1. Point groups classify molecules based on their symmetry elements and operations. 2. Common point groups include C2v, C3v, C2h, D3h, C∞v, and D∞h. 3. C2v contains C2 rotation and 2σv vertical planes of symmetry (e.g. H2O). C3v contains C3 rotation and 3σv planes (e.g. NH3).

1. POINT GROUPS
By,
Dr. Prajakta S. More
Smt. CHM College, Ulhasnagar

2. Sr.
No.
Point
group
Characteristic Symmetry
elements
Example
1. C2v C2, 2σv and E H2O
2. C3v C3, 3σv and E NH3
3. C2h C2, σh, i and E trans-dichloro
ethylene
4. D3h C3, 3C2, 3σv, σh, S3 and E BCl3
5. C∞v C∞ , ∞σv and E HCl
6. D∞h C∞ , ∞C2, ∞σv, σh and E H2
Point groups: It is a collection of all symmetry elements that can be
carried out on a molecule belonging to that group.

4. Cnv Point group: Cn, nσv, E
C2v point group: It is collection of C2, 2σv and E
symmetry operations. e.g. Water molecule.

6. C3v point group: It is collection of C3, 3σV and E symmetry
operations. e.g. Ammonia molecule

8. Cnh point group: Cn, σh, i, E
C2h point group: It is collection of C2, σh, i and E
symmetry operations. e.g. Trans dichloro ethylene

10. Dnh point group: Cn, nC2, nσv, σh, E
D3h point group: It is collection of C3, 3C2, 3σv, S3, σh
and E symmetry operation. e.g. BCl3 molecule.
Three vertical plane of
symmetry 3σv
One horizontal plane of symmetry σh
C3 axis perpendicular to
three C2 axes

11. Point groups of linear molecules:
C∞v point group:
It contains C∞, ∞σv and E
symmetry operation.
e.g. Hetero nuclear
diatomic molecule like
HCl
D∞h point group:
It contains C∞, ∞C2, ∞σv,
σh, i and E symmetry
operations.
e.g. Homonuclear
diatomic molecule like H2

12. Additional points

13. Classification of point groups:
Elements Point group Example
C type point group
Cn Cn H2O2
Cn + nσv Cnv H2O, NH3
Cn+ σh Cnh Trans dichloro
ethylene
D type point group (possess Cn perpendicular to C2 axis)
Cn + nC2 Dn [Cu(en)2] +2
Cn + nC2 + nσV +
σh
Dnh BCl3
Cn + nC2 + σd Dnd Allene
Higher symmetry point groups
Tetrahedral Td CH4, CCl4
Octahedral Oh SF6

14. Order of
group
Point
group
Characteristic Symmetry
elements / operations
Example
4 C2v C2, 2σv and E H2O
6 C3v 2C3, 3σv and E NH3
4 C2h C2, σh, i and E trans-dichloro
ethylene
12 D3h 2C3, 3C2, 3σv, σh, 2S3 and E BCl3
∞
C∞v C∞ , ∞σv and E HCl
∞
D∞h C∞ , ∞C2, ∞σv, σh and E H2
Order of group: The total number of symmetry elements present in the
group is called order of group and it is denoted by h.

15. Ammonia (as well as BCl3) has only one C3 axis, then how 2C3 , if order of
group is to be calculated?
Ans: Yes ammonia has only one C3 axis. However, one C3 axis can produce
three C3 operations namely
• 120º rotation i.e. C3
1
• 240º rotation i.e. C3
2
• 360º rotation i.e. C3
3 ( it is identity E )
Out of these three, 120º rotation and 240º rotation represents 2C3 and
360ºrotation represents E