Reduction formula for point group D2d

Your representation

E 2S4 C2 (z) 2C'2 2d
12 0 0 0 2

can be reduced to

A1 A2 B1 B2 E
2 1 1 2 3

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
2 0 1 1 1



Force field analysis

Infrared and Raman activities (harmonic approximation)
Method A1 A2 B1 B2 E
Infrared - - - + +
Raman + - + + +

Number of force field parameters
Force field No. 1 No. 2 No. 3
linear 6 6 2
quadratic 36 21 6
cubic 216 56 12
quartic 1296 126 25
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 B1 B2 E
linear 2 0 1 1 1
quadratic 6 1 3 3 4
cubic 12 4 8 8 12
quartic 25 11 17 17 28

Number of independant internal coordinates 2

Literature




Character tables for chemically important point groups Character table for point group D2d Jacobs University Bremen