Reduction formula for point group D2d

Your representation

E 2S4 C2 (z) 2C'2 2d
21 -1 -3 -3 3

can be reduced to

A1 A2 B1 B2 E
2 2 1 4 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
2 1 1 3 4



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 15 15 2
quadratic 225 120 21
cubic 3375 680 89
quartic 50625 3060 415
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 1 1 3 4
quadratic 21 11 15 17 28
cubic 89 79 75 93 172
quartic 415 361 377 395 756

Number of independant internal coordinates 2

Literature




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