Reduction formula for point group Ih

Your representation

E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15
36 3.2361 -1.2361 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 0 1 2 0 2 1 1 1

Substraction of translational and rotational contributions results in

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



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 30 30 1
quadratic 900 465 9
cubic 27000 4960 56
quartic 810000 40920 393
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 0 1 2 0 1 1 1 1
quadratic 9 7 7 16 25 3 12 12 15 18
cubic 56 111 111 167 218 38 129 129 167 200
quartic 393 975 975 1368 1761 327 1033 1033 1360 1687

Number of independant internal coordinates 1

Literature




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