Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
36 0 0 0 0 0 0 4

can be reduced to

Ag Eg Tg Au Eu Tu
2 2 4 1 1 5

Substraction of translational and rotational contributions results in

Ag Eg Tg Au Eu Tu
2 2 3 1 1 4



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 30 30 2
quadratic 900 465 25
cubic 27000 4960 223
quartic 810000 40920 1761
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 2 2 3 1 1 4
quadratic 25 25 55 18 18 57
cubic 223 218 607 205 200 625
quartic 1761 1761 5079 1687 1687 5113

Number of independant internal coordinates 2

Literature




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