Reduction formula for point group S4

Your representation

E S4 C2 (S4)3
78 0 -2 0

can be reduced to

A B E
19 19 20

Substraction of translational and rotational contributions results in

A B E
18 18 18



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 72 72 18
quadratic 5184 2628 666
cubic 373248 64824 16206
quartic 26873856 1215450 304038
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 18 18 18
quadratic 666 666 648
cubic 16206 16206 16206
quartic 304038 304020 303696

Number of independant internal coordinates 18

Literature




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