Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
21 0 -1 -3 0 3

can be reduced to

A1g A2g Eg A1u A2u Eu
2 1 3 1 3 4

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
2 0 2 1 2 3



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 15 15 2
quadratic 225 120 16
cubic 3375 680 64
quartic 50625 3060 288
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 2 3
quadratic 16 6 22 8 10 18
cubic 64 46 108 55 65 117
quartic 288 234 522 240 258 498

Number of independant internal coordinates 2

Literature




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