Reduction formula for point group D3

Your representation

E 2C3 (z) 3C'2
21 0 -1

can be reduced to

A1 A2 E
3 4 7

Substraction of translational and rotational contributions results in

A1 A2 E
3 2 5



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1 A2 E
Infrared - + +
Raman + - +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 15 15 3
quadratic 225 120 24
cubic 3375 680 119
quartic 50625 3060 528
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 A1 A2 E
linear 3 2 5
quadratic 24 16 40
cubic 119 111 225
quartic 528 492 1020

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Character table for point group D3 Jacobs University Bremen