Reduction formula for point group D3h

Your representation

E 2C3 (z) 3C'2 h (xy) 2S3 3v
18 0 -2 4 -2 4

can be reduced to

A'1 A'2 E' A''1 A''2 E''
2 1 4 0 3 2

Substraction of translational and rotational contributions results in

A'1 A'2 E' A''1 A''2 E''
2 0 3 0 2 1



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A'1 A'2 E' A''1 A''2 E''
Infrared - - + - + -
Raman + - + - - +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 12 12 2
quadratic 144 78 13
cubic 1728 364 43
quartic 20736 1365 147
quintic 248832 4368 423
sextic 2985984 12376 1162
No. 1 : Total number of force constants .
No. 2 : Total number of force constants k.
No. 3 : Total number of nonvanishing force constants k.

Characters for symmetric tensor products of internal modes
Force field Tensor
Order
E 2C3 (z) 3C'2 h (xy) 2S3 3v
linear 1 12 0 0 4 -2 4
quadratic 2 78 0 6 14 2 14
cubic 3 364 4 0 36 0 36
quadratic 4 1365 0 21 85 -2 85
quintic 5 4368 0 0 176 2 176
sextic 6 12376 10 56 344 2 344


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 2 0 3 0 2 1
quadratic 2 13 3 15 3 7 11
cubic 3 43 25 66 19 37 54
quartic 4 147 94 242 91 123 213
quintic 5 423 335 757 305 393 699
sextic 6 1162 962 2118 932 1076 2004

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Character table for point group D3h Jacobs University Bremen