Reduction formula for point group D2d

Your representation

E 2S4 C2 (z) 2C'2 2d
15 -1 -1 -1 3

can be reduced to

A1 A2 B1 B2 E
2 1 1 3 4

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
2 0 1 2 2



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 9 9 2
quadratic 81 45 10
cubic 729 165 27
quartic 6561 495 78
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 2 2
quadratic 10 3 5 7 10
cubic 27 15 18 25 40
quartic 78 51 57 69 120

Number of independant internal coordinates 2

Literature




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