Reduction formula for point group D2

Your representation

E C2 (z) C2 (y) C2 (x)
15 -1 -1 -1

can be reduced to

A B1 B2 B3
3 4 4 4

Substraction of translational and rotational contributions results in

A B1 B2 B3
3 2 2 2



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 9 9 3
quadratic 81 45 15
cubic 729 165 45
quartic 6561 495 135
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 2 2 2
quadratic 15 10 10 10
cubic 45 40 40 40
quartic 135 120 120 120

Number of independant internal coordinates 3

Literature




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