Operations of C3v Symmetry Group Applied to Ammonia

first symmetry operation

E

+

C

3

-

C

3

σ

v

′

σ

v

′′

σ

v

second symmetry operation

E

+

C

3

-

C

3

σ

v

′

σ

v

′′

σ

v

	E	+ C 3	- C 3	σ v	σ v '	σ v ''
E	E	+ C 3	- C 3	σ v	σ v '	σ v ''
+ C 3	+ C 3	- C 3	E	σ v ''	σ v	σ v '
- C 3	- C 3	E	+ C 3	σ v '	σ v ''	σ v
σ v	σ v	σ v '	σ v ''	E	+ C 3	- C 3
σ v '	σ v '	σ v ''	σ v	- C 3	E	+ C 3
σ v ''	σ v ''	σ v	σ v '	+ C 3	- C 3	E

This Demonstration shows the effect of successive symmetry operations of the

C

3v

group applied to the ammonia molecule and how this corresponds to the multiplication table of the group.

Set the buttons to apply one of these group operations:

E

, the identity operator;

+

C

3

, clockwise rotation by 120°;

-

C

3

, counterclockwise rotation by 120°; and the three reflection operators

σ

v

,

σ

v

'

and

σ

v

''

, corresponding to the plane going through the three N-H bonds.

You can apply two symmetry operations successively and show that the combined operations generate another operation, in accordance with the multiplication table of the group. The direct application of the product operator is shown in the lower row of the diagram.