Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
36 0 0 0

can be reduced to

A B E
9 9 9

Substraction of translational and rotational contributions results in

A B E
8 8 7



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 30 30 8
quadratic 900 465 121
cubic 27000 4960 1248
quartic 810000 40920 10272
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 8 8 7
quadratic 121 120 112
cubic 1248 1248 1232
quartic 10272 10264 10192

Number of independant internal coordinates 8

Literature




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