Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
180 0 0 0 0 0 0 4

can be reduced to

Ag Eg Tg Au Eu Tu
8 8 22 7 7 23

Substraction of translational and rotational contributions results in

Ag Eg Tg Au Eu Tu
8 8 21 7 7 22



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method Ag Eg Tg Au Eu Tu
Infrared - - - - - +
Raman + + + - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 174 174 8
quadratic 30276 15225 661
cubic 5268024 893200 37303
quartic 916636176 39524100 1648065
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 Ag Eg Tg Au Eu Tu
linear 8 8 21 7 7 22
quadratic 661 661 1891 630 630 1893
cubic 37303 37274 111583 37213 37184 111673
quartic 1648065 1648065 4939923 1646611 1646611 4940101

Number of independant internal coordinates 8

Literature




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