Reduction formula for point group Th

Your representation

E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 3h
48 0 0 0 0 0 0 0

can be reduced to

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

Substraction of translational and rotational contributions results in

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



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 42 42 2
quadratic 1764 903 44
cubic 74088 13244 562
quartic 3111696 148995 6281
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 5 2 2 5
quadratic 44 44 110 37 37 110
cubic 562 555 1650 562 555 1650
quartic 6281 6281 18590 6204 6204 18590

Number of independant internal coordinates 2

Literature




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