Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
18 0 0 0 0 2

can be reduced to

A1g A2g Eg A1u A2u Eu
2 1 3 1 2 3

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
2 0 2 1 1 2



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 12 12 2
quadratic 144 78 11
cubic 1728 364 38
quartic 20736 1365 133
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 2 0 2 1 1 2
quadratic 11 3 14 6 6 12
cubic 38 24 60 31 31 60
quartic 133 98 231 112 112 224

Number of independant internal coordinates 2

Literature




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