Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
15 -1 -1 -1

can be reduced to

A B E
3 4 4

Substraction of translational and rotational contributions results in

A B E
2 3 2



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 9 9 2
quadratic 81 45 13
cubic 729 165 42
quartic 6561 495 129
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 3 2
quadratic 13 12 10
cubic 42 43 40
quartic 129 126 120

Number of independant internal coordinates 2

Literature




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