Reduction formula for point group Oh

Your representation

E 8C3 6C2 6C4 3C2 =(C4)2 i 6S4 8S6 3h 6d
21 0 -1 3 -3 -3 -1 0 5 3

can be reduced to

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

Substraction of translational and rotational contributions results in

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



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 15 15 1
quadratic 225 120 7
cubic 3375 680 22
quartic 50625 3060 92
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 1 0 1 0 1 0 0 0 2 1
quadratic 7 2 9 4 9 1 2 3 8 7
cubic 22 13 33 33 42 9 14 20 51 46
quartic 92 63 155 171 196 50 59 109 199 190

Number of independant internal coordinates 1

Literature




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