Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
180 0 0 0 0 4

can be reduced to

A1g A2g Eg A1u A2u Eu
16 14 30 14 16 30

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
16 13 29 14 15 29



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 174 174 16
quadratic 30276 15225 1322
cubic 5268024 893200 74577
quartic 916636176 39524100 3296130
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 16 13 29 14 15 29
quadratic 1322 1230 2552 1260 1263 2523
cubic 74577 74309 148857 74397 74489 148857
quartic 3296130 3291858 6587988 3293222 3293490 6586712

Number of independant internal coordinates 16

Literature




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