a Cn axis and
nC2 axis perpendicular to it belongs to Dn point group.
Higher Symmetry point group: large no of symmetry
elements and symmetry operations e.g Td and Oh point
group.
Point Groups
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19. •H2, N2, O2, Cl2, CO2, C2H2 Molecules
•{E, i, C, C2, σh σv}
•h = 
•Point group = Dh
H2 Molecule
C2
i
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20.  Heteronuclear diatomic
 HCl, HCN etc.
 {E, C , σv}
 h = 
 Point group = Cv
HCl MoleculeDr. Julekha Shaikh
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21. H2O Molecule
•E
•C2
•2σv
•h = 4
•Point group = C2v
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22. NH3 Molecule
•E
•2C3
•3σv
•h = 6
•C3v
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23. trans-dichloro ethylene (C2H2Cl2)
•E
•i
•C2
•σh
•h = 4
•Point Group = C2h C2
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24. BCl3 / BF3Molecule
•E
•2C3
•3C2
•σh
•3σv
•2S3
•h = 12
•Point group = D3h Dr. Julekha Shaikh 24

25. Some examples of Point Groups
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26. Dr. Julekha Shaikh 26
Examples of Some High Symmetry Point Groups

27. Dr. Julekha Shaikh 27
Identifying Point Groups

28. Dr. Julekha Shaikh 28
References
• Molecular symmetry and group theory by Robert L. Carter –
second edition.
• Introduction to Molecular Symmetry by J. S. Ogden
• Molecular Symmetry and Group Theory by Alan Vincent –
second edition.
• Inorganic Chemistry by D. Shriver, M. Weller, T. Overton
J. Rourke, F. Armstrong – sixth edition.
• Inorganic Chemistry by Catherine E. Housecroft and Alan
G. Sharpe – second edition

29. Thank You!
Dr. Julekha Shaikh 29