Reduction formula for point group D2d

Your representation

E 2S4 C2 (z) 2C'2 2d
24 0 0 0 4

can be reduced to

A1 A2 B1 B2 E
4 2 2 4 6

Substraction of translational and rotational contributions results in

A1 A2 B1 B2 E
4 1 2 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 18 18 4
quadratic 324 171 30
cubic 5832 1140 162
quartic 104976 5985 807
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 4 1 2 3 4
quadratic 30 16 21 24 40
cubic 162 128 138 152 280
quartic 807 708 738 772 1480

Number of independant internal coordinates 4

Literature




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