Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
72 0 0 0 0 8

can be reduced to

A1g A2g Eg A1u A2u Eu
8 4 12 4 8 12

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
8 3 11 4 7 11



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 66 66 8
quadratic 4356 2211 212
cubic 287496 50116 4285
quartic 18974736 864501 72698
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 8 3 11 4 7 11
quadratic 212 162 374 174 189 363
cubic 4285 4075 8349 4109 4251 8349
quartic 72698 71479 144177 71700 72290 143990

Number of independant internal coordinates 8

Literature




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