Reduction formula for point group Ih

Your representation

E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15
60 0.0000 -0.0000 0 0 0 0.0000 -0.0000 0 4

can be reduced to

Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 1 1 2 3 0 2 2 2 2

Substraction of translational and rotational contributions results in

Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 0 1 2 3 0 1 2 2 2



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
Infrared - - - - - - + - - -
Raman + - - - + - - - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 54 54 1
quadratic 2916 1485 21
cubic 157464 27720 255
quartic 8503056 395010 3426
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 T1g T2g Gg Hg Au T1u T2u Gu Hu
linear 1 0 1 2 3 0 1 2 2 2
quadratic 21 31 29 50 71 12 38 37 48 60
cubic 255 670 671 928 1174 225 700 701 928 1144
quartic 3426 9755 9754 13179 16605 3267 9889 9887 13154 16421

Number of independant internal coordinates 1

Literature




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