Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
21 -1 -3 -1

can be reduced to

A B E
4 5 6

Substraction of translational and rotational contributions results in

A B E
3 4 4



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 15 15 3
quadratic 225 120 32
cubic 3375 680 168
quartic 50625 3060 776
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 3 4 4
quadratic 32 32 28
cubic 168 168 172
quartic 776 772 756

Number of independant internal coordinates 3

Literature




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