Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
120 0 0 0 0 8

can be reduced to

A1g A2g Eg A1u A2u Eu
12 8 20 8 12 20

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
12 7 19 8 11 19



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 114 114 12
quadratic 12996 6555 588
cubic 1481544 253460 21293
quartic 168896016 7413705 619306
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 12 7 19 8 11 19
quadratic 588 514 1102 534 549 1083
cubic 21293 20963 42237 21021 21235 42237
quartic 619306 616587 1235893 617196 618146 1235342

Number of independant internal coordinates 12

Literature




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