Reduction formula for point group C2v

Your representation

E C2 (z) v(xz) v(yz)
21 -3 3 3

can be reduced to

A1 A2 B1 B2
6 3 6 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2
5 2 4 4



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 15 15 5
quadratic 225 120 38
cubic 3375 680 182
quartic 50625 3060 810
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 5 2 4 4
quadratic 38 26 28 28
cubic 182 154 172 172
quartic 810 738 756 756

Number of independant internal coordinates 5

Literature




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