Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
12 0 0 0

can be reduced to

A B E
3 3 3

Substraction of translational and rotational contributions results in

A B E
2 2 1



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A B E
Infrared - + +
Raman + + +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 6 6 2
quadratic 36 21 7
cubic 216 56 16
quartic 1296 126 36
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 A B E
linear 2 2 1
quadratic 7 6 4
cubic 16 16 12
quartic 36 34 28

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Character table for point group S4 Jacobs University Bremen