Reduction formula for point group Oh

Your representation

E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
48 0 0 0 0 0 0 0 0 8

can be reduced to

A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
2 0 2 2 4 0 2 2 4 2

Substraction of translational and rotational contributions results in

A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
2 0 2 1 4 0 2 2 3 2



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
Infrared - - - - - - - - + -
Raman + - + - + - - - - -

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 42 42 2
quadratic 1764 903 32
cubic 74088 13244 318
quartic 3111696 148995 3315
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 A1g A2g Eg T1g T2g A1u A2u Eu T1u T2u
linear 2 0 2 1 4 0 2 2 3 2
quadratic 32 12 44 46 64 15 22 37 59 51
cubic 318 244 555 787 863 254 308 555 851 799
quartic 3315 2966 6281 9127 9463 3000 3204 6204 9398 9192

Number of independant internal coordinates 2

Literature




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