Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
21 0 0 -3 -3 0 0 5

can be reduced to

Ag Eg Tg Au Eu Tu
1 1 2 0 0 4

Substraction of translational and rotational contributions results in

Ag Eg Tg Au Eu Tu
1 1 1 0 0 3



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 15 15 1
quadratic 225 120 9
cubic 3375 680 35
quartic 50625 3060 155
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 1 1 1 0 0 3
quadratic 9 9 13 3 3 15
cubic 35 33 75 23 20 97
quartic 155 155 367 109 109 389

Number of independant internal coordinates 1

Literature




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