Reduction formula for point group C2v

Your representation

E C2 (z) v(xz) v(yz)
30 -2 10 2

can be reduced to

A1 A2 B1 B2
10 4 10 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2
9 3 8 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 24 24 9
quadratic 576 300 97
cubic 13824 2600 729
quartic 331776 17550 4715
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 9 3 8 4
quadratic 97 59 84 60
cubic 729 571 716 584
quartic 4715 4099 4624 4112

Number of independant internal coordinates 9

Literature




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