Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
51 -1 -1 -1

can be reduced to

A B E
12 13 13

Substraction of translational and rotational contributions results in

A B E
11 12 11



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 45 45 11
quadratic 2025 1035 265
cubic 91125 16215 4059
quartic 4100625 194580 48720
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 11 12 11
quadratic 265 264 253
cubic 4059 4060 4048
quartic 48720 48708 48576

Number of independant internal coordinates 11

Literature




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