Reduction formula for point group D2d

Your representation

E 2S4 C2 (z) 2C'2 2d
66 0 -2 -2 6

can be reduced to

A1 A2 B1 B2 E
9 7 6 10 17

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
9 6 6 9 15



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 60 60 9
quadratic 3600 1830 252
cubic 216000 37820 4782
quartic 12960000 595665 74904
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 9 6 6 9 15
quadratic 252 213 228 237 450
cubic 4782 4673 4673 4782 9455
quartic 74904 74136 74361 74664 148800

Number of independant internal coordinates 9

Literature




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