Reduction formula for point group D3d

Your representation

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

can be reduced to

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

Substraction of translational and rotational contributions results in

A1g A2g Eg A1u A2u Eu
4 1 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 4
quadratic 900 465 50
cubic 27000 4960 441
quartic 810000 40920 3522
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 4 1 5 2 3 5
quadratic 50 30 80 36 39 75
cubic 441 389 825 405 425 825
quartic 3522 3318 6840 3374 3426 6800

Number of independant internal coordinates 4

Literature




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