Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
57 0 0 -3 -3 0 0 9

can be reduced to

Ag Eg Tg Au Eu Tu
3 3 6 1 1 9

Substraction of translational and rotational contributions results in

Ag Eg Tg Au Eu Tu
3 3 5 1 1 8



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 51 51 3
quadratic 2601 1326 68
cubic 132651 23426 1019
quartic 6765201 316251 13449
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 5 1 1 8
quadratic 68 68 158 49 49 167
cubic 1019 1011 2877 938 929 2986
quartic 13449 13449 39336 12993 12993 39639

Number of independant internal coordinates 3

Literature




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