Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
66 0 -2 0

can be reduced to

A B E
16 16 17

Substraction of translational and rotational contributions results in

A B E
15 15 15



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 60 60 15
quadratic 3600 1830 465
cubic 216000 37820 9455
quartic 12960000 595665 149040
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 15 15 15
quadratic 465 465 450
cubic 9455 9455 9455
quartic 149040 149025 148800

Number of independant internal coordinates 15

Literature




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