Reduction formula for point group C2v

Your representation

E C2 (z) v(xz) v(yz)
15 -3 5 3

can be reduced to

A1 A2 B1 B2
5 1 5 4

Substraction of translational and rotational contributions results in

A1 A2 B1 B2
4 0 3 2



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 9 9 4
quadratic 81 45 19
cubic 729 165 56
quartic 6561 495 163
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 4 0 3 2
quadratic 19 6 12 8
cubic 56 24 49 36
quartic 163 92 136 104

Number of independant internal coordinates 4

Literature




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