Reduction formula for point group C3v

Your representation

E 2C3 (z) 3v
18 0 4

can be reduced to

A1 A2 E
5 1 6

Substraction of translational and rotational contributions results in

A1 A2 E
4 0 4



Force field analysis

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

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 12 12 4
quadratic 144 78 20
cubic 1728 364 80
quartic 20736 1365 270
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 E
linear 4 0 4
quadratic 20 6 26
cubic 80 44 120
quartic 270 185 455

Number of independant internal coordinates 4

Literature




Character tables for chemically important point groups Character table for point group C3v Jacobs University Bremen