Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
48 0 0 0 0 8

can be reduced to

A1g A2g Eg A1u A2u Eu
6 2 8 2 6 8

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
6 1 7 2 5 7



Force field analysis

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

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 42 42 6
quadratic 1764 903 96
cubic 74088 13244 1181
quartic 3111696 148995 12778
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 A1u A2u Eu
linear 6 1 7 2 5 7
quadratic 96 58 154 66 81 147
cubic 1181 1031 2205 1053 1159 2205
quartic 12778 12093 24871 12192 12602 24794

Number of independant internal coordinates 6

Literature




Character tables for chemically important point groups Character table for point group D3d Jacobs University Bremen