Reduction formula for point group D3d

Your representation

E 2C3 3C'2 i 2S6 3d
36 0 -4 0 0 0

can be reduced to

A1g A2g Eg A1u A2u Eu
2 4 6 2 4 6

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
2 3 5 2 3 5



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 30 30 2
quadratic 900 465 48
cubic 27000 4960 407
quartic 810000 40920 3488
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 3 5 2 3 5
quadratic 48 32 80 38 37 75
cubic 407 423 825 407 423 825
quartic 3488 3352 6840 3408 3392 6800

Number of independant internal coordinates 2

Literature




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