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example 1 - NH3


 

The vibrational modes associated with the N-H bonds in NH3

The NH3 molecule belongs to the C3v point group.

The number of bonds that remain unshifted by the operations are represented by the following:

 

 

E

2C3

3sv

G3H

3

0

1



This set of characters can be generated by adding the A1 and E rows together. (This is readily seen by noting that the '0' in the 2C3 column requires adding a +1 and a -1 so the E row must be used. The '1' in the 3sv column then requires that the A1 row is used).

 

 

E

2C3

3sv

 

 A1

 1

 1

 +

 E

 2

 -1

 0

 

 

 

 

 

 

 G3H

 3

 0

 

The representation reduces to A1 and E:

G3H = A1 + E

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