Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
60 0 0 0 0 4

can be reduced to

A1g A2g Eg A1u A2u Eu
6 4 10 4 6 10

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
6 3 9 4 5 9



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 54 54 6
quadratic 2916 1485 142
cubic 157464 27720 2357
quartic 8503056 395010 33210
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 3 9 4 5 9
quadratic 142 110 252 120 123 243
cubic 2357 2269 4617 2297 2329 4617
quartic 33210 32688 65898 32842 32930 65772

Number of independant internal coordinates 6

Literature




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