Reduction formula for point group C3v

Your representation

E 2C3 (z) 3v
15 0 3

can be reduced to

A1 A2 E
4 1 5

Substraction of translational and rotational contributions results in

A1 A2 E
3 0 3



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 9 9 3
quadratic 81 45 12
cubic 729 165 38
quartic 6561 495 102
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 3 0 3
quadratic 12 3 15
cubic 38 19 54
quartic 102 63 165

Number of independant internal coordinates 3

Literature




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