Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
60 0 0 0 0 0 0 4

can be reduced to

Ag Eg Tg Au Eu Tu
3 3 7 2 2 8

Substraction of translational and rotational contributions results in

Ag Eg Tg Au Eu Tu
3 3 6 2 2 7



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 54 54 3
quadratic 2916 1485 71
cubic 157464 27720 1183
quartic 8503056 395010 16605
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 3 3 6 2 2 7
quadratic 71 71 181 60 60 183
cubic 1183 1174 3443 1153 1144 3473
quartic 16605 16605 49293 16421 16421 49351

Number of independant internal coordinates 3

Literature




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