Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
72 0 0 0 0 0 0 8

can be reduced to

Ag Eg Tg Au Eu Tu
4 4 8 2 2 10

Substraction of translational and rotational contributions results in

Ag Eg Tg Au Eu Tu
4 4 7 2 2 9



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 66 66 4
quadratic 4356 2211 106
cubic 287496 50116 2148
quartic 18974736 864501 36349
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 4 4 7 2 2 9
quadratic 106 106 268 87 87 276
cubic 2148 2137 6212 2060 2049 6300
quartic 36349 36349 107828 35850 35850 108140

Number of independant internal coordinates 4

Literature




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