Reduction formula for point group D3h

Your representation

E 2C3 (z) 3C'2 h (xy) 2S3 3v
12 0 -2 4 -2 2

can be reduced to

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

Substraction of translational and rotational contributions results in

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



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 6 6 1
quadratic 36 21 5
cubic 216 56 9
quartic 1296 126 19
quintic 7776 252 33
sextic 46656 462 60
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 6 0 0 4 -2 2
quadratic 2 21 0 3 11 2 5
cubic 3 56 2 0 24 0 8
quadratic 4 126 0 6 46 -2 14
quintic 5 252 0 0 80 2 20
sextic 6 462 3 10 130 1 30


Decomposition into Irreducible representations
Force field Tensor
Order
A'1 A'2 E' A''1 A''2 E''
linear 1 1 0 2 0 1 0
quadratic 2 5 1 5 0 1 2
cubic 3 9 5 13 1 5 5
quartic 4 19 9 29 5 9 13
quintic 5 33 23 55 9 19 29
sextic 6 60 40 98 23 33 55

Number of independant internal coordinates 1

Literature




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