Reduction formula for point group Ih

Your representation

E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15
180 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
2 4 4 6 8 1 5 5 6 7

Substraction of translational and rotational contributions results in

Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
2 3 4 6 8 1 4 5 6 7



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 174 174 2
quadratic 30276 15225 151
cubic 5268024 893200 7519
quartic 916636176 39524100 330468
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 3 4 6 8 1 4 5 6 7
quadratic 151 361 359 510 661 126 380 379 504 630
cubic 7519 22262 22263 29784 37274 7429 22352 22353 29784 37184
quartic 330468 987131 987130 1317597 1648065 329269 988075 988073 1317342 1646611

Number of independant internal coordinates 2

Literature




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