Reduction formula for point group Ih

Your representation

E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15
72 6.4721 -2.4721 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 0 2 4 0 4 2 2 2

Substraction of translational and rotational contributions results in

Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
2 1 0 2 4 0 3 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 66 66 2
quadratic 4356 2211 32
cubic 287496 50116 474
quartic 18974736 864501 7514
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 0 2 4 0 3 2 2 2
quadratic 32 44 44 74 106 15 59 58 72 87
cubic 474 1201 1200 1674 2137 386 1289 1288 1674 2049
quartic 7514 21322 21322 28835 36349 7052 21746 21746 28798 35850

Number of independant internal coordinates 2

Literature




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