Reduction formula for point group D2

Your representation

E C2 (z) C2 (y) C2 (x)
21 -3 -3 -3

can be reduced to

A B1 B2 B3
3 6 6 6

Substraction of translational and rotational contributions results in

A B1 B2 B3
3 4 4 4



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A B1 B2 B3
Infrared - + + +
Raman + + + +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 15 15 3
quadratic 225 120 36
cubic 3375 680 164
quartic 50625 3060 792
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 A B1 B2 B3
linear 3 4 4 4
quadratic 36 28 28 28
cubic 164 172 172 172
quartic 792 756 756 756

Number of independant internal coordinates 3

Literature




Character tables for chemically important point groups Character table for point group D2 Jacobs University Bremen