Reduction formula for point group C2v

Your representation

E C2 (z) v(xz) v(yz)
12 0 4 0

can be reduced to

A1 A2 B1 B2
4 2 4 2

Substraction of translational and rotational contributions results in

A1 A2 B1 B2
3 1 2 0



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1 A2 B1 B2
Infrared + - + +
Raman + + + +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 6 6 3
quadratic 36 21 10
cubic 216 56 22
quartic 1296 126 48
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.

Symmetry properties of force field parameters
Force field A1 A2 B1 B2
linear 3 1 2 0
quadratic 10 3 6 2
cubic 22 10 18 6
quartic 48 22 38 18

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Character table for point group C2v Jacobs University Bremen