Reduction formula for point group C4v

Your representation

E 2C4 (z) C2 2v 2d
21 3 -3 5 3

can be reduced to

A1 A2 B1 B2 E
5 1 2 1 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
4 0 2 1 4



Force field analysis

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

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 15 15 4
quadratic 225 120 24
cubic 3375 680 106
quartic 50625 3060 446
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 E
linear 4 0 2 1 4
quadratic 24 8 18 14 28
cubic 106 62 92 76 172
quartic 446 330 408 364 756

Number of independant internal coordinates 4

Literature




Character tables for chemically important point groups Character table for point group C4v Jacobs University Bremen