Reduction formula for point group Ih

Your representation

E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15
120 0.0000 -0.0000 0 0 0 0.0000 -0.0000 0 8

can be reduced to

Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
2 2 2 4 6 0 4 4 4 4

Substraction of translational and rotational contributions results in

Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
2 1 2 4 6 0 3 4 4 4



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 114 114 2
quadratic 12996 6555 74
cubic 1481544 253460 2200
quartic 168896016 7413705 62475
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 2 1 2 4 6 0 3 4 4 4
quadratic 74 148 146 220 294 51 167 166 216 267
cubic 2200 6253 6254 8456 10637 2064 6389 6390 8456 10501
quartic 62475 184705 184704 247178 309653 61530 185540 185538 247068 308598

Number of independant internal coordinates 2

Literature




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